Fig. 1.
Overview of the modelling framework. a, Response to therapy modelled as a second-order function of drug exposure: Pt210's ex vivo response to 0.05 μM of carfilzomib (blue scatter plot) was fit to a second-order sigmoidal function that accounts for tumour drug-specific threshold modelled as a precursor to cell death (EMMA, solid blue line). The EMMA model fit is compared to linear decay rate model (red solid line) and first-order Michaelis-Menten kinetic model (solid green line) to show that it is necessary to account for exposure-driven threshold that traditional models ignore. b, Illustration of the drug-agnostic mechanism of response to single agent therapy: The drug-agnostic mechanism of cell death is based on drug occupancy theory, where the interaction of a drug with a receptor is governed by a reaction-kinetic equation that results in a drug-receptor complex (β), which initiates cell death beyond a clonal-specific threshold (τ) via cell death trigger (α). c, Tumour growth model: A simple doubling time equation is used to estimate tumour growth, where 1% to 3% (LI) of the population is assumed to double every 24 hours. d, Synergy is a dynamic phenomenon: Pt290's ex vivo response to 0.05 μM of carfilzomib (solid red line), 0.05 μM of panobinostat (solid green line), their combination (solid blue line), and the theoretical additive response (dashed blue line) computed from the two single agent response curves assuming Bliss independence are shown. The synergistic effect is measured as the difference in response between theoretical additive and the actual combination. It can be seen that synergistic interaction is a dynamic phenomenon and requires quantification using finely spaced temporal response data. e, Illustration of the two-way pharmacodynamic modelling framework: The path from dose to response for a two-drug combination obeys the same mechanism of cell death as the single agent model but accounts for the two-way combination effect at the pharmacodynamic level by augmenting the reaction-kinetic equations used in computing the drug-receptor complex (βA and βB) for single agents with a nonlinear combination effect term (βBA and βAB) as shown in the differential equations for βA and βB. The combination response is computed from the fraction population remaining estimates for the two drugs as if they were statistically independent. Abbreviations: CFZ, carfilzomib; EMMA, Ex Vivo Mathematical Malignancy Advisor; h/hA/hB, stoichiometric coefficient of the pharmacodynamic equation; LI, Labelling Index; M, Molar; Pt, Patient; p/pA/pB, predicted tumour burden; R/RA/RB, drug concentration; t, time; α/αA/αB, cell death trigger; β/βA/βB, drug-induced damage; δ, drug-specific factor; εAB/εBA, combination effect quadratic coefficient; γAB/γBA, combination effect linear coefficient; κ/κA/κB, cell dissociation coefficient in the pharmacodynamics equation; τ, tumour-specific threshold.