Modeling spatial evolution of multi-drug resistance under drug environmental gradients
Fig 9
Drug-resistance selection outcomes for periodic 2 drugs as a function of their spatial periods T1 and T2.
A. Synergistic drugs. B. Independent drugs. C. Antagonistic drugs. Shaded blue region: single-resistance to drug 1 has higher fitness, shaded red region: single-resistance to drug 2 has higher fitness, shaded purple region: double resistant mutant with intermediate resistance to each drug has the higher fitness. The periodic variations of drug 1 and drug 2 over one-dimensional space z ∈ [0, 1] are constructed in such way as to keep the total amount of each drug equal to 1. The periodic function parameters are initially specified as: k1 = A1 = k2 = A2 for any combination of periods T1 and T2, and then immediately scaled by the integral of the periodic function over space, to obtain a total amount of drug equal to unity in each case. Assumed diffusion coefficient is D = 0.01. The growth functions of each mutant over space are obtained following Eqs. 16 together with the assumption that a mutant with traits (αi, βi) experiences the two drugs at concentrations αix and βiy. The interaction strength is fixed at q = 0.5 both in the case of synergistic and antagonistic interaction. In the case of synergistic/antagonistic interaction, the effect is to decrease/increase the growth rate of bacteria relative to the simple additive effect of the two drugs. See Fig D (S1 Text) for the analogous figure under a more complex drug interaction function, highlighting the sensitivity to fitness landscape.