title: Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance.
abstract: The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness landscape with the algebraic properties of a Markov chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Using this formalism, we analyze 15 empirical fitness landscapes of E. coli under selection by different β-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be either hindered or promoted by different sequences of drug application. Specifically, we demonstrate that the majority, approximately 70%, of sequential drug treatments with 2-4 drugs promote resistance to the final antibiotic. Further, we derive optimal drug application sequences with which we can probabilistically 'steer' the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic-resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy.
authors.affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom; Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida, United States of America.
authors.forename: Daniel
authors.initials: D
authors.lastname: Nichol
authors.affiliation: Department of Computer Science, University of Oxford, Oxford, United Kingdom.
authors.forename: Peter
authors.initials: P
authors.lastname: Jeavons
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
authors.forename: Alexander G
authors.initials: AG
authors.lastname: Fletcher
authors.affiliation: Department of Medicine, Louis Stokes Department of Veterans Affairs Hospital, Cleveland Ohio, United States of America.
authors.forename: Robert A
authors.initials: RA
authors.lastname: Bonomo
authors.affiliation: Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
authors.forename: Philip K
authors.initials: PK
authors.lastname: Maini
authors.affiliation: School of Electrical Engineering and Computing Systems, University of Cincinnati, Cincinnati, Ohio, United States of America.
authors.forename: Jerome L
authors.initials: JL
authors.lastname: Paul
authors.affiliation: Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida, United States of America.
authors.forename: Robert A
authors.initials: RA
authors.lastname: Gatenby
authors.affiliation: Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida, United States of America.
authors.forename: Alexander R A
authors.initials: AR
authors.lastname: Anderson
authors.affiliation: Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida, United States of America; Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
authors.forename: Jacob G
authors.initials: JG
authors.lastname: Scott
mesh_terms: D000900:Anti-Bacterial Agents / Q000494:pharmacology*; D019295:Computational Biology; D024881:Drug Resistance, Bacterial / Q000187:drug effects* / Q000235:genetics; D004926:Escherichia coli / Q000187:drug effects / Q000235:genetics; D004927:Escherichia coli Infections / Q000382:microbiology; D019143:Evolution, Molecular; D056084:Genetic Fitness / Q000187:drug effects* / Q000235:genetics; D006801:Humans; D008954:Models, Biological; D012641:Selection, Genetic / Q000187:drug effects* / Q000235:genetics
chemical_list: D000900:Anti-Bacterial Agents