Synergistic and antagonistic drug combinations depend on network topology

Abstract

Drug combinations may exhibit synergistic or antagonistic effects. Rational design of synergistic drug combinations remains a challenge despite active experimental and computational efforts. Because drugs manifest their action via their targets, the effects of drug combinations should depend on the interaction of their targets in a network manner. We therefore modeled the effects of drug combinations along with their targets interacting in a network, trying to elucidate the relationships between the network topology involving drug targets and drug combination effects. We used three-node enzymatic networks with various topologies and parameters to study two-drug combinations. These networks can be simplifications of more complex networks involving drug targets, or closely connected target networks themselves. We found that the effects of most of the combinations were not sensitive to parameter variation, indicating that drug combinational effects largely depend on network topology. We then identified and analyzed consistent synergistic or antagonistic drug combination motifs. Synergistic motifs encompass a diverse range of patterns, including both serial and parallel combinations, while antagonistic combinations are relatively less common and homogenous, mostly composed of a positive feedback loop and a downstream link. Overall our study indicated that designing novel synergistic drug combinations based on network topology could be promising, and the motifs we identified could be a useful catalog for rational drug combination design in enzymatic systems.

Figure 1. Modeling process to study drug combinations.

(A) Illustration of the drug modelling process. An example enzymatic network with corresponding ODEs is shown. Solid links represent inter-node regulatory relationships, broken lines are background regulations. With the addition of drugs to chosen links (shown by crosses), the equations are modified by incorporating drugs as competitive inhibitors. (B) An example isobologram calculated from the combination of links 1 and 2 in (A). Points on isobloles represent dose combinations with the same efficacy. The black isobole (solid line) is concave, suggesting a synergistic interaction between the two links. The tipping point is the point where CI reaches minimum (or maximum for antagonistic cases). Inhibition strength is defined as [I]/Ki, i. e. the concentration of the inhibitor divided by its inhibition constant. The combination indices calculated from inhibition strengths are identical with those calculated with concentrations since K_I's cancel. The whole process depicted here was repeated for all (16,038) networks and 100,000 sampled parameter sets.

Figure 2. Distribution of percentage of synergistic cases under various parameter sets for all combinations studied.

Consistently synergistic and antagonistic combinations are marked, showing their stark contrast in number.

Figure 3. Distribution of CI_t values for several combinations.

The combinations are shown in insets and the targets inhibited marked by crosses. These combinations are all highly consistent in showing either synergy or antagonism under 90% of parameterizing conditions.

Figure 4. List of basic motifs that could result in drug synergy.

Red dotted arrows indicate inhibitory actions, while blue arrows indicate activations. The targeting links of the drug combinations are marked by crosses in each network.

Figure 5. Comparison of distributions of average CI_t's for parallel and serial combinations.

Definitions of parallel and serial combinations are presented in the main text.

Figure 6. List of antagonistic combinations found in our study.

Figure 7. Basic structure of the growth factor signaling pathway, showing examples of serial and parallel combinations.