-- a FAIR tool for drug combination discovery





Mirror site 1: https://synergyfinder.org/

Mirror site 2: https://tangsoftwarelab.shinyapps.io/synergyfinder/

Standalone download: https://sourceforge.net/projects/synergyfinder/





Drug Information


Download Drug Information

Drug Target Information


* Potent targets are defined as the targets displaying binding affinities <= 1,000 nM from the bioactivity databases, or targets recorded in the unary databases. The information comes from MICHA , which integrates the data from 6 databases: DTC , chEMBL , BindingDB , DrugBank , Guide to Pharmacology , DGIdb .

Download Drug Target Information

Cell Line Information


Download Cell Information

Monotherapy

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Download plot (svg)

Combination

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Synergy Map

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Combination Index Table

Synergy Barometer


Selected dose


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Tips:

  1. Click on a row in the bar plot to choose a particular dose combination. The barometer will be updated accordingly.
  2. Double click on a panel in the bar plot will sort the entire plot according to that panel.


Combination Sensitivity Table

Synergy-Sensitivity plot (SS plot)

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Select blocks

Download reports

Static PDF report

Dynamic HTML report

Note: The multi-drug surface plot will not be shown in the static report.

Download data tables

Summary table

Synergy score table

Download R object

R object

What’s New

07.09.2024-R-3.10.3

Bugs

  • Documentation about CI. CI = 1 indicates additive, not CI = 0

06.3.2024-R-3.10.3

Features

16.01.2024-R-3.8.2-dev

Bugs

  • A bug in ZIP function will cause error when the single drug dose response cannot be fitted in high-order drug combinations.

26.09.2023-R-3.8.2-dev

Features

02.09.2023-R-3.8.2-dev

Features

  • Security updates

04.06.2023-R-3.8.2-dev

Bugs

Restrictions

  • We recommend the Bioconductor/R pacakge for large data analysis
  • max number of doses in a matrix: 20
  • max number of rows in an input file: 1250
  • max number of input files in the same session: 10
  • max number of 2-drug combinations in an input file: 12
  • max number of high order drug combinations in an input file: 2

30.04.2023-R-3.8.2

Features

  • Tips are provided for illustrating functionality of the buttons, as well as interpretations of the results
  • Synchronized with the recent updates in the Bioconductor R package version 3.8.2

16.04.2023-R-3.6.3-dev

Features

6.04.2023-R-3.6.3-dev

Restrictions

  • Synergyfinder Plus (SynergyFinder+) is currently under cyber attack. Please be patient if the server is down.
  • Synergyfinder Plus (SynergyFinder+) is compatible with the input files of SynergyFinder3. No format changes are needed.
  • Maximal number of blocks in an input file is 6.
  • Each user has a quota of generated report files. If quota is reached, restart the program.
  • We recommend using the Bioconductor R package for large data analysis.

Features

  • Combination Index is provided as part of synergy result.
  • Missing values before and after imputation can be visualized.

Bugs

  • Synergy barometer is updated when choosing different blocks.
  • Handling of missing values is enabled when calculating statistics.
  • Handling of error catch when monotherapy data is totally missing.

1 Prepare Input Data

1.1 Data Format

1.1.1 Table Format

In the Table format, the dose-response data is represented as a long table where each row represent one observation in the dose-response matrix (Fig.1). Fig.1 Input file in Table format.

Fig.1 Input file in Table format.

The input table must contain the following columns (The column naming style used in the old SynergyFinder or DrugComb, i.e. ‘Alternative Column names’ are accepted):

Required Columns Alternative Column names Description
block_id PairIndex, BlockId Identifier for the drug combination blocks.
drug1 Drug1, drug_row, DrugRow Name of the first tested drug.
drug2 Drug2, drug_col, DrugCol Name of the second tested drug.
conc1 Conc1, conc_row, ConcRow Concentration of first tested drug.
conc2 Conc2, conc_col, ConcCol Concentration of second tested drug.
response Response, inhibition, Inhibition Cell response to the drug treatment (%inhibition or %viability).
conc_unit ConcUnit Unit of concentration for drugs. This column could be replaced by multiple separated columns for each tested drugs (see table below), while different unit was used for measuring the concentrations.
Optional Columns Alternative Column names Description
conc_unit1 conc_r_unit Unit of concentration for the first drug. Used if the concentration units are not identical across the drugs tested in one block.
conc_unit2 conc_c_unit Unit of concentration for the second drug. Used if the concentration units are not identical across the drugs in test one block.
drug[n] Name of the n_th_ tested drug. For example, “drug3” for the third tested drug. Used for higher-order drug combination data point.
conc[n] Concentration of n_th_ tested drug. Used for higher-order drug combination data point.
conc_unit[n] Unit of concentration for n_th drug. Used if the concentration units are not identical across the drugs in test one block.
cell_line_name Name of the cell line. The cell line names will be used for “data annotation”.

Note:

  1. The duplicated concentration combinations in one block (with the same “block_id”) will be treated as replicates.
  2. There is no restriction on the number of drug combinations for the input file. The data should however, contain at least three concentrations for each drug, so that sensible synergy scores can be calculated.
  3. SynergyFinder allows for missing values in the dose-response matrix. The missing value will be automatically imputed by mice R package.

1.1.2 Matrix Format

In the Matrix format, the dose-response matrix is represented in a matrix with drug concentrations shown along the left (for Drug1) and top (for Drug2) edges of the matrix (Fig.2). The three rows below should precede each dose-response matrix:

  1. Drug1 name of the first drug
  2. Drug2 name of the second drug
  3. ConcUnit unit of concentration

Fig.2 An input file in Matrix format. Two dose-response matrices (for AT-406 & Navitoclax and NVP-LGK974 & Alpelisib drug combinations) are provided as an example.

Fig.2 An input file in Matrix format. Two dose-response matrices are provided as an example.

Note:

  1. Matrix format only works on 2 drug combination data. Please use table format for combinations with more than 3 drugs.
  2. The drug concentrations should be located at the top and left side of the matrix, where concentrations located at the left side correspond to Drug1 and concentrations located at the top correspond to the Drug2.
  3. There is no restriction on the number of drug combinations for the input file. The data should however, contain at least three concentrations for each drug, so that sensible synergy scores can be calculated.
  4. SynergyFinder allows for missing values in the dose-response matrix. The missing value will be automatically imputed by mice R package.

1.2 File Format

SynergyFinder accepts following file formats:

  • EXCLE file with extension “.xlsx”
  • comma-delimited CSV file, with extension “.csv”
  • tab-delimited TXT file, with extension “.txt”

1.3 Example Data

SynergyFinderPlus provides 3 example data:

  1. ONEILTable: It is an example data in table format for 2-drug combinations with 4 replicates. The is information extracted from a pan-cancer drug screening study [O’Neil et al. 2016]. It contains two representative drug combinations (MK-1775 & Niraparib and Paclitaxel & L-778123 free base) for which the %inhibition of a cell line OCUBM and NCIH2122 was assayed using a 5 by 5 dose matrix design with four replicates.

  2. ONEILMatrix: It is an example data in matrix format for 2-drug combinations without replicates. The data resource is the sample as previous example data. The %inhibition value in the matrix are the average response value from 4 replicates.

  3. NCATSTable: It is an example data in table format for 3-drug combinations without replicate. The information is extracted from a triple drug screening study on malaria [Ansbro et al. 2020]. It contains two representative drug combinations (Piperaquine & Pyronaridine Tetraphosphate & Darunavir Ethanolate and Piperaquine & Pyronaridine Tetraphosphate & Lopinavir) for which the %inhibition of malaria was assayed using a 10 by 10 by 12 dose matrix design with four replicates.

User can directly upload these data sets or download all of them in 3 different file formats (xlsx, csv, and txt) on the websites (see Fig3).

The files are also downloadable from here.

2 Upload File

The “Upload Data” tab is designed for user to upload file. Figure 3 shows the user interface.

Fig.3 User Interface of the “Upload Data” tab

Fig.3 User Interface of the "Upload Data" tab

  1. Choose the data format used in the uploaded file. Please check section “1.1 Data Format” for more details.
  2. Select the file to upload from your local directory. Please check section “1 Prepare Input Data” for more details. Alternatively you can select one of the example data tables from the dropdown list for analysis.
  3. Choose the phenotypic response metric of uploaded drug combinations. Available options in SynergyFinder are: inhibition (% inhibition to cell growth or other signals. Normalized by negative control.) viabillity (% cell viability after treatment. Normalized by negative control. In case of %viability response type, the provided %viability values will be converted to %inhibition by the formula: \(\%inhibition = 100 - \%viability\).) Once a response type is selected, a new tab “Dose Response Map” will be shown in the left sidebar. User could click it to visualize dose-response map (see the next page of the user guide).
  4. A button to download the example data. The example data sets include 2 drug combination screening data, 3 drug combination screening data.
  5. A switch for data annotation. It will be shown once the data is successfully uploaded.By turning it on, the program will query the external databases the annotate the drugs and cell lines in the input data table.
  6. The overview for the input data in table format. It will be shown while the file is successfully uploaded and formatted.

3. Annotation

SynergyFinder provides three tables for annotation(Fig.4):

Fig.4 Annotation for drug and cell line

Fig.4 Annotation for drug and cell line

Drug Information: It contains the basic information for drugs tested in input data tables. It includes columns:

  • Drug Name: The name for drugs in the input data table.

  • InChIKey: They The IUPAC International Chemical Identifier for drugs. (Information from PubChem.[Kim et al., 2021])

  • Isomeric SMILES: The isomeric SMILES for drugs from input data table. (Information from PubChem.[Kim et al., 2021])

  • Molecular Formula: The molecular formula for the drugs. (Information from MICHA[Tanoli et al., 2021])

  • Max Phase: The maximum phase for clinical trial for the compounds (drugs) in input data table. (Information from MICHA[Tanoli et al., 2021])

    • 0: Compound has not yet reached phase I clinical trials
    • 1: Compound has reached phase I clinical trials
    • 2: Compound has reached phase II clinical trials
    • 3: Compound has reached phase III clinical trials
    • 4: Compound has been approved in at least one country/area
  • Cross Reference: The drug identifiers used in other databases (PubChem, BindingDB, chEMBL, DrugBank, PharmGKB, Guide to Pharmacology, ChEBI, Selleck, ZINC). Clicking on the IDs directs user to corresponding drug pages on the external databases.

  • Disease Indication: The drug is used to treat these diseases. (Information from MICHA[Tanoli et al., 2021])

Drug Target Information: It contains the information for drug targets. It includes columns:

  • Drug Name: The name for drugs in the input data table.
  • InChIKey: They The IUPAC International Chemical Identifier for drugs. (Information from PubChem.[Kim et al., 2021])
  • Primary Target Name: The name for the primary target of the drug. (Information from MICHA[Tanoli et al., 2021])
  • Primary Target ID: The UniProt ID for the primary target of the drug. (Information from MICHA[Tanoli et al., 2021])
  • Potent Target Name: The potent targets are defined as the targets displaying binding affinities <= 1,000 nM from the bioactivity databases, or targets recorded in the unary databases. The information comes from MICHA, which integrates the data from 6 databases: DTC, chEMBL, BindingDB, DrugBank, Guide to Pharmacology, DGIdb. (Information from MICHA[Tanoli et al., 2021])

Cell Line Information: It contains the information about the cell line from Cellosaurus database.[Bairoch, 2018] It shows only when the cell line names are included in the input data table. It includes columns:

  • Cell Name: The cell line name extracted from input data table.
  • Synonyms: The synonyms for cell line
  • Cellosaurus Accession: The identifier for cell lines used in Cellosaurus
  • Tissue: The tissue from which cell line is collected
  • Disease Name: The disease from which cell line is collected
  • Disease NCIt ID: The NCI Thesaurus (NCIt) for the disease

Reference

[Bairoch, 2018] Bairoch,A. (2018) The Cellosaurus, a Cell-Line Knowledge Resource. J Biomol Tech, 29, 25–38.

[Kim et al., 2021] Kim,S., Chen,J., Cheng,T., Gindulyte,A., He,J., He,S., Li,Q., Shoemaker,B.A., Thiessen,P.A., Yu,B., et al. (2021) PubChem in 2021: new data content and improved web interfaces. Nucleic Acids Research, 49, D1388–D1395.

[O’Neil et al. 2016] O’Neil, Jennifer, Yair Benita, Igor Feldman, Melissa Chenard, Brian Roberts, Yaping Liu, Jing Li, et al. 2016. “An Unbiased Oncology Compound Screen to Identify Novel Combination Strategies.” Molecular Cancer Therapeutics 15 (6): 1155–62.

[Tanoli et al., 2021] Tanoli,Z., Aldahdooh,J., Alam,F., Wang,Y., Seemab,U., Fratelli,M., Pavlis,P., Hajduch,M., Bietrix,F., Gribbon,P., et al. (2021) Minimal information for Chemosensitivity assays (MICHA): A next-generation pipeline to enable the FAIRification of drug screening experiments. bioRxiv, 10.1101/2020.12.03.409409.

1 User Interface

This tab contains the dose-response curve and dose-response map for visualizing the input data. Figure 1 shows the user interface.

Fig.1 User Interface of the “Dose Response Map” tab

Fig.1 User Interface of the "Dose Response Map" tab

  1. Select the block to visualize.
  2. Plotting area. All of the plots can be customized and downloaded. Please check sections below for more details.
  3. The “Synergy Map” tab appears in the sidebar. By clicking on it, user will be directed to visualization for synergy level of the combinations.

2 Dose Response Curve

Fig.2 Dose-response curve

Fig.2 Dose-response curve

SynergyFinder extracts the data of the single drug treatment from the input data. Each drug’s dose-response is modeled using 4-parameter log-logistic curve and visualized in this panel. SynergyFinder provides various widgets to help user customize the plot:

  1. Plotting area for dose response curve.
  2. Select the one of the drugs in the combination to visualize.
  3. Select the color for the data points.
  4. Select whether the grid is shown in the background.
  5. Select the color for the curve.
  6. Download the plot as “SVG” file.

3 Dose Response Map (2 Drugs Combination)

Fig.3 Two drugs combination dose-response map

Fig.3 Two drugs combination dose-response map

SynergyFinder extracts the data for all possible drug combinations from the data and visualize them in as dose response maps. Two types of plot are available: Heatmap and interactive 3D surface (Fig.3). SynergyFinder provides various widgets to help user customize the plot:

  1. Interactive plotting area powered by plotly.Buttons at the top-right corner help user modify the plotting view and download the plot as “SVG” file.
  2. Select the drug pair to visualize. If input data is 2-drug combination, only one option is available.
  3. Adjust the text size for plot title, axis titles, axis texts, legend titles, and legend tick texts.
  4. Select the summary statistic shown on the top of the top. It could be mean, median, 25% quantile or 75% quantile of the response values in the whole combination matrix. If there are replications in the input data, the p value (comparing to 0% inhibition) will be shown after the mean value.
  5. Select the plot type to be Heatmap or 3D surface.
  6. Select the color for the highest value in the Heatmap/surface.
  7. Select the color for the lowest value in the Heatmap/surface.
  8. (Only for Heatmap) Adjust the text size for the labels within Heatmap.
  9. (Only for Heatmap and replicated data) Select the statistics shown below the Heatmap text labels. Available statistics are “90% confidence interval” or “standard error of mean”.
  10. (Only for Heatmap) Select the color for the text Heatmap on the Heatmap.
  11. (Only for 3D surface) Whether to show the grids on the surface in the plot.

4 Dose Response Map (Multiple Drugs Combination)

Fig.4 Multiple drugs combination dose-response map

Fig.4 Multiple drugs combination dose-response map

This plot is designed for visualizing high-order drug combinations. The two-dimensional coordinates of each drug dose combination are determined by multi-dimensional scaling based on the similarity of their dose ranges. The response (% inhibition) is visualized as the height of a 3D surface. Observed data points are plotted as dots on the surface.

  1. Interactive plotting area powered by plotly. Buttons at the top-right corner help user modify the plotting view and download the plot as “SVG” file. Hovering mouse on the data points will show the concentration information of the drugs and corresponding % inhibition value.
  2. Select whether to show the observed data points.
  3. Select the color of the data points.
  4. Select the color for the highest value in the surface plot.
  5. Select the color for the lowest value in the surface plot.

1 Synergy Score Calculation

The synergistic effect can be determined as the excess of observed effect over expected effect calculated by a reference models (synergy scoring models). All of the models make different assumptions regarding the expected effect. Currently, 4 reference models are available in SynergyFinder.

  • Highest Single Agent (HSA) [Berenbaum, 1989] states that the expected combination effect equals to the higher effect of individual drugs:

$$y_{HSA} = max(y_1, y_2)$$

  • Loewe additivity model [Loewe, 1953] defines the expected effect \(y_{LOEWE}\) as if a drug was combined with itself. Unlike the HSA and the Bliss independence models, which give a point estimate using different assumptions, the Loewe additivity model considers the dose-response curves of individual drugs. The expected effect \(y_{LOEWE}\) must satisfy:

$$ \frac {x_1}{\chi_{LOEWE}^1} + \frac{x_2}{\chi_{LOEWE}^2} = 1 $$

, where \(x_{1,2}\) are drug doses and \(\chi_{LOEWE}^1,\ \chi_{LOEWE}^2\) are the doses of drug 1 and 2 alone that produce \(y_{LOEWE}\). Using 4-parameter log-logistic (4PL) curves to describe dose-response curves the following parametric form of previous equation is derived:

$$ \frac {x_1}{m_1(\frac{y_{LOEWE}-E_{min}^1}{E_{max}^1 - y_{LOEWE}})^{\frac{1}{\lambda_1}}} + \frac{x_2}{m_2(\frac{y_{LOEWE}-E_{min}^2}{E_{max}^2 - y_{LOEWE}})^{\frac{1}{\lambda_2}}} = 1 $$ , where \(E_{min}, E_{max}\in[0,1]\) are minimal and maximal effects of the drug, \(m_{1,2}\) are the doses of drugs that produce the midpoint effect of \(E_{min} + E_{max}\), also known as relative \(EC_{50}\) or \(IC_{50}\), and \(\lambda_{1,2}(\lambda>0)\) are the shape parameters indicating the sigmoidicity or slope of dose-response curves. A numerical nonlinear solver can be then used to determine \(y_{LOEWE}\) for ($x_1$, \(x_2\)).

  • Bliss model [Bliss, 1939] assumes a stochastic process in which two drugs exert their effects independently, and the expected combination effect can be calculated based on the probability of independent events as:

$$ y_{BLISS} = y_1 + y_2 - y_1 \cdot y_2 $$

  • Zero Interaction Potency (ZIP) [Yadav et al., 2015] calculates the expected effect of two drugs under the assumption that they do not potentiate each other:

$$ y_{ZIP} = \frac{(\frac{x_1}{m_1}) ^ {\lambda_1}}{(1 + \frac{x_1}{m_1})^{\lambda_1}}+\frac{(\frac{x_2}{m_2})^{\lambda_2}}{(1 + \frac{x_2}{m_2})^{\lambda_2}} - \frac{(\frac{x_1}{m_1})^{\lambda_1}}{(1 + \frac{x_1}{m_1})^{\lambda_1}} \cdot \frac{(\frac{x_2}{m_2})^{\lambda_2}}{(1 + \frac{x_2}{m_2})^{\lambda_2}} $$

2 Correct Baseline

Typically, the models for estimating synergy or sensitivity of drug combinations expect that the drug’s effect to be expressed as continuous values ranged between 0 and 1 (or between 0% and 100%). However, in practice the readouts from the drug combination screening could be negative. In this cases, the technical error might be introduced in the dose-response data. The base line correction function is designed to adjust the “baseline” of the dose-response data closer to 0. Following is the main steps for the process of “baseline correction”:

  1. Extract all the single drug treatment (monotherapy) dose-response data from the combination;
  2. Fit the four-parameter log logistic model for each monotherapy with the data table from step 1;
  3. Pick the minimum fitted response value from all the models fitted in step 2 as “baseline”;
  4. Adjusted response value = observed response value - ((100 – observed response value) / 100 * baseline).

We provides 3 options for baseline correction:

  • “non” - do not correct base line;
  • “part” - correct base line but only adjust negative response values in matrix;
  • “all” - correct base line with adjusting all values in matrix.

3 User Interface

This tab visualizes the synergy scores for the inputted drug combination screening data. Figure 1 shows the user interface.

Fig.1 User Interface of the “Synergy Score” tab

Fig.1 User Interface of the "Synergy Score" tab

  1. A selector to select the block to visualize.
  2. A selector to select the method for baseline correction. This function adjusts the baseline of drug combination dose-response matrix closer to 0. There are three options:

“Non” - no baseline correction (default value);

“Part” - only the negative values in the matrix will be adjusted;

“All” - adjusts all values in the matrix.

Once the baseline correction method is selected, the calculation for synergy scores and sensitivity scores will be triggered. After the calculation, two new tabs (“Sensitivity Scores” and “Download Report”) will be shown. Please check corresponding pages for more details. 3. Plotting area. The customizable plots will be shown in this area. All of the plots are able to be downloaded. Please check sections below for more details.

4 Synergy Map (2 Drugs Combination)

Fig.2 Synergy Map (2 Drugs Combination)

Fig.2 Synergy Map (2 Drugs Combination)

SynergyFinder extracts the data for all the possible drug combination pairs from the data and visualize the synergy map calculated from 4 synergy scoring models. There are 3 types of plot are available: Heatmap, contour plot and interactive 3D surface (Fig.2). SynergyFinder provides various widgets to help user customize the plots:

  1. Interactive plotting area powered by plotly. Several buttons will be shown at the top-right corner while hovering to help user modify the plotting view and download the plot as “SVG” file.
  2. Select the drug pair to visualize. If input data is 2-drug combination, only one option is available.
  3. Select the plot type to be Heatmap, contour plot or 3D surface.
  4. Select the summary statistic shown on the top of the top. It could be mean, median, 25% quantile or 75% quantile of the response values in the whole combination matrix. If there are replications in the input data, the p value (comparing to 0% inhibition) will be shown after the mean value.
  5. Adjust the text size for plot title, axis titles, axis texts, legend titles, and legend tick texts.
  6. Select the color for the highest value in the plot.
  7. Select the color for the lowest value in the plot.
  8. (Only for Heatmap and replicated data) Select the statistics shown below the Heatmap text labels. Available statistics are “90% confidence interval” or “standard error of mean”.
  9. (Only for Heatmap) Adjust the text size for the labels within Heatmap.
  10. (Only for Heatmap) Select the color for the text Heatmap on the Heatmap.
  11. (For 3D surface and 2D contour plot) Whether to show the grids on the surface in the plot.

5 Synergy Map (Multiple Drugs Combination)

Fig.4 Multiple drugs combination synergy map

Fig.4 Multiple drugs combination synergy map

This plot is designed for visualizing high-order drug combinations. The two-dimensional coordinates of each drug dose combination are determined by multi-dimensional scaling based on the similarity of their dose ranges. The synergy scores are visualized as the height of a 3D surface. Observed data points are plotted as dots on the surface.

  1. Interactive plotting area powered by plotly. Buttons at the top-right corner help user modify the plotting view and download the plot as “SVG” file. Hovering mouse on the data points will show the concentration information of the drugs and corresponding synergy score.
  2. Select whether to show the observed data points.
  3. Select the color of the data points.
  4. Select the color for the highest value in the surface plot.
  5. Select the color for the lowest value in the surface plot.

6 Bar and Barometer Plots

Fig.3 Bar and Barometer Plots

Fig.3 Bar and Barometer Plots

SynergyFinder visualize the whole matrix’s dose response and synergy scores in a group of bar plot. The barometer plot is provided for user to compare the synergy scores from different synergy scoring models (Fig.3). SynergyFinder provides various widgets to help user customize the plot:

  1. A table for the information at the selected data point (one drug dose combination in the matrix) in the Bar plot.
  2. Barometer plot for the selected data point in Bar plot. Then needle points to the observed response value. The 4 ticks on the color bar mark the reference additive effect response value calculated by different models.
  3. An interactive bar plot to show the over all information of the whole combination matrix. Clicking on a specific row of bars will highlight it and show it’s information in the table and barometer above. Double click on certain panel will sort the bars according to the values of that panel.
  4. Adjust the text size for the panel title.
  5. Adjust the text size for the axis texts.
  6. Adjust the text size of the text label on highlighted bars.
  7. Select the color for the 100% inhibition in the barometer.
  8. Select the color for the bars of positive value.
  9. Select the color for the bars of negative value.
  10. Select the color for the highlighted bars of positive value.
  11. Select the color for the highlighted bars of negative value.
  12. Download Bar plot as “SVG” file.
  13. Download Barometer as “SVG” file.

Reference

[Berenbaum, 1989] Berenbaum, M. C. (1989). What is synergy? Pharmacol. Rev., 41(2):93–141.

[Bliss, 1939] Bliss, C. I. (1939). The toxicity of poisons applied jointly1. Annals of Applied Biology, 26(3):585–615.

[Loewe, 1953] Loewe, S. (1953). The problem of synergism and antagonism of combined drugs. Arzneimit- telforschung, 3(6):285–290.

[Yadav et al., 2015] Yadav, B., Wennerberg, K., Aittokallio, T., and Tang, J. (2015). Searching for Drug Synergy in Complex Dose-Response Landscapes Using an Interaction Potency Model. Comput Struct Biotechnol J, 13:504– 513.

1 Sensitivity Score Calculation

SynergyFinder mainly calculates 3 sensitive scores: relative IC50 and relative inhibition (RI) for single drug treatment, and combination sensitivity score (CSS) for drug combinations.

1.1 Relative IC50

SynergyFinder extracts the single drug treatment response data from the combination matrix to fit the 4-parameter log-logistic curve:

$$y = y_{min} + \frac{y_{max} - y_{min}}{1 + 10^{\lambda(log_{10}IC_{50} - x')}}$$ where \(y_{min}, y_{max}\) are minimal and maximal inhibition and \(x' = log_{10}x\)

1.2 Relative Inhibition (RI)

RI is the abbreviation of “relative inhibition”. It is the proportion of the area under the dose-response curve (fitted by four parameter log logistic model), to the maximal area that one drug can achieve at the same dose range (Fig.1). For example, RI of 40 suggests that the drug is able to achieve 40% of the maximal of inhibition (e.g. a positive control where the cell is 100% inhibited in each dose that in the range). RI is comparable between different scenarios, even for the same drug-cell pair but tested in different concentration ranges.

Fig.1 Concept of RI

Fig.1 IC50 and area under the dose-response curve

## 1.3 Combination Sensitivity Score (CSS)

CSS - drug combination sensitivity score is derived using relative IC50 values of compounds and the area under their dose-response curves. CSS of a drug combination is calculated such that each of the compounds (background drug) is used at a fixed concentration (its relative IC50) and another is at varying concentrations (foreground drug) resulting in two CSS values, which are then averaged. Each drug’s dose-response is modeled using 4-parameter log-logistic curve. The area under the log-scaled dose-response curve (AUC) is then determined according to:

$$AUC = \int_{c_1}^{c_2}y_{min} + \frac{y_{max}-y_{min}}{1 + 10^{\lambda(log_{10}IC_{50}-x')}}dx'$$ where \([c_1, c_2]\) is the concentration of the foreground drug tested. [Malyutina et al., 2019]

2 User Interface

This tab visualizes the sensitivity scores for the inputted drug combination screening data. Figure 2 shows the user interface.

Fig.2 User Interface of the “Sensitive Score” tab

Fig.2 User Interface of the "Sensitivity Map" tab

  1. Summary table for sensitivity scores. Please check section 2.1 below for more details.
  2. Plotting area for Synergy-Sensitivity plot(S-S plot).All of the plots can be customized and downloaded. Please check section 2.2 below for more details.

2.1 Sensitivity score summary table

The table contains following columns:

  • block_id: The identifier for combination tests.
  • drug[n]: The drug names tested in the combination.
  • ic50_[n]: The relative IC50 for corresponding drug.
  • ri_[n]: The relative inhibition(RI) for corresponding drug.
  • css[n]_ic50[m]: The CSS for foreground drug[n] while the background drug is drug[m].
  • css: The overall combination sensitivity score for whole combination matrix.

2.2 S-S Plots

Fig.3 Synergy-Sensitivity Plots

Fig.3 Synergy-Sensitivity Plots

SynergyFinder plots the CSS together with different synergy scores for each combination in the input data as Synergy-Sensitivity Plot (Fig.3). It helps user to explore the combinations that not only have synergistic effect but also have high sensitivity on tested cells. The synergy scores or CSS scores shown in this plot are the summarized scores for whole combination matrix. SynergyFinder provides various widgets to help user customize the plot:

  1. Interactive plotting area powered by plotly. Several buttons will be shown at the top-right corner while hovering to help user modify the plotting view and download the plot as “SVG” file.
  2. Select the color for the data points.
  3. Adjust the size for the data points in “mm” unit.
  4. Select the color for the text label.
  5. Adjust the size for the text label in “pt” unit.
  6. Select whether to show the text label on the plots.

Reference

[Malyutina et.al, 2019] Malyutina, A., Majumder, M. M., Wang, W., Pessia, A., Heckman, C. A., Tang, J. Drug Combination Sensitivity Scoring Facilitates the Discovery of Synergistic and Efficacious Drug Combinations in Cancer. PLOS Computational Biology 2019, 15 (5), e1006752.

User Interface

This tab provides the functions to download the analysis results. Figure 1 shows the user interface.

Fig.1 User Interface of the “Download Report” tab

Fig.1 User Interface of the "Download Report" tab

  1. Select the blocks to be shown in the reports.
  2. Download the reports for analysis results with summary tables and plots. There are two kinds of reports available: static PDF reports and dynamic HTML reports. The setting of the plots are partially depends on the options token in the application.
  3. Download the data tables for synergy and sensitivity scores. Three file formats are available: “CSV”, “TXT”, “XLSX”. Two tables are available for downloading: “Summary Table” - The summarized synergy score and CSS score for all the combination blocks; “Synergy Score Table” - The synergy scores, reference additive effects and the fitted effects (only for ZIP) for all the drug concentration combinations in each block.
  4. Download the R list object in “RDS” file. It could be used as the input data for the SynergyFinder R package.

A Brief Introduction to SynergyFinder+

A Tour for SynergyFinder+ Web Application

How do I report a technical issue on SynergyFinder+?

Contact: jing.tang@helsinki.fi

You may also report the technical issues to our GitHub repositories at: TangSoftwareLab/SynergyFinderWeb web application, or TangSoftwareLab/SynergyFinderR for R package.

Mathematical modelling in SynergyFinder+ and SynergyFinder2

Author: Jing Tang, Faculty of Medicine, University of Helsinki


There are substantial differences between SynergyFinder2 and SynergyFinderPlus. For assessing the degree of synergy for higher-order drug combinations, SynergyFinderPlus develops novel mathematical models for BLISS, LOEWE and ZIP, which are distinct from those developed in SynergyFinder2 (Table 1). In fact, we found that mathematical models used in SynergyFinder2 are incompatible with the assumptions of BLISS, LOEWE and ZIP. Therefore, it might be suboptimal to use SynergyFinder2 for the analysis of high-order drug combination data. Please find the detailed explanations as below, using the three-drug combination data as an example:

Table 1. Differences in mathematical modelling for higher-order drug combinations

SynergyFinderPlus SynergyFinder2
BLISS \(S_{BLISS}=E_{A,B,C}-(E_A + E_b + E_c - E_AE_B - E_AE_C - E_BE_C + E_AE_BE_C)\) \(S_{BLISS}=E_{A,B,C}-(E_A + E_b + E_c - E_AE_B - E_AE_C - E_BE_C - E_AE_BE_C)\)
LOEWE \(S_{LOEWE}=E_{A,B,C}-E_{LOEWE},\)
\(s.t. \sum_{i\in \{A,B,C\}}(\frac{x_i}{f_i^{-1}(E_{LOEWE})}) = 1\)
\(S_{LOEWE}=\frac{a}{A} + \frac{b}{B} + \frac{c}{C}\)
ZIP \(S_{ZIP} = \hat{E}_{A,B,C} - (\hat{E}_A + \hat{E}_B + \hat{E}_C - \hat{E}_A\hat{E}_B - \hat{E}_A\hat{E}_C - \hat{E}_B\hat{E}_C + \hat{E}_A\hat{E}_B\hat{E}_C)\)
\(\hat{E}_{A,B,C} = \frac{1}{3}(\frac{\hat{E}_{-A} + (\frac{x_A}{\hat{m}_A})^{\hat{\lambda}_A}}{1+(\frac{x_A}{\hat{m}_A})^{\hat{\lambda}_A}}+\frac{\hat{E}_{-B} + (\frac{x_B}{\hat{m}_B})^{\hat{\lambda}_B}}{1+(\frac{x_B}{\hat{m}_B})^{\hat{\lambda}_B}} + \frac{\hat{E}_{-C} + (\frac{x_C}{\hat{m}_C})^{\hat{\lambda}_C}}{1+(\frac{x_C}{\hat{m}_C})^{\hat{\lambda}_C}})\)
\(S_{ZIP} = E_{A,B,C} - (\hat{E}_A + \hat{E}_B + \hat{E}_C - \hat{E}_A\hat{E}_B - \hat{E}_A\hat{E}_C - \hat{E}_B\hat{E}_C - \hat{E}_A\hat{E}_B\hat{E}_C)\)
Website www.synergyfinderplus.org or www.synergyfinder.org https://synergyfinder.fimm.fi
Source code https://www.bioconductor.org/packages/release/bioc/html/synergyfinder.html Not available
Publication Zheng, S.; Wang, W.; Aldahdooh, J.; Malyutina, A.; Shadbahr, T.; Tanoli Z; Pessia, A.; Jing, T*. SynergyFinder Plus: Toward Better Interpretation and Annotation of Drug Combination Screening Datasets. Genomics, Proteomics & Bioinformatics 2022. doi:10.1016/j.gpb.2022.01.004 Ianevski, A.; Giri, A. K.; Aittokallio, T. SynergyFinder 2.0: Visual Analytics of Multi-Drug Combination Synergies. Nucleic Acids Research 2020, 48 (W1), W488–W493. doi:10.1093/nar/gkaa216

The BLISS model

For the BLISS model, SynergyFinder2 used the Equation (1) to determine the expected drug combination response:

$$S_{BLISS}=E_{A,B,\dots,N}-(E_A + E_b + \dots + E_N - E_AE_B - E_AE_N - E_BE_N - \dots - E_AE_B...E_C)\ \ \ \ (1)$$

where \(E_{A, B,...,N}\) is the combination response and \(E_A,E_B,… E_N\) are the single drug responses (i.e. % inhibitions) for drug \(A,B,…N\), respectively.

However, equation (1) does not converge to the BLISS model which assumes the probabilistic independence. For example, in the case of three drugs ($A,B,C$), according to (1):

$$S_{BLISS}=E_{A,B,C}-(E_A + E_b + E_c - E_AE_B - E_AE_C - E_BE_C - E_AE_BE_C)\ \ \ \ (2)$$

while the correct BLISS model should be:

$$S_{BLISS}=E_{A,B,C}-(E_A + E_b + E_c - E_AE_B - E_AE_C - E_BE_C + E_AE_BE_C)\ \ \ \ (3)$$

Equation (2) and (3) differs only at the last term but mathematically they are different. If we assume the probabilistic independence as defined in the BLISS model, then (3) should be the correct formula.

For example, in a scenario where \(E_{A,B,C}=E_A=E_B=E_C=1\), that all the single drugs and their combination reach 100% inhibition, no BLISS synergy should be detected. However, we found inflated synergy score of \(S_{BLISS}=2\) if using (2). Instead, (3) leads to correct synergy score of \(S_{BLISS}=0\). In SynergyFinderPlus, we used the formula that leads to (3), and thus provides a more compatible BLISS model for higher-order drug combinations.

The LOEWE model

For the LOEWE model, SynergyFinder2 used the Equation (4):

$$S_{LOEWE} = \frac{a}{A} + \frac{b}{B} + \dots + \frac{n}{N}\ \ \ \ (4)$$

where \(a,b,…n\) are the doses of the single drugs required to produce the combination effect \(E_{A,B,…,N}\). By such a definition, \(S_{LOEWE}\) takes the values from \((0,+\infty)\) and it can never be negative. This is incompatible with the other scores such as \(S_{BLISS}\), for which a positive score implies synergy, and a negative score implies antagonism. In fact, (4) is the Combination Index that takes a value of 1 for non-interaction, a value in \((0,1)\) for synergy and a value in \((1,+\infty)\) for antagonism, which is totally in opposite direction as the other types of synergy scores.

In contrast, in SynergyFinderPlus we have utilized a different formula as

$$S_{LOEWE}=E_{A,B,...,N}-E_{LOEWE},\\ s.t.\sum_{i= A,B,...,N}(\frac{x_i}{f_i^{-1}(E_{LOEWE})}) = 1\ \ \ \ (5)$$

Our implementation makes sure that the LOEWE score for multiple drug combinations is well defined with zero as the reference point, i.e. \(E_{A,B,…,N}=E_{LOEWE}\) lead to \(S_{LOEWE}=0\).

The ZIP model

Take again the three-drug scenario for example, SynergyFinder2 uses the following formula for \(S_{ZIP}\): $$S_{ZIP} = E_{A,B,C} - (\hat{E}_A + \hat{E}_B + \hat{E}_C - \hat{E}_A\hat{E}_B - \hat{E}_A\hat{E}_C - \hat{E}_B\hat{E}_C - \hat{E}_A\hat{E}_B\hat{E}_C)\ \ \ \ (6)$$ where \(\hat{E}_A, \hat{E}_B, ..., \hat{E}_N\) are fitted response using four-parameter log-logistic model for the single drugs, e.g.

$$\hat{E}_{A} = \frac{(\frac{x_A}{m_A})^{\lambda_A}}{1+(\frac{x_A}{m_A})^{\lambda_A}} \ \ \ \ (7)$$

There are two limitations in Equation (6): a) Similar to Equation (1), the signs of the multiplicative terms in Equation (6) should be flipped. b) Equation (6) is inconsistent, as it is using fitted drug response only for the reference model but not for the observed response The ZIP model should also fit the combination response with the four-parameter log-logistic model, i.e.

$$\hat{E}_{A,B,...,N} = \frac{1}{n}\sum_{i = A, B,..., N}\frac{(\hat{E}_{-i} + \frac{x_i}{\hat{m}_i})^{\hat{\lambda}_i}}{1+(\frac{x_i}{\hat{m_i}})^{\hat{\lambda}_i}} \ \ \ \ (8)$$

where \(\hat{E}_{-i}\) is the combination response while drug \(i\) is absent.

Therefore, the correct formula for S_ZIP, which is proposed in SynergyFinderPlus is

$$S_{ZIP} = \hat{E}_{A,B,C} - (\hat{E}_A + \hat{E}_B + \hat{E}_C - \hat{E}_A\hat{E}_B - \hat{E}_A\hat{E}_C - \hat{E}_B\hat{E}_C + \hat{E}_A\hat{E}_B\hat{E}_C)\ \ \ \ (9)$$

where

$$\hat{E}_{A,B,C} = \frac{1}{3}(\frac{\hat{E}_{-A} + (\frac{x_A}{\hat{m}_A})^{\hat{\lambda}_A}}{1+(\frac{x_A}{\hat{m}_A})^{\hat{\lambda}_A}}+\frac{\hat{E}_{-B} + (\frac{x_B}{\hat{m}_B})^{\hat{\lambda}_B}}{1+(\frac{x_B}{\hat{m}_B})^{\hat{\lambda}_B}} + \frac{\hat{E}_{-C} + (\frac{x_C}{\hat{m}_C})^{\hat{\lambda}_C}}{1+(\frac{x_C}{\hat{m}_C})^{\hat{\lambda}_C}}) \ \ \ \ (10)$$

In summary, we provided new mathematical formulation for the BLISS, LOEWE and ZIP models that are compatible with their assumptions. The new formulation in SynergyFinderPLus overcomes the limitation of the models that were proposed in SynergyFinder2.

Reference

[1] SynergyFinderPlus website: www.synergyfinder.org; www.synergyfinderplus.org

[2] SynergyFinderPlus R package: https://www.bioconductor.org/packages/release/bioc/html/synergyfinder.html

[3] SynergyFinder2 website: www.synergyfinder.fimm.fi

[4] SynergyFinderPlus publication:

Zheng S., Wang W., Aldahdooh J., Malyutina A., Shadbahr T., Pessia A., Tang J.* (2022). SynergyFinder Plus: towards a better interpretation and annotation of drug combination screening datasets. Genomics Proteomics Bioinformatics. https://doi.org/10.1016/j.gpb.2022.01.004.

[5] SynergyFinder2 publication:

Ianevski A, Giri, ZK, and Aittokallio T. (2020) SynergyFinder 2.0: visual analytics of multi-drug combination synergies. Nucleic Acids Res. 48(W1):W488-W493. doi: 10.1093/nar/gkaa216.

[6] Mathematical modelling of HSA, BLISS, LOEWE and ZIP:

Yadav, B., Wennerberg, K., Aittokallio T., Tang J.* (2015) Searching for drug synergy in complex dose–response landscapes using an interaction potency model. Comput Struct Biotechnol J. 13:504-13. doi: 10.1016/j.csbj.2015.09.001

[7] SynergyFinder1 publication:

Ianevski A., He L., Aittokallio T., Tang J.* (2017) SynergyFinder: a web application for analyzing drug combination dose-response matrix data. Bioinformatics 33(15):2413-2415.

He L., Kulesskiy E, Saarela J., Turunen L., Wennerberg, K., Aittokallio T., Tang J.* (2018) Methods for high-throughput drug combination screening and synergy scoring. Methods Mol Biol. 1711:351-398. doi: 10.1007/978-1-4939-7493-1_17

Mathematical modelling in SynergyFinder2/3 is inconsistent

On July 2022, the authors of SynergyFinder2 published ‘Correction to ‘SynergyFinder 2.0: visual analytics of multi-drug combination synergies’’ at https://doi.org/10.1093/nar/gkac552. It stated that “In the originally published version of this manuscript, there is an error in the Bliss and ZIP equations. There should be a ‘+’ sign instead of ‘-’, before the last term. However, the authors advise that the formulas are correct in the codes used for calculation on the website, so the error doesn’t affect any previous or future analysis with SynergyFinder.”

However, the statement was false. The sign before the last term should depend on the parity in the combination. If the number of drugs is odd, e.g. a 3-drug combination, then the sign should be ‘+’, as the authors corrected. However, if the number is even, e.g. a 4-drug combination, the sign should be ‘-’.

Furthermore, the erratum did not solve the issues concerning the Loewe model. If SynergyFinder3 continues to use the formula \(S_{LOEWE}=\frac{a}{A} + \frac{b}{B}\) to determine the Loewe synergy score, then it is still inconsistent with the definition of Loewe models. The problem of Loewe model may be inherent irrespective of the size of the combination, which may explain why the results between SynergyFinder⅔ and SynergyFinder+ are different, even for 2-drug combinations.

Baseline correction in SynergyFinder2/3 may lead to false positive synergies

The original idea of ‘baseline correction’ was to increase the efficacy of monotherapies (see the example below). Fig.1

By such a baseline correction, the monotherapies will become more effective, and thus lead to a lower synergy score. In other words, we should take a conservative view by decreasing the synergy score, when users choose the baseline correction. However, the Baseline correction function in SynergyFinder3 does the opposite. Namely, if the baseline correction function is chosen, the synergy score will become higher. The example below shows a dose response matrix, where the Bliss score of 0 is expected, as the combination response is generated by Bliss independence. Using SynergyFinder3 with the baseline correction option, the Bliss synergy score becomes 6.43, significantly higher than the true value (Figure below). Fig.2

Fig.3

Therefore, SynergyFinder3 tend to provide false positive synergies if the baseline correction is chosen. In contrast, SynergyFinder+ provides the correct synergy score as 0 (Figure below): Fig.4

When to use the ‘baseline correction’ option? We suggest the use of ‘baseline correction’ when there is quality issue of the data: Whether you need to do baseline correction depends on how you treat the negative % inhibition data points (i.e. when viability > 100%). If viability > 100% is real, then no need to correct it. If it is due to the use of poor negative/positive control, then yes.

HOW TO CITE

SynergyFinder+ is a powerful tool that offers reliable mathematical models for identifying genuine drug combinations with high accuracy. Its algorithms consistently deliver precise results, enabling researchers to distinguish true positive synergies from false positives with confidence. Please cite the following publications when producing the results:

For use of the SynergyFinder R package or the SynergyFinder+ web application:

[1] Zheng, S.; Wang, W.; Aldahdooh, J.; Malyutina, A.; Shadbahr, T.; Tanoli Z; Pessia, A.; Tang, J. SynergyFinder Plus: Toward Better Interpretation and Annotation of Drug Combination Screening Datasets. Genomics, Proteomics & Bioinformatics 2022, 20, 587-596 doi:10.1016/j.gpb.2022.01.004

For use of the ZIP synergy scoring:

[2] Yadav, B.; Wennerberg, K.; Aittokallio, T.; Tang, J. Searching for Drug Synergy in Complex Dose-Response Landscapes Using an Interaction Potency Model. Comput Struct Biotechnol J 2015, 13, 504–513. doi:10.1016/j.csbj.2015.09.001

For how to harmonize the different synergy scoring methods:

[3] Tang, J.; Wennerberg, K.; Aittokallio, T. What Is Synergy? The Saariselkä Agreement Revisited. Front Pharmacol 2015, 6, 181. doi:10.3389/fphar.2015.00181

For general ideas of drug combination therapies:

[4] Tang, J. Informatics Approaches for Predicting, Understanding, and Testing Cancer Drug Combinations. Methods Mol Biol 2017, 1636, 485–506. doi:10.1007/978-1-4939-7154-1_30

For retrieving the most comprehensive drug combination data resources at the DrugComb database:

https://drugcomb.org/

[5] Zheng, S.; Aldahdooh, J.; Shadbahr, T.; Wang, Y.; Aldahdooh, D.; Bao, J.; Wang, W.; Tang, J. DrugComb update: a more comprehensive drug sensitivity data repository and analysis portal. Nucleic Acids Res 2021, W174-W184 doi:10.1093/nar/gkab438

[6] Zagidullin, B.; Aldahdooh, J.; Zheng, S.; Wang, W.; Wang, Y.; Saad, J.; Malyutina, A.; Jafari, M.; Tanoli, Z.; Pessia, A.; Tang, J. DrugComb: An Integrative Cancer Drug Combination Data Portal. Nucleic Acids Res 2019, 47 (W1), W43–W51. doi:10.1093/nar/gkz337

For use of drug combination sensitivity score (CSS):

[7] Malyutina, A.; Majumder, M. M.; Wang, W.; Pessia, A.; Heckman, C. A.; Tang, J. Drug Combination Sensitivity Scoring Facilitates the Discovery of Synergistic and Efficacious Drug Combinations in Cancer. PLoS Comput Biol 2019, 15 (5), e1006752. 10.1371/journal.pcbi.1006752

ABOUT US

SynergyFinder is developed by the Network Pharmacology for Precision Medicine in the Research Program of System Oncology, Faculty of Medicine at University of Helsinki , Helsinki, Finland.

SynergyFinder Plus (SynergyFinder+) is an interactive tool for analyzing drug combination dose response data. It enables efficient implementations for all the popular synergy scoring models, including HSA, Loewe, Bliss and ZIP to quantify the degree of drug synergy. The Bioconductor/R package 'synergyfinder' is available for R programmers.

OTHER TOOLS

THE TEAM

Jing Tang
Group Leader
Associate Professor

Wenyu Wang
R Package Development
PhD Researcher

Alina Malyutina
Method Development
PhD Researcher

Ziaurrehman Tanoli
Database Manager
Senior Researcher

Liye He
Package Developer
Former PhD Researcher

Shuyu Zheng
Software Development & R Package Maintainer
PhD Researcher

Jehad Aldahdooh
Server Manager
PhD Researcher

Tolou Shadbahr
Method Development
PhD Researcher

Alberto Pessia
Method Development
Postdoc Researcher

CONTACT US

Building: Biomedicum Helsinki 1 Office B325
Strees Address: Haartmaninkatu 8
Faculty of Medicine
00014 University of Helsinki
Finland

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