Population genetics of non-genetic traits: Evolutionary roles of stochasticity in gene expression

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

"Bet hedging" against climate change in developing and adult animals: roles for stochastic gene expression, phenotypic plasticity, epigenetic inheritance and adaptation

Animals from embryos to adults experiencing stress from climate change have numerous mechanisms available for enhancing their long-term survival. In this review we consider these options, and how viable they are in a world increasingly experiencing extreme weather associated with climate change. A deeply understood mechanism involves natural selection, leading to evolution of new adaptations that help cope with extreme and stochastic weather events associated with climate change. While potentially effective at staving off environmental challenges, such adaptations typically occur very slowly and incrementally over evolutionary time. Consequently, adaptation through natural selection is in most instances regarded as too slow to aid survival in rapidly changing environments, especially when considering the stochastic nature of extreme weather events associated with climate change. Alternative mechanisms operating in a much shorter time frame than adaptation involve the rapid creation of alternate phenotypes within a life cycle or a few generations. Stochastic gene expression creates multiple phenotypes from the same genotype even in the absence of environmental cues. In contrast, other mechanisms for phenotype change that are externally driven by environmental clues include well-understood developmental phenotypic plasticity (variation, flexibility), which can enable rapid, within-generation changes. Increasingly appreciated are epigenetic influences during development leading to rapid phenotypic changes that can also immediately be very widespread throughout a population, rather than confined to a few individuals as in the case of favorable gene mutations. Such epigenetically-induced phenotypic plasticity can arise rapidly in response to stressors within a generation or across a few generations and just as rapidly be "sunsetted" when the stressor dissipates, providing some capability to withstand environmental stressors emerging from climate change. Importantly, survival mechanisms resulting from adaptations and developmental phenotypic plasticity are not necessarily mutually exclusive, allowing for classic "bet hedging". Thus, the appearance of multiple phenotypes within a single population provides for a phenotype potentially optimal for some future environment. This enhances survival during stochastic extreme weather events associated with climate change. Finally, we end with recommendations for future physiological experiments, recommending in particular that experiments investigating phenotypic flexibility adopt more realistic protocols that reflect the stochastic nature of weather.

Heterogeneity is not always a source of noise: Stochastic gene expression in regulatory heterozygote

Zygosity of diploid genome (i.e., degree to which two parental alleles of a gene have varied genetic sequences) adds another dimension to stochastic gene expression. The allelic imbalance in chromatin accessibility or divergence in regulatory sequences leads to fitness effects but the quantitative aspects thereof are largely left unexplored. We investigate diploid gene expression systems with homozygous (the same) and heterozygous (varied) combination of alleles in cis-regulatory sequences, not in structural gene loci, and characterize the zygosity-associated stochastic fluctuations in protein abundance. An emerging feat of heterozygosity is its counterintuitive capacity for genetic noise control. Especially when the noise is dominantly contributed to by the fluctuations in duty cycle ("reliability") rather than in process speed ("productivity") of gene expression machinery, its interallelic discrepancy acts to reduce the gene expression noise. These findings offer a novel insight into the rich repertoire of balancing selection enriched in the regulatory elements of immune response genes.

Gene expression noise can promote the fixation of beneficial mutations in fluctuating environments

Nongenetic phenotypic variation can either speed up or slow down adaptive evolution. We show that it can speed up evolution in environments where available carbon and energy sources change over time. To this end, we use an experimentally validated model of Escherichia coli growth on two alternative carbon sources, glucose and acetate. On the superior carbon source (glucose), all cells achieve high growth rates, while on the inferior carbon source (acetate) only a small fraction of the population manages to initiate growth. Consequently, populations experience a bottleneck when the environment changes from the superior to the inferior carbon source. Growth on the inferior carbon source depends on a circuit under the control of a transcription factor that is repressed in the presence of the superior carbon source. We show that noise in the expression of this transcription factor can increase the probability that cells start growing on the inferior carbon source. In doing so, it can decrease the severity of the bottleneck and increase mean population fitness whenever this fitness is low. A modest amount of noise can also enhance the fitness effects of a beneficial allele that increases the fraction of a population initiating growth on acetate. Additionally, noise can protect this allele from extinction, accelerate its spread, and increase its likelihood of going to fixation. Central to the adaptation-enhancing principle we identify is the ability of noise to mitigate population bottlenecks, particularly in environments that fluctuate periodically. Because such bottlenecks are frequent in fluctuating environments, and because periodically fluctuating environments themselves are common, this principle may apply to a broad range of environments and organisms.

Phenotypic noise and the cost of complexity

Experimental studies demonstrate the existence of phenotypic diversity despite constant genotype and environment. Theoretical models based on a single phenotypic character predict that during an adaptation event, phenotypic noise should be positively selected far from the fitness optimum because it increases the fitness of the genotype, and then be selected against when the population reaches the optimum. It is suggested that because of this fitness gain, phenotypic noise should promote adaptive evolution. However, it is unclear how the selective advantage of phenotypic noise is linked to the rate of evolution, and whether any advantage would hold for more realistic, multidimensional phenotypes. Indeed, complex organisms suffer a cost of complexity, where beneficial mutations become rarer as the number of phenotypic characters increases. Using a quantitative genetics approach, we first show that for a one-dimensional phenotype, phenotypic noise promotes adaptive evolution on plateaus of positive fitness, independently from the direct selective advantage on fitness. Second, we show that for multidimensional phenotypes, phenotypic noise evolves to a low-dimensional configuration, with elevated noise in the direction of the fitness optimum. Such a dimensionality reduction of the phenotypic noise promotes adaptive evolution and numerical simulations show that it reduces the cost of complexity.

Hormonal pleiotropy and the evolution of allocation trade-offs

Recent empirical evidence suggests that trade-off relationships can evolve, challenging the classical image of their high entrenchment. For energy reliant traits, this relationship should depend on the endocrine system that regulates resource allocation. Here, we model changes in this system by mutating the expression and conformation of its constitutive hormones and receptors. We show that the shape of trade-offs can indeed evolve in this model through the combined action of genetic drift and selection, such that their evolutionarily expected curvature and length depend on context. In particular, the shape of a trade-off should depend on the cost associated with resource storage, itself depending on the traded resource and on the ecological context. Despite this convergence at the phenotypic level, we show that a variety of physiological mechanisms may evolve in similar simulations, suggesting redundancy at the genetic level. This model should provide a useful framework to interpret and unify the overly complex observations of evolutionary endocrinology and evolutionary ecology.

Links between evolutionary processes and phenotypic robustness in microbes

The costs and benefits of random phenotypic heterogeneity in microbes have been vigorously debated and experimental tested for decades; yet, this conversation is largely independent from discussion of phenotypic robustness in other disciplines. In this review I connect microbial examples of stochasticity with studies on the ecological and population-genetic consequences of phenotypic variability. These topics illustrate the complexity of selection pressures on phenotypic robustness and provide inspiration that this complexity can be parsed with theoretical advances and the experimental power of microbial systems.

Computational Investigation of Environment-Noise Interaction in Single-Cell Organisms: The Merit of Expression Stochasticity Depends on the Quality of Environmental Fluctuations

Organisms need to adapt to changing environments and they do so by using a broad spectrum of strategies. These strategies include finding the right balance between expressing genes before or when they are needed, and adjusting the degree of noise inherent in gene expression. We investigated the interplay between different nutritional environments and the inhabiting organisms’ metabolic and genetic adaptations by applying an evolutionary algorithm to an agent-based model of a concise bacterial metabolism. Our results show that constant environments and rapidly fluctuating environments produce similar adaptations in the organisms, making the predictability of the environment a major factor in determining optimal adaptation. We show that exploitation of expression noise occurs only in some types of fluctuating environment and is strongly dependent on the quality and availability of nutrients: stochasticity is generally detrimental in fluctuating environments and beneficial only at equal periods of nutrient availability and above a threshold environmental richness. Moreover, depending on the availability and nutritional value of nutrients, nutrient-dependent and stochastic expression are both strategies used to deal with environmental changes. Overall, we comprehensively characterize the interplay between the quality and periodicity of an environment and the resulting optimal deterministic and stochastic regulation strategies of nutrient-catabolizing pathways.

Mistranslation can enhance fitness through purging of deleterious mutations

Phenotypic mutations are amino acid changes caused by mistranslation. How phenotypic mutations affect the adaptive evolution of new protein functions is unknown. Here we evolve the antibiotic resistance protein TEM-1 towards resistance on the antibiotic cefotaxime in an Escherichia coli strain with a high mistranslation rate. TEM-1 populations evolved in such strains endow host cells with a general growth advantage, not only on cefotaxime but also on several other antibiotics that ancestral TEM-1 had been unable to deactivate. High-throughput sequencing of TEM-1 populations shows that this advantage is associated with a lower incidence of weakly deleterious genotypic mutations. Our observations show that mistranslation is not just a source of noise that delays adaptive evolution. It could even facilitate adaptive evolution by exacerbating the effects of deleterious mutations and leading to their more efficient purging. The ubiquity of mistranslation and its effects render mistranslation an important factor in adaptive protein evolution.

Mistranslation results in amino acid changes in proteins known as phenotypic mutations and these occur at a much higher rate than DNA mutations. Here, the authors show that mistranslation can increase the response to directional selection by exacerbating the fitness effects of deleterious DNA mutations.

Extreme calorie restriction in yeast retentostats induces uniform non-quiescent growth arrest

Non-dividing Saccharomyces cerevisiae cultures are highly relevant for fundamental and applied studies. However, cultivation conditions in which non-dividing cells retain substantial metabolic activity are lacking. Unlike stationary-phase (SP) batch cultures, the current experimental paradigm for non-dividing yeast cultures, cultivation under extreme calorie restriction (ECR) in retentostat enables non-dividing yeast cells to retain substantial metabolic activity and to prevent rapid cellular deterioration. Distribution of F-actin structures and single-cell copy numbers of specific transcripts revealed that cultivation under ECR yields highly homogeneous cultures, in contrast to SP cultures that differentiate into quiescent and non-quiescent subpopulations. Combined with previous physiological studies, these results indicate that yeast cells subjected to ECR survive in an extended G₁ phase. This study demonstrates that yeast cells exposed to ECR differ from carbon-starved cells and offer a promising experimental model for studying non-dividing, metabolically active, and robust eukaryotic cells.

An Individual-Based Diploid Model Predicts Limited Conditions Under Which Stochastic Gene Expression Becomes Advantageous

Recent studies suggest the existence of a stochasticity in gene expression (SGE) in many organisms, and its non-negligible effect on their phenotype and fitness. To date, however, how SGE affects the key parameters of population genetics are not well understood. SGE can increase the phenotypic variation and act as a load for individuals, if they are at the adaptive optimum in a stable environment. On the other hand, part of the phenotypic variation caused by SGE might become advantageous if individuals at the adaptive optimum become genetically less-adaptive, for example due to an environmental change. Furthermore, SGE of unimportant genes might have little or no fitness consequences. Thus, SGE can be advantageous, disadvantageous, or selectively neutral depending on its context. In addition, there might be a genetic basis that regulates magnitude of SGE, which is often referred to as “modifier genes,” but little is known about the conditions under which such an SGE-modifier gene evolves. In the present study, we conducted individual-based computer simulations to examine these conditions in a diploid model. In the simulations, we considered a single locus that determines organismal fitness for simplicity, and that SGE on the locus creates fitness variation in a stochastic manner. We also considered another locus that modifies the magnitude of SGE. Our results suggested that SGE was always deleterious in stable environments and increased the fixation probability of deleterious mutations in this model. Even under frequently changing environmental conditions, only very strong natural selection made SGE adaptive. These results suggest that the evolution of SGE-modifier genes requires strict balance among the strength of natural selection, magnitude of SGE, and frequency of environmental changes. However, the degree of dominance affected the condition under which SGE becomes advantageous, indicating a better opportunity for the evolution of SGE in different genetic models.

Variation is function: Are single cell differences functionally important?: Testing the hypothesis that single cell variation is required for aggregate function

There is a growing appreciation of the extent of transcriptome variation across individual cells of the same cell type. While expression variation may be a byproduct of, for example, dynamic or homeostatic processes, here we consider whether single-cell molecular variation per se might be crucial for population-level function. Under this hypothesis, molecular variation indicates a diversity of hidden functional capacities within an ensemble of identical cells, and this functional diversity facilitates collective behavior that would be inaccessible to a homogenous population. In reviewing this topic, we explore possible functions that might be carried by a heterogeneous ensemble of cells; however, this question has proven difficult to test, both because methods to manipulate molecular variation are limited and because it is complicated to define, and measure, population-level function. We consider several possible methods to further pursue the hypothesis that variation is function through the use of comparative analysis and novel experimental techniques.