Diversity in times of adversity: probabilistic strategies in microbial survival games

Evolution of a bistable genetic system in fluctuating and nonfluctuating environments

Epigenetic mechanisms can generate bacterial lineages capable of spontaneously switching between distinct phenotypes. Currently, mathematical models and simulations propose epigenetic switches as a mechanism of adaptation to deal with fluctuating environments. However, bacterial evolution experiments for testing these predictions are lacking. Here, we exploit an epigenetic switch in Salmonella enterica, the opvAB operon, to show clear evidence that OpvAB bistability persists in changing environments but not in stable conditions. Epigenetic control of transcription in the opvAB operon produces OpvABOFF (phage-sensitive) and OpvABON (phage-resistant) cells in a reversible manner and may be interpreted as an example of bet-hedging to preadapt Salmonella populations to the encounter with phages. Our experimental observations and computational simulations illustrate the adaptive value of epigenetic variation as an evolutionary strategy for mutation avoidance in fluctuating environments. In addition, our study provides experimental support to game theory models predicting that phenotypic heterogeneity is advantageous in changing and unpredictable environments.

Fitness cost associated with cell phenotypic switching drives population diversification dynamics and controllability

Isogenic cell populations can cope with stress conditions by switching to alternative phenotypes. Even if it can lead to increased fitness in a natural context, this feature is typically unwanted for a range of applications (e.g., bioproduction, synthetic biology, and biomedicine) where it tends to make cellular response unpredictable. However, little is known about the diversification profiles that can be adopted by a cell population. Here, we characterize the diversification dynamics for various systems (bacteria and yeast) and for different phenotypes (utilization of alternative carbon sources, general stress response and more complex development patterns). Our results suggest that the diversification dynamics and the fitness cost associated with cell switching are coupled. To quantify the contribution of the switching cost on population dynamics, we design a stochastic model that let us reproduce the dynamics observed experimentally and identify three diversification regimes, i.e., constrained (at low switching cost), dispersed (at medium and high switching cost), and bursty (for very high switching cost). Furthermore, we use a cell-machine interface called Segregostat to demonstrate that different levels of control can be applied to these diversification regimes, enabling applications involving more precise cellular responses.

Noise-induced Parrondo's paradox in discrete-time quantum walks

Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. We show that noise can induce Parrondo's paradox in one-dimensional discrete-time quantum walks with deterministic periodic as well as aperiodic sequences of two-state quantum coins where this paradox does not occur in the absence of noise. Moreover, we show how the noise-induced Parrondo's paradox affects the time evolution of quantum entanglement for such quantum walks.

Neuronal temperature perception induces specific defenses that enable C. elegans to cope with the enhanced reactivity of hydrogen peroxide at high temperature

Hydrogen peroxide is the most common reactive chemical that organisms face on the microbial battlefield. The rate with which hydrogen peroxide damages biomolecules required for life increases with temperature, yet little is known about how organisms cope with this temperature-dependent threat. Here, we show that Caenorhabditis elegans nematodes use temperature information perceived by sensory neurons to cope with the temperature-dependent threat of hydrogen peroxide produced by the pathogenic bacterium Enterococcus faecium. These nematodes preemptively induce the expression of specific hydrogen peroxide defenses in response to perception of high temperature by a pair of sensory neurons. These neurons communicate temperature information to target tissues expressing those defenses via an insulin/IGF1 hormone. This is the first example of a multicellular organism inducing their defenses to a chemical when they sense an inherent enhancer of the reactivity of that chemical.

Parrondo's paradox in quantum walks with three coins

Parrondo's paradox refers to the apparently paradoxical effect whereby a certain combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's paradox can occur not only in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of two quantum coins but also in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of three quantum coins. Moreover, we show how Parrondo's paradox affects the time evolution of quantum entanglement for such quantum walks.

Diversity of bet-hedging strategies in microbial communities-Recent cases and insights

Microbial communities are continuously exposed to unpredictable changes in their environment. To thrive in such dynamic habitats, microorganisms have developed the ability to readily switch phenotypes, resulting in a number of differently adapted subpopulations expressing various traits. In evolutionary biology, a particular case of phenotypic heterogeneity that evolved in an unpredictably changing environment has been defined as bet‐hedging. Bet‐hedging is a risk‐spreading strategy where isogenic populations stochastically (randomly) diversify their phenotypes, often resulting in maladapted individuals that suffer lower reproductive success. This fitness trade‐off in a specific environment may have a selective advantage upon the sudden environmental shift. Thus, a bet‐hedging strategy allows populations to persist in very dynamic habitats, but with a particular fitness cost. In recent years, numerous examples of phenotypic heterogeneity in different microorganisms have been observed, some suggesting bet‐hedging. Here, we highlight the latest reports concerning bet‐hedging phenomena in various microorganisms to show how versatile this strategy is within the microbial realms.

This article is categorized under:

Infectious Diseases > Molecular and Cellular Physiology

Modulation of sensory perception by hydrogen peroxide enables Caenorhabditis elegans to find a niche that provides both food and protection from hydrogen peroxide

Hydrogen peroxide (H2O2) is the most common chemical threat that organisms face. Here, we show that H2O2 alters the bacterial food preference of Caenorhabditis elegans, enabling the nematodes to find a safe environment with food. H2O2 induces the nematodes to leave food patches of laboratory and microbiome bacteria when those bacterial communities have insufficient H2O2-degrading capacity. The nematode's behavior is directed by H2O2-sensing neurons that promote escape from H2O2 and by bacteria-sensing neurons that promote attraction to bacteria. However, the input for H2O2-sensing neurons is removed by bacterial H2O2-degrading enzymes and the bacteria-sensing neurons' perception of bacteria is prevented by H2O2. The resulting cross-attenuation provides a general mechanism that ensures the nematode's behavior is faithful to the lethal threat of hydrogen peroxide, increasing the nematode's chances of finding a niche that provides both food and protection from hydrogen peroxide.

Parrondo's paradox in quantum walks with deterministic aperiodic sequence of coins

Parrondo's effect is a well-known apparent paradox where a combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's effect can occur not only in the case of one-dimensional discrete quantum walks with random or deterministic periodic sequence of two- or multistate quantum coins but also in the case of one-dimensional discrete quantum walks with deterministic aperiodic sequence of two-state quantum coins. Moreover, we show how Parrondo's effect affects the time evolution of the walker-coin quantum entanglement.

Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments

Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

Waddington's Landscapes in the Bacterial World

Conrad Waddington’s epigenetic landscape, a visual metaphor for the development of multicellular organisms, is appropriate to depict the formation of phenotypic variants of bacterial cells. Examples of bacterial differentiation that result in morphological change have been known for decades. In addition, bacterial populations contain phenotypic cell variants that lack morphological change, and the advent of fluorescent protein technology and single-cell analysis has unveiled scores of examples. Cell-specific gene expression patterns can have a random origin or arise as a programmed event. When phenotypic cell-to-cell differences are heritable, bacterial lineages are formed. The mechanisms that transmit epigenetic states to daughter cells can have strikingly different levels of complexity, from the propagation of simple feedback loops to the formation of complex DNA methylation patterns. Game theory predicts that phenotypic heterogeneity can facilitate bacterial adaptation to hostile or unpredictable environments, serving either as a division of labor or as a bet hedging that anticipates future challenges. Experimental observation confirms the existence of both types of strategies in the bacterial world.

Does Cancer Biology Rely on Parrondo's Principles?

Simple Summary

Parrondo’s paradox, whereby losing strategies or deleterious effects can combine to provide a winning outcome, has been increasingly applied by biologists to explain complex adaptations in many living systems. Here, we suggest that considering this paradox in oncology, particularly in relation to the phenotypic diversity of malignant cells, could also be a promising approach to understand several puzzling aspects of cancer biology. For example, the high genetic and epigenetic instability of cancer cells, their metastatic behavior and their capacity to enter dormancy could be explained by Parrondo’s theory. We also discuss the relevance of Parrondo’s paradox in a therapeutical framework using different examples. This work provides a compelling argument that the traditional separation between medicine and other disciplines remains a fundamental limitation that needs to be overcome if complex processes, such as oncogenesis, are to be completely understood.

Abstract

Many aspects of cancer biology remain puzzling, including the proliferative and survival success of malignant cells in spite of their high genetic and epigenetic instability as well as their ability to express migrating phenotypes and/or enter dormancy despite possible fitness loss. Understanding the potential adaptive value of these phenotypic traits is confounded by the fact that, when considered separately, they seem to be rather detrimental at the cell level, at least in the short term. Here, we argue that cancer’s biology and success could frequently be governed by processes underlying Parrondo’s paradox, whereby combinations of intrinsically losing strategies may result in winning outcomes. Oncogenic selection would favor Parrondo’s dynamics because, given the environmental adversity in which malignant cells emerge and evolve, alternating between various less optimal strategies would represent the sole viable option to counteract the changing and deleterious environments cells are exposed to during tumorigenesis. We suggest that malignant processes could be viewed through this lens, and we discuss how Parrondo’s principles are also important when designing therapies against cancer.

Long-term iron deprivation and subsequent recovery uncover heterogeneity in the response of cyanobacterial populations

Cyanobacteria are globally important primary producers and nitrogen fixers. They are frequently limited by iron bioavailability in natural environments that often fluctuate due to rapid consumption and irregular influx of external Fe. Here we identify a succession of physiological changes in Synechocystis sp. PCC 6803 occurring over 14-16 days of iron deprivation and subsequent recovery. We observe several adaptive strategies that allow cells to push their metabolic limits under the restriction of declining intracellular Fe quotas. Interestingly, cyanobacterial populations exposed to prolonged iron deprivation showed discernible heterogeneity in cellular auto-fluorescence during the recovery process. Using FACS and microscopy techniques we revealed that only cells with high auto-fluorescence were able to grow and reconstitute thylakoid membranes. We propose that ROS-mediated damage is likely to be associated with the emergence of the two subpopulations, and, indeed, a rapid increase in intracellular ROS content was observed during the first hours following iron addition to Fe-starved cultures. These results suggest that an increasing iron supply is a double-edged sword - posing both an opportunity and a risk. Therefore, phenotypic heterogeneity within populations is crucial for the survival and proliferation of organisms facing iron fluctuations within natural environments.

Persistence as an Optimal Hedging Strategy

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new, to our knowledge, theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation and design. Overall, we provide a new, to our knowledge, way of conceptualizing and modeling cellular decision making in volatile environments by explicitly unifying theory from mathematical biology and finance.

Drivers and sites of diversity in the DNA adenine methylomes of 93 Mycobacterium tuberculosis complex clinical isolates

This study assembles DNA adenine methylomes for 93 Mycobacterium tuberculosis complex (MTBC) isolates from seven lineages paired with fully-annotated, finished, de novo assembled genomes. Integrative analysis yielded four key results. First, methyltransferase allele-methylome mapping corrected methyltransferase variant effects previously obscured by reference-based variant calling. Second, heterogeneity analysis of partially active methyltransferase alleles revealed that intracellular stochastic methylation generates a mosaic of methylomes within isogenic cultures, which we formalize as ‘intercellular mosaic methylation’ (IMM). Mutation-driven IMM was nearly ubiquitous in the globally prominent Beijing sublineage. Third, promoter methylation is widespread and associated with differential expression in the ΔhsdM transcriptome, suggesting promoter HsdM-methylation directly influences transcription. Finally, comparative and functional analyses identified 351 sites hypervariable across isolates and numerous putative regulatory interactions. This multi-omic integration revealed features of methylomic variability in clinical isolates and provides a rational basis for hypothesizing the functions of DNA adenine methylation in MTBC physiology and adaptive evolution.

From Microbial Communities to Distributed Computing Systems

A distributed biological system can be defined as a system whose components are located in different subpopulations, which communicate and coordinate their actions through interpopulation messages and interactions. We see that distributed systems are pervasive in nature, performing computation across all scales, from microbial communities to a flock of birds. We often observe that information processing within communities exhibits a complexity far greater than any single organism. Synthetic biology is an area of research which aims to design and build synthetic biological machines from biological parts to perform a defined function, in a manner similar to the engineering disciplines. However, the field has reached a bottleneck in the complexity of the genetic networks that we can implement using monocultures, facing constraints from metabolic burden and genetic interference. This makes building distributed biological systems an attractive prospect for synthetic biology that would alleviate these constraints and allow us to expand the applications of our systems into areas including complex biosensing and diagnostic tools, bioprocess control and the monitoring of industrial processes. In this review we will discuss the fundamental limitations we face when engineering functionality with a monoculture, and the key areas where distributed systems can provide an advantage. We cite evidence from natural systems that support arguments in favor of distributed systems to overcome the limitations of monocultures. Following this we conduct a comprehensive overview of the synthetic communities that have been built to date, and the components that have been used. The potential computational capabilities of communities are discussed, along with some of the applications that these will be useful for. We discuss some of the challenges with building co-cultures, including the problem of competitive exclusion and maintenance of desired community composition. Finally, we assess computational frameworks currently available to aide in the design of microbial communities and identify areas where we lack the necessary tools.

Parrondo paradoxical walk using four-sided quantum coins

Two losing games can be played in a certain manner to produce a winning outcome-a phenomenon known as Parrondo's paradox. Of particular interest is the emergence of quantum game theory and the attempt to model known Parrondo's games through quantum computation notation. In this article, we investigate whether flipping four-sided quantum coins will result in the emergence of Parrondo's paradox. We discover that by playing two losing games A and B in a sequential order, a winning scenario can be derived. Furthermore, four-sided quantum coin is the first instance where the ratcheting effect from the classical Parrondo's game is necessary. Crucially, our study is designed with quantum protocols as its basis and does not have a direct classical counterpart.

Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon

Models of adaptive bet-hedging commonly adopt insights from Kelly’s famous work on optimal gambling strategies and the financial value of information. In particular, such models seek evolutionary solutions that maximize long-term average growth rate of lineages, even in the face of highly stochastic growth trajectories. Here, we argue for extensive departures from the standard approach to better account for evolutionary contingencies. Crucially, we incorporate considerations of volatility minimization, motivated by interim extinction risk in finite populations, within a finite time horizon approach to growth maximization. We find that a game-theoretic competitive optimality approach best captures these additional constraints and derive the equilibria solutions under straightforward fitness payoff functions and extinction risks. We show that for both maximal growth and minimal time relative payoffs, the log-optimal strategy is a unique pure strategy symmetric equilibrium, invariant with evolutionary time horizon and robust to low extinction risks.

Perturbation-Driven Entropy as a Source of Cancer Cell Heterogeneity

Intratumor heterogeneity is a key hallmark of cancer that contributes to progression and therapeutic resistance. Phenotypic heterogeneity is in part caused by Darwinian selection of subclones that arise by random (epi)genetic aberrations. In addition, cancer cells are endowed with increased cellular plasticity compared with their normal counterparts, further adding to their heterogeneous behavior. However, the molecular mechanisms underpinning cancer cell plasticity are incompletely understood. Here, I outline the hypothesis that cancer-associated perturbations collectively disrupt normal gene regulatory networks (GRNs) by increasing their entropy. Importantly, in this model both somatic driver and passenger alterations contribute to 'perturbation-driven entropy', thereby increasing phenotypic heterogeneity and evolvability. This additional layer of heterogeneity may contribute to our understanding of cancer evolution and therapeutic resistance.

Paradoxical Survival: Examining the Parrondo Effect across Biology

Parrondo's paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; a plethora of exciting applications has also been found in biology at an astounding pace. In this review paper, the authors examine a large range of recent developments of Parrondo's paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. Intriguing connections between numerous works are identified and analyzed, culminating in an emergent pattern of nested recurrent mechanics that appear to span the entire biological gamut, from the smallest of spatial and temporal scales to the largest-from the subcellular to the complete biosphere. In analyzing the macro perspective, the pivotal role that the paradox plays in the shaping of biological life becomes apparent, and its identity as a potential universal principle underlying biological diversity and persistence is uncovered. Directions for future research are also discussed in light of this new perspective.

Model genotype-phenotype mappings and the algorithmic structure of evolution

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Evolutionary regain of lost gene circuit function

Natural or synthetic genetic modules can lose their function over long-term evolution if the function is costly. How populations can evolve to restore such broken function is poorly understood. To test the reversibility of evolutionary breakdown, we use yeast cell populations with a chromosomally integrated synthetic gene circuit. In previous evolution experiments the gene circuit lost its costly function through various mutations. By exposing such mutant populations to conditions where regaining gene circuit function would be beneficial, we find adaptation scenarios with or without repairing lost gene circuit function. These results are important for drug resistance or future synthetic biology applications where evolutionary loss and regain of function play a significant role.

Evolutionary reversibility—the ability to regain a lost function—is an important problem both in evolutionary and synthetic biology, where repairing natural or synthetic systems broken by evolutionary processes may be valuable. Here, we use a synthetic positive-feedback (PF) gene circuit integrated into haploid Saccharomyces cerevisiae cells to test if the population can restore lost PF function. In previous evolution experiments, mutations in a gene eliminated the fitness costs of PF activation. Since PF activation also provides drug resistance, exposing such compromised or broken mutants to both drug and inducer should create selection pressure to regain drug resistance and possibly PF function. Indeed, evolving 7 PF mutant strains in the presence of drug revealed 3 adaptation scenarios through genomic, PF-external mutations that elevate PF basal expression, possibly by affecting transcription, translation, degradation, and other fundamental cellular processes. Nonfunctional mutants gained drug resistance without ever developing high expression, while quasifunctional and dysfunctional PF mutants developed high expression nongenetically, which then diminished, although more slowly for dysfunctional mutants where revertant clones arose. These results highlight how intracellular context, such as the growth rate, can affect regulatory network dynamics and evolutionary dynamics, which has important consequences for understanding the evolution of drug resistance and developing future synthetic biology applications.

Epigenetic switching as a strategy for quick adaptation while attenuating biochemical noise

Epigenetic switches are bistable, molecular systems built from self-reinforcing feedback loops that can spontaneously switch between heritable phenotypes in the absence of DNA mutation. It has been hypothesized that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation, but the evolutionary trajectories and conditions by which an epigenetic switch can outcompete adaptation through genetic mutation remain unknown. Here, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically through mutation and exhibit epigenetic switching. We evolved these genetic circuits under a fluctuating environment that alternatively selected for low and high protein expression levels. In all tested conditions, the population first evolved by genetic mutation towards a region of genotypes where genetic adaptation can occur faster after each environmental transition. Once in this region, the self-activating genetic circuit can exhibit epigenetic switching, which starts competing with genetic adaptation. We show a trade-off between either minimizing the adaptation time or increasing the robustness of the phenotype to biochemical noise. Epigenetic switching was superior in a fast fluctuating environment because it adapted faster than genetic mutation after an environmental transition, while still attenuating the effect of biochemical noise on the phenotype. Conversely, genetic adaptation was favored in a slowly fluctuating environment because it maximized the phenotypic robustness to biochemical noise during the constant environment between transitions, even if this resulted in slower adaptation. This simple trade-off predicts the conditions and trajectories under which an epigenetic switch evolved to outcompete genetic adaptation, shedding light on possible mechanisms by which bet-hedging strategies might emerge and persist in natural populations.

Epigenetic switches regulate cell fate decisions during development in multicellular organisms, but their origin predates multicellularity because they are found in viruses, bacteria, and unicellular eukaryotes. It has been suggested that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation to fluctuating environments. To discern the evolutionary pressures that select for epigenetic switches, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically and exhibit epigenetic switching. Unlike laboratory evolution experiments, this in silico experiment was run many times over a range of evolutionary parameters (population size, selection pressure, mutation step-size, fluctuation frequency) and different model assumptions to uncover statistical regularities in the evolutionary trajectories. Using this computational approach, we could elucidate simple principles that predict the conditions that favor adaptation by epigenetic switching over genetic mutation in a fluctuating environment.

(In)exhaustible Suppliers for Evolution? Epistatic Selection Tunes the Adaptive Potential of Nongenetic Inheritance

Nongenetic inheritance media-from methyl-accepting cytosines to culture-tend to mutate more frequently than DNA sequences. Whether this makes them inexhaustible suppliers for adaptive evolution will depend on the effect of nongenetic mutations (hereafter, epimutations) on fitness-related traits. Here we investigate how these effects might themselves evolve, specifically whether natural selection may set boundaries to the adaptive potential of nongenetic inheritance media because of their higher mutability. In our model, the genetic and epigenetic contributions to a nonneutral phenotype are controlled by an epistatic modifier locus, which evolves under the combined effects of drift and selection. We show that a pure genetic control evolves when the environment is stable-provided that the population is large-such that the phenotype becomes robust to frequent epimutations. When the environment fluctuates, however, selection on the modifier locus also fluctuates and can overall produce a large nongenetic contribution to the phenotype, especially when the epimutation rate matches the rate of environmental variation. We further show that selection on the modifier locus is generally insensitive to recombination, meaning it is mostly direct, that is, not relying on subsequent effects in future generations. These results suggest that unstable inheritance media might significantly contribute to fitness variation of traits subject to highly variable selective pressures but little to traits responding to scarcely variable aspects of the environment. More generally, our study demonstrates that the rate of mutation and the adaptive potential of any inheritance media should not be seen as independent properties.

Metabolic constraints drive self-organization of specialized cell groups

How phenotypically distinct states in isogenic cell populations appear and stably co-exist remains unresolved. We find that within a mature, clonal yeast colony developing in low glucose, cells arrange into metabolically disparate cell groups. Using this system, we model and experimentally identify metabolic constraints sufficient to drive such self-assembly. Beginning in a uniformly gluconeogenic state, cells exhibiting a contrary, high pentose phosphate pathway activity state, spontaneously appear and proliferate, in a spatially constrained manner. Gluconeogenic cells in the colony produce and provide a resource, which we identify as trehalose. Above threshold concentrations of external trehalose, cells switch to the new metabolic state and proliferate. A self-organized system establishes, where cells in this new state are sustained by trehalose consumption, which thereby restrains other cells in the trehalose producing, gluconeogenic state. Our work suggests simple physico-chemical principles that determine how isogenic cells spontaneously self-organize into structured assemblies in complimentary, specialized states.

Bet-hedging strategies in expanding populations

In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic diversity observed even in clonal populations. Bet-hedging in well-mixed populations is rather well understood. However, many species underwent range expansions during their evolutionary history, and the importance of phenotypic diversity in such scenarios still needs to be understood. In this paper, we develop a theory of bet-hedging for populations colonizing new, unknown environments that fluctuate either in space or time. In this case, we find that bet-hedging is a more favorable strategy than in well-mixed populations. For slow rates of variation, temporal and spatial fluctuations lead to different outcomes. In spatially fluctuating environments, bet-hedging is favored compared to temporally fluctuating environments. In the limit of frequent environmental variation, no opportunity for bet-hedging exists, regardless of the nature of the environmental fluctuations. For the same model, bet-hedging is never an advantageous strategy in the well-mixed case, supporting the view that range expansions strongly promote diversification. These conclusions are robust against stochasticity induced by finite population sizes. Our findings shed light on the importance of phenotypic heterogeneity in range expansions, paving the way to novel approaches to understand how biodiversity emerges and is maintained.

Ecological populations are often exposed to unpredictable and variable environmental conditions. A number of strategies have evolved to cope with such uncertainty. One of them is stochastic phenotypic switching, by which some individuals in the community are enabled to tackle adverse conditions, even at the price of reducing overall growth in the short term. In this paper, we study the effectiveness of these “bet-hedging” strategies for a population in the process of colonizing new territory. We show that bet-hedging is more advantageous when the environment varies spatially rather than temporally, and infrequently rather than frequently.

Unpredictable homeodynamic and ambient constraints on irrational decision making of aneural and neural foragers

Foraging for nutritional sustenance represents common significant learned/heritable survival strategies evolved for phylum-diverse cellular life on Earth. Unicellular aneural to multicellular neural foragers display conserved rational or irrational decision making depending on outcome predictions for noise-susceptible real/illusory homeodynamic and ambient dietary cues. Such context-dependent heuristic-guided foraging enables optimal, suboptimal, or fallacious decisions that drive organismal adaptation, health, longevity, and life history.

Shortsighted Evolution Constrains the Efficacy of Long-Term Bet Hedging

To survive unpredictable environmental change, many organisms adopt bet-hedging strategies that are initially costly but provide a long-term fitness benefit. The temporal extent of these deferred fitness benefits determines whether bet-hedging organisms can survive long enough to realize them. In this article, we examine a model of microbial bet hedging in which there are two paths to extinction: unpredictable environmental change and demographic stochasticity. In temporally correlated environments, these drivers of extinction select for different switching strategies. Rapid phenotype switching ensures survival in the face of unpredictable environmental change, while slower-switching organisms become extinct. However, when both switching strategies are present in the same population, then demographic stochasticity-enforced by a limited population size-leads to extinction of the faster-switching organism. As a result, we find a novel form of evolutionary suicide whereby selection in a fluctuating environment can favor bet-hedging strategies that ultimately increase the risk of extinction. Population structures with multiple subpopulations and dispersal can reduce the risk of extinction from unpredictable environmental change and shift the balance so as to facilitate the evolution of slower-switching organisms.

Phenotype affinity mediated interactions can facilitate the evolution of cooperation

We study the coevolutionary dynamics of the diversity of phenotype and the evolution of cooperation in the Prisoner's Dilemma. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with phenotypes. Individuals each carry a set of potentially expressible traits and expresses a number of such traits at a cost proportional to the number. The set of traits expressed constitutes phenotype. Phenotypes and thus the rate of interaction are evolvable over time. Our results show that nonnegligible cost of expressing traits restrains phenotype diversity, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few traits. It pays for cooperative strains to express a very few traits. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates the rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype can mutually reinforce each other. Our results may help better understand the coevolution of cooperation and the diversity of phenotype.

Evolutionary highways to persistent bacterial infection

Persistent infections require bacteria to evolve from their naïve colonization state by optimizing fitness in the host via simultaneous adaptation of multiple traits, which can obscure evolutionary trends and complicate infection management. Accordingly, here we screen 8 infection-relevant phenotypes of 443 longitudinal Pseudomonas aeruginosa isolates from 39 young cystic fibrosis patients over 10 years. Using statistical modeling, we map evolutionary trajectories and identify trait correlations accounting for patient-specific influences. By integrating previous genetic analyses of 474 isolates, we provide a window into early adaptation to the host, finding: (1) a 2–3 year timeline of rapid adaptation after colonization, (2) variant “naïve” and “adapted” states reflecting discordance between phenotypic and genetic adaptation, (3) adaptive trajectories leading to persistent infection via three distinct evolutionary modes, and (4) new associations between phenotypes and pathoadaptive mutations. Ultimately, we effectively deconvolute complex trait adaptation, offering a framework for evolutionary studies and precision medicine in clinical microbiology.

The pathogen Pseudomonas aeruginosa undergoes complex trait adaptation within cystic fibrosis patients. Here, Bartell, Sommer, and colleagues use statistical modeling of longitudinal isolates to characterize the joint genetic and phenotypic evolutionary trajectories of P. aeruginosa within hosts.

Bacterial growth: a statistical physicist's guide

Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background, discusses recent applications of statistical physics in this field, and highlights the potential for future research.

Bacterial spores, from ecology to biotechnology

The production of a highly specialized cell structure called a spore is a remarkable example of a survival strategy displayed by bacteria in response to challenging environmental conditions. The detailed analysis and description of the process of sporulation in selected model organisms have generated a solid background to understand the cellular processes leading to the formation of this specialized cell. However, much less is known regarding the ecology of spore-formers. This research gap needs to be filled as the feature of resistance has important implications not only on the survival of spore-formers and their ecology, but also on the use of spores for environmental prospection and biotechnological applications.

Solution of the Crow-Kimura model with changing population size and Allee effect

The Crow-Kimura model is commonly used in the modeling of genetic evolution in the presence of mutations and associated selection pressures. We consider a modified version of the Crow-Kimura model, in which population sizes are not fixed and Allee saturation effects are present. We demonstrate the evolutionary dynamics in this system through an analytical approach, examining both symmetric and single-peak fitness landscape cases. Especially interesting are the dynamics of the populations near extinction. A special version of the model with saturation and degradation on the single-peak fitness landscape is investigated as a candidate of the Allee effect in evolution, revealing reduction tendencies of excessively large populations, and extinction tendencies for small populations. The analytical solutions for these dynamics are presented with accuracy O(1/N), where N is the number of nucleotides in the genome.

Formation of phenotypic lineages in Salmonella enterica by a pleiotropic fimbrial switch

The std locus of Salmonella enterica, an operon acquired by horizontal transfer, encodes fimbriae that permit adhesion to epithelial cells in the large intestine. Expression of the std operon is bistable, yielding a major subpopulation of Std^OFF cells (99.7%) and a minor subpopulation of Std^ON cells (0.3%). In addition to fimbrial proteins, the std operon encodes two proteins, StdE and StdF, that have DNA binding capacity and control transcription of loci involved in flagellar synthesis, chemotaxis, virulence, conjugal transfer, biofilm formation, and other cellular functions. As a consequence of StdEF pleiotropic transcriptional control, Std^ON and Std^OFF subpopulations may differ not only in the presence or absence of Std fimbriae but also in additional phenotypic traits. Separation of Std^OFF and Std^ON lineages by cell sorting confirms the occurrence of lineage-specific features. Formation of Std^OFF and Std^ON lineages may thus be viewed as a rudimentary bacterial differentiation program.

We show that the std fimbrial operon of Salmonella enterica undergoes bistable expression, a trait far from exceptional among loci that encode components of the bacterial envelope. However, an unsuspected trait of the std operon is the presence of two genes that encode pleiotropic regulators of gene expression. Indeed, StdE and StdF are DNA-binding proteins that control transcription of hundreds of genes. As a consequence, StdEF govern multiple phenotypic traits, and the fimbriated and non-fimbriated Salmonella lineages may differ in motility, virulence, conjugal transfer, biofilm formation, and potentially in other phenotypic features. We hypothesize that pleiotropic control of gene expression by StdEF may contribute to adapt the non-fimbriated lineage to acute infection and the fimbriated lineage to chronic infection.

Evolution of joint cooperation under phenotypic variations

Effects of phenotypic variation on the species-environment systems and the evolution of cooperation under prescribed phenotypic diversity have been well addressed respectively. Interspecies interactions in the context of evolvable phenotypic diversity remain largely unconsidered. We address the evolutionary dynamics by considering evolvable phenotypic variations under group interactions. Each individual carries a capacitor of phenotypes and pays a cost proportional to its volume. A random phenotype from the capacitor is expressed and the population is thus divided into subpopulations. Group interactions happen in each of these subpopulations, respectively. Competition is global. Results show that phenotypic diversity coevolves with cooperation under a wide range of conditions and that tradeoff between expanding capacitor and rising cost leads to an optimal level of phenotypic diversity best promoting cooperation. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other.

Bistability and phase variation in Salmonella enterica

Cell-to-cell differences in bacterial gene expression can merely reflect the occurrence of noise. In certain cases, however, heterogeneous gene expression is a programmed event that results in bistable expression. If bistability is heritable, bacterial lineages are formed. When programmed bistability is reversible, the phenomenon is known as phase variation. In certain cases, bistability is controlled by genetic mechanisms (e. g., DNA rearrangement). In other cases, bistability has epigenetic origin. A robust epigenetic mechanism for the formation of bacterial lineages is the formation of heritable DNA methylation patterns. However, bistability can also arise upon propagation of gene expression patterns by feedback loops that are stable upon cell division. This review describes examples of bistability and phase variation in Salmonella enterica and discusses their adaptive value, sometimes in a speculative manner.

The emergence of metabolic heterogeneity and diverse growth responses in isogenic bacterial cells

Microorganisms adapt to frequent environmental changes through population diversification. Previous studies demonstrated phenotypic diversity in a clonal population and its important effects on microbial ecology. However, the dynamic changes of phenotypic composition have rarely been characterized. Also, cellular variations and environmental factors responsible for phenotypic diversity remain poorly understood. Here, we studied phenotypic diversity driven by metabolic heterogeneity. We characterized metabolic activities and growth kinetics of starved Escherichia coli cells subject to nutrient upshift at single-cell resolution. We observed three subpopulations with distinct metabolic activities and growth phenotypes. One subpopulation was metabolically active and immediately grew upon nutrient upshift. One subpopulation was metabolically inactive and non-viable. The other subpopulation was metabolically partially active, and did not grow upon nutrient upshift. The ratio of these subpopulations changed dynamically during starvation. A long-term observation of cells with partial metabolic activities indicated that their metabolism was later spontaneously restored, leading to growth recovery. Further investigations showed that oxidative stress can induce the emergence of a subpopulation with partial metabolic activities. Our findings reveal the emergence of metabolic heterogeneity and associated dynamic changes in phenotypic composition. In addition, the results shed new light on microbial dormancy, which has important implications in microbial ecology and biomedicine.

Genetic Competence Drives Genome Diversity in Bacillus subtilis

Prokaryote genomes are the result of a dynamic flux of genes, with increases achieved via horizontal gene transfer and reductions occurring through gene loss. The ecological and selective forces that drive this genomic flexibility vary across species. Bacillus subtilis is a naturally competent bacterium that occupies various environments, including plant-associated, soil, and marine niches, and the gut of both invertebrates and vertebrates. Here, we quantify the genomic diversity of B. subtilis and infer the genome dynamics that explain the high genetic and phenotypic diversity observed. Phylogenomic and comparative genomic analyses of 42 B. subtilis genomes uncover a remarkable genome diversity that translates into a core genome of 1,659 genes and an asymptotic pangenome growth rate of 57 new genes per new genome added. This diversity is due to a large proportion of low-frequency genes that are acquired from closely related species. We find no gene-loss bias among wild isolates, which explains why the cloud genome, 43% of the species pangenome, represents only a small proportion of each genome. We show that B. subtilis can acquire xenologous copies of core genes that propagate laterally among strains within a niche. While not excluding the contributions of other mechanisms, our results strongly suggest a process of gene acquisition that is largely driven by competence, where the long-term maintenance of acquired genes depends on local and global fitness effects. This competence-driven genomic diversity provides B. subtilis with its generalist character, enabling it to occupy a wide range of ecological niches and cycle through them.

Molecular and cellular bases of adaptation to a changing environment in microorganisms

Environmental heterogeneity constitutes an evolutionary challenge for organisms. While evolutionary dynamics under variable conditions has been explored for decades, we still know relatively little about the cellular and molecular mechanisms involved. It is of paramount importance to examine these molecular bases because they may play an important role in shaping the course of evolution. In this review, we examine the diversity of adaptive mechanisms in the face of environmental changes. We exploit the recent literature on microbial systems because those have benefited the most from the recent emergence of genetic engineering and experimental evolution followed by genome sequencing. We identify four emerging trends: (i) an adaptive molecular change in a pathway often results in fitness trade-off in alternative environments but the effects are dependent on a mutation's genetic background; (ii) adaptive changes often modify transcriptional and signalling pathways; (iii) several adaptive changes may occur within the same molecular pathway but be associated with pleiotropy of different signs across environments; (iv) because of their large associated costs, macromolecular changes such as gene amplification and aneuploidy may be a rapid mechanism of adaptation in the short-term only. The course of adaptation in a variable environment, therefore, depends on the complexity of the environment but also on the molecular relationships among the genes involved and between the genes and the phenotypes under selection.

Allison mixture and the two-envelope problem

In the present study, we have investigated the Allison mixture, a variant of the Parrondo's games where random mixing of two random sequences creates autocorrelation. We have obtained the autocorrelation function and mutual entropy of two elements. Our analysis shows that the mutual information is nonzero even if two distributions have identical average values. We have also considered the two-envelope problem and solved for its exact probability distribution.

An efficient and assumption-free method to approximate protein level distribution in the two-states gene expression model

Stochastic fluctuations at each step of gene expression might influence protein levels distributions across cell populations. However, current methods to model protein distribution of intrinsic gene expression dynamics are either computationally inefficient or rely on ad hoc assumptions, e.g., that the gene is always active. Taking advantage of the simple form of lower-order moments of distribution, we developed an efficient and assumption-free protein distribution approximation method (EFPD), for the two state gene expression model to accurately approximate the distribution. By EFPD, we computed nearly identical intensity of gene expression regulation at mRNA and protein level, implying a profound link between transcription and translation. Finally, by extending EFPD to approximate the distribution of protein level at any arbitrary temporal state, we proposed an explanation for the role of stochastic noise in gene expression in the context of a continuously changing environment. EFPD can be a powerful tool for modeling the particular molecular mechanisms of targeted gene expression pattern.

The impact of bottlenecks on microbial survival, adaptation, and phenotypic switching in host-pathogen interactions

Microbial pathogens and viruses can often maintain sufficient population diversity to evade a wide range of host immune responses. However, when populations experience bottlenecks, as occurs frequently during initiation of new infections, pathogens require specialized mechanisms to regenerate diversity. We address the evolution of such mechanisms, known as stochastic phenotype switches, which are prevalent in pathogenic bacteria. We analyze a model of pathogen diversification in a changing host environment that accounts for selective bottlenecks, wherein different phenotypes have distinct transmission probabilities between hosts. We show that under stringent bottlenecks, such that only one phenotype can initiate new infections, there exists a threshold stochastic switching rate below which all pathogen lineages go extinct, and above which survival is a near certainty. We determine how quickly stochastic switching rates can evolve by computing a fitness landscape for the evolutionary dynamics of switching rates, and analyzing its dependence on both the stringency of bottlenecks and the duration of within-host growth periods. We show that increasing the stringency of bottlenecks or decreasing the period of growth results in faster adaptation of switching rates. Our model provides strong theoretical evidence that bottlenecks play a critical role in accelerating the evolutionary dynamics of pathogens.

A kinetic model of multiple phenotypic states for breast cancer cells

Quantitative modeling of microscopic genes regulatory mechanisms in an individual cell is a crucial step towards understanding various macroscopic physiological phenomena of cell populations. Based on the regulatory mechanisms of genes zeb1 and cdh1 in the growth and development of breast cancer cells, we propose a kinetic model at the level of single cell. By constructing the effective landscape of underlying stationary probability for the genes expressions, it is found that (i) each breast cancer cell has three phenotypic states (i.e., the stem-like, basal, and luminal states) which correspond to three attractions of the probability landscape. (ii) The interconversions between phenotypic states can be induced by the noise intensity and the property of phenotypic switching is quantified by the mean first-passage time. (iii) Under certain conditions, the probabilities of each cancer cell appearing in the three states are consistent with the macroscopic phenotypic equilibrium proportions in the breast cancer SUM159 cell line. (iv) Our kinetic model involving the TGF-β signal can also qualitatively explain several macroscopic physiological phenomena of breast cancer cells, such as the "TGF-β paradox" in tumor therapy, the five clinical subtypes of breast cancer cells, and the effects of transient TGF-β on breast cancer metastasis.

Noise in a phosphorelay drives stochastic entry into sporulation in Bacillus subtilis

Entry into sporulation in Bacillus subtilis is governed by a phosphorelay in which phosphoryl groups from a histidine kinase are successively transferred via relay proteins to the response regulator Spo0A. Spo0A~P, in turn, sets in motion events that lead to asymmetric division and activation of the cell-specific transcription factor σ^F, a hallmark for entry into sporulation. Here, we have used a microfluidics-based platform to investigate the activation of Spo0A and σ^F in individual cells held under constant, sporulation-inducing conditions. The principal conclusions were that: (i) activation of σ^F occurs with an approximately constant probability after adaptation to conditions of nutrient limitation; (ii) activation of σ^F is tightly correlated with, and preceded by, Spo0A~P reaching a high threshold level; (iii) activation of Spo0A takes place abruptly just prior to asymmetric division; and (iv) the primary source of noise in the activation of Spo0A is the phosphorelay. We propose that cells exhibit a constant probability of attaining a high threshold level of Spo0A~P due to fluctuations in the flux of phosphoryl groups through the phosphorelay.

Review of stochastic hybrid systems with applications in biological systems modeling and analysis

Stochastic hybrid systems (SHS) have attracted a lot of research interests in recent years. In this paper, we review some of the recent applications of SHS to biological systems modeling and analysis. Due to the nature of molecular interactions, many biological processes can be conveniently described as a mixture of continuous and discrete phenomena employing SHS models. With the advancement of SHS theory, it is expected that insights can be obtained about biological processes such as drug effects on gene regulation. Furthermore, combining with advanced experimental methods, in silico simulations using SHS modeling techniques can be carried out for massive and rapid verification or falsification of biological hypotheses. The hope is to substitute costly and time-consuming in vitro or in vivo experiments or provide guidance for those experiments and generate better hypotheses.

Phenotypic Diversity Using Bimodal and Unimodal Expression of Stress Response Proteins

Populations of cells need to express proteins to survive the sudden appearance of stressors. However, these mechanisms may be taxing. Populations can introduce diversity, allowing individual cells to stochastically switch between fast-growing and stress-tolerant states. One way to achieve this is to use genetic networks coupled with noise to generate bimodal distributions with two distinct subpopulations, each adapted to a stress condition. Another survival strategy is to rely on random fluctuations in gene expression to produce continuous, unimodal distributions of the stress response protein. To quantify the environmental conditions where bimodal versus unimodal expression is beneficial, we used a differential evolution algorithm to evolve optimal distributions of stress response proteins given environments with sudden fluctuations between low and high stress. We found that bimodality evolved for a large range of environmental conditions. However, we asked whether these findings were an artifact of considering two well-defined stress environments (low and high stress). As noise in the environment increases, or when there is an intermediate environment (medium stress), the benefits of bimodality decrease. Our results indicate that under realistic conditions, a continuum of resistance phenotypes generated through a unimodal distribution is sufficient to ensure survival without a high cost to the population.

Asymmetric cellular memory in bacteria exposed to antibiotics

Background

The ability to form a cellular memory and use it for cellular decision-making could help bacteria to cope with recurrent stress conditions. We analyzed whether bacteria would form a cellular memory specifically if past events are predictive of future conditions. We worked with the asymmetrically dividing bacterium Caulobacter crescentus where past events are expected to only be informative for one of the two cells emerging from division, the sessile cell that remains in the same microenvironment and does not migrate.

Results

Time-resolved analysis of individual cells revealed that past exposure to low levels of antibiotics increases tolerance to future exposure for the sessile but not for the motile cell. Using computer simulations, we found that such an asymmetry in cellular memory could be an evolutionary response to situations where the two cells emerging from division will experience different future conditions.

Conclusions

Our results raise the question whether bacteria can evolve the ability to form and use cellular memory conditionally in situations where it is beneficial.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-017-0884-4) contains supplementary material, which is available to authorized users.

Coevolutionary dynamics of phenotypic diversity and contingent cooperation

Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.

Phenotypic variation is commonly observed from human cells to the intestinal pathogen Salmonella enterica serovar Typhimurium to the wrinkly-spreader morphs. Such phenotypic diversity proves effective in promoting cooperation, or confers survival advantage against unfavorable environmental changes. Prior studies show that interactions based on phenotypic similarity can promote cooperation. Yet in these models, the level of phenotypic diversity is prescribed such that individuals each possess the same number of available phenotypes, and thereby no evolution of phenotypic diversity per se. We here take into consideration important aspects of the diversity of phenotype and contingent cooperation and show that phenotypic diversity coevolves with cooperation under a variety of conditions. Our work provides a potential mechanism for the evolution of cooperation, and individuals, especially cooperators, endowed with diverse phenotypes constitute the backbone in inducing the coevolution.

Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction

Organisms often exhibit behavioral or phenotypic diversity to improve population fitness in the face of environmental variability. When each behavior or phenotype is individually maladaptive, alternating between these losing strategies can counter-intuitively result in population persistence-an outcome similar to the Parrondo's paradox. Instead of the capital or history dependence that characterize traditional Parrondo games, most ecological models which exhibit such paradoxical behavior depend on the presence of exogenous environmental variation. Here we present a population model that exhibits Parrondo's paradox through capital and history-dependent dynamics. Two sub-populations comprise our model: nomads, who live independently without competition or cooperation, and colonists, who engage in competition, cooperation, and long-term habitat destruction. Nomads and colonists may alternate behaviors in response to changes in the colonial habitat. Even when nomadism and colonialism individually lead to extinction, switching between these strategies at the appropriate moments can paradoxically enable both population persistence and long-term growth.

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Nongenetic variation in phenotypes, or bet-hedging, has been observed as a driver of drug resistance in both bacterial infections and cancers. Here, we study how bet-hedging emerges in genotype-phenotype (GP) mapping through a simple interaction model: a molecular switch. We use simple chemical reaction networks to implement stochastic switches that map gene products to phenotypes, and investigate the impact of structurally distinct mappings on the evolution of phenotypic heterogeneity. Bet-hedging naturally emerges within this model, and is robust to evolutionary loss through mutations to both the expression of individual genes, and to the network itself. This robustness explains an apparent paradox of bet-hedging-why does it persist in environments where natural selection necessarily acts to remove it? The structure of the underlying molecular mechanism, itself subject to selection, can slow the evolutionary loss of bet-hedging to ensure a survival mechanism against environmental catastrophes even when they are rare. Critically, these properties, taken together, have profound implications for the use of treatment-holidays to combat bet-hedging-driven resistant disease, as the efficacy of breaks from treatment will ultimately be determined by the structure of the GP mapping.