Charting the Fragmented Landscape of Drug Synergy

Abstract

Even as the clinical impact of drug combinations continues to accelerate, no consensus on how to quantify drug synergy has emerged. Rather, surveying the landscape of drug synergy reveals the persistence of historical fissures regarding the appropriate domains of conflicting synergy models - fissures impacting all aspects of combination therapy discovery and deployment. Herein we chronicle the impact of these divisions on: (i) the design, interpretation, and reproducibility of high-throughput combination screens; (ii) the performance of algorithms to predict synergistic mixtures; and (iii) the search for higher-order synergistic interactions. Further progress in each of these subfields hinges on reaching a consensus regarding the long-standing rifts in the field.

Keywords: Bliss Independence; Loewe Additivity; drug synergy.

Figure 1:. Timeline of developments in drug synergy highlights the persistence of historical rifts in the field.

A) Developments in drug synergy span four distinct epochs. During the Foundational Principles period, the major drug synergy principles were first described. Subsequent work in the 1980s rederived the DEP and MSP based on a mass-action model of drug effect resulting in two equations. The DEP-based equation became known as the Combination Index (CI). A series of studies during a critical period in the 1990s highlighted the incongruence of the DEP and MSP culminating in the recommendation studies should explicitly state how synergy was calculated. The modern era is characterized by an expansion of synergy models that seek to extend the DEP and MSP (Table 1). Substantial developments have also occurred in related subfields such as software, sampling methods, computational prediction, and higher-order interactions. B) Publications (in Google Scholar) which include the term “drug synergy.” Publications are grouped by those mentioning MSP (blue), DEP (red), both (purple), or neither (gray). Papers the terms “dose equivalence principle” or “isobologram” or “loewe” or “combination index” or “Chou and Talalay” or “isobole” containing the terms “dose equivalence principle” or “isobole” or “Loewe” or “combination index” were considered to reference the DEP. Papers containing the terms “multiplicative survival principle” or “bliss” or “fractional product method” were considered to reference the MSP. The time span included was: 1993–2019. The search date was 01/16/2020. Over 84% of publications continue to use the term synergy without referencing a particular model. Of those that do, < 6% acknowledge the existence of multiple frameworks.

Figure 2:. Conflicting results between synergy software packages impairs reproducibility.

A) Percent effect (color-bar bottom, numbers in boxes) of nvpbgl226 (PI3K/mTor inhibitor) and emetine (anti-protozoal) against HB3 strain of malaria. Data from Mott et al. [25]. The percent effect can be greater than 100% because static endpoint measures of drug effect rely on normalization to untreated controls. If the treated condition has more cells than the control, the normalized percent effect is >100%. This highlights the difference between percent affect (which can never exceed 100%) and percent effect. B) Combenefit and SynergyFinder calculate Bliss (color scale bottom) for this combination differently resulting in conflicting synergy classification based on the mean across the surface. Gray boxes are undefined as synergy is only calculated for combination conditions. Syn=synergy, Ant=Antagonism. The color scale is the same for both heatmaps. This disparity may arise from different approaches to deal with effects >100%. C) The frequency of agreement between SynergyFinder and Combenefit in the anti-malarial dataset is synergy metric dependent.

Figure 3:. Dose-dependent synergy frameworks perform inconsistently when using summary statistics.

A) Different summary statistics for dose-dependent synergy metrics (Table 1, Dose-Independent) prioritize different combinations for follow-up. Anti-malarial combinations are ranked from left to right in order of increasing maximum observed Loewe synergy (calculation by Combenefit). The rank-order correlation between the maximum Loewe and mean Loewe is 0.13 (Figure S3A) and combinations with high maximum synergy are often antagonistic by mean (red lines bottom panel). The top 5% of antagonistic combinations by the mean fall in the top 32% of synergistic combinations by the max. -log(Loewe) <0 is antagonistic and >0 is synergistic. B) Percent effect (color scale bottom, numbers in boxes) of amodiaquine (polymerase inhibitor) and artemether (proposed to function by inhibiting anti-oxidant enzymes) on the HB3 strain of malaria. C) The combination is antagonistic (Ant) by Bliss (color scale bottom) according to SynergyFinder at three different combination doses (purple, orange, green lines); however, the combination is synergistic (Syn) by mean over the surface. Gray boxes are undefined as synergy is only calculated at combination conditions.

Figure 4:. Top, machine learning-predicted, combinations depend on the synergy metric.

A) We trained DeepSynergy [46], a machine-learning algorithm to predict drug synergy from gene expression and drug physicochemical properties, on the O’Neil et al. dataset [24] with Bliss (purple), HSA (green), or Loewe (orange) as the measure of synergy. The top-predicted synergistic combinations were different depending on which metric was used. The mixture of mk-2206 (AKT inhibitor) plus sunitinib (tyrosine kinase inhibitor) in A2780 cells was the top combination present in the rank-orderings of all three metrics at the 6^th, 8^th, and 263^rd position for HSA, Bliss, and Loewe respectively (red highlight). The top 5 predicted synergistic interactions in Loewe are all in HT144 cells (malignant melanoma) while in Bliss and HSA all are in A2780 (ovarian carcinoma).

Figure 5:. Seeking consensus on the existence and nature of higher-order interactions.

A) Average Loewe synergy decreases for an increasing number of drugs in three datasets (Russ et al. [56], Katzir et al. [59], and Tekin et al. [34]). The black dot is the mean value of the distribution. Red-line demarcates synergy (Syn) from antagonism (Ant). The species tested in each paper are indicated in the panel title. B) Distribution of Bliss synergy as a function of increasing numbers of drugs. Accounting for the difference between percent effect and percent affect reduced the bias toward antagonism for ultra-high order combinations in the Katzir et al. data (Figure S6A).