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. 2015 Jun 2;112(22):E2874-83.
doi: 10.1073/pnas.1424184112. Epub 2015 May 18.

Imperfect drug penetration leads to spatial monotherapy and rapid evolution of multidrug resistance

Stefany Moreno-Gamez  1 , Alison L Hill  2 , Daniel I S Rosenbloom  3 , Dmitri A Petrov  4 , Martin A Nowak  2 , Pleuni S Pennings  5
Affiliations

Imperfect drug penetration leads to spatial monotherapy and rapid evolution of multidrug resistance

Stefany Moreno-Gamez et al. Proc Natl Acad Sci U S A. .

Abstract

Infections with rapidly evolving pathogens are often treated using combinations of drugs with different mechanisms of action. One of the major goal of combination therapy is to reduce the risk of drug resistance emerging during a patient's treatment. Although this strategy generally has significant benefits over monotherapy, it may also select for multidrug-resistant strains, particularly during long-term treatment for chronic infections. Infections with these strains present an important clinical and public health problem. Complicating this issue, for many antimicrobial treatment regimes, individual drugs have imperfect penetration throughout the body, so there may be regions where only one drug reaches an effective concentration. Here we propose that mismatched drug coverage can greatly speed up the evolution of multidrug resistance by allowing mutations to accumulate in a stepwise fashion. We develop a mathematical model of within-host pathogen evolution under spatially heterogeneous drug coverage and demonstrate that even very small single-drug compartments lead to dramatically higher resistance risk. We find that it is often better to use drug combinations with matched penetration profiles, although there may be a trade-off between preventing eventual treatment failure due to resistance in this way and temporarily reducing pathogen levels systemically. Our results show that drugs with the most extensive distribution are likely to be the most vulnerable to resistance. We conclude that optimal combination treatments should be designed to prevent this spatial effective monotherapy. These results are widely applicable to diverse microbial infections including viruses, bacteria, and parasites.

Keywords: combination therapy; drug resistance; drug sanctuaries; pathogen evolution; spatial structure.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Compartment model for combination therapy with two drugs. The box represents a patient’s body and the red and blue shaded areas indicate the presence of drug 1 and drug 2, respectively. Mismatched drug penetration creates regions in the body where only one drug from the combination is present. We refer to these regions as single-drug compartments. Colored circles represent the pathogen genotypes: wild type (light gray), mutant resistant to drug 1 (blue), mutant resistant to drug 2 (red), and double-drug-resistant mutant (purple). In the sanctuary all of the pathogen genotypes can grow because none of the drugs is present. In the single-drug compartments only pathogens carrying a resistance mutation against the active drug can grow; that is, each drug alone suppresses pathogen growth. Finally, in the double-drug compartment only the double-drug-resistant mutant can grow. All of the compartments are connected by migration as indicated by the black arrows. Treatment failure occurs when the double-drug compartment, which always composes the majority of the body, is colonized by the double mutant. Note that we do not always require that both single-drug compartments exist, and the compartment sizes may not follow this particular geometric relationship.
Fig. 2.
Fig. 2.
Resistance evolution in the presence of a single-drug compartment. Even a small single-drug compartment can considerably speed up the evolution of double-drug resistance. (A and B) The shaded area gives the fraction of simulated patients that failed treatment after 1 year or 10 years as a function of the size of the single-drug compartment containing drug 1 (SDC1) relative to the size of the double-drug compartment (DDC). We further indicate whether treatment failure occurred via direct (gray circles) or stepwise (pink circles) evolution. Solid lines are analytic calculations (SI Appendix, sections 5 and 6). The vertical dotted lines are further simplified, closed-form analytical expressions for the point where the stepwise path to resistance becomes more important than the direct path (SI Appendix, sections 4.2 and 7). (C and D) Evolution of drug resistance over time for a simulated patient in the absence (C) or presence (D) of SDC1. When there are no single-drug compartments, mutants resistant to drug 1 go to extinction recurrently by competition with the wild type in the sanctuary, whereas in the presence of SDC1, mutants resistant to drug 1 can escape competition and establish a continuous population (blue line) from which a doubly resistant strain can evolve (purple). Parameters: RWT=4,ϵ1=0.99,ϵ2=0.99,dy=1d−1,dx=0.1d−1,m=0.1d−1,s1=0.05,s2=0.05, μ1=10−5,μ2=10−5,NSAN=105cells,NSDC2=0cells,NDDC=107 cells. NSDC1 changes along the x axis for A and B and for each value of NSDC1 treatment has failed in at least 2,000 simulated patients. NSDC1=0 for C and NSDC1=5×104cells for D.
Fig. 3.
Fig. 3.
Trade-off between total drug coverage and the presence of single-drug compartments. (A) The adaptation rate (purple circles, left y axis) and time-averaged infection size (orange circles, right y axis) are plotted as a function of the size of the single-drug compartment with drug 1 (NSDC1), assuming that the sum of the sizes of the sanctuary (NSAN) and SDC1 is constant. Diagrams below the x axis illustrate the changes in compartment sizes, following the style of Fig. 1. The adaptation rate is defined as the inverse of the mean time to treatment failure and is plotted relative to the rate when NSDC1=0. We show adaptation rate only from acquired genetic variation (solid circles) and from both acquired and standing genetic variation (i.e., preexisting resistance, open circles); the difference is shown by the gray area and the vertical lines. The infection size is calculated as the mean of the time-averaged number of infected cells in all compartments before treatment failure occurs. Increasing the size of the single-drug compartment provides better control of the infection before treatment fails, but strongly favors resistance evolution if the reduction of the sanctuary is not large enough. (B) Ratio of the rate of adaptation from standing and acquired genetic variation (RSGV+AGV) to the rate of adaptation only from acquired genetic variation (RAGV). The relative contribution of standing genetic variation to treatment failure increases with the size of the SDC. Parameters: RWT=4,ϵ1=0.99,ϵ2=0.99,dy=1d−1,dx=0.1d−1,m=0.1d−1,s1=0.05,s2=0.05, μ1=10−5,μ2=10−5,NSAN=105−NSDC1,NSDC2=0cells,NDDC=107 cells. Each point is an average over at least 30,000 simulated patients.
Fig. 4.
Fig. 4.
Stepwise resistance evolution in the presence of two single-drug compartments. (A–C) Fraction of simulated patients that failed via the path where the single-drug compartment with drug 1 is colonized before treatment failure (P(SDC1): SAN→ SDC1→ DDC) relative to the fraction that failed via the path where the single-drug compartment with drug 2 is colonized before (P(SDC2): SAN→ SDC2→ DDC) as a function of (A) compartment sizes, (B) mutation rates, and (C) mutation costs. (A) The x axis corresponds to the ratio of the size of the single-drug compartment with drug 1 (NSDC1) to the size of the single-drug compartment with drug 2 (NSDC2). (B) The x axis corresponds to the ratio of the mutation rate for resistance to drug 1 (μ1) to the mutation rate for resistance to drug 2 (μ2). (C) The x axis corresponds to the ratio of the cost of a resistance mutation to drug 1 (s1) to the cost of a resistance mutation to drug 2 (s2). Simulation results (circles) are overlaid with the lines y=x (A and B) or y=1/x (C). Parameters: RWT=4,ϵ1=0.99,ϵ2=0.99,dy=1d−1,dx=0.1d−1,m=0.1d−1,s1=0.05,s2=0.05,μ1=10−5,μ2=10−5,NSAN=105cells,NSDC1=104cells,NSDC2=104cells,NDDC=107 cells. NSDC1 changes along the x axis (A), μ1 changes along the x axis (B), and s1 changes along the x axis (C). The total number of simulated patients for each point is at least 6,000.
Fig. 5.
Fig. 5.
Summary of the evolution of resistance with imperfect drug coverage. (A) When both drugs have high, matched penetration throughout the body, the evolution of multidrug resistance is slow, because it requires either preexisting multidrug resistance or near-simultaneous acquisition of both mutations along with migration out of a sanctuary site. If one drug (B) or both drugs (C) have a lower penetration, treatment outcomes may suffer in different ways. (B) If there are regions where only one drug reaches an effective concentration, then the evolution of multidrug resistance speeds up, because mutations may emerge in a stepwise fashion via single-drug compartments. Single mutations can arise de novo from a wild-type pathogen in the sanctuary or be selected from preexisting mutations in the single-drug compartment when treatment is started. (C) If the sanctuary is larger but both drugs reach the same regions of the body, then resistance still evolves slowly, but the infection size before treatment failure will be larger. Therefore, if high penetration of all drugs is impossible, there is a trade-off when choosing which drugs to pair in combinations: halting growth of the wild-type pathogen immediately (B) or preventing the sequential accumulation of resistance mutations (C).
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References

    1. Chernish RN, Aaron SD. Approach to resistant gram-negative bacterial pulmonary infections in patients with cystic fibrosis. Curr Opin Pulm Med. 2003;9(6):509–515. - PubMed
    1. Gupta RK, et al. Global trends in antiretroviral resistance in treatment-naive individuals with HIV after rollout of antiretroviral treatment in resource-limited settings: A global collaborative study and meta-regression analysis. Lancet. 2012;380(9849):1250–1258. - PMC - PubMed
    1. Tana MM, Ghany MG. Hepatitis B virus treatment: Management of antiviral drug resistance. Clin Liver Dis. 2013;2(1):24–28. - PMC - PubMed
    1. Pawlotsky J-M. Treatment failure and resistance with direct-acting antiviral drugs against hepatitis C virus. Hepatology. 2011;53(5):1742–1751. - PubMed
    1. Zumla A, et al. Drug-resistant tuberculosis—current dilemmas, unanswered questions, challenges, and priority needs. J Infect Dis. 2012;205(Suppl 2):S228–S240. - PubMed

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