Mutational Pathway Determines Whether Drug Gradients Accelerate Evolution of Drug-Resistant Cells (original) (raw)
Abstract
Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anticancer drugs. We use a statistical physics model to study the evolution of a population of malignant cells exposed to drug gradients, where drug resistance emerges via a mutational pathway involving multiple mutations. We show that a nonuniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients. These predictions can be verified experimentally, and may help to improve strategies for combating the emergence of resistance.
- Received 2 March 2012
DOI:https://doi.org/10.1103/PhysRevLett.109.088101
© 2012 American Physical Society
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Authors & Affiliations
Philip Greulich, Bartłomiej Waclaw, and Rosalind J. Allen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
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Figure 1
Simulation snapshots for the cases of a uniform and an exponentially increasing drug concentration (left and right, respectively). Blue thick lines show the drug concentration (left axes), while the colors (shades of gray in gray scale) represent the populations of the different genotypes (right axes). Parameter values are K=100, L=500, M=6, μ=5×10−6, βm=4m−1, and the drug concentration c=0.3 (left panel) and c(x)=eαx−1 with α=0.012 (right panel). For corresponding movies, see the Supplemental Material [38].Reuse & Permissions
Figure 2
Average time to resistance τ¯ for uniform [(a),(d), circles] and nonuniform [(b),(e), circles] drug concentrations, for M=6, L=500, K=100, and μ=5×10−6. Top panels (a),(b): exponentially increasing MIC [shown in (c)]. Bottom panels (d),(e): fitness valley [shown in (f)]. For the nonuniform case (b),(e), the dashed lines show the minimal value of τ¯ obtained for the uniform case [i.e., the minimum of τ¯(c) from (a),(d)]. The solid lines show the theoretical predictions: (a) τ¯≈126 642/c3/2 [see also Eq. (IV.11) in the Supplemental Material [38], Sec. IV], (b) Eq. (3), (d) Eq. (4), and (e) Eq. (5). The insets in (b) show simulation snapshots taken just before the first occurrence of genotype m=6, for two values of α (indicated by arrows).Reuse & Permissions
Figure 3
Average time τ¯ to full resistance as a function of the mutational pathway length M for uniform (c=0.9; triangles) and nonuniform (α=0.07; crosses) drug distribution. In both cases L=300, K=100, and μ=10−4. Solid lines are theoretical predictions for the nonuniform case [calculated numerically from Eqs. (2, 3)] and uniform case (calculated as explained in the Supplemental Material [38], Sec. V).Reuse & Permissions
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