Chemical combination effects predict connectivity in biological systems

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Joseph Lehár^1,2, Grant R Zimmermann¹, Andrew S Krueger², Raymond A Molnar¹, Jebediah T Ledell¹, Adrian M Heilbut¹, Glenn F Short, III¹, Leanne C Giusti¹, Garry P Nolan¹, Omar A Magid¹, Margaret S Lee¹, Alexis A Borisy¹, Brent R Stockwell³ & Curtis T Keith¹

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Synopsis

Living organisms are built of interacting components, whose function and dysfunction can be described through dynamic network models (Davidson et al, 2002). Systems Biology involves the iterative construction of such models (Ideker et al, 2001), and may eventually improve the understanding of diseases using in silico simulations. Such simulations may eventually permit drugs to be prioritized for clinical trials, reducing potential risks and increasing the likelihood of successful outcomes. Given the complexity of biological systems, constructing realistic models will require large and diverse sets of connectivity data.

Chemical combinations provide a new window into biological connectivity. Information gleaned from targeted combinations, such as paired mutations (Tong et al, 2004), has proven to be especially useful for revealing functional interactions between components. We have been screening chemical combinations for therapeutic synergies (Borisy et al, 2003; Zimmermann et al, 2007), collecting full-dose matrices where combinations are tested in all possible pairings of serially diluted single agent doses (Figure 1). Such screens yield a variety of response surfaces with distinct shapes for combinations that work through different known mechanisms, suggesting that combination effects may contain information on the nature of functional connections between drug targets.

Figure 1

The morphology of cell-based dose-matrix responses to chemical combinations differs between mechanisms. Data for two synergistic antibacterial combinations using a methicillin-resistant Staphylococcus aureus strain are shown in three-dimensional projections. In Augmentin^® (A), clavulanate disables a bacterial defence against penicillin drugs, whereas both agents in Bactrim^® (B) inhibit enzymes in folate metabolism. The mechanisms of action differ between the two combinations, as do the shapes of their response surfaces. Dose-matrix response surfaces show the inhibition of growth (1-treated/untreated) for each pairwise permutation of the serially diluted single agent doses. The 2D maps (C, D) show a top-down view of the surface, using the same colours for inhibition levels, to better display mathematical descriptions of the shape without obscuring any data, and permit many matrices to be shown together with clarity.

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Simulations of biological pathways predict synergistic responses to inhibitors that depend on target connectivity. We explored theoretical predictions by simulating a metabolic pathway with pairs of inhibitors aimed at different targets with varying doses. We found that the shape of each combination response depended on how the inhibitor pair's targets were connected in the pathway (Figure 2). The predicted response shapes were robust to plausible variations in the simulated pathway that did not affect the network topology (e.g., kinetic assumptions, parameter values, and nonlinear response functions), but were very sensitive to topological alterations in the modelled network (e.g., feedback regulation or changing the type of junction at a branch point). These findings suggest that connectivity of the inhibitor targets has a major influence on combination response morphology.

Figure 2

Combination response shape models that describe many of the observed response morphologies. Each model (shown using the same colour scale as Figures 1 and 3) is used to calculate an expected combination effect I_model at any concentration X,Y, based on the single agent response curves. (A) HSA is a superposition of the X and Y single agent responses, calculated from the inhibitions I_X at X and I_Y at Y. (B) Loewe additivity (Loewe, 1928) is the drug-with-itself reference for synergy, where I_Loewe at X,Y yields additive doses relative to the components' effective concentrations X_I,Y_I at I_Loewe. (C) Bliss boosting describes combinations with a variable boost above E_max (the greater of the single agent limiting efficacies E_X,E_Y), at high combined concentrations. Useful reference levels for Bliss boosting are 'cancelling', 'suppressing', 'masking', 'multiplicative' corresponding to Bliss independence (Bliss, 1939), and 'saturating' (see Materials and methods). Finally, (D) potentiation can characterize responses similar to those of Bactrim^® (Figure 1), where one single agent's curve I_X(C) is shifted with a power-law slope p above an enhancer concentration Y_pot, and superposed on the enhancer's own activity. These models can be extended to higher-order combinations, and used in the same form (with adjustments to Bliss boosting) for any type of measurement, provided that the activities of both agents vary monotonically with concentration. Of these models, only Loewe additivity has an a priori mechanistic basis.

Figure 3

Simulations of a multiply inhibited network yield distinct response shapes that depend on target connectivity. Substrates (black nodes) are metabolized through a series of Michaelis–Menten reactions (grey circles) from sources with constant reaction velocities to a limitless sink at the end-point. We calculated dose-matrix inhibitions of the end point velocity at R_E to paired competitive inhibitors at various enzymes. The response surfaces for some combinations are shown, with the inhibitors indicated by joined markers. For Pathway A, same-target pairs produced Loewe additivity, and separated targets led to various Bliss boosts depending on where the targets were placed. Pathway B was added to investigate combination effects across pathways, with a bypass to ensure clear distinctions between cross-pathway boosting levels. Because both inputs are required for R_AB, the junction is equivalent to a logical AND function. The negative feedback in Pathway B was introduced to represent processes like sterol biosynthesis in yeast. Inhibiting across pathways produced HSA-like masking effects, and inhibiting within the negative feedback loop yielded potentiation effects.

Full figure and legend (329K)Figures & Tables index

Full figure and legend (171K)Figures & Tables index

The predicted shapes were experimentally confirmed in yeast combination experiments. The proliferation experiment used drugs focused on the sterol biosynthesis pathway, which is mostly linear between the targets covered in this study, and is known to be regulated by negative feedback (Gardner et al, 2001). The combinations between sterol inhibitors confirmed expectations from our simulations, showing dose-additive responses for pairs targeting the same enzyme and strong synergies across enzymes of the shape predicted in our simulations for linear pathways under negative feedback. Combinations across pathways showed much more variable responses with a trend towards less synergy on average.

Further experimental support was obtained from human cells. A combination screen of 90 annotated drugs in a human tumour cell line (HCT116) proliferation assay produced strong synergies for combinations within pathways and more variable effects between targeted functions. Synergy profiles (sets of all synergy scores involving each drug) also showed a greater degree of similarity for pairs of drugs with related targets. Finally, the most extreme outliers were dominated by inhibitors of kinases that are especially critical for HCT116 proliferation (Awwad et al, 2003), with effects that are consistent across mechanistic replicates, showing that chemical combinations can highlight biologically relevant cellular processes.

This study demonstrates the potential of chemical combinations for exploring functional connectivity in biological systems. This information complements genetic studies by providing more details through variable dosing, by directly targeting single domains of multi-domain proteins, and by probing cell types that are not amenable to mutagenesis. Responses from large chemical combination screens can be used to identify molecular targets through chemical–genetic profiling (Macdonald et al, 2006), or to directly constrain network models by means of a prediction-validation procedure (Ideker et al, 2001). This initial exploration can be extended to cover a wider range of response shapes and network topologies, as well as to combinations of three or more chemical agents. Moreover, this approach may even be applicable to non-biological systems where responses to targeted perturbations can be measured.

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