Drug Combinations

Details of the original SynergyFinder implementation and its features for synergy assessment between two drugs have been described previously (13 (link)). Here, we primarily focus on the enhancements made to support synergy scoring for higher-order combinations, in addition to other web-tool improvements. More specifically, SynergyFinder 2.0 implements (i) efficient synergy estimation for multi-drug combinations, (ii) various curve-fitting algorithms for single drug dose–responses, (iii) automatic outlier detection in multi-drug combination screening data, (iv) novel visualization and export options and (v) statistical treatment of replicate measurements. A detailed comparison between the features of SynergyFinder release 1.0 and 2.0 is provided in Table 1.

To demonstrate the performance of the ZIP-based delta scoring, we considered a recent cancer drug screen study involving ibrutinib in combination with 466 compounds for the activated B-cell-like subtype (ABC) of diffuse large B-cell lymphoma (DLBCL) [14] (link). Ibrutinib is a small molecule targeting Bruton's tyrosine kinase (BTK) approved for the treatment of mantle cell lymphoma and chronic lymphocytic leukemia [16] (link). In this study, a high-throughput drug combination screening was used to identify other compounds that can synergistically interact with ibrutinib to improve its anticancer efficacy and circumvent drug resistance. For each drug pair, a 6 × 6 dose–response matrix design was utilized, where the drug effect was measured as percentage of cell viability using TMD8 cancer cell line. The raw combination data was provided by the authors via personal communication, but can now be downloaded from https://tripod.nih.gov/matrix-client/rest/matrix/export/241. We transformed the original percentage viability data into the percentage inhibition data before applying the drug combination analysis to be compatible with the mathematical formulation defined in the Methods section.
We ran the ZIP model on the drug combination data and calculated a summary delta score Δ for each drug pair by taking the average of all the delta scores over its dose combinations, i.e., $\Delta =\frac{1}{n}{\displaystyle \sum _{i=1}^n\delta }\text{,}$ where n is the number of dose combinations and n = 25 for a 6 × 6 dose–response matrix (monotherapy responses were removed). We compared the summary delta scores with the other scores derived from the HSA-, Bliss- and Loewe-based models. For HSA and Bliss, there were existing scores implemented in the original study [14] (link), which were based on the following methods: 1) NumExcess is the number of wells in the dose matrix that produced higher effect than both of the individual drug effects; 2) ExcessHSA is the sum of differences between the combination effect and the expected HSA effect; 3) MedianExcess is the median of the HSA excess; 4) ExcessCRX is an extension of the HSA model that was adjusted by dilution factors; 5) LS3 × 3 is the ExcessHSA applied to a 3 × 3 block showing the best HSA synergy in the dose matrix; 6) Beta (β) is the interaction parameter minimizing the deviance from the Bliss independence model over all dose combinations defined as $\underset{\beta }{argmin}\left({\displaystyle \sum {\left(1-y_c-\beta \left(1-y_1\right)\left(1-y_2\right)\right)}^2}\right)$ ; and 7) Gamma (γ) is a combination of HSA and Bliss models minimizing $\underset{\gamma }{argmin}\left({\displaystyle \sum {\left(1-y_c-\gamma max\left(1-y_1,1-y_2\right)\right)}^2}\right)\text{.}$ For the Loewe-based models, we calculated the two common interaction indices CI (Eq. (8)) and alpha(a) (Eq. (9)). The CI was calculated using an R package SYNERGY [13] (link) and the alpha score was estimated using the R package drc[12] .

Similar to SynergyFinder 1.0, version2.0 supports interactive analysis of two-drug combination data, based on the user-uploaded dose–response matrices (Figure 1A). As a result, interactive synergy distribution plots, together with summary synergy scores, are generated for each pair of drugs. In addition, SynergyFinder 2.0 supports the analysis of higher-order drug combinations by implementing interactive dose–response tensors for each triplet of the drugs (Figure 1B). Furthermore, barplots of synergy scores are produced separately for each sub-combination (pairs, triplets, etc.), depending on the number of drugs in the combinations. For more systematic analysis of the contribution of each drug to the joint higher-order combination effect, 3D synergy landscape plots for each of the two-drug sub-combinations are visualized enabling their further investigation (Figure 1C).
SynergyFinder 2.0. implements four reference synergy models (HSA, Bliss, Loewe and ZIP), and their extensions to calculate synergy scores for higher-order combination data. These models quantify the degree of synergy either as the excess over the maximum single drug response (HSA), multiplicative effect of single drugs as if they acted independently (Bliss), expected response corresponding to an additive effect as if the single drugs were the same compound (Loewe), and expected response corresponding to the effect as if the single drugs did not affect the potency of each other (ZIP). More specifically, the following higher-order formulations were used to quantify the drug combination synergy (S) for the measured multi-drug combination effect between N drugs :
Here, are the measured responses of the single drugs, while a, b and n are the doses of the single drugs required to produce the combination effect . For the ZIP model, is the dose of N^th drug fitted with four-parameter log-logistic (4PL) function, whereas is the dose that produces the half-maximum effect (also known as relative or , depending on the readout), and is the shape parameter indicating the slope of the dose–response curve.

The minimum inhibitory concentration (MIC) values of EVL alone or in combination with ITC, VRC, POS, or AMB against various dematiaceous fungi were assessed as per the guidelines established by the Clinical and Laboratory Standards Institute (CLSI) M38-A2. The working concentrations for the tested drugs were 0.06-4 μg/mL for ITC, VRC, POS, and AMB, and 0.25-16 μg/mL for EVL. Briefly, 50 μl of serially diluted EVL solutions were added to horizontal rows of a 96-well plate containing the conidia suspension prepared above (100 μl/well), followed by the addition of 50 μl of serially diluted ITC, VRC, POS, or AMB in the vertical columns of this plate. Plates were then incubated for 4 days at 28°C, with MIC values then being established based on the minimum drug concentration necessary to suppress 100% of fungal growth relative to control conditions.
Interactions between EVL and specific antifungal drugs were assessed based on the fractional inhibitory concentration index (FICI) as follows: FICI = (MIC_Ac/MIC_Aa) + (MIC_Bc/MIC_Ba), where MIC_Ac and MIC_Bc respectively correspond to test drug combinations, and MIC_Aa and MIC_Ba correspond to the MIC values for drugs A and B when used as single-agent treatments. A FICI ≤ 0.5 was indicative of synergism, while 0.5 < FICI < 4 indicated no interaction or indifference, and FICI ≥ 4 indicated antagonism. All experiments were independently repeated in triplicate.

When available, antimicrobial susceptibility veterinary breakpoints from the Clinical Laboratory Standards Institute (CLSI) were used to interpret MIC results [Clinical and Laboratory Standards Institute (CLSI), 2020 ], while human CLSI breakpoints were used for bacterial-drug combinations without veterinary breakpoints [Clinical and Laboratory Standards Institute (CLSI), 2020 ; Clinical Lab Standards Institute (CLSI), 2022 ]. All breakpoints used in this study were for the bacterium indicated. For antimicrobials in which the BOPO7F Vet AST Plate dilutions included the established breakpoint, “resistant” status was assigned if the isolate grew in or beyond the breakpoint dilution (ampicillin, ceftiofur, sulfadimethoxine, and trimethoprim/sulfamethoxazole for E. coli and ampicillin for Enterococcus). For antimicrobials in which the testing plate included only dilutions below the established breakpoint, “non-susceptible” status was assigned and included isolates in the intermediate range according to CLSI guidelines or isolates that grew in the highest dilution available. Resistance or non-susceptible status was only assigned to antimicrobials for which breakpoints were available and for which in-vivo activity and antimicrobial spectrum were applicable. For antimicrobials that were assigned non-susceptible status (florfenicol and tetracycline for E. coli and penicillin and tetracycline for Enterococcus), it was not possible to establish resistance because the drug dilutions did not reach the threshold breakpoint; hence growth or no growth at or beyond the breakpoint could not be established. Antimicrobial breakpoints used and dilution ranges for the BOPO7F Vet AST Plate can be found in Table 1.