presentation of experimental data and results

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• How Do I Present Findings From My Experiment in a Report?
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Many believe that a scientist’s most difficult job is not conducting an experiment but presenting the results in an effective and coherent way. Even when your methods and technique are sound and your notes are comprehensive, writing a report can be a challenge because organizing and communicating scientific findings requires patience and a thorough grasp of certain conventions. Having a clear understanding of the typical goals and strategies for writing an effective lab report can make the process much less troubling.

General Considerations

It is useful to note that effective scientific writing serves the same purpose that your lab report should. Good scientific writing explains:

• The goal(s) of your experiment
• How you performed the experiment
• The results you obtained
• Why these results are important

While it’s unlikely that you’re going to win the Nobel Prize for your work in an undergraduate laboratory course, tailoring your writing strategies in imitation of professional journals is easier than you might think, since they all follow a consistent pattern. However, your instructor has the final say in determining how your report should be structured and what should appear in each section. Please use the following explanations only to supplement your given writing criteria, rather than thinking of them as an indication of how all lab reports must be written.

In Practice

The structure of a report.

The traditional experimental report is structured using the acronym “IMRAD” which stands for I ntroduction, M ethods, R esults and D iscussion. The “ A ” is sometimes used to stand for A bstract. For help writing abstracts, please see Sweetland’s resource entitled “What is an abstract, and how do I write one?”

Introduction: “What am I doing here?”

The introduction should accomplish what any good introduction does: draw the reader into the paper. To simplify things, follow the “inverted pyramid” structure, which involves narrowing information from the most broad (providing context for your experiment’s place in science) to the most specific (what exactly your experiment is about). Consider the example below.

Most broad: “Caffeine is a mild stimulant that is found in many common beverages, including coffee.”

Less broad: “Common reactions to caffeine use include increased heart rate and increased respiratory rate.”

Slightly more specific (moving closer to your experiment): Previous research has shown that people who consume multiple caffeinated beverages per day are also more likely to be irritable.

Most specific (your experiment): This study examines the emotional states of college students (ages 18-22) after they have consumed three cups of coffee each day.

See how that worked? Each idea became slightly more focused, ending with a brief description of your particular experiment. Here are a couple more tips to keep in mind when writing an introduction:

• Include an overview of the topic in question, including relevant literature A good example: “In 1991, Rogers and Hammerstein concluded that drinking coffee improves alertness and mental focus (citation 1991).
• Explain what your experiment might contribute to past findings A good example: “Despite these established benefits, coffee may negatively impact mood and behavior. This study aims to investigate the emotions of college coffee drinkers during finals week.”
• Keep the introduction brief There’s no real advantage to writing a long introduction. Most people reading your paper already know what coffee is, and where it comes from, so what’s the point of giving them a detailed history of the coffee bean? A good example: “Caffeine is a psychoactive stimulant, much like nicotine.” (Appropriate information, because it gives context to caffeine—the molecule of study) A bad example: “Some of the more popular coffee drinks in America include cappuccinos, lattés, and espresso.” (Inappropriate for your introduction. This information is useless for your audience, because not only is it already familiar, but it doesn’t mention anything about caffeine or its effects, which is the reason that you’re doing the experiment.)
• Avoid giving away the detailed technique and data you gathered in your experiment A good example: “A sample of coffee-drinking college students was observed during end-of-semester exams.” ( Appropriate for an introduction ) A bad example: “25 college students were studied, and each given 10oz of premium dark roast coffee (containing 175mg caffeine/serving, except for Folgers, which has significantly lower caffeine content) three times a day through a plastic straw, with intervals of two hours, for three weeks.” ( Too detailed for an intro. More in-depth information should appear in your “Methods” or “Results” sections. )

Methods: “Where am I going to get all that coffee…?”

A “methods” section should include all the information necessary for someone else to recreate your experiment. Your experimental notes will be very useful for this section of the report. More or less, this section will resemble a recipe for your experiment. Don’t concern yourself with writing clever, engaging prose. Just say what you did, as clearly as possible. Address the types of questions listed below:

• Where did you perform the experiment? (This one is especially important in field research— work done outside the laboratory.)
• How much did you use? (Be precise.)
• Did you change anything about them? (i.e. Each 5 oz of coffee was diluted with 2 oz distilled water.)
• Did you use any special method for recording data? (i.e. After drinking coffee, students’ happiness was measured using the Walter Gumdrop Rating System, on a scale of 1-10.)
• Did you use any techniques/methods that are significant for the research? (i.e. Maybe you did a double blinded experiment with X and Y as controls. Was your control a placebo? Be specific.)
• Any unusual/unique methods for collecting data? If so, why did you use them?

After you have determined the basic content for your “methods” section, consider these other tips:

• Decide between using active or passive voice

There has been much debate over the use of passive voice in scientific writing. “Passive voice” is when the subject of a sentence is the recipient of the action.

• For example: Coffee was given to the students.

“Active voice” is when the subject of a sentence performs the action.

• For example: I gave coffee to the students.

The merits of using passive voice are obvious in some cases. For instance, scientific reports are about what is being studied, and not about YOU. Using too many personal pronouns can make your writing sound more like a narrative and less like a report. For that reason, many people recommend using passive voice to create a more objective, professional tone, emphasizing what was done TO your subject. However, active voice is becoming increasingly common in scientific writing, especially in social sciences, so the ultimate decision of passive vs. active voice is up to you (and whoever is grading your report).

• Units are important When using numbers, it is important to always list units, and keep them consistent throughout the section. There is a big difference between giving someone 150 milligrams of coffee and 150 grams of coffee—the first will keep you awake for a while, and the latter will put you to sleep indefinitely. So make sure you’re consistent in this regard.
• Don’t needlessly explain common techniques If you’re working in a chemistry lab, for example, and you want to take the melting point of caffeine, there’s no point saying “I used the “Melting point-ometer 3000” to take a melting point of caffeine. First I plugged it in…then I turned it on…” Your reader can extrapolate these techniques for him or herself, so a simple “Melting point was recorded” will work just fine.
• If it isn’t important to your results, don’t include it No one cares if you bought the coffee for your experiment on “3 dollar latte day”. The price of the coffee won’t affect the outcome of your experiment, so don’t bore your reader with it. Simply record all the things that WILL affect your results (i.e. masses, volumes, numbers of trials, etc).

Results: The only thing worth reading?

The “results” section is the place to tell your reader what you observed. However, don’t do anything more than “tell.” Things like explaining and analyzing belong in your discussion section. If you find yourself using words like “because” or “which suggests” in your results section, then STOP! You’re giving too much analysis.

A good example: “In this study, 50% of subjects exhibited symptoms of increased anger and annoyance in response to hearing Celine Dion music.” ( Appropriate for a “results” section—it doesn’t get caught up in explaining WHY they were annoyed. )

In your “results” section, you should:

• Display facts and figures in tables and graphs whenever possible. Avoid listing results like “In trial one, there were 5 students out of 10 who showed irritable behavior in response to caffeine. In trial two…” Instead, make a graph or table. Just be sure to label it so you can refer to it in your writing (i.e. “As Table 1 shows, the number of swear words spoken by students increased in proportion to the amount of coffee consumed.”) Likewise, be sure to label every axis/heading on a chart or graph (a good visual representation can be understood on its own without any textual explanation). The following example clearly shows what happened during each trial of an experiment, making the trends visually apparent, and thus saving the experimenter from having to explain each trial with words.

• Identify only the most significant trends. Don’t try to include every single bit of data in this section, because much of it won’t be relevant to your hypothesis. Just pick out the biggest trends, or what is most significant to your goals.

The principles of presenting statistical results using figures

Jae hong park.

1 Department of Anesthesiology and Pain Medicine, Haeundae Paik Hospital, Inje University College of Medicine, Busan, Korea

Dong Kyu Lee

2 Department of Anesthesiology and Pain Medicine, Dongguk University Ilsan Hospital, Goyang, Korea

3 Department of Anesthesiology and Pain Medicine, Chung-Ang University College of Medicine, Seoul, Korea

Jong Hae Kim

4 Department of Anesthesiology and Pain Medicine, Daegu Catholic University School of Medicine, Daegu, Korea

Francis Sahngun Nahm

5 Department of Anesthesiology and Pain Medicine, Seoul National University Bundang Hospital, Seongnam, Korea

Sang Gyu Kwak

6 Department of Medical Statistics, Daegu Catholic University School of Medicine, Daegu, Korea

Chi-Yeon Lim

7 Department of Biostatistics, Dongguk University College of Medicine, Goyang, Korea

Associated Data

Tables and figures are commonly adopted methods for presenting specific data or statistical analysis results. Figures can be used to display characteristics and distributions of data, allowing for intuitive understanding through visualization and thus making it easier to interpret the statistical results. To maximize the positive aspects of figure presentation and increase the accuracy of the content, in this article, the authors will describe how to choose an appropriate figure type and the necessary components to include. Additionally, this article includes examples of figures that are commonly used in research and their essential components using virtual data.

Introduction

All studies based on scientific approaches in anesthesia and pain medicine must involve an analysis of data to support a theory. After establishing a hypothesis and determining the research subjects, the researcher organizes the data obtained into specific categories. In most cases, data are composed of numbers or letters, but can also be stored as photos or figures, depending on the type of research. After researchers classify and index the data, they must decide which statistical analysis method to use. In general, data composed of numbers or letters are stored in tables with rows and columns. This can easily be accomplished using spreadsheet-based computer programs. The simple functions provided by spreadsheet programs, such as classification and sorting, facilitate the interpretation of the essential characteristics of the data, such as structure and frequency. In addition, some spreadsheet programs can show the results of these simple functions as graphs (such as dots, straight lines, or bars) such that the structure and characteristics of the data can be grasped quickly through visualization.

Graphs can be used to present the statistical analysis results in such a way as to make them intuitively easy to understand. For many research papers, the statistical results are illustrated using graphs to support their theory and to enable visual comparisons with other study results. Even though presenting data and statistical results using visual graphs have many advantages, representative values of variables are not presented as exact numbers. Therefore, it is essential to follow some basic principles that allow for graphical representations to be both transparent and precise so information is not misinterpreted. A previous Statistical Round article has covered the general principles of presenting statistical results as text, tables, and figures [ 1 ]. The current article provides further examples of how to present basic statistical results as graphs and essential aspects to consider to prevent distorted interpretations.

Common considerations

In this section, general considerations for presenting graphs are described. Although not all aspects are essential, we have summarized the key points to improve accuracy and minimize errors when using graphs for information transfer and interpretation.

When data are expressed using dots, lines, diagrams, etc., the axes of the graph should have ticks on a scale sufficient to identify the value corresponding to the position of each mark. Both major ticks and minor ticks can be used to indicate the scale on an axis; however, a corresponding value should at least be presented as a major tick. The axis title should include the name of the measurement variable or result and the unit of measurement. If the scale of the axis is an arithmetic distribution, the interval between the marks should be displayed uniformly. When the value of a variable is transformed during analysis or if the measured value has already been transformed, the interval between the marks should be adjusted according to the characteristics of the data. In this case, the type of transformation or measurement scale used should be included in the graph legend ( Fig. 1 ).

Histogram and accompanying density plot of baseline BNP. The baseline BNP shows a right-skewed distribution. The X-axis scale is logarithmic, and an explanation regarding the x-axis scale should be included in the footnote. Note the difference between the most frequently observed value and the representative value (dashed line). BNP: B-type natriuretic peptide, hsTnI: high-sensitivity troponin I, POD: postoperative day. From the previously-published article: "Moon YJ, Kwon HM, Jung KW, et al. Preoperative high-sensitivity troponin I and B-type natriuretic peptide, alone and in combination, for risk stratification of mortality after liver transplantation. Korean J Anesthesiol 2021; 74: 242-53."

If a part of the axis is removed, it is recommended that a break be inserted into the axis and the scales before and after the break be the same ( Fig. 2 ). If the numbering of an axis has to start from a non-zero value, or if the scales before and after the break must be different, an explanation should be included.

An example of a line and dot plot. Note that there is a break on the y-axis, which is inserted to reduce the white space. The measured value at each time point is on those at the adjacent time points. The interpolated line between dots (markers) indicates their changing trend. The statistical method used was the two-way mixed ANOVA with one within- and one between-factor, and post-hoc Bonferroni adjusted pairwise comparisons. There was statistical intergroup difference (F[1,112] = 6.542, P = 0.012) and a significant interaction between group and time (F[3, 336.4] = 3.535, P = 0.015). * P < 0.05 between groups, † P < 0.05 between groups at each time point.

Each axis should have an appropriate range to distinguish between the data presented in the graph. In the case that the range is too large or too small for the displayed data values, the visual comparison of the data may appear exaggerated or the difference may not be recognizable.

Two-dimensional graphs with orthogonally oriented horizontal and vertical axes (x-axis and y-axis, respectively) that cross at a reference point of zero are most commonly used. However, an additional vertical axis can be included on the opposite side of the existing vertical axis if necessary to represent two variables with different measurement units in a single diagram. 1)

Representative values

The preferred type of graph should be chosen based on the representative value of the data (absolute value, fraction, average, median, etc.). Choosing the most-commonly used graph type for a specific representative value helps the reader to interpret the data or statistical results accurately. However, in the case that the use of an uncommon type of graph is unavoidable, an explanation of the representative value and error term must be provided to prevent misunderstanding.

Symbols, lines, and diagrams for representative values

When a symbol, line, or diagram is used to indicate the representative value of the data, the size or thickness of the line should be adjusted appropriately. Additionally, the degree of adjustment should be uniform so that different sizes or thicknesses are not misunderstood as large or small values. In addition, the size and thickness should be adjusted to indicate real values. When symbols or lines are expressed in overlapping or very close proximity, they must have an appropriate size and thickness to allow for an accurate comparison of the values ( Fig. 2 ). A statistical program or other types of program that draws a professional graph rather than a picture-editing tool should be used to accurately represent the positions of symbols, lines, and diagrams with the corresponding values. The graph tools provided by most statistical programs offer user-selected symbols and lines that can be accurately marked according to the corresponding values.

It is recommended that the same symbols be used every time a representative value is represented. However, to distinguish between different groups, different symbols can be used to improve discrimination. The use of different symbols to present the representative values of the same group is not recommended.

A line can be used either when every point represents a specific value or when it visually indicates a change between two symbols ( Fig. 3 ). In the latter case, adding lines between symbols can make the interpretation difficult if the change is not meaningful. Different lines should be used for different groups or situations ( Fig. 2 ). Sometimes, it may be difficult to distinguish between different dashes owing to the line thickness, the size of the graph, or overlapping lines. Therefore, different line types should be adjusted to allow for easy discernability. One option may be to use a color graph; however, this is recommended only when it is impossible to express the information accurately in black and white. Because some readers may have difficulty distinguishing colors, care must be taken regarding color selection.

An example of a dot-line graph. Dots and error bars indicate the means and SDs. The interpolated line allows for enhanced estimation of the changing trend. Bar plots could also be used to represent this kind of statistical result.

The representative value can also be presented using a shape. If the area or form of the shape is proportional to the value, an explanation of this fact should be included. For a diagram expressed at regular intervals where the height or length corresponds to the value (such as a histogram), precautions similar to those regarding symbols or lines should be applied.

Various colors or specific patterns can be used inside the diagram to facilitate interpretation. It is good practice to set different colors or patterns for each group or to use them differently to allow for data before and after an event to be distinguishable. However, such a graph may become complicated as a result of too many colors and patterns or a lack of unified notation.

A description of the variable or situation, represented by lines, symbols, or shapes, should be included in the graph legend. The legend can be located inside or outside the graph, as long as it does not interfere with interpretation. Explanations of values that the symbols, lines, and/or diagrams represent should be included. If abbreviations are used, their definitions should be included in the figure legend. Borders of the legend box can be added as needed around the legend to make it easier to read, and it may be helpful to match the order of data as it appears in both the legend and the graph.

Statistically inferred representative values and their corresponding errors can be indicated on the graph in various ways. Most commonly, whisker-shaped symbols are used to express errors. Depending on the type of graph, it is typically expressed by the length of a line or an area. When there are many representative values or considerable overlap, the symbols used to express the error will also overlap, making it difficult to distinguish between them. If the spread of data is equal on both sides, such as with a normal distribution, it can be presented in only one direction; however, both errors should be presented when the data are skewed to one side. Alternatively, to avoid overlap, the positions of the corresponding values may be moved forward or backward slightly; however, an explanation of this should be included in the figure legend. For example, if it is difficult to distinguish between the means and standard deviations of blood pressure measured at 5 sec after medication in two groups, the representative values of each group can be displayed at 4.9, and 5.1 sec. It is recommended to describe an explanation that the blood pressure values of the two groups measured at specific time point are displayed separately in the figure legend ( Fig. 2 ). For representative examples, refer to the previous Statistical Round article [ 1 ].

Annotations can be added to the graph to explain specific values or statistically significant differences. Annotations are also used to highlight visible differences in the graphs (in which case, instead of an annotation, an explanation should be included in the figure legend). Symbols can be used for annotations that explain statistical differences and should be consistent in type and order throughout the paper. As specified in the instructions to the authors for the Korean Journal of Anesthesiology, it usually follows the order: * (asterisk), † (dagger), ‡ (double dagger, diesis), § (silcrow), and ¶ (pilcrow) [ 2 , 3 ].

Figure legend

In order for readers to know what is contained in a figure and the results of any statistical analysis conducted, a figure legend should be included. A figure legend usually consists of a graph title, a brief description of the graph content, statistical methods, and results. Definitions of any abbreviations and/or symbols used should also be included to facilitate interpretation.

Commonly used graphs

Scatter plots.

A scatter plot shows the associations between two numerical variables measured from one subject ( Fig. 4 ). By adding another variable, three-dimensional expression is also possible. Scatter plots can also be used for ordered categorical variables, at the expense of reduced readability. A scatter plot displays the coordinates of the measured values on an orthogonal plane with two variables as axes using specific symbols, such as dots. The two variables may be independent of each other or may have a cause-effect relationship. Scatter plots are primarily used in the data exploration stage to examine the relationship between two variables, and a trend line 2) can be added to indicate a statistically significant relationship between the two variables. Scatter plots help the reader to understand the relationship between two variables and contribute considerably to the visual expression and understanding of correlation or regression analyses.

An example of a scatter plot. This plot presents the cardiac output value for the same patients using two different measurement methods: EDCO (esophageal doppler cardiac output) and TDCO (continuous thermodilution method). From the previously-published article: “Shim YH, Oh YJ, Nam SB, et. al. Cardiac output estimations by esophageal Doppler cannot replace estimations by the thermodilution method in off-pump coronary artery bypass surgery patients. Korean J Anesthesiol 2003; 45: 456–61.”

As described above, a scatter plot usually demonstrates the relationship between the actual values between two variables. In addition, however, a scatter plot is used for interpretation in some statistical methods. One example is the Bland-Altman scatter plot, which is a method used to analyze the agreement between two measurements ( Fig. 5 ). In addition, scatter plots are often used to evaluate residuals in regression analyses or visually check the fit of a statistically estimated model.

Bland-Altman scatter plot comparing the standard frontal position with an alternative mandibular position. The dotted horizontal line represents the mean difference between the two measures. The dashed horizontal lines represent the 95% limit of agreement between the two measures. The 95% limit of agreement is drawn at the mean difference +/- 1.96 times the standard deviation of the difference. The solid line is the line of equality which indicates the exact same value between two measures.

A line plot is a graph that connects a series of repeatedly measured data points using a straight or curved line, based on a scatter plot. This type of graph is used in several fields to represent various statistical results. A commonly used example is any case in which the data are measured at a set time interval. A run chart (run-sequential plot) is a line plot that displays the data in chronological order. When applying a continuous variable on one axis, such as time, caution must be taken regarding the scale interval. Ordered categorical variables are also candidates for line plots. With scatter plots, measured values are mainly used to examine the data distribution; however, line plots are used primarily for averages, which are representative values of the measured data under specific conditions in the relevant group. As previously mentioned, the errors (such as the standard deviation) must be displayed on a line plot with the representative values.

For bar charts, the height or length of each bar represents the value of the variables, and the ratio between them makes it easy to visualize the differences between categorical variables. On either the horizontal or vertical axis, the values are presented as scale values, whereas on the other axis, the values are presented by other measurement parameters. This type of graph can also be used to express continuous variables, and it is possible to express multiple measured values as cumulative or grouped values using different bar appearances.

A histogram is a graph used to represent the frequency distribution of the data ( Fig. 1 ). Each column’s height indicates the number of samples corresponding to each bin, divided by a fixed interval. Because the variable corresponding to the bin has the characteristics of a continuous variable, the bins are adjacent to each other but do not overlap. Bar plots differ from histograms. In a bar plot, the bars are separated from each other because they represent the values of categorical variables. Each column’s height in a histogram can also be normalized in the form of the frequency of the samples for the total sample size. In this case, mathematical methods, such as kernel density estimation, can be used to smooth the overall shape (smoothing) and estimate a density plot that can be used to represent the distribution of the data.

Boxplots and box-and-whisker plots

A boxplot is a graph that is used to express the median and quartiles of data using a box shape. It is often used to represent nonparametric statistics ( Fig. 6 , Supplementary R code ). A whisker, which is represented by a line extending from each box, can be used to indicate the range of the data (box-and-whisker plot). The range of data defined using whiskers can be set according to the researchers’ needs. For example, the ends of both whiskers can be the maximum and minimum values or values corresponding to 10% and 90% of the entire data range. If both ends of the whiskers are set to values that correspond to the first quartile minus 1.5 times the interquartile range (IQR) and the third quartile plus 1.5 times the IQR, data outside this range can be defined as outliers. The box-and-whisker plot enables recognition of the distribution of data without a specific distribution assumption and displays data dispersion and kurtosis. Depending on the data spread, one of the quartiles and the median may overlap. In this case, the location of the median should be clearly expressed. Violin and bee-swarm plots are improved versions of the box-and-whisker plot and can be used to represent the frequency of data at specific values along with the spread of data.

An example of a box-whisker plot. Estimated median (Q1, Q3) [min:max] from the sample data is 1.1 (0.8, 1.3) [0.1:2.1]. This graph includes explanations of the components of the box-whisker plot. These are not necessary for the general purpose of publication. A significance marker can be added, though it was not used in this graph. If a significance maker is added, it should be located on the shoulder or alongside the whisker. If markers are located over the mid-top of the whiskers, these could be interpreted as outliers if no detailed explanation is provided. The limits of the whiskers can be varied depending on the purpose.

Other commonly used graphs

In addition to the basic graphs previously introduced, various graphs have also been used to present the results or evaluate the analysis process for a specific statistical method. Some examples include receiver operating characteristic (ROC) curves [ 4 ], survival curves, regression curves by linear regression analysis, and dose-response curves. These graphs deliver information on a specific relationship between interpreted statistical results or indicate the trend of independent and dependent variables expressed as functions. These graphs have predetermined components that reflect the characteristics of the data and analysis, and these components must be included in the graph. Additional information must also be included with these graphs to facilitate interpretation, such as corresponding statistics, tables, trend lines, and guidelines. The graph output from a statistics program includes most of the basic requirements, but some parts may need to be added or removed in some cases. In addition, the graph should be composed according to the guidelines of the target journal because the requirements may vary.

Graphs for specific statistical analysis methods

In general, statistical analyses begin with the selection of a specific statistical method according to the characteristics of the collected variables and the expected relationship between them. Most statistical methods require particular features and relationships between variables, and the estimated results are formalized. The following sections include graphs that express specific statistical results. The following graphs are only examples, and other graph types may be appropriate, depending on the characteristics of the data collected.

All of the example graphs were created using R software 4.1.0 for Windows (R Development Core Team, Austria, 2021). The ggplot2 package used in the R software provides various options for creating graphs in the medical field and a user-centered graph editing function. All examples are fictitious data assuming clinical or experimental conditions and should not be interpreted as actual data. All virtual data and R codes are provided in the Supplementary Materials ( Supplementary material 1; R code ).

Independent t-tests

For the first example, data on the time from administration of a neuromuscular blocking agent antagonist to the patients’ first movement after general anesthesia between two different agents are compared ( Supplementary material 2; reverse.csv ). In total, 218 patients were included in this study. Both groups satisfied the assumption of normal distribution but violated the equality of variance; therefore, an unequal variance t -test was performed ( Table 1 ). Fig. 7 shows a graph of the results in the form of a vertical bar graph ( Supplementary material 1; R code ). 3)

An example of a horizontal bar plot with an error bar. Positive-sided error bars are marked because the SDs are located at the same distance from the mean. The recommended legend for this figure is: “The elapsed time from administration to first movement for two different reversal agents: an anticholinergic (n = 109) and a new drug (n = 109); *two-sided P value < 0.05 with the unequal variances t -test”.

Time to Movement After Two Neuromuscular Reversal Agents

Data are presented as mean ± SD.

Paired t-tests

The next example includes virtual data on the required air volume to ensure endotracheal cuff sealing during general anesthesia ( Supplementary material 3; cuff_pressure.csv ). After tracheal intubation with an adequately sized tube, cuff sealing was achieved through either an arbitrary volume that prevented end-inspiratory leak or by a volume resulting in a cuff pressure of 25 mmHg. The two alternative volumes necessary for the two cuff sealing methods were measured for each patient, and a total of 100 patients were included. A paired t -test was performed because the two methods were conducted on each patient. The results are presented in Table 2 . Fig. 3 shows a graphical representation of the results ( Supplementary material 1; R code ).

Cuff Inflation Volume to Prevent End-inspiratory Gas Leakage

Values are presented as mean ± SD.

Comparisons between more than three independent groups

For the following example, information on the amount of opioids administered for pain control after three types of surgery were obtained ( Supplementary material 4; opioid_surgery.csv ). The total number of patients was 171 (57 in each group).

One-way analysis of variance (ANOVA) was performed, and there was a statistically significant difference in the opioid dose administered according to the surgery type. Tukey’s test was performed for post-hoc testing. The results showed that the opioid dose administered after operation C was significantly higher than that administered after operations A or B ( Table 3 ).

Postoperative Opioid Requirements according to Three Different Types of Surgery

A graph of the statistical results is shown in Fig. 8 . As the three groups were not related to each other, they are expressed as bar graphs. The results of the statistical tests are presented in the Supplementary material 1; R code .

An example of a vertical bar plot. The asterisk (*) is used to represent a comparative statistically significant result.

Comparisons for repeatedly measured data

In the following example, virtual data on the effect of an antihypertensive drug on diastolic blood pressure were used ( Supplementary material 5; dbpmedication.csv ). A total of 114 patients were included, and the control and treatment groups were equally allocated. Data were measured six times at 5-second intervals, including the time of drug administration. For statistical analysis, two-way mixed ANOVA with one within-factor and one between-factor was used. There was a statistically significant difference between the treatment and control groups (F[1,112] = 6.542, P = 0.012), and there was a statistically significant interaction between the treatment and the time (F[3, 336.4] = 3.535, P = 0.015). The treatment group showed significant differences at 15, 20, and 25 s after administration (adjusted P = 0.004, P = 0.003, and P = 0.006, respectively; Table 4 ). The detailed statistical analysis process was omitted, but a graph of the results is shown in Fig. 2 . The graphs are slightly shifted to the left and right so that they can be distinguished from each other, and a gap is set on the y-axis. These methods make the results easier to visualize by preventing the graphs from overlapping and reducing the whitespace ( Supplementary material 1; R code ).

Changes in Diastolic Blood Pressure after Antihypertensive Treatment

Values are presented as mean ± SD. Two-way mixed analysis of variance with one within factor and one between factor. A statistically significant intergroup difference (F[1,112] = 6.542, P = 0.012) and a significant interaction between group and time (F[3, 336.4] = 3.535, P = 0.015) are seen.

Categorical data comparisons

For the following example, two categorical variables (endotracheal intubation success and sore throat occurrence) were assessed in relation to two different intubation techniques ( Supplementary material 6; sorethr.csv ). The data included two observations from 106 patients (53 patients in each group). The chi-square test with Yate’s correction showed that the success rate of the new tracheal intubation technique was significantly higher than that of the conventional technique (P = 0.018), whereas there was no statistical difference in sore throat occurrence ( Table 5 ). The results are represented using a bar graph classified by observation ( Fig. 9 ). Because the 95% CIs are not symmetrically distributed with respect to the representative values, both error bars are presented and statistical significance is indicated using symbols. To better represent the data, the sample size may also be displayed ( Supplementary material 1; R code ).

An example of a grouped bar plot. The height of each bar indicates the observed rate. If the CIs of the rate are not distributed symmetrically from the observed rate, both sides of the error bar should be presented. The asterisk indicates statistical significance.

Observed Intubation Success and Presence of Sore Throat after the Conventional and New Intubation Technique

Values are presented as numbers (percentiles).

Other commonly used statistical graphs

Correlation analyses, linear regression.

As an example of correlation analysis, the blood concentrations of three intravenous anesthetic adjuvants were measured during propofol general anesthesia ( Supplementary material 7; pretxlevel.csv ). All three adjuvants (A, B, and C) showed a positive correlation with exposure time (correlation coefficient r = 0.71, r = 0.65, and r = 0.42, respectively), but only the coefficient of adjuvant A was statistically significant (P = 0.014, P = 0.117, and P = 0.132, respectively; Fig. 10 ). Various diagrams can be used to show these correlations. However, in this article, a scatter plot with a trend line for the group, and the statistical analysis results are presented ( Supplementary material 1; R code ).

An example of a scatter plot with a linear trend line for the correlation analysis. The asterisk indicates statistical significance.

A scatter plot with a trend line clearly represents the data and is used more often in linear regression analyses than in correlation analyses. For the linear regression example graph, blood glucose concentrations and the degree of glucose deposition in the mitral valve node were used in patients with type 2 diabetes with rheumatic mitral valve insufficiency ( Supplementary material 8; dmmvi.csv ). Linear regression analysis was performed with blood glucose concentration as the independent variable and the degree of glucose deposition in the mitral valve as the dependent variable. The regression equation was estimated to be “Glucose in nodule = 0.048 × Blood glucose concentration + 32.98 (P < 0.001)”. The graph in Fig. 11 shows the observed values with a regression line and other necessary information ( Supplementary R code ).

An example of a scatter plot with a trend line for the linear regression. Around the regression line, the shadowed area indicates the range of the 95% CI of the estimated coefficient. The estimated regression line formula is also presented in the graph with statistics.

Logistic regression

For the following example, virtual data showed the influence of five factors on specific test results ( Supplementary material 9; five_factors.csv ). The test result is a yes/no dichotomous variable, whereas all five factors (F1 to F5) are continuous variables. Although logistic regression analyses involve various assumptions that must be verified before statistical analysis to obtain accurate results, the contents of such verification processes have been omitted. The model estimated by logistic regression provides the odds ratio (OR) for each independent variable ( Table 6 ). A graphic representation of ORs allows for a clearer interpretation than a table in the case of multiple independent variables or ORs with many numbers ( Fig. 12 , Supplementary material 1; R code ).

An example of a dot plot with an error bar. For each level of factors (y-axis), corresponding odds ratio (OR) and 95% CIs are presented using dots and accompanying horizontal error bar. The dotted line indicates the reference value of 1. The estimated OR would not be different from 1.0 statistically if its error bar crossed this reference line.

Estimated OR and 95% CI of Logistic Regression Model

OR: odds ratio.

Survival analysis

Survival analysis is a statistical method that can be applied to mortality data and various types of longitudinal data. There are various methods, from the nonparametric Kaplan-Meier method to more complex methods involving different parametric models. Kaplan-Meier survival analysis and Cox regression models are widely used in the medical field. Survival analysis results usually accompany the survival curve, which can increase the reader’s understanding of the results through visualization. For details on the survival curve, refer to the previous Statistical Round article [ 5 , 6 ]. An example of a survival curve is shown in Fig. 13 . In addition to several important pieces of information that should be included, the survival table must be attached to the survival curve because the number at risk is reduced at the end of the observation. This can minimize the likelihood of misinterpretation.

An example of a survival curve. Two survival curves with 95% CIs are presented. The median survival time is also indicated for each curve. Because the number at risk decreases at the end of observation, the survival table should be incorporated with curves to clarify the statistical inference process. From the previously-published article: "In J, Lee DK. Survival analysis: part II - applied clinical data analysis. Korean J Anesthesiol 2019; 72: 441-57."

Dose-response curve

For this example, various concentrations of two antibiotics were assessed by measuring the absorbance of a specific light known to be proportional to the normal bacterial flora amount in a culture medium ( Supplementary material 10; antiobsorp.csv ). The data were fitted using a 4-parameter log-logistic model; the estimated parameters are summarized in Table 7 . A graph of the fitted model is presented in Fig. 14 ( Supplementary material 1; R code ). The absorbance values for the doses of the two antibiotics are expressed using symbols, and a dose-response curve was drawn. Compared to a table that includes only numbers, using a graph is more intuitive and easier to interpret.

An example of multiple dose-response curves. Observed values are plotted using dot symbols: filled circles and triangles. The straight solid and dashed lines indicate the ED50 value of each curve. Be aware that the x-axis is log scaled.

Dose-response Curve Model Fit Result

Dose-response curve fit using a 4-parameter log-logistic model. Values are presented as estimates (95% CI). ED: effective dose at a certain response level indicated by the following number as the percentile.

Conclusions

There are many types of graphs for various statistical methods that can be used to represent data and results, depending on their characteristics. Trying out a few types of graphs that show the characteristics well and then choosing the best one among them is recommended. Presenting results with a table and a figure simultaneously takes up space and can distract readers. Therefore, it is recommended to use graphs and discuss significant results in the body of the manuscript, and tables of granular information can be moved to the supplementary material or vice versa.

1) In addition to a two-dimensional graph consisting of a horizontal (x-axis) and a vertical axis (y-axis), a three-dimensional graph using a third axis (z-axis) perpendicular to both axes is also widely used in specific fields. In this article, we will focus on two-dimensional graphs.

2) The trend line is a type of regression graph that provides useful information regarding the relationship between two variables and can be fitted as linear, quadratic, or cubic formulas.

3) When the range of error has both positive and negative values, like a continuous variable, the histogram contains the possibility of error in a strict sense. This is because, when expressed as a bar graph, the error range on one side does not appear on the graph (as shown in Fig. 7). While there is a way to express both sides when the range of error is different, it is not commonly used. In most medical papers, they are used without distinction given the general perception that the error range expressed in the bar graph is naturally distributed equally on both sides.

Conflicts of Interest

No potential conflict of interest relevant to this article was reported.

Author Contributions

Jae Hong Park (Conceptualization; Methodology; Validation; Writing – review & editing)

Dong Kyu Lee (Data curation; Formal analysis; Methodology; Supervision; Validation; Writing – original draft; Writing – review & editing)

Hyun Kang (Conceptualization; Data curation; Writing – review & editing)

Jong Hae Kim (Conceptualization; Data curation; Writing – review & editing)

Francis Sahngun Nahm (Conceptualization; Data curation; Writing – review & editing)

EunJin Ahn (Conceptualization; Data curation; Writing – review & editing)

Junyong In (Conceptualization; Data curation; Validation; Writing – review & editing)

Sang Gyu Kwak (Conceptualization; Data curation; Writing – review & editing)

Chi-Yeon Lim (Conceptualization; Data curation; Writing – review & editing)

Supplementary Materials

Supplementary material 1., supplementary material 2., supplementary material 3..

cuff pressure

Supplementary Material 4.

opioid_surgery

Supplementary Material 5.

dbpmedication

Supplementary Material 6.

Supplementary material 7., supplementary material 8., supplementary material 9..

five factors

Supplementary Material 10.

• Analysis and Presentation of Experimental Results
• January 2017
• Publisher: Springer International Publishing
• ISBN: 978-3-319-53345-2

• National Technical University of Athens

• Université de Mons

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Statistics By Jim

Making statistics intuitive

Experimental Design: Definition and Types

By Jim Frost 3 Comments

What is Experimental Design?

An experimental design is a detailed plan for collecting and using data to identify causal relationships. Through careful planning, the design of experiments allows your data collection efforts to have a reasonable chance of detecting effects and testing hypotheses that answer your research questions.

An experiment is a data collection procedure that occurs in controlled conditions to identify and understand causal relationships between variables. Researchers can use many potential designs. The ultimate choice depends on their research question, resources, goals, and constraints. In some fields of study, researchers refer to experimental design as the design of experiments (DOE). Both terms are synonymous.

Ultimately, the design of experiments helps ensure that your procedures and data will evaluate your research question effectively. Without an experimental design, you might waste your efforts in a process that, for many potential reasons, can’t answer your research question. In short, it helps you trust your results.

Learn more about Independent and Dependent Variables .

Design of Experiments: Goals & Settings

Experiments occur in many settings, ranging from psychology, social sciences, medicine, physics, engineering, and industrial and service sectors. Typically, experimental goals are to discover a previously unknown effect , confirm a known effect, or test a hypothesis.

Effects represent causal relationships between variables. For example, in a medical experiment, does the new medicine cause an improvement in health outcomes? If so, the medicine has a causal effect on the outcome.

An experimental design’s focus depends on the subject area and can include the following goals:

• Understanding the relationships between variables.
• Identifying the variables that have the largest impact on the outcomes.
• Finding the input variable settings that produce an optimal result.

For example, psychologists have conducted experiments to understand how conformity affects decision-making. Sociologists have performed experiments to determine whether ethnicity affects the public reaction to staged bike thefts. These experiments map out the causal relationships between variables, and their primary goal is to understand the role of various factors.

Conversely, in a manufacturing environment, the researchers might use an experimental design to find the factors that most effectively improve their product’s strength, identify the optimal manufacturing settings, and do all that while accounting for various constraints. In short, a manufacturer’s goal is often to use experiments to improve their products cost-effectively.

In a medical experiment, the goal might be to quantify the medicine’s effect and find the optimum dosage.

Developing an Experimental Design

Developing an experimental design involves planning that maximizes the potential to collect data that is both trustworthy and able to detect causal relationships. Specifically, these studies aim to see effects when they exist in the population the researchers are studying, preferentially favor causal effects, isolate each factor’s true effect from potential confounders, and produce conclusions that you can generalize to the real world.

To accomplish these goals, experimental designs carefully manage data validity and reliability , and internal and external experimental validity. When your experiment is valid and reliable, you can expect your procedures and data to produce trustworthy results.

An excellent experimental design involves the following:

• Lots of preplanning.
• Developing experimental treatments.
• Determining how to assign subjects to treatment groups.

The remainder of this article focuses on how experimental designs incorporate these essential items to accomplish their research goals.

Learn more about Data Reliability vs. Validity and Internal and External Experimental Validity .

Preplanning, Defining, and Operationalizing for Design of Experiments

This phase of the design of experiments helps you identify critical variables, know how to measure them while ensuring reliability and validity, and understand the relationships between them. The review can also help you find ways to reduce sources of variability, which increases your ability to detect treatment effects. Notably, the literature review allows you to learn how similar studies designed their experiments and the challenges they faced.

Operationalizing a study involves taking your research question, using the background information you gathered, and formulating an actionable plan.

This process should produce a specific and testable hypothesis using data that you can reasonably collect given the resources available to the experiment.

• Null hypothesis : The jumping exercise intervention does not affect bone density.
• Alternative hypothesis : The jumping exercise intervention affects bone density.

To learn more about this early phase, read Five Steps for Conducting Scientific Studies with Statistical Analyses .

Formulating Treatments in Experimental Designs

In an experimental design, treatments are variables that the researchers control. They are the primary independent variables of interest. Researchers administer the treatment to the subjects or items in the experiment and want to know whether it causes changes in the outcome.

As the name implies, a treatment can be medical in nature, such as a new medicine or vaccine. But it’s a general term that applies to other things such as training programs, manufacturing settings, teaching methods, and types of fertilizers. I helped run an experiment where the treatment was a jumping exercise intervention that we hoped would increase bone density. All these treatment examples are things that potentially influence a measurable outcome.

Even when you know your treatment generally, you must carefully consider the amount. How large of a dose? If you’re comparing three different temperatures in a manufacturing process, how far apart are they? For my bone mineral density study, we had to determine how frequently the exercise sessions would occur and how long each lasted.

How you define the treatments in the design of experiments can affect your findings and the generalizability of your results.

Assigning Subjects to Experimental Groups

A crucial decision for all experimental designs is determining how researchers assign subjects to the experimental conditions—the treatment and control groups. The control group is often, but not always, the lack of a treatment. It serves as a basis for comparison by showing outcomes for subjects who don’t receive a treatment. Learn more about Control Groups .

How your experimental design assigns subjects to the groups affects how confident you can be that the findings represent true causal effects rather than mere correlation caused by confounders. Indeed, the assignment method influences how you control for confounding variables. This is the difference between correlation and causation .

Imagine a study finds that vitamin consumption correlates with better health outcomes. As a researcher, you want to be able to say that vitamin consumption causes the improvements. However, with the wrong experimental design, you might only be able to say there is an association. A confounder, and not the vitamins, might actually cause the health benefits.

Let’s explore some of the ways to assign subjects in design of experiments.

Completely Randomized Designs

A completely randomized experimental design randomly assigns all subjects to the treatment and control groups. You simply take each participant and use a random process to determine their group assignment. You can flip coins, roll a die, or use a computer. Randomized experiments must be prospective studies because they need to be able to control group assignment.

Random assignment in the design of experiments helps ensure that the groups are roughly equivalent at the beginning of the study. This equivalence at the start increases your confidence that any differences you see at the end were caused by the treatments. The randomization tends to equalize confounders between the experimental groups and, thereby, cancels out their effects, leaving only the treatment effects.

For example, in a vitamin study, the researchers can randomly assign participants to either the control or vitamin group. Because the groups are approximately equal when the experiment starts, if the health outcomes are different at the end of the study, the researchers can be confident that the vitamins caused those improvements.

Statisticians consider randomized experimental designs to be the best for identifying causal relationships.

If you can’t randomly assign subjects but want to draw causal conclusions about an intervention, consider using a quasi-experimental design .

Learn more about Randomized Controlled Trials and Random Assignment in Experiments .

Randomized Block Designs

Nuisance factors are variables that can affect the outcome, but they are not the researcher’s primary interest. Unfortunately, they can hide or distort the treatment results. When experimenters know about specific nuisance factors, they can use a randomized block design to minimize their impact.

This experimental design takes subjects with a shared “nuisance” characteristic and groups them into blocks. The participants in each block are then randomly assigned to the experimental groups. This process allows the experiment to control for known nuisance factors.

Blocking in the design of experiments reduces the impact of nuisance factors on experimental error. The analysis assesses the effects of the treatment within each block, which removes the variability between blocks. The result is that blocked experimental designs can reduce the impact of nuisance variables, increasing the ability to detect treatment effects accurately.

Suppose you’re testing various teaching methods. Because grade level likely affects educational outcomes, you might use grade level as a blocking factor. To use a randomized block design for this scenario, divide the participants by grade level and then randomly assign the members of each grade level to the experimental groups.

A standard guideline for an experimental design is to “Block what you can, randomize what you cannot.” Use blocking for a few primary nuisance factors. Then use random assignment to distribute the unblocked nuisance factors equally between the experimental conditions.

You can also use covariates to control nuisance factors. Learn about Covariates: Definition and Uses .

Observational Studies

In some experimental designs, randomly assigning subjects to the experimental conditions is impossible or unethical. The researchers simply can’t assign participants to the experimental groups. However, they can observe them in their natural groupings, measure the essential variables, and look for correlations. These observational studies are also known as quasi-experimental designs. Retrospective studies must be observational in nature because they look back at past events.

Imagine you’re studying the effects of depression on an activity. Clearly, you can’t randomly assign participants to the depression and control groups. But you can observe participants with and without depression and see how their task performance differs.

Observational studies let you perform research when you can’t control the treatment. However, quasi-experimental designs increase the problem of confounding variables. For this design of experiments, correlation does not necessarily imply causation. While special procedures can help control confounders in an observational study, you’re ultimately less confident that the results represent causal findings.

Learn more about Observational Studies .

For a good comparison, learn about the differences and tradeoffs between Observational Studies and Randomized Experiments .

Between-Subjects vs. Within-Subjects Experimental Designs

When you think of the design of experiments, you probably picture a treatment and control group. Researchers assign participants to only one of these groups, so each group contains entirely different subjects than the other groups. Analysts compare the groups at the end of the experiment. Statisticians refer to this method as a between-subjects, or independent measures, experimental design.

In a between-subjects design , you can have more than one treatment group, but each subject is exposed to only one condition, the control group or one of the treatment groups.

A potential downside to this approach is that differences between groups at the beginning can affect the results at the end. As you’ve read earlier, random assignment can reduce those differences, but it is imperfect. There will always be some variability between the groups.

In a  within-subjects experimental design , also known as repeated measures, subjects experience all treatment conditions and are measured for each. Each subject acts as their own control, which reduces variability and increases the statistical power to detect effects.

In this experimental design, you minimize pre-existing differences between the experimental conditions because they all contain the same subjects. However, the order of treatments can affect the results. Beware of practice and fatigue effects. Learn more about Repeated Measures Designs .

Design of Experiments Examples

For example, a bone density study has three experimental groups—a control group, a stretching exercise group, and a jumping exercise group.

In a between-subjects experimental design, scientists randomly assign each participant to one of the three groups.

In a within-subjects design, all subjects experience the three conditions sequentially while the researchers measure bone density repeatedly. The procedure can switch the order of treatments for the participants to help reduce order effects.

Matched Pairs Experimental Design

A matched pairs experimental design is a between-subjects study that uses pairs of similar subjects. Researchers use this approach to reduce pre-existing differences between experimental groups. It’s yet another design of experiments method for reducing sources of variability.

Researchers identify variables likely to affect the outcome, such as demographics. When they pick a subject with a set of characteristics, they try to locate another participant with similar attributes to create a matched pair. Scientists randomly assign one member of a pair to the treatment group and the other to the control group.

On the plus side, this process creates two similar groups, and it doesn’t create treatment order effects. While matched pairs do not produce the perfectly matched groups of a within-subjects design (which uses the same subjects in all conditions), it aims to reduce variability between groups relative to a between-subjects study.

On the downside, finding matched pairs is very time-consuming. Additionally, if one member of a matched pair drops out, the other subject must leave the study too.

Learn more about Matched Pairs Design: Uses & Examples .

Another consideration is whether you’ll use a cross-sectional design (one point in time) or use a longitudinal study to track changes over time .

A case study is a research method that often serves as a precursor to a more rigorous experimental design by identifying research questions, variables, and hypotheses to test. Learn more about What is a Case Study? Definition & Examples .

In conclusion, the design of experiments is extremely sensitive to subject area concerns and the time and resources available to the researchers. Developing a suitable experimental design requires balancing a multitude of considerations. A successful design is necessary to obtain trustworthy answers to your research question and to have a reasonable chance of detecting treatment effects when they exist.

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Reader Interactions

March 23, 2024 at 2:35 pm

Dear Jim You wrote a superb document, I will use it in my Buistatistics course, along with your three books. Thank you very much! Miguel

March 23, 2024 at 5:43 pm

Thanks so much, Miguel! Glad this post was helpful and I trust the books will be as well.

April 10, 2023 at 4:36 am

What are the purpose and uses of experimental research design?

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Yield should be presented in parentheses after the compound name (or its equivalent). Weight and percentage should be separated by a comma – for example, the lactone (7.1 g, 56%).

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For the presentation of elemental analyses, both forms (Found: C, 63.1; H, 5.4. C 13 H 13 NO 4 requires C, 63.2; H, 5.3%) and (Found: C, 62.95; H, 5.4. Calc. for C 13 H 13 NO 4 : C, 63.2; H, 5.3%) are acceptable. Analyses are normally quoted to the nearest 0.1%, but a 5 in the second place of decimals is retained.

If a molecular weight is to be included, the appropriate form is: [Found: C, 63.1; H, 5.4%; M (mass spectrum), 352 (or simply M+, 352). C 13 H 13 NO 4 requires C, 63.2; H, 5.3%; M, 352].

We encourage authors to provide instrumental details and the chromatograms of the performed measurements in the Supplementary Information where possible.

These should be given in the form λmax(EtOH)/nm 228 (ε/dm 3  mol -1  cm -1  40 900), 262 (19 200) and 302 (11 500). Inflections and shoulders are specified as 228infl or 262sh. Alternatively the following form may be used: λmax (EtOH)/nm 228, 262 and 302 (ε/dm 3  mol -1  cm -1  40 900, 19 200 and 11 500); log ε may be quoted instead of ε.

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A broad signal may be denoted by br, such as 2.43 (1 H, br s, NH). Order of citation in parentheses: (i) number of equivalent nuclei (by integration), (ii) multiplicity (s, d, t, q), (iii) coupling constant – for example,  J 1,2  2,  J A B 4, (iv) assignment; italicisation can be used to specify the nuclei concerned (for example, CH3CH2). The proton attached to C-6 may be designated C(6)H or 6-H; the methyl attached to C-6, 6-Me or C(6)Me.

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P. Cui, D. P. McMahon, P. R. Spackman, B. M. Alston, M. A. Little, G. M. Day and A. I. Cooper, 2019, CCDC Experimental Crystal Structure Determination: 1915306, DOI: 10.5517/ccdc.csd.cc22912j

Please also refer to the guidelines from the relevant repository on which information to provide in a citation.

When a study involves the use of live animal subjects, authors should adhere to the Animal Research: Reporting In Vivo Experiments (ARRIVE) 2.0 guidelines. When a study involves the use of human subjects, authors should adhere to the general principles set out in the Declaration of Helsinki .

Authors must include in the "methods/experimental" section of the manuscript a statement that all experiments were performed in compliance with the relevant guidelines. The statement must name the institutional/local ethics committee that has approved the study, and where possible the approval or case number should be provided.

Details of all guidelines followed should be provided. A statement regarding informed consent is required for all studies involving human subjects. Reviewers may be asked to comment specifically on any cases in which concerns arise.

For studies involving the use of animal subjects, authors are encouraged to make the completed ARRIVE 2.0 checklist available during peer review, for example by sharing it as part of the Supplementary Information (SI) or citing the deposited item.

The journals’ editorial teams reserve the right to request additional information in relation to experiments on vertebrates or higher invertebrates as necessary for the evaluation of the manuscript e.g., in the context of appropriate animal welfare or studies that involve death as an experimental endpoint.

Authors and referees should note the following guidelines for articles reporting electrochemical data and setup of batteries. It is the authors’ responsibility to ensure that the following information is provided in the main manuscript or Supplementary Information as appropriate.

The setup used for electrochemical testing should be clearly specified in the Experimental Information. For example, full or half cells, reference electrode (if used), testing temperature, etc.

When reporting electrochemical performance data, the authors should clearly state how many experimental runs these data are based on. The electrochemical performance value calculations should be clearly explained (including information on using charging or discharging values). All electrochemical data should be reported to an appropriate number of significant figures, along with standard deviation and error bars on graphs.

When reporting electrode performance values , the thickness of the electrode and the mass percentage of all electrode components (active material, additive, binder, etc.), the total mass of the electrode, and the geometric area of the electrode should be provided.

When reporting device-level performance values, the mass percentage of all battery components (active material, additive, binder, casing, current collector, electrolyte, separator, etc.), the total mass of the battery, and the geometric area of the electrode should be reported.

The mass percent and theoretical capacity of the active material should be provided if the theoretical capacity of the studied material is known. The theoretical capacity should be used to calculate C-rate. Alternatively, a rigorous use of A g -1 is recommended.

Pre-cycling and/or first cycle data should be reported.

Calculations of battery capacity should report the capacity obtained (in mAh g -1 ; if appropriate, volumetric values can be added in the unit of mAh cm -3 ) with the cycling rate and at what cycle number this capacity was obtained clearly stated. Average capacities for ≥3 cells with standard deviation are preferred.

It is the authors’ responsibility to provide rigorous evidence for the identity and purity of the biomolecules (for example, enzymes, proteins, DNA/RNA, oligosaccharides, oligonucleotides) described.

The identity of the biomolecule should be substantiated by employing at least one appropriate method, which may include one or more of the following:

Mass spectrometry

• Sequencing data (for proteins and oligonucleotides)
• High field 1 H or 13 C NMR

The purity should be established by one or more of the following

• Gel electrophoresis
• Capillary electrophoresis

Sequence verification should also be carried out for nucleic acids in molecular biology, including all mutants; for new protein or gene sequences, the entire sequence should be provided. For organic synthesis involving DNA, RNA oligonucleotides, their derivatives or mimics, purity should be established using HPLC and mass spectrometry as a minimum.

Provide usual organic chemistry analytical requirements for the novel monomer ( see Organic compounds ). However, it is not necessary to provide this level of characterisation for the oligonucleotide into which the novel monomer is incorporated.

Provide sufficient detail to identify the species being used. Specific information on antibodies is essential. Commercial sources and, if new antibodies are generated, full experimental details such as immunogen/phage, species, protocols for mAb-) should be given. We strongly recommend authors use unique Resource Identifiers for model organisms, antibodies, and tools, and publish them with full descriptions.

Present scatter plots of data, sensitivity, and specificity values with confidence intervals and results of receiver operating characteristic curve analysis. If a marker is already routinely used for that disease, comparison with that marker should be included.

Where the screening of new catalysts is reported, authors should provide a mass balance for all reactions (using, for example, an internal standard in their analysis technique). Recycling efficiencies should be based on reaction rates measurements and not product yield as a function of cycle. It is highly desirable to report the reaction rate for the catalysts as turnover frequency or mass-specific activity or, for heterogeneous catalysts, as surface-specific activity.

It is the responsibility of authors to provide fully convincing evidence for the homogeneity and identity of all compounds whose preparations they describe. Evidence of both purity and identity is required to establish that the properties and constants reported are those of a compound as claimed.

Reviewers will assess the evidence in support of the homogeneity and structure of all new compounds. No hard and fast rules can be laid down to cover all types of compound, but evidence for the unequivocal identification of new compounds should, wherever possible, include good elemental analytical data – an accurate mass measurement of a molecular ion does not provide evidence of purity of a compound and should be accompanied by independent evidence of homogeneity.

Where elemental analytical data cannot be obtained, appropriate evidence that is convincing to an expert in the field may be acceptable. Normally, for diamagnetic compounds this entails, at a minimum, a high resolution mass spectrometry measurement along with assigned 1 H and/or 13 C NMR spectra devoid of visible impurities.

Spectroscopic information necessary for the assignment of structure should be given. How complete this information should be depends upon the circumstances; the structure of a compound obtained from an unusual reaction or isolated from a natural source should be supported by stronger evidence than one that was produced by a standard reaction from a precursor of undisputed structure.

Particular care should be taken in supporting the assignments of stereochemistry (both relative and absolute) of chiral compounds reported, for example by one of the following:

• NMR spectroscopy
• Polarimetry
• Correlation with known compounds of undisputed configuration

In cases where mixtures of isomers are generated (for example, E-Z isomers, enantiomers, diastereoisomers), the constitution of the mixture should usually be established using appropriate analytical techniques (for example, NMR spectroscopy, GC, HPLC) and reported in an unambiguous fashion.

For an asymmetric reaction in which an enantiomeric mixture is prepared, the direct measurement of the enantiomer ratio expressed as the enantiomeric excess (ee) is recommended, and is preferred to less reliable polarimetry methods.

If a compound is new more detailed characterisation will be required. A compound is considered to be new if:

• it has not been prepared before
• it has been prepared before but not adequately purified
• it has been purified but not adequately characterised
• it has been assigned an erroneous composition previously
• it is a natural product isolated or synthesized for the first time

We encourage authors reporting various compounds or compound libraries to apply the FAIR principles and include a summary file of these compounds as part of the submission. This file should be deposited in an appropriate repository or be provided as part of the Supplementary Information, and should adhere to the following:

• format - CSV (*.csv), TSV (*.tsv) or SDF (*.sdf)
• for chemical structures - relevant headers including SMILES , InChI  and InChIKey
• for chemical names - Name and Synonym
• for other comments - such data, metadata, etc

These instructions are based on FAIR chemical structures in the Journal of Cheminformatics (E.L. Schymanski & E.E. Bolton, Journal of Cheminformatics , 2021, 13 , 50).

We recommend that authors follow the guidelines for the nomenclature of new radiolabelled compounds, as laid out in Consensus nomenclature rules for radiopharmaceutical chemistry - setting the record straight (C.H.H., G.A.D. et al., Nuclear Medicine and Biology , 2017, 55 , v – xi).

Authors should provide sufficient information to enable readers to reproduce any computational results. If software was used for calculations and is generally available, it should be properly cited in the references. References to the methods upon which the software is based should also be provided.

Equations, data, geometric parameters/coordinates, or other numerical parameters essential to the reproduction of the computational results (or adequate references when available in the open literature) should be provided. Authors who report the results of electronic structure calculations in relative energies should also include the absolute energies obtained directly from the computational output files. These may be deposited in an appropriate repository and cited, or provided in the Supplementary Information (SI).

We ask that the following information be provided where possible:

• As a minimum, papers reporting QM work should include the atomic coordinates, energies, and number of imaginary frequencies for all computed stationary points
• The level of theory used for computations should be mentioned in the text, and/or in the caption of the first figure that reports the results of those computations
• Where calculations are performed with density functional theory, the integration grid used for the calculations should be specified
• All relevant total energies (potential energies, enthalpies, Gibbs free energies, etc.) should be reported for each computed species. For transition states (TSs), the magnitude of the frequency of the imaginary vibrational mode may also be reported
• For intrinsic reaction coordinate (IRC) calculations, any shoulders in the IRC plots should be noted. If IRC calculations reveal that a TS corresponded to a reaction pathway different from that suggested by simple animation of its imaginary mode, then the IRC results (plots and details of reactants/products) should be deposited in an appropriate repository and cited
• Where computational work is included as part of a synthetic study, full details of any theoretical characterization (for example, computational NMR or VCD) of products and/or important synthetic intermediates should be documented

We also strongly encourage xyz, .mol2 or .pdb files for coordinates to be shared via deposition in an appropriate repository.

It is the responsibility of the authors to provide the raw data for all electrophoretic gel and blot data, ensuring sufficient evidence to support their conclusions.

All Western blot and other electrophoresis data should be supported by the underlying raw images. The image of the full gel and blot, uncropped and unprocessed, should be made available on submission. We suggest authors deposit their data in an appropriate repository. Where this isn’t possible, we ask authors to include the data as part of the Supplementary Information. All samples and controls used for a comparative analysis should be run on the same gel or blot.

When illustrating the result, any cropping or rearrangement of lanes within an image should be stated in the figure legend and with lane boundaries clearly delineated. Alterations should be kept to a minimum required for clarity.

Each image should be appropriately labelled, with the closest molecular mass markers and lanes labelled. All details should be visible; over or underexposed gels and blots are not acceptable. Authors should be able to provide raw data for all replicate experiments upon request.

Studies on fluorescence sensor systems should include titrations covering a full range of analyte concentration, from the absence of analyte to a stoichiometric excess, taking the following factors into account:

• If the analyte shows significant absorption at the excitation or emission frequencies corrections should be carried out for Inner Filter Effects (IFEs). (note: fluorescence probes where the response mechanism is based on the Inner Filter Effect are not suitable for publication in NJC)
• A plateau should be observed at high analyte concentrations for the intensity vs. concentration plot when the sensing mechanism is based on association
• Calculated Limits of Detection (LoD) should be supported by experimental data at similar concentrations
• The intensity vs. concentration relationship should be fitted using suitable software. The Benesi-Hildebrand linearization method for the determination of the association constant should not be used without extensive consideration of the limitations that arise from the method’s assumptions ( see Chemical Society Reviews Tutorial 10.1039/C0CS00062K for further details.)

Plots reporting the Stern-Volmer relationship (I°/I vs. concentration; the same should be valid for its reciprocal I/I°) should show an intercept of 1. Significant variation from this is not acceptable.

The Stern-Volmer relationship should be justified by reference to an appropriate quenching mechanism, e.g. dynamic quenching should show a linear relationship, while static quenching can present an upward curvature for relatively high association constants (see Chemical Society Reviews Tutorial 10.1039/D1CS00422K for further discussion)

The performance of all sensor systems should be compared to the current state-of-the-art sensors for the same analyte, with any differences in requirements (e.g. solvent system) clearly stated; a suitable (and justified) set of interferences should also be tested and discussed.

A new chemical substance (molecule or extended solid) should have a homogeneous composition and structure. Where the compound is molecular, authors should provide data to unequivocally establish its homogeneity, purity and identification as described above.

In general, this should include elemental analyses or a justification for the omission of this data.

This is particularly important for NMR silent paramagnetic compounds where NMR data tends to be less useful in establishing purity. In some instances an assigned 1 H NMR spectrum of a paramagnetic compound that is demonstrably devoid of impurities may be acceptable.

It may be possible to substitute elemental analyses with high-resolution mass spectrometric molecular weights. This is appropriate, for example, with trivial derivatives of thoroughly characterised substances or routine synthetic intermediates. In all cases, relevant spectroscopic data (NMR, IR, UV-vis, etc.) should be provided in tabulated form or as reproduced spectra. These may be deposited in an appropriate repository and cited, or provided in the Supplementary Information (SI). However, it should be noted that, in general, mass spectrometric and spectroscopic data do not constitute proof of purity, and, in the absence of elemental analyses, additional evidence of purity should be provided (melting points, PXRD data, etc.).

Where the compound is an extended solid, it is important to unequivocally establish the chemical structure and bulk composition. Single crystal X-ray diffraction does not determine the bulk structure. Reviewers will normally look to see evidence of bulk homogeneity. A fully indexed powder diffraction pattern that agrees with single crystal data may be used as evidence of a bulk homogeneous structure, and chemical analysis may be used to establish purity and homogeneous composition.

Detailed information on the reporting requirements for X-ray crystallography, including small molecule single crystal data and powder diffraction data is available in the section on X-ray crystallography.

Novel macromolecular structures and newly reported nucleic acid or protein sequences and microarray data should be deposited in appropriate repositories. It is the responsibility of the authors to provide relevant accession numbers prior to publication.

A Data Availability Statement with suitable links to the deposited data should be included. Please see our Data Sharing policy for more details. For high-throughput studies, we encourage authors to refer to Minimum Information Standards as determined and maintained by the relevant communities. For further details see:

• Minimum information standard - Wikipedia
• Minimum Information for Biological and Biomedical Investigations - FAIRsharing Information Resource

The following should be supplied for macromolecular X-ray structures:

• R merge , completeness, multiplicity and I /sigma(I) - both overall and in the outer resolution shell - for data, and
• R cryst , R free and the bond and angle deviations for coordinates
• a Ramachandran plot, and preferably
• real space R -factor

For NMR structures equivalent data plus resonance assignments should be supplied - number of restraints (NOEs and  J -couplings), RMS restraint deviation, etc, plus resonance assignments should be supplied.

All the above information should be included as summary data tables in the manuscript or may be deposited in an appropriate repository and cited, or provided in the Supplementary Information.

Magnetic measurements

If data from magnetic measurements are presented, the authors should provide a thorough description of the experimental details pertaining to how the sample was measured. If the data have been corrected for sample or sample holder diamagnetism, the diamagnetic correction term should be provided and the manner in which it was determined should be stated.

Any fit of magnetic data (for example, χ(T), χ(1/T), χT(T), μ(T), M(H), etc.) to an analytical expression should be accompanied by the Hamiltonian from which the analytical expression is derived, the analytical expression itself, and the fitting parameters. If the expression is lengthy, it may be deposited in an appropriate repository and cited, or relegated to the Supplementary Information to conserve space. When an exchange coupling constant (J) is quoted in the abstract, the form of the Hamiltonian should also be included in the abstract.

For nanomaterials (such as quantum dots, nanoparticles, nanotubes, nanowires), it is the authors’ responsibility not only to provide a detailed characterisation of individual components (see Inorganic and organometallic compounds ) but also a comprehensive characterisation of the bulk composition. Characterisation of the bulk sample could require determination of the chemical composition and size distribution over large portions of the sample.

All nanoparticulate materials should have been purified from synthesis by-products and residual parent compounds, ions etc. If they are to be applied in dispersed form (for example, as a nanoparticulate drug carrier), sufficient data on the dispersion state should be provided (for example, by dynamic light scattering, centrifugal analysis, nanoparticle tracking analysis).

SEM or TEM images for hybrid inorganic-organic nanoparticles should be provided in at least three different levels of magnification. Bar scales should be clearly visible. Images may be deposited in an appropriate repository and cited, or provided in the Supplementary Information (SI).

It is the responsibility of the authors to provide unequivocal support for the purity and assigned structure of all compounds using a combination of the following characterisation techniques.

Elemental analysis is recommended to confirm sample purity and corroborate isomeric purity. We encourage authors to provide instrumental details and the chromatograms of the performed measurements in the Supplementary Information where possible. Authors are also requested to provide 1 H, 13 C NMR spectra and/or GC/HPLC traces if satisfactory elemental analysis cannot be obtained.

For libraries of compounds, HPLC traces should be submitted as proof of purity. The determination of enantiomeric excess of nonracemic, chiral substances should be supported with either GC/HPLC traces with retention times for both enantiomers and separation conditions (that is, chiral support, solvent and flow rate) or for Mosher Ester/Chiral Shift Reagent analysis, copies of the spectra.

Important physical properties, for example, boiling or melting point, specific rotation, refractive index, including conditions and a comparison to the literature for known compounds, should be provided. For crystalline compounds, the method used for recrystallisation should also be documented (that is, solvent etc.).

Mass spectra and a complete numerical listing of 1 H, 13 C NMR peaks in support of the assigned structure, including relevant 2D NMR and related experiments (that is, NOE, etc.) are required. As noted in Analytical , authors are requested to provide copies of these spectra. Infrared spectra that support functional group modifications, including other diagnostic assignments, should be included. High-resolution mass spectra are acceptable as proof of the molecular weight providing the purity of the sample has been accurately determined as outlined above.

For all soluble polymers, an estimation of molecular weight should be provided by size exclusion chromatography, including details of columns, eluents and calibration standards, intrinsic viscosity, MALDI TOF, etc. In addition, full NMR characterisation ( 1 H, 13 C) as for organic compound characterisation above.

For Gel Permeation Chromatography, molecular weight (Mw), molecular number (Mn) polydispersity index (PDI), and internal standards used should be specified, and associated images/spectra should be made available on submission. We suggest authors deposit their data in an appropriate repository. Where this isn’t possible, we ask authors to include the data as part of the article Supplementary Information (SI).

These should be described in enough detail so that a skilled researcher is able to repeat them. They should include the specific reagents, products and solvents with all of their amounts (g, mmol, for products: %), as well as clearly stating how the percentage yields are calculated.

• Reaction times, temperature and solvent quantities should be reported
• Reactions requiring heating - provide the heat source
• Reactions conducted using microwave heating - information on the type of vessel used and how the temperature was monitored should be given as well as the temperature reached or maintained
• Light-promoted reactions - report the light source and specific conditions
• Describe purification methods in detail
• GC or HPLC traces should be supported with retention times and separation conditions (support, solvent and flow rate)
• Centrifugation  - includes rotation speed, centrifugation/dialysis time, solution for resuspension, resuspension time and procedure for each centrifugation step

Synthetic procedures should also include all the characterisation data for the prepared compound or material. For a series of related compounds at least one representative procedure that outlines a specific example that is described in the text or in a table and that is representative of the other cases should be provided. For a multistep synthesis, spectra of key compounds and the final product should be included.

Systems Biology Markup Language (SBML) is a computer-readable format for representing models of biochemical reaction networks. SBML is applicable to metabolic networks, cell-signalling pathways, regulatory networks, and many others.

We encourage authors to prepare models of biochemical reaction networks using SBML and to deposit the model in an open database such as the BioModels database  or  MetabolicAtlas .

Include some physical or experimental validation. Studies that screen a molecule against a set of receptors with no link to physical or experimental data are not suitable for publication.

These guidelines provide details for the presentation of single crystal and powder diffraction data; they apply to submissions to any of our journals.

Authors should present their crystal data in a CIF (Crystallographic Information File) format and deposit this with the  Cambridge Crystallographic Data Centre (CCDC) before submission. Data will be held in the CCDC's confidential archive until publication of the article, but it will be made accessible to reviewers and the publisher assigned to review the data.

At the point of publication, any deposited data will be made publicly available through the CCDC Access Structures service. In addition, organic and metal-organic structures will be curated into the Cambridge Structural Database, and inorganic structures will be curated into the Inorganic Crystal Structures Database (FIZ Karlsruhe).

Upon deposition, each data set is assigned a Digital Object Identifier (DOI), so that the crystal structure is unambiguously identified and registered.

Include CCDC or ICSD numbers in the manuscript prior to submission as part of a Data Availability Statement . During submission authors will be asked to cite CCDC or ICSD reference numbers; CIFs should not be submitted with the manuscript. Any revised CIFs should be deposited directly with the CCDC before the revised manuscript is submitted to us.

In addition, authors are required to provide a checkCIF report for their reported crystal data. The checkCIF report can be obtained via the  International Union of Crystallography's (IUCr) free checkCIF service , or as part of the CCDC deposition process. Any ‘level A' alerts in the report should be explained in the submission details for the article or an explanation provided within the submitted CIF. Authors should submit the checkCIF reports to the Royal Society of Chemistry along with the manuscript files.

If the editor deems it necessary during the peer-review process, the crystallography associated with the manuscript may undergo specialist crystallographic assessment, in which case a report will be provided along with the other reports from reviewers. Any points raised in this assessment should be attended to and all revised CIFs should be deposited with the CCDC prior to uploading the revised manuscript.

For recommended information to include in your CIF, please see the CCDC CIF Deposition Guidelines.  If SQUEEZE or MASK procedures are used, this should be noted in the CIF file.

We encourage authors to include hkl data in the deposited CIF file. Alternatively authors can submit hkl data and the structure files (.fcf) separately during deposition with the CCDC. Raw data accompanying a structure should be made available by the authors for the review process, on request.

Details of the data collection and CCDC numbers should be given in the Data Availability Statement.

For relevant structures that are published as CSD communications, and that have not appeared in the manuscript or a previous journal publication, details should be included in the Data Availability Statement and the appropriate DOI should be cited as a reference in the manuscript.

Where there is significant discussion about the crystallography, the description may be given in textual or tabular form, although the latter is more appropriate if several structure determinations are being reported in one paper. A table of selected bond lengths and angles, with estimated standard deviations, should be restricted to significant dimensions only. Average values may be given with a range of E.S.D.s for chemically equivalent groups or for similar bonds.

Procedures for data collection and structure analysis can be provided as part of the Supplementary Information. The following data are recommended:

• Chemical formula and formula weight ( M )
• Crystal system
• Unit cell dimensions (Å or pm, degrees) and volume, with estimated standard deviations, temperature
• Space group symbol (if non-standard setting give related standard setting)
• Number of formula units in unit cell ( Z )
• Number of reflections measured and/or number of independent reflections, R int
• Final R values (and whether quoted for all or observed data)
• Flack or Rogers parameter (if appropriate)

For example:

Single crystals of [Pd{C(CO 2 Me)[C(CO 2 Me)C(CO 2 Me)=

C(CO 2 Me)C(CO 2 Me)=C(CO 2 Me)]C 6 H 3 [CH(Me)NH 2 ]-2-NO 2 -5}Br] 4 were recrystallised from dichloromethane, mounted in inert oil and transferred to the cold gas stream of the diffractometer.

Crystal structure determination of complex 4:

Crystal data. C 28 H 31 BrCl 4 N 2 O 14 Pd, M = 947.66, orthorhombic, a = 11.096(1), b  = 17.197(2), c = 19.604(3) Å, U = 3741.0(9) Å 3 , T = 173 K, space group P2 1 2 1 2 1 (no.19), Z = 4, 6013 reflections measured, 5665 unique (R int = 0.031), which were used in all calculations. The final wR(F 2 ) was 0.099 (all data).

There may be cases where authors do not wish to include details or extensive discussion of a crystal structure determination. Examples include where only the connectivity has been established, data is marked as low quality at the CCDC, the structure is not integral to the conclusions of the article, or the structure has been discussed in a previous publication. Authors should be mindful of unnecessary fragmentation and the editor’s decision on this will be final.

Authors are encouraged to submit powder diffraction crystallographic data as a CIF (Crystallographic Information File) file to an appropriate repository,such as the ICDD or CCDC, please see the  Data Sharing policy  for further details. For powder diffraction data, please do not include CCDC numbers as part of the manuscript submission process. The reference numbers and DOIs should be cited in a data availability statement. For information on how to cite crystallographic data in your manuscript, please  see the section on Data Citation .  

Authors should combine multiple data sets for a given manuscript into a single file. The individual structures in the combined file should be separated from each other by the sequence #===END at the beginning of a line.

Authors should identify the manuscript with which the electronic file is associated when they submit the file by entering the name of the manuscript at the top of the electronic file.

The information required for deposition includes the following:

• A table of final fractional atomic coordinates
• Any calculated coordinates (for example, hydrogen)
• A full list of bond lengths and angles with estimated standard deviations
• A full list of displacement parameters in the form B ij   or U ij   (in Å 2 or pm 2 )
• Full details of the refinement
• Profile difference plots for all analyses. Where a range of similar analyses are presented a minimum number of representative plots may be given

Unrefined powder diffraction data should normally be reported only if the data form part of the discussion presented in the paper, and should be restricted to new materials. In such cases, the following experimental details should be provided in either textual or tabular format:

• Diffractometer name and model
• Radiation wavelength (Å)
• Temperature of data collection
• Unit cell dimensions (Å or pm, degrees), if determined

Tables of 2 θ  data, or diagrams showing diffraction patterns of reaction products, should not normally be published in print unless they have some distinct feature of relevance that requires such detail to be present. In most cases, such data may be provided as Supplementary Information (SI).

For cases where the materials are new , but have similar powder data to other well-characterised materials, such data should not usually be included in the paper but can be deposited in an appropriate repository, with the relevant reference number included in a Data Availability Statement, and cited.

For refined powder diffraction data  (where atomic coordinates have been determined), if the procedures for data collection and structure analysis were routine, their description may be concise. When the analysis has not been of a routine nature, the authors should briefly detail the procedures used. In most cases, a table of atomic coordinates may be provided, which should give details of occupancies that are less than unity.

Anisotropic thermal parameters may be included if they form an important aspect of the study. Selected bond lengths and angles, with estimated standard deviations, should be given.

For Rietveld refinements, an observed + calculated + difference profile plot should normally be given for each structure determination, except where a significant number of similar refinements have been carried out. In such cases, only the minimum number of representative plots should be included in the article, with additional plots being deposited in an appropriate repository and cited, or included in the SI.

The following information should be provided:

• Unit cell dimensions (Å or pm, degrees)
• Space group
• Number of formula units in unit cell ( Z ) 
• Number of reflections
• Final R values ( R wp , R exp and R l ) and method of background treatment

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Data sharing guidance and policy, author guidelines and information.

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Presenting Data – Graphs and Tables

Types of data.

There are different types of data that can be collected in an experiment. Typically, we try to design experiments that collect objective, quantitative data.

Objective  data is fact-based, measurable, and observable. This means that if two people made the same measurement with the same tool, they would get the same answer. The measurement is determined by the object that is being measured. The length of a worm measured with a ruler is an objective measurement. The observation that a chemical reaction in a test tube changed color is an objective measurement. Both of these are observable facts.

Subjective  data is based on opinions, points of view, or emotional judgment. Subjective data might give two different answers when collected by two different people. The measurement is determined by the subject who is doing the measuring. Surveying people about which of two chemicals smells worse is a subjective measurement. Grading the quality of a presentation is a subjective measurement. Rating your relative happiness on a scale of 1-5 is a subjective measurement. All of these depend on the person who is making the observation – someone else might make these measurements differently.

Quantitative  measurements gather numerical data. For example, measuring a worm as being 5cm in length is a quantitative measurement.

Qualitative  measurements describe a quality, rather than a numerical value. Saying that one worm is longer than another worm is a qualitative measurement.

After you have collected data in an experiment, you need to figure out the best way to present that data in a meaningful way. Depending on the type of data, and the story that you are trying to tell using that data, you may present your data in different ways.

Data Tables

The easiest way to organize data is by putting it into a data table. In most data tables, the independent variable (the variable that you are testing or changing on purpose) will be in the column to the left and the dependent variable(s) will be across the top of the table.

Be sure to:

• Label each row and column so that the table can be interpreted
• Include the units that are being used
• Add a descriptive caption for the table

You are evaluating the effect of different types of fertilizers on plant growth. You plant 12 tomato plants and divide them into three groups, where each group contains four plants. To the first group, you do not add fertilizer and the plants are watered with plain water. The second and third groups are watered with two different brands of fertilizer. After three weeks, you measure the growth of each plant in centimeters and calculate the average growth for each type of fertilizer.

Scientific Method Review:  Can you identify the key parts of the scientific method from this experiment?

• Independent variable – Type of treatment (brand of fertilizer)
• Dependent variable – plant growth in cm
• Control group(s) – Plants treated with no fertilizer
• Experimental group(s) – Plants treated with different brands of fertilizer

Graphing data

Graphs are used to display data because it is easier to see trends in the data when it is displayed visually compared to when it is displayed numerically in a table. Complicated data can often be displayed and interpreted more easily in a graph format than in a data table.

In a graph, the X-axis runs horizontally (side to side) and the Y-axis runs vertically (up and down). Typically, the independent variable will be shown on the X axis and the dependent variable will be shown on the Y axis (just like you learned in math class!).

Line graphs are the best type of graph to use when you are displaying a change in something over a continuous range. For example, you could use a line graph to display a change in temperature over time. Time is a continuous variable because it can have any value between two given measurements. It is measured along a continuum. Between 1 minute and 2 minutes are an infinite number of values, such as 1.1 minute or 1.93456 minutes.

Changes in several different samples can be shown on the same graph by using lines that differ in color, symbol, etc.

Bar graphs are used to compare measurements between different groups. Bar graphs should be used when your data is not continuous, but rather is divided into different categories. If you counted the number of birds of different species, each species of bird would be its own category. There is no value between “robin” and “eagle”, so this data is not continuous.

Scatter Plot

Scatter Plots are used to evaluate the relationship between two different continuous variables. These graphs compare changes in two different variables at once. For example, you could look at the relationship between height and weight. Both height and weight are continuous variables. You could not use a scatter plot to look at the relationship between number of children in a family and weight of each child because the number of children in a family is not a continuous variable: you can’t have 2.3 children in a family.

How to make a graph

• Identify your independent and dependent variables.
• Choose the correct type of graph by determining whether each variable is continuous or not.
• Determine the values that are going to go on the X and Y axis. If the values are continuous, they need to be evenly spaced based on the value.
• Label the X and Y axis, including units.
• Graph your data.
• Add a descriptive caption to your graph. Note that data tables are titled above the figure and graphs are captioned below the figure.

Let’s go back to the data from our fertilizer experiment and use it to make a graph. I’ve decided to graph only the average growth for the four plants because that is the most important piece of data. Including every single data point would make the graph very confusing.

• The independent variable is type of treatment and the dependent variable is plant growth (in cm).
• Type of treatment is not a continuous variable. There is no midpoint value between fertilizer brands (Brand A 1/2 doesn’t make sense). Plant growth is a continuous variable. It makes sense to sub-divide centimeters into smaller values. Since the independent variable is categorical and the dependent variable is continuous, this graph should be a bar graph.
• Plant growth (the dependent variable) should go on the Y axis and type of treatment (the independent variable) should go on the X axis.
• Notice that the values on the Y axis are continuous and evenly spaced. Each line represents an increase of 5cm.
• Notice that both the X and the Y axis have labels that include units (when required).
• Notice that the graph has a descriptive caption that allows the figure to stand alone without additional information given from the procedure: you know that this graph shows the average of the measurements taken from four tomato plants.

Descriptive captions

All figures that present data should stand alone – this means that you should be able to interpret the information contained in the figure without referring to anything else (such as the methods section of the paper). This means that all figures should have a descriptive caption that gives information about the independent and dependent variable. Another way to state this is that the caption should describe what you are testing and what you are measuring. A good starting point to developing a caption is “the effect of [the independent variable] on the [dependent variable].”

Here are some examples of good caption for figures:

• The effect of exercise on heart rate
• Growth rates of E. coli at different temperatures
• The relationship between heat shock time and transformation efficiency

Here are a few less effective captions:

• Heart rate and exercise
• Graph of E. coli temperature growth
• Table for experiment 1

Principles of Biology Copyright © 2017 by Lisa Bartee, Walter Shriner, and Catherine Creech is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• How to write an APA results section

Reporting Research Results in APA Style | Tips & Examples

Published on December 21, 2020 by Pritha Bhandari . Revised on January 17, 2024.

The results section of a quantitative research paper is where you summarize your data and report the findings of any relevant statistical analyses.

The APA manual provides rigorous guidelines for what to report in quantitative research papers in the fields of psychology, education, and other social sciences.

Use these standards to answer your research questions and report your data analyses in a complete and transparent way.

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Table of contents

What goes in your results section, introduce your data, summarize your data, report statistical results, presenting numbers effectively, what doesn’t belong in your results section, frequently asked questions about results in apa.

In APA style, the results section includes preliminary information about the participants and data, descriptive and inferential statistics, and the results of any exploratory analyses.

Include these in your results section:

• Participant flow and recruitment period. Report the number of participants at every stage of the study, as well as the dates when recruitment took place.
• Missing data . Identify the proportion of data that wasn’t included in your final analysis and state the reasons.
• Any adverse events. Make sure to report any unexpected events or side effects (for clinical studies).
• Descriptive statistics . Summarize the primary and secondary outcomes of the study.
• Inferential statistics , including confidence intervals and effect sizes. Address the primary and secondary research questions by reporting the detailed results of your main analyses.
• Results of subgroup or exploratory analyses, if applicable. Place detailed results in supplementary materials.

Write up the results in the past tense because you’re describing the outcomes of a completed research study.

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Before diving into your research findings, first describe the flow of participants at every stage of your study and whether any data were excluded from the final analysis.

Participant flow and recruitment period

It’s necessary to report any attrition, which is the decline in participants at every sequential stage of a study. That’s because an uneven number of participants across groups sometimes threatens internal validity and makes it difficult to compare groups. Be sure to also state all reasons for attrition.

If your study has multiple stages (e.g., pre-test, intervention, and post-test) and groups (e.g., experimental and control groups), a flow chart is the best way to report the number of participants in each group per stage and reasons for attrition.

Also report the dates for when you recruited participants or performed follow-up sessions.

Missing data

Another key issue is the completeness of your dataset. It’s necessary to report both the amount and reasons for data that was missing or excluded.

Data can become unusable due to equipment malfunctions, improper storage, unexpected events, participant ineligibility, and so on. For each case, state the reason why the data were unusable.

Some data points may be removed from the final analysis because they are outliers—but you must be able to justify how you decided what to exclude.

If you applied any techniques for overcoming or compensating for lost data, report those as well.

Adverse events

For clinical studies, report all events with serious consequences or any side effects that occured.

Descriptive statistics summarize your data for the reader. Present descriptive statistics for each primary, secondary, and subgroup analysis.

Don’t provide formulas or citations for commonly used statistics (e.g., standard deviation) – but do provide them for new or rare equations.

Descriptive statistics

The exact descriptive statistics that you report depends on the types of data in your study. Categorical variables can be reported using proportions, while quantitative data can be reported using means and standard deviations . For a large set of numbers, a table is the most effective presentation format.

Include sample sizes (overall and for each group) as well as appropriate measures of central tendency and variability for the outcomes in your results section. For every point estimate , add a clearly labelled measure of variability as well.

Be sure to note how you combined data to come up with variables of interest. For every variable of interest, explain how you operationalized it.

According to APA journal standards, it’s necessary to report all relevant hypothesis tests performed, estimates of effect sizes, and confidence intervals.

When reporting statistical results, you should first address primary research questions before moving onto secondary research questions and any exploratory or subgroup analyses.

Present the results of tests in the order that you performed them—report the outcomes of main tests before post-hoc tests, for example. Don’t leave out any relevant results, even if they don’t support your hypothesis.

Inferential statistics

For each statistical test performed, first restate the hypothesis , then state whether your hypothesis was supported and provide the outcomes that led you to that conclusion.

Report the following for each hypothesis test:

• the test statistic value,
• the degrees of freedom ,
• the exact p- value (unless it is less than 0.001),
• the magnitude and direction of the effect.

When reporting complex data analyses, such as factor analysis or multivariate analysis, present the models estimated in detail, and state the statistical software used. Make sure to report any violations of statistical assumptions or problems with estimation.

Effect sizes and confidence intervals

For each hypothesis test performed, you should present confidence intervals and estimates of effect sizes .

Confidence intervals are useful for showing the variability around point estimates. They should be included whenever you report population parameter estimates.

Effect sizes indicate how impactful the outcomes of a study are. But since they are estimates, it’s recommended that you also provide confidence intervals of effect sizes.

Subgroup or exploratory analyses

Briefly report the results of any other planned or exploratory analyses you performed. These may include subgroup analyses as well.

Subgroup analyses come with a high chance of false positive results, because performing a large number of comparison or correlation tests increases the chances of finding significant results.

If you find significant results in these analyses, make sure to appropriately report them as exploratory (rather than confirmatory) results to avoid overstating their importance.

While these analyses can be reported in less detail in the main text, you can provide the full analyses in supplementary materials.

To effectively present numbers, use a mix of text, tables , and figures where appropriate:

• To present three or fewer numbers, try a sentence ,
• To present between 4 and 20 numbers, try a table ,
• To present more than 20 numbers, try a figure .

Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.

Tables and figures should be numbered and have titles, along with relevant notes. Make sure to present data only once throughout the paper and refer to any tables and figures in the text.

Formatting statistics and numbers

It’s important to follow capitalization , italicization, and abbreviation rules when referring to statistics in your paper. There are specific format guidelines for reporting statistics in APA , as well as general rules about writing numbers .

If you are unsure of how to present specific symbols, look up the detailed APA guidelines or other papers in your field.

It’s important to provide a complete picture of your data analyses and outcomes in a concise way. For that reason, raw data and any interpretations of your results are not included in the results section.

It’s rarely appropriate to include raw data in your results section. Instead, you should always save the raw data securely and make them available and accessible to any other researchers who request them.

Making scientific research available to others is a key part of academic integrity and open science.

Interpretation or discussion of results

This belongs in your discussion section. Your results section is where you objectively report all relevant findings and leave them open for interpretation by readers.

While you should state whether the findings of statistical tests lend support to your hypotheses, refrain from forming conclusions to your research questions in the results section.

Explanation of how statistics tests work

For the sake of concise writing, you can safely assume that readers of your paper have professional knowledge of how statistical inferences work.

In an APA results section , you should generally report the following:

• Participant flow and recruitment period.
• Missing data and any adverse events.
• Descriptive statistics about your samples.
• Inferential statistics , including confidence intervals and effect sizes.
• Results of any subgroup or exploratory analyses, if applicable.

According to the APA guidelines, you should report enough detail on inferential statistics so that your readers understand your analyses.

• the test statistic value
• the degrees of freedom
• the exact p value (unless it is less than 0.001)
• the magnitude and direction of the effect

You should also present confidence intervals and estimates of effect sizes where relevant.

In APA style, statistics can be presented in the main text or as tables or figures . To decide how to present numbers, you can follow APA guidelines:

• To present three or fewer numbers, try a sentence,
• To present between 4 and 20 numbers, try a table,
• To present more than 20 numbers, try a figure.

Results are usually written in the past tense , because they are describing the outcome of completed actions.

The results chapter or section simply and objectively reports what you found, without speculating on why you found these results. The discussion interprets the meaning of the results, puts them in context, and explains why they matter.

In qualitative research , results and discussion are sometimes combined. But in quantitative research , it’s considered important to separate the objective results from your interpretation of them.

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• > Experimental Methods for Science and Engineering Students
• > Graphical Presentation of Data

Book contents

• Experimental Methods for Science and Engineering Students
• Copyright page
• Preface to the Second Edition
• Preface to the First Edition
• 1 Introduction to Experimentation
• 2 Characteristics of Experimental Data
• 3 Graphical Presentation of Data
• 4 Dealing with Uncertainties
• 5 Statistical Approach to Variability in Measurements
• 6 Fitting a Line to x–y Data Using the Method of Least Squares
• 7 Report Writing and Presentations
• 8 Using Excel to Present and Analyse Data
• 9 Computer-Aided Data Capture
• Solutions to Exercises and Problems
• Further Reading

3 - Graphical Presentation of Data

Published online by Cambridge University Press:  24 August 2019

Graphs are a powerful and concise way to communicate information. Representing data from an experiment in the form of an x - y graph allows relationships to be examined, scatter in data to be assessed and allows for the rapid identification of special or unusual features. A well laid out graph containing all the components discussed in this chapter can act as a 'one stop' summary of a whole experiment. Someone studying an account of an experiment will often examine the graph(s) included in the account first to gain an overall picture of the outcome of an experiment. The importance of graphs, therefore, cannot be overstated as they so often play a central role in the communication of the key findings of an experiment. This chapter contains many examples of graphs and includes exercises and end of chapter problems which reinforce the graph-plotting principles.

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• Graphical Presentation of Data
• Les Kirkup , University of Technology, Sydney
• Book: Experimental Methods for Science and Engineering Students
• Online publication: 24 August 2019
• Chapter DOI: https://doi.org/10.1017/9781108290104.005

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Nanoconfinement of polyoxometalates in cyclodextrin: computational inspections of the binding affinity and experimental demonstrations of reactivity modulation †

First published on 5th September 2024

Chaotropic polyoxometalates (POMs) form robust host–guest complexes with γ-cyclodextrin (γ-CD), offering promising applications in catalysis, electrochemical energy storage, and nanotechnology. In this article, we provide the first computational insights on the supramolecular binding mechanisms using density-functional theory and classical molecular dynamics simulations. Focusing on the encapsulation of archetypal Keggin-type POMs (PW 12 O 40 3− , SiW 12 O 40 4− and BW 12 O 40 5− ), our findings reveal that the lowest-charged POM, namely PW 12 O 40 3− spontaneously confines within the wider rim of γ-CD, but BW 12 O 40 5− does not exhibit this behaviour. This striking affinity for the hydrophobic pocket of γ-CD originates from the structural characteristics of water molecules surrounding PW 12 O 40 3− . Moreover, through validation using 31 P NMR spectroscopy, we demonstrate that this nanoconfinement regulates drastically the POM reactivity, including its capability to undergo electron transfer and intermolecular metalate Mo/W exchanges. Finally, we exploit this nanoconfinement strategy to isolate the elusive mixed addenda POM PW 11 MoO 40 3− .

Introduction

It has become increasingly evident that water transcends its role as merely a “solvent” and can be seen as a matrix that actively connects and interacts closely with ions. The structure and dynamics of the hydration shell around ions appear to influence the behaviour of both the ions and the water molecules, creating an interplay between the two entities. Recent insights show conceptual similarity between large ions and weakly solvated ions in the Hofmeister series, categorized as chaotropic. 16 The name comes from the idea that these ions disrupt the structure of water, a notion currently subject to controversy. 19,20 POMs exhibiting behaviour akin to chaotropic ions but with heightened intensity, are labelled as (super)chaotropic. 19,21 Since the first mention of the chaotropicity of POMs by Thouvenot in 1978, 22 the terms “high energy water” or “disordered water” are usually used to describe the water surrounding POMs. This description remains quite vague and unsatisfying however probing experimentally the water structure at solute/liquid interfaces is extremely challenging. 23–26 In context, using theoretical tools appears as an efficient strategy to investigate the origin of the chaotropic effect. In recent literature, the study of the chaotropic system's effects has emerged as a topic of growing interest. This is underscored by the recent publication of two computational studies—one classifying nano-ions within the Hofmeister series and the other investigating the water's ordering in salt solutions. 19,27 In both cases, very simple spherical models were used to describe the nano-ions. The chaotropicity of POMs and the related phenomena are unexplored, indeed previous simulations about the solution behaviour of POMs were mostly focused on ion-pairing effects. 28–34 Actually, the only molecular dynamics studies of POMs performed under the prism of the chaotropic effect were conducted to link the potential affinity of POMs with hen egg-white lysozyme, although these studies were not supported by experimental data. 35,36

The complexation of Keggin-type POMs with γ-cyclodextrin (notated γ-CD), a natural oligosaccharide made up of eight glucopyranose units, represents certainly one of the most significant chaotropically-driven systems reported so far since it leads to potential applications in catalysis, energy storage, iodine capture, or nanotechnologies. 37–42 The adequate size matching between γ-CD cavity and the Keggin-type POM leads to a wide variety of host–guest complexes. 6,15,43–47 As observed, the global charge density of the Keggin-type POMs dramatically influences both the binding constant and the nature of the aggregates. 15,43 For instance, solution investigations using NMR evidenced that both primary and secondary faces contribute to the POM's complexation. 15 Calorimetric studies revealed that this process is orthogonal to the classical hydrophobic effect since it is enthalpically driven accompanied by an entropic penalty. 15 It is worth noting that this embedment within the hydrophobic cavity can be viewed as a nanoconfinement similar to those observed in Mo-storage proteins, in which the protein binding pocket acts not only as a template and nucleation site for polynuclear Mo-based entities but also offers a protecting barrier again hydrolytic attacks. 48,49 In biological systems, nanoconfinement represents a widely used strategy to ensure vital functions such as oxygen transport in the blood or enzyme catalysis. In context, the supramolecular association between Keggin-type POMs and γ-CD represents appealing models for studying the chemical reactivity of POMs entrapped in a hydrophobic pocket.

In this article, we first report the computational inspection of the supramolecular binding process of three archetypal Keggin-type POM (PW 12 O 40 3− , SiW 12 O 40 4− and BW 12 O 40 5− ) with γ-CD using Density-Functional Theory (DFT) and classical Molecular Dynamics (MD) simulations. This theoretical study shows that the super-chaotropic character of PW 12 O 40 3− is responsible for its strong affinity with γ-CD host. Then, we demonstrate experimentally using 31 P NMR studies that the nanoconfinement of PW 12 O 40 3− provides a way to control its chemical reactivity, allowing tuning of the intermolecular electron-transfer rates and the exchange of metalate ions between Keggin-type POMs. Finally, we employ this strategy to prepare the elusive mixed-metal Keggin anion PW 11 MoO 40 3− with high purity.

Results and discussion

Theoretical studies of the encapsulation process.

To computationally determine preferential configurations along the series, two factors were investigated using DFT methods: the POM size and host–guest interaction energies. The computed molecular surface area for PW 12 O 40 3− , SiW 12 O 40 4− , and BW 12 O 40 5− is 1687.53, 1679.82 and 1662.71 Å 2 , respectively. Considering the insignificant differences in their molecular area, we confirm that size is not the determining factor for diverse preferential configurations observed experimentally. To determine the host–guest binding energies between POM and γ-CD in water solution, we dissected the binding process using a standard thermodynamic cycle: Δ G bind aq = Δ G bind gas + Δ G solv whereas Δ G solv = POM-CD Δ G solv − POM Δ G solv − γ-CD Δ G solv (for more details see Section 1.a of ESI † ). The DFT Gibbs solvation and binding energies are reported in Table 1 . This indicates the POM-CD binding is an enthalpic driven process with and small entropic penalty. Importantly, Δ G solvation energies play an important role in conformers relative energies. For the most charged system [BW 12 O 40 ] 5− the desolvation energy effect is more significant than POM-CD intermolecular interactions, resulting in the most stable conformer being the one with least contact, referred to as external. For medium charged system [SiW 12 O 40 ] 4− in gas phase and when solvent is included implicitly, secondary configuration is the most preferred. For the most chaotropic system [PW 12 O 40 ] 3− , the penalty of Δ G solvation energies for secondary configuration, the most penetrating one, is half that of [BW 12 O 40 ] 5− highlighting the importance of enthalpy as a driving binding force for chaotropic systems. Hence, what is crucial here is the effect of the anion on the surrounding water molecules, as expected for the chaotropically-driven self-assemblies. 50 Thus, the dynamic solvation sphere of the POMs is likely to play a significant role in the formation of the adducts. To incorporate the effects of hydration and the structural and dynamic properties of water, we employed explicit classical MD simulations.

We computed the Radial Distribution Function (RDF) between the center of the Keggin-type POMs and the γ-CD center to analyse the average number of supramolecular adducts formed over time (see Fig. 2 ). Firstly, our goal was to determine the stability of various adducts. To achieve this, we conducted MD simulations using two initial box systems: one with all POMs complexed by the primary face and another with all POMs bounded to the secondary faces. Secondly, we aimed to identify the predominant adduct formed in aqueous solution. For this purpose, we initialized a periodic simulation box with POMs and γ-CD randomly distributed as free molecules, not complexed (see Fig. S1 † ). It's worth noting that each supramolecular assembly had a specific distance between the POM and center of γ-CD. Consequently, each peak observed in the RDF corresponds to one specific supramolecular adduct.

Regarding the low-charged PW 12 O 40 3− , when starting from the secondary configuration (green curve in Fig. 2 ), the secondary adducts remain stable from beginning to end of the simulation, exhibiting the highest peak intensity compared to other starting systems confirming the highest stability of the secondary configuration. There is also an appearance over time of a lower intensity peak around 800–1000 pm, which corresponds to the newly proposed side-secondary adduct. On the other hand, when starting from the primary configuration (pink curve), the primary adducts show stability over time. However, when starting from an initial free configuration (black curve), various adducts are formed during the simulation, but the secondary and external adducts exhibit the highest intensities in contrast with side adducts. For the free initial state simulation of PW 12 O 40 3− , note that for longer simulation times, the peak corresponding to the external site decrease intensity, thus demonstrating that although the system did not reach equilibrium, the position and intensity of the peak corresponding to the secondary structure persists. This demonstrates that the POM and CD assemble spontaneously in explicit water solution, and that the preferred binding mode derived from the simulations precisely coincides with that observed in experiments.

In the medium-charged SiW 12 O 40 4− , when starting from the secondary and primary configurations, some initial supramolecular assemblies persist over all the simulations. However, when starting from a free configuration, the predominant adducts formed in solution are the side-primary and external adducts, with minor contributions from the side-secondary adducts observed in the spatial distribution functions within the range of 800–1000 pm. Overall, the intensity of the peaks is lower compared to PW 12 O 40 3− . One intriguing aspect of this result is the appearance of the newly proposed side-primary configuration as one of the two most prevalent adducts.

Moving on to the high-charged Keggin-type POMs, namely BW 12 O 40 5− , when starting from the secondary and primary configurations, both do not remain stable over time. In all initial cases, only the external adducts are formed during the dynamics. The RDF exhibits peaks of extra low intensity in all cases.

We compared our predictions with experimental findings obtained from 1 H NMR data (titration experiment) that provide valuable insights into the formation and stability of supramolecular association of Keggin-type POMs and γ-CD in water. 15 Specifically, the chemical shifts of H3, H5, and H6 exhibit distinct alterations after the addition of various equivalents of Keggin-type POMs (see Table 2 ). These observed changes in chemical shifts indicate different interactions and recognition processes. The most exposed hydrogens of γ-CD to POM are H3 and H5, located inside the cavity, as well as H6, located on the methoxy group outside the ring. In addition, other hydrogen atoms able to form hydrogen bonds with the Keggin anions are the in-ring and out-ring hydroxo groups, labelled H7 and H8, respectively (see Fig. 1 ).

For PW 12 O 40 3− , the experimental chemical shifts exhibit the highest shift for H3, followed by smaller shifts for H5 and H6. 15 Our MD simulations indicate that main configurations, secondary, external, and to a lesser extent, side-secondary and side-primary adducts, assemble over time. The structural DFT parameters calculated for complexation by the secondary face reveal close contacts between the POM H3 and H5. Additionally, our proposed new solution structure, the side-primary adduct, exhibits close contact with H6. The observed chemical shifts can be explained utilizing MD by the presence of a combination of secondary and to a lesser extent side-primary, and external adduct configurations. The experimental 1 H NMR study revealed that the addition of SiW 12 O 40 4− to γ-CD induces a strong shift of the H6 signal and a smaller one for H5. 15 Our MD simulations reveal that silicotungstate anions spontaneously assemble mostly external and side-primary adducts. Optimized DFT structures further confirm the presence of close contacts between the side-primary configuration and H6, while side-secondary configurations predominantly interact with the proton of hydroxo H7. The observed chemical shifts align well with the co-existence of side-primary and external adduct configurations. The dynamic behaviour of side- and external adduct systems is particularly intriguing, as the analysis of the MD trajectories for external configurations reveals a region of possible near-side primary configurations where the POM exhibits some motion over time. Some of these configurations involve potential interactions between the POM and H5. Similarly, in the case of BW 12 O 40 5− , the highest chemical shift is observed for H6, followed by a smaller shift for H5. From our MD simulations, it is evident that only external adducts are spontaneously formed, which correlates with the observed chemical shift in H6. These findings demonstrate a good agreement between the experimentally observed chemical shifts and the adduct configurations formed during molecular dynamics simulations. Also, similar chemical shifts can originate from different adducts, highlighting the complexity of solution assemblies. The combination of NMR spectroscopy and MD simulations is a useful methodology for extracting valuable information about the assembly behaviour in solution and provides information on the structural characteristics of the adducts.

Our results reveal distinct patterns of adduct formation based on the charge density of the Keggin-type POMs. For the POM exhibiting the lowest charge density, the secondary and external adducts dominate in solution. In the case of Keggin with the global anionic charge of −4, there is less aggregation, and both side-primary and external adducts are observed with higher abundance. However, for the highest charged Keggin, the formation of adducts is quite limited since only external adducts are observed, implying an interaction without losing its hydration shell. Oppositely, the deep penetration of PW 12 O 40 3− within the hydrophobic cavity of the CD allows its full dehydration.

Globally, the MD results are consistent with the experimental results and explain the tendencies of the Keggin-type anions within the Hofmeister series.

Nanoconfinement effect on the intermolecular electron transfer

To highlight the nanoconfinement effect of PW 12 O 40 3− embedded within γ-CD, we revisited the classical Baker's experiment 54,55 in which he studied the electron transfer between one-electron reduced POM and its non-reduced form using 31 P NMR measurements. It must be noted, that all of our experiments were carried out at room temperature and involved equimolar aqueous solution of one-electron reduced and non-reduced form ([PW 12 O 40 3− ] = [PW 12 O 40 3− ] = 25 mM in 0.1 M HCl), and various equivalents of γ-CD (from 0 to 6 equivalents).

Nanoconfinement effect on the intermolecular metalate Mo/W exchanges

In the absence of γ-CD, the spectrum recorded after 24 hours consists of a statistical distribution of 31 P NMR resonances centered at about −8.5 ppm (see Fig. 5 ). The chemical shift of the central phosphorous of Keggin-type POMs is known to be sensitive to the ratio of molybdenum to tungsten and the 31 P NMR spectrum is consistent with a complete distribution including all the possible mixed-metal POMs PW 12− x Mo x O 40 3− in solution. It must be noted the spectra are very complex due to the existence of positional isomers for all POMs with x varying from 2 to 10. For instance, the theoretical number of positional isomers for PW 6 Mo 6 O 40 3− is 48. 59 We also note that the 31 P NMR signals of PW 12 O 40 3− and PMo 12 O 40 3− completely disappeared.

The experiments performed in the presence of variable quantities of γ-CD (50 and 100 mM) show that the intermolecular metalate Mo/W exchanges are dramatically slowed down by the presence of the γ-CD (see Fig. 5 ). In the presence of 100 mM of γ-CD, the spectrum measured after 24 hours exhibits only two peaks observed at −3 and −14.8 ppm, corresponding to the homometallic Keggin anions PMo 12 O 40 3− and PW 12 O 40 3− , respectively.

When 50 mM in γ-CD (CD/POM = 1) is introduced, the situation is quite complex since a multimodal distribution of 31 P resonances is observed after 24 hours. In this condition, the exchange process is strongly slowed down and it becomes possible to study the intermediate stages of the metalate exchanges ( 31 P NMR spectra and the species distribution are shown in Fig S2 and S3 † ). This evolution revealed a different reactivity between the POM rich in Mo centers and those rich in W centers. Similarly, quantitative analysis evidences that the quantities of mixed metal POM rich in W centers ( x = 1 or 2) remain very low during all processes while the POM entities rich in Mo centers ( x = 10 or 11) reach highest concentration at the beginning of the process. This reveals that W exchange process involving PW 11 MoO 40 3− and PW 10 Mo 2 O 40 3− species proceeds faster than PW 12 O 40 3− and that the kinetic stability of Mo-rich Keggin globally increases by introducing W centres in the metal oxo frameworks. All these observations are fully consistent with the well-known POM behaviour suggesting that the kinetic stability of POM is higher for W-rich POM than for Mo-rich POMs. 2,14 Nevertheless, it appears the complexation of the Keggin-type anion by γ-CD provides a way to control to a large extent the metalate exchange processes.

To quantify the impact of the γ-CD concentration on the intermolecular metalate exchanges, we determined the decrease of homometallic POMs concentration can be roughly described as first-order kinetics (Fig. S4 † ). The rate constant ( k ) and half-life of a first-order reaction ( t 1/2 ) for the decomposition of PMo 12 O 40 3− and PW 12 O 40 3− are reported in Table S2. † These results evidenced that the embedment POMs within the macrocyclic host produced a dramatic increase of the half-life of POMs that is multiplied by more than three orders of magnitude when only two equivalents of γ-CD are introduced in the solution (Table S2 † ).

Toward the stereoselective synthesis of elusive POM

The classical way to prepare monosubstituted Keggin-type POMs consists of a condensation process of a metalate species to a monovacant polyoxotungstate XW 11 O 39 n − ( X = P V or Si IV ). Although this process is highly selective for the formation of the SiW 11 MoO 40 4− ion, that of the phosphato analogue PW 11 MoO 40 3− is hindered by formation of numerous side-products mainly driven by the M/W metalate exchanges. Indeed, addition of the cationic MoO 2 2+ species to a solution containing preformed PW 11 O 39 7− as Li + salt leads to in a few minutes the fast precipitation of an insoluble pale-yellow solid while the supernatant analysis by 31 P NMR revealed that the desired anion PW 11 MoO 40 3− correspond to only 18% of the total compounds. The other side-products are mainly mixed-metal POMs PW 12− x Mo x O 40 3− (with x from 0 to 3) (see Fig. 6 ). The situation is dramatically different when six equivalents of γ-CD per PW 11 O 39 7− precursor were initially introduced in the synthesis solution. In such conditions, no precipitation was observed and the 31 P NMR analysis of the mixture contains PW 11 MoO 40 3− with high purity (>97%) as revealed by 31 P NMR analysis (see Fig. 6 ). This result can be easily understood if we consider that the chaotropic PW 11 MoO 40 3− ions is protected until its formation by γ-CD. The resulting host–guest aggregate creates a hydrophobic shell that stabilizes chaotropic POMs by cancelling out metalate exchange.

This article does not only decipher the forces behind the encapsulation process of POMs by macrocyclic hosts but also demonstrates experimentally that the striking affinity of super-chaotropic POMs with γ-CD allows it to modulate to a large extent its physical-chemical behaviour such as efficiency of electron transfers or metalates exchange. Furthermore, the chatropically-induced nanoconfinement can be exploited to mimic hydrophobic conditions in aqueous solution.

All these results, both theoretical and experimental, confirm that the solvent effect, often neglected, is ubiquitous in polyoxometalate chemistry, and provide a better understanding of aggregation processes with hydrophobic organic substances and, in fine, alterations to their intrinsic physical-chemical properties.

Data availability

Author contributions, conflicts of interest, acknowledgements.

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Moral Preferences of Investors : Experimental Evidence -- Replication Package

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This package allows to replicate the results of "The Moral Preferences of Investors: Experimental Evidence", by Bonnefon, Landier, Sastry and Thesmar. It contains codes and experimental data. Please read the readme file in the root of the folder for details.

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All details on experiment in the paper: "The Moral Preferences of Investors: Experimental Evidence", by Bonnefon, Landier, Sastry and Thesmar.

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Prediction of the germination rate and antioxidant properties of VD20 Rice by utilizing Artificial neural network-coupled response surface methodology and product characterization

• Original Paper
• Published: 10 September 2024

Cite this article

• Le Thi Kim Loan 1 ,
• Truong Quoc Tat 2 ,
• Pham Do Trang Minh 1 ,
• Vo Thi Thu Thao 1 ,
• Pham Thi Minh Hoang 1 ,
• Tran Thi Yen Nhi 3 ,
• Bach Long Giang 3 ,
• Dao Tan Phat 3 &
• Ngo Van Tai   ORCID: orcid.org/0000-0002-5383-0142 4  

The current research aims to predict and optimize process conditions to produce germinated VD20 with a high rate of germination and antioxidant properties. Box-Behnken design (BBD) was used to build models with three factors [soaking time (ST: 4–6 h), germination time (GT: 18–22 h), and germination temperature (33–37 °C)] and three replications. The data set from the BBD experiment was used to create an artificial neural network (ANN) model that estimated the change in responses by variable factors. The ANN model was extremely accurate, with an overall correlation coefficient (R) of 0.9997 and showed the best fit with actual and predicted data. The germination conditions were further optimized using multi-objective RSM, which revealed that the optimal conditions were ST of 5.34 h, GT of 20.78 h, and germination temperature of 35.6 °C. The experimental validation revealed a high level of agreement between the results of the BBD models forecasted and the actual experimental values. The ANN-coupled BBD methodology is a promising hybrid method for modeling, forecasting, and optimizing the impact of process conditions on the quality of germinated grain. In addition, the raw and germinated VD20 rice were analyzed for their techno-functional properties, estimated glycemic index (eGI), and FTIR. Lower peak viscosity, values of breakdown and setback, and phytic acid were found after rice was germinated. The result revealed that high antioxidant content and activity, which were confirmed by the FTIR pattern, and low digestion behaviors (eGI = 64.23) were the attributes of the germinated product. Furthermore, the results of pasting, thermal, swelling power, and solubility showed the wide range of further application of this material, which should receive more consideration in future research.

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Acknowledgements

The researchers would like to express their appreciation to Mr. Damian Laryea for his assistance in editing grammar and proofreading this manuscript.

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Faculty of Agriculture and Food Technology, Tien Giang University, My Tho City, Tien Giang Province, Vietnam

Le Thi Kim Loan, Pham Do Trang Minh, Vo Thi Thu Thao & Pham Thi Minh Hoang

Faculty of Technology and Engineering, Dong Thap University, Dong Thap, Vietnam

Truong Quoc Tat

Institute of Applied Technology and Sustainable Development, Nguyen Tat Thanh University, Ho Chi Minh city, Vietnam

Tran Thi Yen Nhi, Bach Long Giang & Dao Tan Phat

School of Food Industry, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

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• Published: 10 September 2024

VEGF-A-mediated venous endothelial cell proliferation results in neoangiogenesis during neuroinflammation

• Sanjid Shahriar   ORCID: orcid.org/0000-0003-4911-9742 1 , 2   na1 ,
• Saptarshi Biswas 3   na1 ,
• Kaitao Zhao 3 ,
• Uğur Akcan 3 ,
• Mary Claire Tuohy   ORCID: orcid.org/0000-0003-0600-9834 3 ,
• Michael D. Glendinning 3 ,
• Ali Kurt 3 ,
• Charlotte R. Wayne 3 ,
• Grace Prochilo 4 ,
• Maxwell Z. Price   ORCID: orcid.org/0000-0001-7480-7008 4 ,
• Heidi Stuhlmann   ORCID: orcid.org/0000-0001-7217-768X 5 ,
• Rolf A. Brekken 6 ,
• Vilas Menon   ORCID: orcid.org/0000-0002-4096-8601 3   na2 &
• Dritan Agalliu   ORCID: orcid.org/0000-0002-5375-4143 1 , 3   na2  

Nature Neuroscience ( 2024 ) Cite this article

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• Blood–brain barrier
• Multiple sclerosis

Newly formed leaky vessels and blood–brain barrier (BBB) damage are present in demyelinating acute and chronic lesions in multiple sclerosis (MS) and experimental autoimmune encephalomyelitis (EAE). However, the endothelial cell subtypes and signaling pathways contributing to these leaky neovessels are unclear. Here, using single-cell transcriptional profiling and in vivo validation studies, we show that venous endothelial cells express neoangiogenesis gene signatures and show increased proliferation resulting in enlarged veins and higher venous coverage in acute and chronic EAE lesions in female adult mice. These changes correlate with the upregulation of vascular endothelial growth factor A (VEGF-A) signaling. We also confirmed increased expression of neoangiogenic markers in acute and chronic human MS lesions. Treatment with a VEGF-A blocking antibody diminishes the neoangiogenic transcriptomic signatures and vascular proliferation in female adult mice with EAE, but it does not restore BBB function or ameliorate EAE pathology. Our data demonstrate that venous endothelial cells contribute to neoangiogenesis in demyelinating neuroinflammatory conditions.

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Data availability.

The raw and analyzed mouse CNS EC scRNA-seq and bulk RNA-seq datasets supporting this paper are archived at the NIH Gene Expression Omnibus (GEO) repository under accession GSE210776 . For performing congruency analysis comparing EAE neoangiogenic signature to tumor angiogenesis and developmental angiogenesis, scRNA-seq data from ref. 38 (lung tumor: E-MTAB- 7458 ) and ref. 39 (E14.5 mouse forebrain: GSE51619 ) were used, and differential expression analysis was performed using the Seurat FindMarkers function (Supplementary Table 2 ). Line plots summarizing neoangiogenic marker mRNA detection in WM, GM or the sulcus area relative to MS lesion borders in SPMS cases were generated using spatial transcriptomics data from ref. 47 ( GSE174647 ). Source data are provided with this paper.

Code availability

The code used for the scRNA-seq analysis can be found in the source data associated with this paper.

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Acknowledgements

We thank J. Bastiaans at Weill Cornell Medical College, New York, for assistance in optimizing the EGFL7 protein staining in the human brain, T. Cutforth for advice with the preparation of mRNA probes and FISH experiments, M. Kissner (at the Columbia Stem Cell Initiative Flow Cytometry Core) and E. Bush (at the Columbia Single-Cell RNA sequencing facility) for their advice and help with FACS isolation and scRNA-seq experiments, respectively. The work was supported by grants from the National Multiple Sclerosis Society (RG-1901-33218) and NIH (National Institute of Mental Health (NIMH) (R01 MH112849), National Eye Institute (NEI) (R01 EY033994), National Heart, Lung, and Blood Institute (NHLBI) (R61/33HL159949) and National Institute of Neurological Disorders and Stroke (NINDS) (R21 NS118891 and R21 NS130265). This research made use of the Genomics and High Throughput Screening Shared Resource Facility, funded in part by the NIH/National Cancer Institute (NCI) grant P30CA013696.

Author information

These authors contributed equally: Sanjid Shahriar, Saptarshi Biswas.

These authors jointly supervised this work: Vilas Menon, Dritan Agalliu.

Authors and Affiliations

Department of Pathology and Cell Biology, Columbia University Irving Medical Center, New York, NY, USA

Sanjid Shahriar & Dritan Agalliu

Wyss Institute for Biologically Inspired Engineering, Boston, MA, USA

Sanjid Shahriar

Department of Neurology, Columbia University Irving Medical Center, New York, NY, USA

Saptarshi Biswas, Kaitao Zhao, Uğur Akcan, Mary Claire Tuohy, Michael D. Glendinning, Ali Kurt, Charlotte R. Wayne, Vilas Menon & Dritan Agalliu

Department of Biological Sciences, Columbia University, New York, NY, USA

Grace Prochilo & Maxwell Z. Price

Department of Cell and Developmental Biology, Weill Cornell Medical College, New York, NY, USA

Heidi Stuhlmann

Department of Surgery, University of Texas Southwestern Medical Center, Dallas, TX, USA

Rolf A. Brekken

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Contributions

S.S., S.B., V.M. and D.A. conceived and designed the study. S.S., S.B., K.Z., U.A., M.C.T., M.D.G., A.K., G.P., M.Z.P. and D.A. performed the experiments and collected the data. S.S., M.C.T. and V.M. performed computational analysis of the RNA-seq data. H.S. and R.A.B. provided some key reagents. S.S., S.B., M.C.T., V.M. and D.A. wrote and revised the paper. S.S. prepared Figs. 1 , 2e , 4 and 6 , and Extended Data Figs. 1 – 3 . S.B. prepared Figs. 3 , 4 and 7a–g , and Extended Data Figs. 3 and 4 . M.C.T. prepared Extended Data Fig. 6 . C.R.W. prepared Figs. 2a–d and 7h . D.A. prepared Fig. 5 and Extended Data Figs. 5 and 7 and revised all the figures. V.M. and D.A. supervised the project. D.A. provided the funds for the project.

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Extended data

Extended data fig. 1 disease course of mog 35–55 eae mice used for single-cell rna sequencing, gating strategy for ec isolation and data analysis..

a , Adult (10–12 weeks old) female mice were immunized with either MOG 35–55 peptide and CFA/Ptx to induce EAE or CFA/Ptx (CFA controls). b – e , Clinical EAE score curves ( b ), peak clinical scores ( c ), day of disease onset ( d ) and score on the day of collection ( e ), for CFA control (yellow), acute (16 d.p.i.; blue) and chronic (29 d.p.i.; magenta) EAE mice used for single-cell RNA sequencing (scRNA-seq). Two mice were pooled for each sample to obtain sufficient endothelial cells (ECs) for scRNA-seq [(n = 6 mice healthy (3 samples); n = 6 female CFA (3 samples), n = 8 female acute EAE (4 samples), n = 8 female chronic EAE mice (4 samples)]. f , FACS plots show the gating strategy for sorting spinal cord ECs from either control (healthy or CFA; n = 6 mice (3 samples per condition)), acute or chronic Tcf / Lef ::H2B::eGFP (Wnt reporter) EAE mice (n = 8 mice (4 samples per condition)) for scRNA-seq. eGFP + and eGFP − spinal cord ECs were pooled prior to performing scRNA-seq from all conditions. g , t-distributed stochastic neighbor embedding (t-SNE) plot, color-coded for each batch. h , t-SNE plot, color-coded for each EC subtype, with and without Harmony batch correction. Re-embedding into t-SNE space after applying Harmony correction does not show big differences visually in the overall organization of EC clusters. i , Individually re-clustered t-SNE plots for each EC subtype (artery, capillary, venule and vein), color-coded by batch, grouped by disease state (healthy, CFA control, acute and chronic EAE). These plots show that all EC subtypes from each distinct disease state cluster together irrespective of the batch, suggesting minimal batch effects in the dataset. j , Violin plot shows very low expression of eGFP mRNA in vECs isolated from Tcf / Lef ::H2B::eGFP EAE mice, indicative of low-to-absent Wnt/β-catenin signaling activity in vein ECs during EAE. Data represent mean ± SEM; *p < 0.05, **p < 0.01; ****p < 0.0001; c and e , one-way ANOVA with Bonferroni correction for multiple testing; d , Student’s unpaired two-sided t-test.

Source data

Extended data fig. 2 angiogenic and tip cell marker transcripts are upregulated in vecs and vnecs in acute and chronic eae..

a – j , Feature plots show expression of angiogenic and tip cell markers in spinal cord vein ECs. The expression of angiogenic and tip cell markers is increased in vECs from acute and chronic EAE. k – o , Feature plots show expression of tip cell markers in spinal cord venule ECs. The expression of tip cell markers is increased in vnECs isolated from acute and chronic EAE.

Extended Data Fig. 3 Congruency in angiogenic gene expression among acute EAE vECs, developing brain and lung tumor ECs.

a – c , Venn diagrams of the overlap in angiogenic gene signatures between developing brain ECs (DECs) and EAE vECs ( a ), tumor lung ECs (TECs) and EAE vECs ( b ) and TECs and DECs ( c ). Venn diagrams show the numbers of common and unique genes between the two populations in each comparison and some of the key gene names. d , f , h , Alkaline phosphatase in situ hybridization for Apln mRNA. e , g , i , Fluorescence in situ hybridization for Apln mRNA combined with immunofluorescence for Caveolin-1 (EC marker) and DAPI, in developing (P3; d , e ), adult ( f , g ) healthy spinal cords and acute EAE spinal cords (16 d.p.i.; score 2.5; h , g ) female mice. Apln mRNA is expressed by many blood vessels in the developing P3 spinal cord ( d , black arrows; e , white arrows) when CNS angiogenesis is ongoing but is absent in the adult spinal cord ( g , white arrow) when CNS angiogenesis is completed. Apln mRNA is expressed in neurons in the adult spinal cord ( f , h , shown with a red arrowhead). Alpn mRNA expression is absent from blood vessels located in white matter lesions in acute EAE spinal cords ( i ), although other angiogenesis markers are expressed in these vessels (see Fig. 4 ). Scale bars: d = 260 μm; f and h  = 575 μm; e , g and i  = 40 μm.

Extended Data Fig. 4 Arterial and capillary ECs and pericytes do not proliferate in EAE.

a , b , Sagittal sections of CFA (control), acute EAE (16 d.p.i.) and chronic EAE (28 d.p.i.) spinal cords were immunostained for alpha-smooth muscle actin (αSMA) to labels arteries, Ki67 (proliferation marker), Mfsd2a (capillary ECs), CD31 (EC marker) and DAPI. There are no proliferative arterial or capillary ECs in EAE. c , Sagittal sections of CFA, acute EAE and chronic EAE spinal cords were immunostained for Pdgfrβ (pericyte marker) and Ki67. Pericytes do not proliferate in EAE. Scale bars = 30 μm. All analyses were done in adult (10–12 weeks old) female mice.

Extended Data Fig. 5 Increased expression of angiogenic markers in human relapsing-remitting and secondary progressive multiple sclerosis.

a – c ″, In situ hybridization for human CLAUDIN-5 ( a – a ″), SERPINE1 ( b – b ″) and ECM1 ( c – c ″) mRNAs show expression of the angiogenesis markers SERPINE1 and ECM1 mRNAs in white matter (WM) multiple sclerosis (MS) lesions, but neither in the normal-appearing white matter (NAWM) from MS patients nor in the NAWM from non-neurological control cases. CLAUDIN-5 mRNA is expressed by all blood vessels in human brain tissues. The fresh frozen MS brain samples were obtained from relapsing-remitting MS (RRMS) cases (N = 4) and non-neurological controls (N = 4). Scale bars = 40 μm. d – g , Line plots summarizing the detection of four angiogenesis mRNAs for EGFL7 ( d ), SERPINE1 ( e ), ECM1 ( f ) and MARCKSL1 ( g ) in either white matter (WM; red line), gray matter (GM, orange) or the sulcus area (purple line), with respect to the distance from the MS lesion border in secondary progressive MS (SPMS) cases from ref. 47 , which used spatial transcriptomics to profile gene expression within an array of 100-μm diameter spots from MS lesion borders. We binned all spots by their distance from the MS lesion border in each tissue type, using bins of 0.5 mm width, and calculated the fraction of spots within each bin where the four angiogenesis genes were detected. White matter spots far away from MS lesions show lower detection for these genes, with SERPINE1 and MARCKSL1 mRNAs showing the most marked effect of all four angiogenesis genes. These mRNAs are expressed at very high levels near the border lesion in the white matter, but not either gray matter or sulcus region.

Extended Data Fig. 6 r84 partially inhibits VEGF-A-mediated reduction in barrier properties and transcriptional changes in primary mouse brain endothelial cells.

a , Trans-endothelial electrical resistance (TEER) over time of primary mouse brain endothelial cells (mBECs) following treatment with VEGF-A (100 ng/mL) in the presence of either human IgG control or r84 antibody at 100-fold molar excess. Time course is shown as average of 8 wells per condition. The experiment was repeated three times. The acute drop in TEER immediately following the treatment (green shading) and the chronic drop (gray shading) are quantified separately (data represent mean ± SEM; *p < 0.05, **p < 0.01, ***p < 0.001,****p < 0.0001, unpaired two-tailed Student’s t-test). b , Principal component analysis (PCA) of bulk RNA sequencing data collected 48 hours after treatment (n = 3 biological samples per condition). c , Heat map visualization of differentially expressed genes (DEGs) driving pathway enrichment in VEGF-A plus r84 versus VEGF-A plus IgG-treated samples. Downregulated DEGs are related to angiogenesis’ (FDR q-val: 0.0012) and inflammation’ (FDR q-val: 0.0011), whereas upregulated DEGs are related to ‘oxidative phosphorylation’ (FDR q-val: 0.0033). There is no change in ‘Wnt/β-catenin signaling’ pathway. Control values are shown for reference.

Extended Data Fig. 7 Treatment of EAE mice with r84 reduces EC proliferation but does affect demyelination, immune cell infiltration and fibrinogen leakage in the spinal cord.

a , b , Sagittal sections of control IgG- and r84-treated (5 mg/kg) chronic (28 d.p.i.) EAE spinal cords immunostained for ( a ) fluoromyelin and CD68 (activated, phagocytic macrophages) and ( b ) fibrinogen and CD4 (T helper cells), as well as DAPI following cardiac perfusion with Lectin-A594 (marker of perfused vessels). c , Dotted bar graph shows Ki67 + ECs numbers/mm 2 with significant reduced EC proliferation in r84- compared to IgG-treated EAE spinal cords (n = 9 IgG, n = 9 r84; p = 0.0315 for r84 versus IgG). d – h , Dotted bar graphs show no significant changes in the number of white matter lesions ( d ), area of demyelination ( e ), number of infiltrating CD4 + T helper cells ( f ), number of infiltrating macrophages ( g ) and fibrinogen leakage ( h ) between IgG- and r84-treated chronic EAE spinal cords (n = 9 mice/condition). Data represent mean ± SEM; *p < 0.05. c , d , e , f , g , h , two-tailed Student’s t test. All analyses were done in adult (10–12 weeks old) female mice.

Supplementary information

Reporting summary, supplementary table 1.

Batch structure for scRNA-seq experiments ( a ). Gene lists used for the GSEA analysis ( b ). Results of differential expression and GSEA analysis between acute versus CFA/healthy aECs ( c ); acute versus CFA/healthy cECs ( d ); chronic versus CFA/healthy cECs ( e ); acute versus CFA/healthy vnECs ( f ); chronic versus CFA/healthy vnECs ( g ); acute versus CFA/healthy vECs ( h ); chronic versus CFA/healthy vECs ( i ). Negative log 2 (FC) values mean that the gene is lower in the disease state compared to CFA/healthy controls, and positive values mean that the gene is higher in the disease state compared to CFA/healthy controls. Differential expression was performed using the edgeRQLF.

Supplementary Table 2

Results of differential expression between acute EAE and CFA spinal cord ECs ( a ), embryonic and healthy adult brain vasculature ECs ( b ) and lung tumor versus normal lung ECs ( c ), used to construct the Venn diagrams in Extended Data Fig. 3a–c .

Supplementary Table 3

Results of differential expression and GSEA analysis between VEGF-A and IgG-treated versus control mouse primary brain endothelial cells (mBECs; a ), VEGF-A and r84-treated versus control mBECs ( b ) and VEGF-A and r84-treated versus VEGF-A and IgG-treated mBECs ( c ). Differential expression was performed using DEseq2.

Supplementary Table 4

Results of differential expression and GSEA analysis between r84- versus IgG-treated venule ECs chronic EAE (sheet a); r84- versus IgG-treated vein ECs chronic EAE (sheet b). Negative log2fc values mean that the gene is lower in the r84 compared to IgG treatment, and positive values mean that the gene is higher in the r84 compared to IgG treatment. Differential expression was performed using the edgeR Quasi-Likelihood F-test (edgeRQLF).

Supplementary Code.

Source data fig. 1.

PRISM file containing statistical source data for Fig. 1k . The code (PDF, word and R language) for the analysis of scRNA-seq data is described in Fig. 1.

Source Data Fig. 2

GSEA input data for Fig. 2a–d .

Source Data Fig. 3

PRISM file containing statistical source data for Fig. 3d–f,h .

Source Data Fig. 4

PRISM file containing statistical source data for Fig. 4i–l .

Source Data Fig. 5

PRISM file containing statistical source data for Fig. 5d–f .

Source Data Fig. 6

PRISM file containing statistical source data for Fig. 6b–e , and GSEA input data for Fig. 6i . The code (PDF, word and R language) for the analysis of scRNA-seq data is described in Fig. 6 .

Source Data Fig. 7

PRISM file containing statistical source data for Fig. 7b,c,e,f,g .

Source Data Extended Data Fig. 1

PRISM file containing statistical source data for Extended Data Fig. 1b–e .

Source Data Extended Data Fig. 5

The code (PDF, word and R language) used to generate the graphs in Extended Data Fig. 5d–g .

Source Data Extended Data Fig. 6

PRISM file containing statistical source data for Extended Data Fig. 6a .

Source Data Extended Data Fig. 7

PRISM file containing statistical source data for Extended Data Fig. 7c–h .

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Shahriar, S., Biswas, S., Zhao, K. et al. VEGF-A-mediated venous endothelial cell proliferation results in neoangiogenesis during neuroinflammation. Nat Neurosci (2024). https://doi.org/10.1038/s41593-024-01746-9

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Received : 15 November 2022

Accepted : 01 August 2024

Published : 10 September 2024

DOI : https://doi.org/10.1038/s41593-024-01746-9

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