Symposium dates: 26 - 28 April 2023
Application deadline: 3 February 2023 (feedback by 10 February 2023)
Drug resistance has become a global threat to human health. The rise of drug resistance has triggered a large number of mathematical studies aimed at obtaining a better understanding of its evolution and how to prevent or delay its emergence. These studies addressing different resistance problems, such as antimicrobial or cancer drug resistance, often use similar theoretical approaches. These approaches involve methods from branching processes, Markov chains, population dynamics, and stochastic numerical simulations. For the modelling of patient treatments, the models need to take into account several factors related to the dynamics of drugs and the host, including, for example, drug interactions, availability of resources in the host, or pharmacodynamics of the drugs.
Given the large number of factors that come into play, a large variety of models on resistance evolution exist. There is no "one-size-fits-all" model to study resistance in bacteria or cancer. While constructing or already working with a model, components of it may change since its advantages and disadvantages become apparent only then. This process is often not shared, although it could benefit other researchers. Generally, there is often no room for detailed discussions of the methods applied to model resistance evolution in scientific meetings.
With this symposium, we want to bring together scientists working on resistance problems (both in bacteria and cancer) to give place to discussions on the theoretical methods employed in the study of resistance evolution. For this purpose, this meeting will include "method sessions" aimed at discussing specific topics relevant to the modelling of antimicrobial resistance (e.g., drug-drug interactions, pharmacodynamics, and population growth models).
There is no registration fee.
A contribution with either a poster or a talk is mandatory for the participation. The presentation details will be sent out once the participants have been selected.
Participants can choose to contribute a short talk (5-10 minutes) to one of the method sessions. More information on this can be found on the registration form.
Some practical information about the Max Planck Institute for Evolutionary Biology can be found here.
In case of any questions or special enquiries, please contact us at: berrios@evolbio.mpg.de or nyhoegen@evolbio.mpg.de.
Stochasticity affects several steps in the evolution of resistance. The appearance of resistant types by mutation or transfer of resistance genes from a source population is a stochastic process. Once resistant types have appeared, they might suffer stochastic loss while rare. During the infection, bottleneck events can lead to further randomness in the dynamics of resistant pathogens. Finally, to persist at the level of the host population, resistant pathogens need to spread to new hosts, which again involves stochasticity -- host encounter (or whatever transmission route is relevant) is not guaranteed, and even if hosts meet, pathogens need to go through a potentially narrow bottleneck and establish a new infection. In this talk, I will present a general and flexible framework based on branching process theory to study aspects of stochasticity at various points on the path to resistance. I will apply it to several scenarios such as the transfer of resistance plasmids from commensals to pathogens or the spread of resistance in a host population.
Bacterial persistence plays a crucial role in determining the number of surviving cells after antibiotic exposure, thereby having an important effect on the effectiveness of antibiotic treatment. Recent evidence suggests that the persister phenotype may also influence the evolvability of antibiotic resistance. The most common hypothesis to explain this link is that persistence leads to a larger reservoir of viable cells, thus ‘buying the population time’ to generate resistance mutations. However, persistence has the potential to affect the evolutionary process in many other ways that have so far remained underexplored. Using an evolutionary simulation approach, we here investigate how persister frequency and lag time influence the probability and speed of fixation of resistance mutations depending on the antibiotic treatment regime. With a simple model we show that lower persister frequency is associated with higher extinction, but a comparatively faster fixation of these mutations if they do fixate. We then present a framework to study the interplay between the antibiotic driven bottleneck size (determined by persistence level) and the lag time of these surviving cells (based on empirical lag time distributions) on the predictability of resistance evolution. More generally, our work stresses the importance of considering the impact of phenotypic heterogeneity on the evolutionary process.
We are interested in modelling Collective antibiotic tolerance (CAT). CAT occurs any time a bacterial population of sufficiently high density survives an antibiotic dose or treatment that a smaller population would succumb to. Various mechanisms have been identified, including cell-to-cell signalling and antibiotic degradation. A known manifestation of CAT is through occurrence of inoculum effect (IE), most often shown through minimum inhibitory concentration (MIC) assays. Definitions of IE and more largely of CAT are slightly inconsistent across the literature and models looking into this effect do so in different ways. Collective responses such as CAT are important to take into account as accurately as possible when designing treatment strategies/regimens. We undertook a systematic review of mathematical models to have a more complete picture of how CAT has been modelled in the literature. To be selected, models should describes population dynamics of one or more bacterial populations facing antibiotic treatment or analogues such as anti-microbial peptides (AMPs). It must include some density-dependent response of bacteria to antibiotic concentration. This effect can be built-in, where response to antibiotic is a function of the MIC, for instance. Or it can be emergent, by including antibiotic removal by bacteria or bacterial product (e.g. enzymes such as beta-lactams). This work gives us metrics to depict the landscape of mathematical modelling associated to CAT. Although those numbers are still preliminary, 47 modelling papers were selected, 85% were published in the past 12 years. ODE systems are over-represented (37). While built-in and emergent implementation of CAT is equally represented, many of the models considered do not explicitly mention CAT, meaning that consequences of CAT are not explored in these. We also observe that very few modelling papers make qualitative predictions on IE, but those that do, do not capture the range of experimental observations. This is combined with a mismatch when comparing model outputs to experimental data. These finding demonstrate a still incomplete understanding of the implications of CAT in bacterial population dynamics. Understanding the consequences of CAT, and how to model these collective effects are very relevant to the way design treatment strategies and understand complex interactions between drugs and bacteria. How, for example, to better link model outputs to reproduce common experimental assays. I am also interested in discussing critically MIC assays as a proxy for measuring IE, in particular in the context of emergence and establishment of resistance. Reliable models of CAT are key to produced testable predictions of how these collective effect impact evolution of resistance.
Antibiotic resistance genes are frequently carried on bacterial plasmids. Because plasmids exist in multiple copies in the host bacterial cell, distinct plasmid copies can carry distinct alleles, allowing for heterozygosity not possible for loci on haploid bacterial chromosomes. This plasmid-mediated heterozygosity of antibiotic resistance alleles can produce multidrug resistance, in which a single bacterial strain is resistant to multiple antibiotics, which is a serious problem in the clinical context. However, the contribution of plasmid-mediated heterozygosity to resistance evolution is limited by the fact that it is subject to constant loss due to random segregation of plasmids on cell division: each division has some probability of producing a homozygous daughter cell. We present a model of the rapid evolution of multidrug resistance in a bacterial population due to plasmid-mediated heterozygosity, focusing on the establishment of a novel resistance allele on a plasmid in a bacterial population already adapted to one antibiotic but undergoing demographic decline due to simultaneous treatment with multiple antibiotics (an evolutionary rescue scenario). We show the probability of population persistence (rescue) of the bacterial population is largely determined by the selective advantage of the heterozygote (multidrug resistant) bacteria and the plasmid copy number. In particular, we determine the threshold on the selective advantage of heterozygotes required to overcome segregative loss and make population persistence possible at all; this threshold decreases with increasing copy number of the plasmid. We further show that the possibility of the formation of plasmid cointegrates from the fusion of plasmids increases the probability of rescue, as cointegrated plasmids which carry both resistance alleles are no longer subject to stochastic loss. These results contribute to our understanding the evolution of antibiotic resistance in complex selective environments and the contribution of plasmid traits, such as copy number to bacterial evolution; future work will include extending the models to the emergence of multidrug resistance by multiple mutations from entirely non-resistant cells, and the incorporation of horizontal gene transfer.
Evolution in changing environments is still poorly understood. We analyze a recently introduced and empirically well-grounded model for antibiotic resistance evolution in bacteria [1]. In this model the corresponding fitness landscape changes with the antibiotic concentration, thereby giving rise to tradeoffs between adaptation to low and high antibiotic concentrations. We show that the adaptive evolution under slowly changing antibiotic concentration exhibits hysteresis loops and memory formation: the selection of a fit genotype not only depends on the current concentration of the antibiotic, but also on the history of concentration changes. Our method of analysis borrows ideas and techniques that were developed for the study of the dynamics driven disordered condensed-matter systems [3]. [1] Suman G. Das, Susana O. L. Direito, Bartlomiej Waclaw, Rosalind J. Allen, Joachim Krug, "Predictable properties of fitness landscapes induced by adaptational tradeoffs," eLife 9 (2020) e55155. [2] Suman G. Das, Joachim Krug, and Muhittin Mungan, "Driven Disordered Systems Approach to Biological Evolution in Changing Environments," Phys. Rev. X 12 (2022) 031040. [3] M. Mungan, "Putting Memories on Paper," PNAS 119 (2022) e2208743119.
Tumors are typically comprised of heterogeneous cell populations exhibiting diverse phenotypes. This heterogeneity, which is correlated with tumor aggressiveness and treatment-failure, confounds current drug screening efforts to identify effective candidate therapies for individual tumors. In the first part of the talk I will present a modeling-driven statistical framework that enables the deconvolution of tumor samples into individual subcomponents exhibiting differential drug-response, using standard bulk drug-screen measurements. In the second part of the talk I will present some efforts towards obtaining insights about tumor evolution from standard genomic data. In particular, we analyze the site frequency spectrum (SFS), a population summary statistic of genomic data, for exponentially growing tumor populations, and we demonstrate how these results can in principle be used to gain insights into tumor evolutionary parameters.
Many pathogenic cellular populations, such as microbial biofilms or solid tumours, are densely packed. However, little is known about how growth-induced collective dynamics - an inherent feature of these systems - reshape the evolution of resistance against antibiotic or anti-cancer therapy. Modelling such emergent phenomena, coupling the mechanical interactions of individual cells to evolutionary outcomes on the population level, is inherently challenging. In my presentation, I will discuss an integrated modelling approach that combines concepts from active granular matter physics and stochastic numerical models with agent-based simulations and data from genetically tailored microbial experiments. Using this strategy, I will show how spatial population expansion and a density-mediated alteration of selection conspire to create an “inflation-selection balance”. The resulting stabilization of less-fit resistant mutants facilitates their continued evolution, including evolutionary rescue via subsequent cost-compensatory mutations. Finally, I will give a brief outlook on how these physical effects could be integrated with other models to inform evolution-based therapy strategies.
Populations of microbial pathogens or cancer cells possess enormous adaptive potential. Such adaptations regularly lead to the failure of treatment, with drastic consequences for individual and public health. From a reductionistic viewpoint, the fundamental processes in such microbial populations are replication, mutation and death. Characterizing these processes by traits allows us to understand adaptation as an uphill walk on a fitness landscape spanned by replication rate and death rate, with mutation rate dictating the walking speed in this picture. Different treatment types exist to tamper with any of these fundamental processes. How such treatment types affect the trajectory of adaptation in trait space is not clear. In this contribution, I will tackle this question and present i) which exact trajectory a population takes in a trait space spanned by replication rate and death rate, ii) how this trajectory is affected by treatment, and iii) how treatments that target either the population size via bottlenecking or the traits via static and toxic drugs differ. Further, I will discuss the fitness gradient(s) that prescribe the adaptation and show that the information on such fitness gradients can guide effective treatment strategies.
Ecological vs. game theoretical models for interaction Both ecologists and evolutionary game theorists study the dynamics in populations of interacting types. Ecologists prefer to use the Lotka-Volterra equations (and non linear generalizations of it), while evolutionary game theorists use the replicator dynamics instead. In their book, Josef Hofbauer and Karl Sigmund have shown that these two approaches are mathematically closely related and lead to the same orbits. Unfortunately, this relation between the two approaches seems less appreciated by experimentalists. On the other hand, a deeper understanding of interactions may emerge from a better understanding of the relationship between the two approaches.
In initially drug-sensitive populations of pathogens or cancerous cells, resistance emerges during drug treatment in some, but not all, populations. This observation of variable outcomes motivates the use of stochastic mathematical models to describe and predict de novo evolution of resistance. Both rate of appearance and fate of resistant mutants depend on the environment, which varies over the course of drug treatment: firstly due to drug dosing and pharmacokinetics, and secondly because the focal population feeds back on its own environment (by consuming and producing substrates). In this talk, I will first outline basic mathematical equations for the probability of emergence of resistance, and how these equations could incorporate environmental variation over time. I will then describe a theoretical case study modelling the emergence of drug resistance in chronic viral infections. This case study illustrates both a general analytical approach, and an example of how environmental feedbacks influence stochastic emergence of resistance. Next, I will present experimental results with Pseudomonas aeruginosa (an opportunistic bacterial pathogen) that give insights into how the environment shapes emergence of resistance. In particular, initial density of the sensitive population plays a surprisingly complex role. This empirical evidence motivates ongoing extensions to our mathematical models.
To alleviate the threat of antimicrobial resistance (AMR), innovative treatment strategies are urgently needed. The phenomenon of collateral sensitivity (CS) may be exploited to achieve this goal using existing antibiotics. CS occurs when resistance to one antibiotic increases the sensitivity to another antibiotic. CS-based combination treatments could potentially suppress resistance, but it remains unclear how to design such treatments. To this end, we use a model-based approach to assess the potential of CS-based treatments to suppress AMR, integrating pharmacokinetics-pharmacodynamics (PK-PD) and principles of evolutionary dynamics. A modelling framework was developed including components accounting for antibiotic PK-PD and population dynamics of bacterial growth and evolution of resistance. Bacterial population dynamics was described using a four-state stochastic hybrid ordinary differential equation model, where each state represents a bacterial subpopulation, including a wild type (WT) population, two single mutant subpopulations, and a double mutant subpopulation. Resistance evolution was modelled according to a stochastic process based on a binomial distribution informed by a mutation rate. Each subpopulation had unique antibiotic sensitivity based on the minimum inhibitory concentration (MIC). Antibiotic sensitivities were incorporated in sigmoidal concentration-effect relationships. The framework was implemented using the RxODE package in R. We used the framework to systematically study how certain pathogen- and drug-specific parameters influence AMR evolution. We simulated different combination dosing regimens with sequential, cyclic, or simultaneous administration using two antibiotics, ABA and ABB, which were assumed to have identical PK and additive bacterial killing effects. Here, in the bacterial model, the two single mutant subpopulations represent resistance to ABA and ABB, respectively, while the double mutant subpopulation was resistant to both ABA and ABB. To understand how antibiotic with different types of PD impact AMR evolution we performed simulations varying the drug-specific parameters relating to the maximal effect and shape of the concentration-effect relationship. We studied the importance of CS reciprocity, effect magnitude, and how pathogen-specific factors including fitness cost and mutation rate, influence the ability of CS to suppress the resistance for different dosing regimens. We find that the impact of reciprocal CS relationships on the probability of resistance at end of treatment is dependent on the drug PD type and dosing regimen. Simultaneous or one-day cycling treatment schedules were most effective dosing regimens to suppress resistance. For these treatments, a CS effect of 50% fully suppressed the resistance when concentration-dependent antibiotics were used. The effect of antibiotic concentration shows that CS-based treatments are most clinically relevant for antibiotics with a narrow therapeutic window. One-directional CS relationships, and not only reciprocal relationships, can be utilized in the design of CS-based treatment schedules. In this analysis, we used modelling and simulation to systematically unravel drug- and pathogen-specific factors influencing optimal design of resistance-pressing CS-based treatment strategies. Our modelling approach addresses important open questions around the topic of CS that are not easily tested experimentally, and provides new insights regarding key design aspects of CS-based treatments, contributing to the unmet need toward innovative strategies to alleviate the threat of AMR.
The evolution of drug resistance in infectious disease and cancer is a serious threat to public health. The mutant selection window (MSW), defined as the range of drug concentrations that selects for a drug resistant strain, has previously been used as a model to predict and avoid resistance. Under the MSW paradigm, drug regimens should be designed to minimize time spent in the MSW. A limitation of the MSW model is that it only offers comparisons between two strains at a time-- i.e. between drug sensitive and drug resistant strains. In contrast, fitness seascapes, which we model as collections of genotype-specific dose-response curves, provide comparisons between many genotypes simultaneously. Furthermore, previous work has shown that MSW comparisons are intrinsically embedded in fitness seascapes. Here, we explore the consequences of modeling evolution with fitness seascapes through the lens of the MSW framework. First, we show how an N-allele fitness seascape embeds N*2N mutant selection window comparisons. Then, we develop mathematical models for drug pharmacokinetics in three clinically-relevant scenarios: serum drug concentration during a daily dosing regimen and drug diffusion in tissue in 1- and 2-dimensions. Each scenario reveals the presence of heterogeneous mutant selection windows. Importantly, we find that different MSWs arise at different times in a treatment regimen, and multiple MSWs appear simultaneously at different points in space. While prior work has analyzed the importance of time spent in a MSW, we argue that both time and space occupied by a MSW impact the probability of drug resistance. This work further explores the connection between mutant selection windows and fitness seascapes using realistic pharmacokinetic and drug diffusion models. Our results highlight the importance of fitness seascapes in modeling evolution when drug concentration varies in time and space. Furthermore, because of the multiplicity of mutant selection window comparisons in a single fitness seascape, this work suggests that two-state mutant selection window models may not be sufficient to predict or control the evolution of drug resistance.
Plasticity and Genetic Evolution
Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete states have been developed. However, seldom do models incorporate both plasticity and mutationally-driven resistance. In this talk, we will use evolutionary game theory, matrix population models, and integral projection models to develop a framework that can incorporate plastic and mutational mechanisms of acquiring resistance in a continuous/discrete and gradualistic fashion, respectively. We use this framework to examine ways in which populations can respond to stress (focusing on polyaneuploid cancer cells, neuroblastoma, and bacteria) and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution.
Development of therapeutic resistance in cancer is typically attributed to natural selection, where a cytotoxic agent eliminates sensitive cells in the population, leaving behind only the resistant ones. However, it appears that non-genetic mechanisms of therapeutic resistance exist as well, and as such they may be reversible through better understanding of underlying biology. Here we discuss two examples of non-genetic resistance to cancer therapy: resistance to PI3K inhibitors that can be reversed through combination therapy that targets metabolism, and resistance to checkpoint inhibitors, which may be addressed through modifying the dosage of drug administration. We discuss existing evidence for these mechanisms, and possible modeling approaches that may be applied to help mitigate non-genetic resistance to cancer therapy.
Tumors are not just collections of mutated cells, they are complex ecosystems of interacting clones and host elements. This type of system is well known to theoretical ecologists, who have been using mathematical models to understand, and even bias, naturally occurring systems like fisheries and game reserves. In this spirit, we have been working to develop mathematical models to describe tumors in this way, and further, to connect these models directly to experimental measurements. Specifically, we have developed an in vitro assay to directly parameterize an evolutionary game theory model, and have begun characterizing cell-cell interactions in heterogeneous model tumors. Using this assay, we have documented evidence of frequency dependent fitness, a necessary condition for adaptive therapy and significant ecological effects on cell fitness which strongly affects the emergence of drug resistance. I will describe our findings in EGFR+ and ALK+ non-small cell lung cancer, and propose both clinical and biological next steps to making personalized adaptive (evolutionary) therapy a reality.
Both bacterial and helminth infections are commonly treatable by suitable drugs. However, these pathogens are constantly evolving ways to escape drug treatment.
Bacteria often protect themselves by forming biofilms - high-density colonies attached to a surface or each other. Such a sedentary lifestyle of biofilm cells comes associated with costs and benefits. While the growth rate of biofilm populations is often significantly lower than that of their free-living counterparts, this cost is repaid once the colony is subjected to antibiotics: biofilms can survive in antibiotic concentrations up to a thousand times higher than those killing their free-living counterparts. Studies have shown that such phenotypic protection influences the evolution of drug resistance in a non-intuitive way.
Helminths, particularly nematodes, are a diverse group of macroscopic parasites causing a plethora of human and animal diseases. Nematodes are diploid organisms with complex sexual reproduction and life cycles often involving multiple hosts, which makes it extremely difficult to study them experimentally. Therefore, many extrinsic and intrinsic factors affecting drug resistance evolution in these creatures are yet poorly understood.
Despite the significant biological differences between these two taxa, fundamental evolutionary principles governing resistance evolution are the same. Here, we take advantage of this similarity and develop a framework combining pharmacodynamics and pharmacokinetics with population genetics, which we apply to investigate drug resistance evolution in bacterial biofilms and parasitic worms.
We explore the effects of various phenotypic mechanisms present in bacterial biofilms on the population dynamics of bacterial populations and investigate their consequences for the evolution of antibiotic resistance. In helminths, we show the effect of population size on the rate of resistance evolution.
Recent experiments on the evolution of drug resistance in bacteria have identified a transition from the preferred substitution of high-rate, low-effect mutations to low-rate, high-effect mutations with increasing population size [1]. The greater mutation supply in large populations increases the probability for rare high-effect mutations to arise, which subsequently outcompete the more frequent low-effect mutations through intensified clonal interference. In this way, the balance between mutation bias and selective differences in their effects on mutation choice is increasingly skewed in favor of selection in large populations. A minimal setting in which the interplay between mutation bias, selection and population size can be quantified is provided by the Yampolsky-Stoltzfus model, which considers the competitive fixation of two mutations, one of which is favored by mutation bias and the other by selection [2]. Using a suite of approximations based on a detailed analysis of the fixation process, we derive accurate expressions for the relative fixation probability of the two mutations that cover all adaptive regimes of interest. This allows us to precisely pinpoint the critical population size beyond which mutation bias is superseded by selection for any choice of mutation rates and selection coefficients. [1] M.F. Schenk et al., Population size mediates the contribution of high-rate and large-benefit mutations to parallel evolution. Nature Ecology & Evolution 6:439-447 (2022) [2] L.V. Yampolsky and A. Stoltzfus, Bias in the introduction of variation as an orienting factor in evolution. Evolution & Development 3:73-83 (2001)
Understanding the evolution of antimicrobial resistance is central for their treatment. In this talk, I want to show a possible way to address this problem from a statistical point of view, namely the hypercubic inference, which we developed and introduced during the last years at the University of Bergen. The basis of this model is a hypercubic transition graph, whose nodes represent possible resistance states and the edges between correspond to the different evolutionary steps. This new approach allows us to efficiently make predictions about the most likely evolutionary pathways leading to AMR and learn their structure and variability. For this we can either use Bayesian inference via Monte Carlo Markov Chain methods or a frequentist approach for the estimation of likelihoods, whereby we only need cross-sectional datasets. The focus of the talk will be the introduction and explanation of the methods themselves, whereby I will address both the advantages and strengths of using a hypercubic structure, but also open problems and ongoing work. In addition, I will also present the results of concrete current applications to real AMR datasets from Klebsiella pneumoniae and Escherichia coli and discuss some biological insights that can be derived from them.
Despite rapid initial responses and low toxicity, targeted therapies commonly fail to provide long-term benefits to cancer patients due to the development of therapy resistance. In multiple solid tumors, this resistance emerges due to gradual, multifactorial adaptation, i.e., a selective process combining genetic and non-genetic methods of cell diversification. This suggests a significant link between the evolution of cancer treatment resistance and evolvability – a selective trait of generating heritable phenotypic variation. However, the interplay between selection, evolvability, and resistance has not yet been fully investigated. We addressed this problem by studying the selection for mutator phenotype. The mutator phenotype is common in many cancers and results from errors in DNA repair mechanisms. This phenotype generates mutations at a higher frequency than other phenotypes. Since mutations can both benefit or reduce cell viability, we hypothesized that the selection for a mutator phenotype changes during the evolution of resistance to cancer targeted therapies. We tested this hypothesis by developing a 2D on-lattice Agent-Based Model (ABM). In the model, a cell can die, divide and mutate, yet mutations have a stochastic impact that can be beneficial, neutral, or deleterious for the individual cell fitness. Consequently, the resistance emerges as a stochastic event depending on the mutation frequency. Our results demonstrate that 1) the mutator phenotype initially accelerates adaptation to treatment, but 2) only intermediate mutation frequencies can sustain high fitness long-term. This work provides a versatile experimental platform that can be adjusted to study the evolution of resistance in other cancers beyond NSCLC and treatments. Moreover, our results challenge the commonly held assumption that resistance develops only due to pre-existing driver mutations and provide an opportunity to integrate evolutionary theory and oncology to improve treatment in cancer patients.
The repeatability of evolution depends strongly on the distribution of fitness effects (DFE) of beneficial mutations. While theoretical modeling has focused mainly on light-tailed DFEs, experiments on antibiotic resistance evolution have also uncovered signatures of heavy-tailed DFEs. We show that in the latter case the repeatability behaves in counter-intuitive ways. Firstly, the evolutionary process is dominated by only a few mutations even in the limit of an infinite number of available beneficial mutations. This enhances the repeatability, but it also implies that the degree of repeatability is less predictable from the DFE. Secondly, the measure of repeatability becomes a non-self-averaging variable which does not converge to its mean. This necessitates a careful conceptual distinction between typical and mean values of the repeatability measure, with important consequences for the quantification of the repeatability of antibiotic resistance evolution from empirical data. I will discuss the theoretical results and illustrate them with experimental data on the DFE of mutations in an antibiotic resistance enzyme.
When multiple antibiotics are combined, they can interact in diverse and difficult-to-predict ways. Two antibiotics may synergize or antagonize, inhibiting bacterial growth more or less than expected. Such drug interactions can strongly influence the dynamics of resistance evolution and, in extreme cases, lead to selection against drug resistance. I will present how drug interactions are quantitatively characterized and show that a theoretical description based on bacterial growth laws, combined with drug uptake and binding kinetics, allows direct prediction of a large fraction of observed drug interactions between antibiotics targeting translation. Additional interactions are explained by "translation bottlenecks": points in the translation cycle where antibiotics block ribosomal progression. In particular, extremely strong antagonistic interactions, where the addition of one antibiotic facilitates bacterial growth in the presence of another, are faithfully captured by a theoretical description based on the totally asymmetric simple exclusion process (TASEP). Finally, I will show how similar theoretical descriptions of bacterial growth can capture quantitative features of the bacterial response to antibiotics with other cellular targets, and discuss the relevance of these phenomena for the dynamics of resistance evolution.