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Register a new userExploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations
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We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.
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Microbial metabolic networks perform the basic function of harvesting energy from nutrients to generate the work and free energy required for survival, growth and replication. The robust physiological outcomes they generate across vastly different organisms in spite of major environmental and genetic differences represent an especially remarkable trait. Most notably, it suggests that metabolic activity in bacteria may follow universal principles, the search for which is a long-standing issue. Most theoretical approaches to modeling metabolism assume that cells optimize specific evolutionarily-motivated objective functions (like their growth rate) under general physico-chemical or regulatory constraints. While conceptually and practically useful in many situations, the idea that certain objectives are optimized is hard to validate in data. Moreover, it is not clear how optimality can be reconciled with the degree of single-cell variability observed within microbial populations. To shed light on these issues, we propose here an inverse modeling framework that connects fitness to variability through the Maximum-Entropy guided inference of metabolic flux distributions from data. While no clear optimization emerges, we find that, as the medium gets richer, Escherichia coli populations slowly approach the theoretically optimal performance defined by minimal reduction of phenotypic variability at given mean growth rate. Inferred flux distributions provide multiple biological insights, including on metabolic reactions that are experimentally inaccessible. These results suggest that bacterial metabolism is crucially shaped by a population-level trade-off between fitness and cell-to-cell heterogeneity.
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits fitness wave solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed. Here we show more generally that evolving fitness distributions are attracted to a one-parameter family of distributions with a fixed parabolic relationship between skewness and kurtosis. Unlike fitness waves, this statistical pattern encompasses both positive and negative (a.k.a. purifying) selection and is not restricted to rapidly adapting populations. Moreover we find that the mean fitness of a population under the selection of pre-existing variation is a power-law function of time, as observed in microbiological evolution experiments but at variance with fitness wave theory. At the conceptual level, our results can be viewed as the resolution of the dynamic insufficiency of Fishers fundamental theorem of natural selection. Our predictions are in good agreement with numerical simulations.
In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a populations growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a populations growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a non-monotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from a set of possible species, which may undergo extinction. How many species survive depends on the properties of the interaction matrix; the size of the resulting food web at stationarity is a property of the system itself in our model, and not a control parameter as in most studies based on random matrix theory. We find that prey-predator relations enhance stability, and that variability of species interactions promotes instability. Complexity of inter-species couplings leads to reduced sizes of ecological communities. Dynamically evolved community size and stability are hence positively correlated.
Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Such optima have been well characterized in several biologically relevant cases over the past decade. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the `capacity) achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.
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