Theory of synergistic effects: Hill-type response surfaces as ‘null-interaction’ models for mixtures

Schindler, Michael

doi:10.1186/s12976-017-0060-y

Cited by 23 publications

(30 citation statements)

References 31 publications

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“…The Hill PDE model has no parameters to fit as the dose-response surface is derived the single dose-response curves. In fact, Schindler does not propose a method to estimate synergy from experimental data, but postulates some implementation of perturbation theory could be used to fit experimental data [10]. Therefore, to calculate the synergy of this model, we defined the sum of residuals between the null surface and the experimental data to the metric of synergy.…”

Section: Methodsmentioning

confidence: 99%

“…The most recent framework is one by Schindler [10] which interpolates a null dose-response surface from the single dose-response curves alone without any fit parameters. This was done by using PDE Hill equations and then imposing boundary conditions as well as sham compliance.…”

Section: Supplemental Materialsmentioning

confidence: 99%

“…More recently, a proliferation of synergy models, derived as extensions of either the DEP or MSP, has further splintered the field [8, 9, 10, 11, 12, 13]. In the absence of a consensus framework for drug synergy, discovery efforts for combinations often calculate all available synergy metrics [14, 15, 16], as first recommended by Greco and colleagues [5] following Saariselkä.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we show that our theory generalizes the DEP and MSP, thereby unifying the field of drug synergy, as sought at Saariselkä. We further map the landscape of current synergy metrics, including: Bliss Independence [4], Loewe Additivity [1], Combination Index (CI) [3], Highest Single Agent (HSA) [22], Effective Dose model by Zimmer et al [8], ZIP [9], a partial differential equation (PDE) Hill model by Schindler [10], and BRAID [13]. In mapping relationships between these various metrics, we identified systematic differences impacting the interpretation of synergy in drug combination experiments.…”

Section: Introductionmentioning

confidence: 99%

“…From the literature, we identified several prominent synergy models beyond Bliss and Loewe including: CI [3], HSA [22], Effective Dose model [8], ZIP [9], and Hill PDE [10]. Table 2 compares key features and assumption of the different synergy models.…”

Section: Introductionmentioning

confidence: 99%

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A Consensus Framework Unifies Multi-Drug Synergy Metrics

Wooten

Meyer

Quaranta

et al. 2019

Preprint

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10Drug combination discovery depends on reliable synergy metrics; however, no consensus exists on the 11 appropriate synergy model to prioritize lead candidates. The fragmented state of the field confounds 12 analysis, reproducibility, and clinical translation of combinations. Here we present a mass-action based 13 efficacy masks synergistic interactions; (2) MSP frameworks are biased toward antagonism for drugs with 54 intermediate efficacy; and (3) DEP frameworks contain a Hill-slope dependent bias. The Hill-slope bias 55 results from satisfying the famous "sham" combination thought experiment, arguing against the merit of 56 sham-compliance as a measure of validity for synergy frameworks. Using two large combination datasets 57 [23, 24], MuSyC identifies real-world examples where the conflicting assumptions of previous drug synergy 58 frameworks misleads or impedes drug discovery efforts through these pervasive and predictable biases. We 59 therefore propose MuSyC as a consensus framework to interpret combination pharmacology and signify its 60 broad applicability to the study of drug mixtures. 61A multi-dimensional formalism to measure multi-drug synergistic effects 62 Low Efficacy High Efficacy High Cooperativity Low Cooperativity h Low Potency High Potency The 4-parameter Hill equation is commonly used to fit dose-response data from in vitro and in vivo assays 63 (see Box 1 equation (3) for derivation and Table 1 for parameter annotation). This equation can be derived64 from the equilibrium of a 2-state model of drug effect based on the Law of Mass Action (Figure 1A left).65 Traditionally, the parameters of the Hill equation are interpreted as a drug's efficacy (E 0 − E 1 ), potency 66 (C), and cooperativity (h), also known as the Hill slope. These parameters correspond to three possible 67 geometric transformations of a dose-response curve (Figure 1A right). To generalize this one-drug formalism 68 to two concurrent drugs, we recently developed a 4-state mass-action model of combination pharmacology 69 (Figure 1B left) [21]. From this model, we derived a two-dimensional (2D) Hill equation for two drugs 70 2 (Box 1 equation 8) defining a dose-response surface (Figure 1B middle). The 2D Hill equation contains five 71 additional parameters, not present in the single-drug Hill equation, which measure different types of drug 72interactions. These additional parameters measure changes in a drug's efficacy (β), potency (α 12 and α 21 ), 73 and cooperativity (γ 12 and γ 21 ) in a combination -representing three distinct types of synergy ( Figure 1B 74 right, Table 1). As we show below, these parameters are conflated in traditional synergy metrics obscuring 75 the true origin and magnitude of drug synergy or antagonism. 76 A bridge between DEP and MSP maps existing synergy approaches onto a com-77 mon landscape 78 In recent years, several alternative synergy models have been proposed. Broadly, these models are derived 79 from one of two guiding principles: the Multiplicative Survival Principle (MSP) and the Drug...

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Section: Methodsmentioning

confidence: 99%

Section: Supplemental Materialsmentioning

confidence: 99%