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The development of reliable methods for restoring susceptibility after antibiotic resistance arises has proven elusive. A greater understanding of the relationship between antibiotic administration and the evolution of resistance is key to overcoming this challenge. Here we present a data-driven mathematical approach for developing antibiotic treat...
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... Current methods for the development of evolutionary therapies require an enormous amount of data on the evolving system. For example, many researchers have optimized treatment by using genotype-phenotype maps to define evolutionary dynamics and model the evolving cell population (16,(25)(26)(27)(28)(29)(30)(31)(32)(33). For instance, Nichol et al. modeled empirical drug fitness landscapes measured in Escherichia coli as a Markov chain to show that different sequences of antibiotics can promote or hinder resistance. ...
... In this study, we developed an approach to discovering evolutionary therapies using a well-studied set of empirical fitness landscapes as a model system (26). We explored "perfect information" optimization methods such as dynamic programming in addition to RL methods that can learn policies given only limited information about a system. ...
... Populations. As a model system, we simulated an evolving population of E. coli using the well-studied fitness landscape paradigm, where each genotype is associated with a certain fitness under selection (16,26,29). To parameterize our evolutionary model, we relied on data from a previously described fitness landscape of the E. coli -lactamase gene (26). ...
Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent, or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that it is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 β -lactam antibiotics with which to treat the simulated Escherichia coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1,024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.
... To combat antibiotic resistance (ABR), we traditionally have confined our attention to discover and design new antibiotics [2]. In addition to the utilization of artificial intelligence in these efforts [3,4], two new lines of research have recently emerged: (i) Developers have repurposed already available drugs against ABR [5,6], or (ii) researchers have prescribed a sequence of antibiotics that exploits the collateral sensitivity of bacterial mutations to slow down or reverse the resistance [7,8]. Even though there were a limited number of clinical observations that raised opposing views [9,10], later experimental and computational studies suggested that there might still exist optimal drug ordering procedures to delimit ABR [11][12][13][14][15][16], including the recently developed reinforcement learning approach [17]. ...
... We conduct extensive computational experiments using the fourallele real dataset from [19] with 23 antibiotics under two probability models from [7]. The results reveal that our SAA-based stochastic optimization models are extraordinarily accurate as the in-sample and out-of-sample values for the probability of reaching the wild type are at most 0.01 away from each other. ...
... An important aspect of the Antibiotics Time Machine Problem is the computation of the transition probability matrices, for which we use the framework from [7]. The authors measure the growth rate of each genotype under the administration of an antibiotic and store it in a vector ∈ R + . ...
... By examining MSWs with the fitness seascape model, we may compare many genotypes simultaneously. For instance, in the binary landcsape model with N mutational sites, each genotype may be simultaneously compared to N adjacent genotypes (genotypes that differ by 1 mutation) [3,[31][32][33][34][35][36][37]. Here, we expand on this idea and explore the MSW model through the lens of fitness seascapes. ...
Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N -allele fitness seascapes allow for N * 2 N −1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.
... Mathematical modeling establishes a high level of control involving factors such as pharmacodynamic (PD) and pharmacokinetic (PK) [65], optimal time of drug exposure [68], between others with relevance on the effects antibiotics have on bacterial growth, inhibition, killing, and mutation [60,30,9,66]. Regarding collateral effects, mathematical models have been developed to evaluate sequential drug regimens in vitro and silico [69,52], to assess the robustness of collateral sensitivity [52], to exploit its statistical structure and designing optimal policies [43], to evaluate possible reversion of evolution towards resistance [48] and to compare cycling vs mixing treatments [55]. None of these models however tackled the CS phenomenon with a combinatorial mutation network which has already been used for multidrug resistance (without collateral effects) on cancer [33], for which it was assumed that a mutation that confers resistance to one drug does not confer resistance to any of the other drugs in use 1 ; framework that leads to a dead-end towards MDR. ...
The use of chemotherapeutics agents in the treatment of bacterial infections have resulted in the emergence of multidrug resistant pathogens. Clinically, with single and even multiple drug intervention strategies, pathogens have developed resistance to one or all drugs utilized. This leads to the reasonable conclusion that the primary effect of any (finite) amount of drugs is delaying resistance development as opposed to prevention. Importantly, it has been shown that in sequential exposure of pathogens to antibiotics, evolution of resistance to some drugs may increase sensitivity toward others previously used, a phenomenon known as collateral sensitivity. This suggests that multidrug resistance could be avoided by an adequate use of the available drugs. Without a framework to do this however, each bug:drugs interaction network would need to be assembled blindly, an arduous experimental process. This study develops a framework for describing qualitatively collateral sensitivity networks, accordingly the interactions between emerging drug-resistant variants are modeled and a dynamic analysis is conducted to predict failure or success of sequential drug therapies.
... Some of these mutations were accumulated during directed evolution or enzyme engineering toward a novel function (phosphotriesterase, PTE; β-lactamase, OXA-48; nitroreductase, NfsA) [27][28][29] . Others were identified from naturally occurring evolutionary trajectories, either through a retrospectively identified path using ancestral sequence reconstruction (methyl-parathion hydrolase, MPH) 19,20 , the presence of clinically relevant mutations (dihydrofolate reductase, DHFR, and β-lactamase, TEM-1) [30][31][32][33][34] , or in the case of alkaline phosphatase (AP), by using previously characterized active site mutations 24 . The final dataset consisted of 56 unique mutations; we ensured that the majority (54) was located within the protein open reading frame, but retained two mutations in the promoter region (in DHFR and TEM-1) 30,33 . ...
... Interestingly, because the SMEs in the reduced dataset were still highly heterogenous ( Supplementary Tables 1 and 2), this dataset can be characterized by a stronger presence of magnitude, as opposed to sign, epistasis. Although several studies have explored the differences in patterns of epistasis within singular enzymes across different selection conditions 20,31,34 , further research is encouraged to provide a rationale for these differences and to better capture global trends across multiple enzymes. ...
... The values of reported functions were divided by the wt background function, or, in the presence of replicates, by the mean of the wt background functions, then log 10 transformed. However, we raised 10 to the power of all the TEM-1 growth rate values from Mira et al. before using them in our standard pipeline 34 , as the growth rates from this study are assumed to be additive and not multiplicative. All processed files are provided (Supplementary Data 1). ...
Enzyme evolution is characterized by constant alterations of the intramolecular residue networks supporting their functions. The rewiring of these network interactions can give rise to epistasis. As mutations accumulate, the epistasis observed across diverse genotypes may appear idiosyncratic, that is, exhibit unique effects in different genetic backgrounds. Here, we unveil a quantitative picture of the prevalence and patterns of epistasis in enzyme evolution by analyzing 41 fitness landscapes generated from seven enzymes. We show that >94% of all mutational and epistatic effects appear highly idiosyncratic, which greatly distorted the functional prediction of the evolved enzymes. By examining seemingly idiosyncratic changes in epistasis along adaptive trajectories, we expose several instances of higher-order, intramolecular rewiring. Using complementary structural data, we outline putative molecular mechanisms explaining higher-order epistasis along two enzyme trajectories. Our work emphasizes the prevalence of epistasis and provides an approach to exploring this phenomenon through a molecular lens.
... Traditional methods to determine fitness are based on growth measurements of 32 reconstructed mutants carrying the mutation of interest. These approaches are generally 33 low-throughput, allowing only a handful of mutations to be assessed each time [5][6][7][8][9]. As 34 the field of evolutionary biology is moving towards a more holistic view, there has been 35 an increased demand in the past decades for techniques that allow evaluation of a large 36 number of mutants in a single assay [10,11]. ...
Transposon insertion site sequencing (TIS) is an extremely powerful tool that has greatly advanced our knowledge of functional genomics. However, studies using TIS often focus on gene essentiality and neglect possibly interesting but subtle differences in the importance of genes for fitness. As shown by other studies, expanding of the analysis of TIS data to allow a quantitative estimate of fitness has important application in genetics and evolutionary biology. Here, we present a method to estimate the fitness of gene disruption mutants on a quantitative level using data obtained from a TIS screen developed for the yeast Saccharomyces cerevisiae called SATAY. We show that using the average read count per transposon insertion site provides a metric for fitness that is robust across biological and technical replicate experiments. Importantly, the ability to resolve differences between gene disruption mutants with low fitness depends crucially on the inclusion of insertion sites that are not observed in the sequencing data to estimate the mean. While our method provides reproducible results between replicate SATAY datasets, the obtained fitness distribution differs substantially from those obtained using other techniques. It remains unclear whether these inconsistencies are due to biological or technical differences between the methods. Finally, we give suggestions for modifications of the SATAY procedure that could improve the resolution of the fitness estimates. Our analysis indicates that increasing the sequencing depth does very little to reduce the uncertainty in the estimates, while replacing the PCR amplification with methods that avoid or reduce the number of amplification cycles will likely be most effective in reducing noise.
... Such factors will not be discussed here. Neither will we discuss more elaborate methods for restoring the original wild-type that depends on sequences of drugs (Mira et al., 2015;Goulart et al., 2013;Tran and Yang., 2017). ...
We use fitness graphs, or directed cube graphs, for analyzing evolutionary reversibility. The main application is antimicrobial drug resistance. Reversible drug resistance has been observed both clinically and experimentally. If drug resistance depends on a single point mutation, then a possible scenario is that the mutation reverts back to the wild-type codon after the drug has been discontinued, so that susceptibility is fully restored. In general, a drug pause does not automatically imply fast elimination of drug resistance. Also if drug resistance is reversible, the threshold concentration for reverse evolution may be lower than for forward evolution. For a theoretical understanding of evolutionary reversibility, including threshold asymmetries, it is necessary to analyze obstacles in fitness landscapes. We compare local and global obstacles, obstacles for forward and reverse evolution, and conjecture that favorable landscapes for forward evolution correlate with evolution being reversible. Both suboptimal peaks and plateaus are analyzed with some observations on the impact of redundancy and dimensionality. Our findings are compared with laboratory studies on irreversible malarial drug resistance.
... A possible direction for future research is the development of algorithms that infer features of the environmental history from the knowledge of evolved genomes using the state transition graph. Conversely, our approach can be used to design treatment protocols that are optimized to avoid or slow down the evolution of drug resistance by controlling the drug concentration or by cycling different antibiotics [77,78]. ...
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organism’s environment, and evolution in changing environments is still poorly understood. We study a particular model of antibiotic resistance evolution in bacteria where the antibiotic concentration is an environmental parameter and the fitness landscapes incorporate trade-offs between adaptation to low and high antibiotic concentration. With evolutionary dynamics that follow fitness gradients, the evolution of the system under slowly changing antibiotic concentration resembles the athermal dynamics of disordered physical systems under external drives. Exploiting this resemblance, we show that our model can be described as a system with interacting hysteretic elements. As in the case of the driven disordered systems, adaptive evolution under antibiotic concentration cycling is found to exhibit hysteresis loops and memory formation. We derive a number of analytical results for quasistatic concentration changes. We also perform numerical simulations to study how these effects are modified under driving protocols in which the concentration is changed in discrete steps. Our approach provides a general framework for studying motifs of evolutionary dynamics in biological systems in a changing environment.
... Combinatorial landscapes analyzed in this study Three mutationally unique trajectories, where each was probed using two inhibitors b Ref.28 explored 15 inhibitors for the same set of four mutations c Two separate mutational trajectories for the same protein and substrate d Ref. 26 explored four mutations using five different substrates; ref. 27 explored both kcat/KM and KI for two mutational trajectories e Ref.25 explored the same five mutations under eight different metal environments f Six mutations were explored using two substrates, one in ref.13 and one outlined in this study (see Methods) ...
Epistasis shapes evolutionary outcomes during protein adaptation. In particular, when the effects of single mutations or mutational interactions are idiosyncratic, that is, unique to a genetic background, the predictability of protein evolution becomes greatly impaired. Here, we unveil a quantitative picture of the prevalence and role of idiosyncrasy in protein evolution by analysing 45 protein fitness landscapes, generated from seven enzymes. We found that mutational effects and epistasis are highly idiosyncratic across the landscapes. Idiosyncrasy obscured functional predictions of mutated proteins when using limited mutational data, and often continued to impair prediction upon incorporation of epistatic information. We show that idiosyncrasy stems from higher-order epistasis, and highlight examples where it permits, or restricts, evolutionary accessibility of certain genotypes. Our work suggests that idiosyncrasy deeply confounds predictions in protein evolution necessitating its incorporation into predictive models and in-depth exploration of its underlying molecular mechanisms.
... Given a list of drugs and a predetermined length of treatment plan, the antibiotics time machine problem seeks to find the optimal drug sequence to be applied so that the probability of reversing the mutations altogether at the end of the treatment is maximized. Although there is significant interest in the biology community in understanding the quantitative aspect of antibiotics resistance (Kim, Lieberman, and Kishony 2014;Nichol et al. 2015;Mira et al. 2015Mira et al. , 2017Yoshida et al. 2017), the only method used to attack the antibiotic times machine problem appears to be complete enumeration. ...
... In this section, the computational results obtained by solving the antibiotics time machine problem using a real dataset from Mira et al. (2015) are presented. The computational effort of complete enumeration is compared with that of MILP (5), and their scalability issues are discussed. ...
... The computational effort of complete enumeration is compared with that of MILP (5), and their scalability issues are discussed. The experimental growth rate data and probability calculations from Mira et al. (2015) are used to obtain the transition probability matrices. In particular, let ω k,j be the growth rate of genotype j under antibiotic k. ...
Optimization problems are considered that involve the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and materials science among others, and are known to be NP-hard for a special case of interest. The underlying structure of such optimization problems is analysed for two particular applications and, depending on the matrix family, compact-size mixed-integer linear or quadratically constrained quadratic programming reformulations are obtained that can be solved via commercial solvers. Finally, the results are presented of computational experiments that demonstrate the success of the author's approach compared to heuristic and enumeration methods predominant in the literature.
