Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance

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.Author Summary: Increasing antibiotic resistance, coupled with the slowing rate of discovery of novel antibiotic agents, is a public health threat which could soon reach crisis point. Indeed, the last decade has seen the emergence of deadly, highly resistant forms of pathogens, such as Escherichia coli, Acenitobacter baumanii, Klebsiella pneumoniae, Enterococcus and Staphylococcus aureus as well as non–bacterial pathogens including malaria and viruses such as HIV. Here, we develop a mathematical model of an evolving bacterial population, which allows us to predict the probability of resistant strains emerging. Using this model we show how sequences of drugs can be prescribed in order to prevent resistance where each drug alone may fail. These model predictions suggest a novel treatment strategy: using sequences of antibiotics to ‘steer’ the evolution of a pathogen to a configuration from which resistance to a final antibiotic cannot emerge. Further, we test the likelihood of resistance emerging when arbitrary sequences of antibiotics are prescribed, finding that approximately 70% of arbitrary sequences of 2–4 drugs promote resistance to the final drug. This result serves as a cautionary warning that we may be inadvertently promoting resistance through careless (or random) prescription of drugs.