SAM: Modeling Synergy in Cancer

Combination therapies have shown improved efficacy with limited addition of toxicity over their single agents. The efficacy of a drug in multiple myeloma varies from one patient to another due to tumor heterogeneity, inherited/acquired resistance, and microenvironmental factors that are specific to a given patient. Patient variability in response to single agents leads to variability in synergistic effects for combination therapies, which require quantification on a patient-to-patient basis. EMMA (Ex vivo Mathematical Malignancy Advisor), a clinical decision support (CDS) tool previously developed, provides a mathematical framework to estimate tumor specific drug sensitivity from patient-derived primary myeloma cells in an ex vivo reconstruction of the bone marrow. EMMA relies on a drug-agnostic mechanistic model that comprises of a dose – effect relationship at the pharmacodynamic level and a cumulative effect – response relationship to estimate percent tumor burden within a clinically actionable time frame. However, in its present form, EMMA lacks the capability to capture synergistic effects for combination therapies. It instead assumes the effect to be additive, as defined by the Bliss independence model.


        We propose a mathematical framework (SAM - Synergy Augmented Model) that predicts efficacy of combination therapies backed by high-throughput ex vivo experiments using patient samples. We tested 130 two-drug combinations in 203 primary MM samples in an ex vivo reconstruction of the bone marrow. Fresh bone marrow aspirate cells enriched for CD138+ expression (MM cells) were seeded in 384 well plates with collagen-I, media supplemented with fetal-bovine serum, human-derived stroma, and freshly obtained patient-derived plasma; left overnight for adhesion; and treated with five serially diluted concentrations for 31 drugs/combinations. Patient-specific responses were estimated nondestructively across time and concentration from sequential bright-field images for a two-drug combination and its constituent single-agents. Dose-time-response data for single agents was fitted to a second-order drug response model to estimate patient-specific parameters, which longitudinally quantify intra- and intertumoral heterogeneity. The improvement of combination response over an additive response was modeled at the pharmacodynamic level, and shown to be sufficiently parameterized by single-agent and fixed-ratio combination response data. Validation of ex vivo model-predicted responses at various concentrations and ratios using actual ex vivo combination response data showed great linear correlation characterized by Pearson’s correlation coefficient values greater than 0.93 across multiple patient samples and combinations. This framework reconciles ex vivo observations from both Loewe and BLISS synergy models, by accounting for the dimension of time, as opposed to focusing on arbitrary time-points or drug effect. We observed a significant inter-sample heterogeneity of combination effect and a number of overall ex vivo synergistic combinations were identified using a volcano plot, which represents the combination effect in terms of its extent and likelihood of synergy. Clinical outcomes of patients were simulated by coupling patient-specific drug combination models with pharmacokinetic (PK) data. Ex vivo synergy in combinations did not necessarily ensure prediction of clinical synergy, thus reinforcing the need for tools that account for drug pharmacokinetics and dosing schedules in addition to interpatient heterogeneity. Out of 46 two-drug combinations (with published PK data) only four were shown to be clinically synergistic with statistical significance (P<0.05).

           Combination screening showed 1 in 5 combinations (21.43% by LD50, 18.42% by AUC) were synergistic ex vivo with statistical significance (P<0.05), but clinical synergy was predicted for only 1 in 10 combinations (8.69%), which was attributed to the role of pharmacokinetics and dosing schedules. Combination AUC and DAUC Synergy (drop in AUC due to synergy) estimated pre-clinically when compared with actual clinical responses for 23 patients showed that patients’ disease statuses were classified with a statistically significant (P<0.05) accuracy.