Evolutionary dynamics in non-Markovian models of microbial populations.

In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.

Scaling concepts in 'omics: Nuclear lamin-B scales with tumor growth and often predicts poor prognosis, unlike fibrosis.

Physicochemical principles such as stoichiometry and fractal assembly can give rise to characteristic scaling between components that potentially include coexpressed transcripts. For key structural factors within the nucleus and extracellular matrix, we discover specific gene-gene scaling exponents across many of the 32 tumor types in The Cancer Genome Atlas, and we demonstrate utility in predicting patient survival as well as scaling-informed machine learning (SIML). All tumors with adjacent tissue data show cancer-elevated proliferation genes, with some genes scaling with the nuclear filament LMNB1, including the transcription factor FOXM1 that we show directly regulates LMNB1 SIML shows that such regulated cancers cluster together with longer overall survival than dysregulated cancers, but high LMNB1 and FOXM1 in half of regulated cancers surprisingly predict poor survival, including for liver cancer. COL1A1 is also studied because it too increases in tumors, and a pan-cancer set of fibrosis genes shows substoichiometric scaling with COL1A1 but predicts patient outcome only for liver cancer-unexpectedly being prosurvival. Single-cell RNA-seq data show nontrivial scaling consistent with power laws from bulk RNA and protein analyses, and SIML segregates synthetic from contractile cancer fibroblasts. Our scaling approach thus yields fundamentals-based power laws relatable to survival, gene function, and experiments.

Cell Size Regulation Induces Sustained Oscillations in the Population Growth Rate.

We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any nonzero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation timescale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.

Universal biology and the statistical mechanics of early life.

All known life on the Earth exhibits at least two non-trivial common features: the canonical genetic code and biological homochirality, both of which emerged prior to the Last Universal Common Ancestor state. This article describes recent efforts to provide a narrative of this epoch using tools from statistical mechanics. During the emergence of self-replicating life far from equilibrium in a period of chemical evolution, minimal models of autocatalysis show that homochirality would have necessarily co-evolved along with the efficiency of early-life self-replicators. Dynamical system models of the evolution of the genetic code must explain its universality and its highly refined error-minimization properties. These have both been accounted for in a scenario where life arose from a collective, networked phase where there was no notion of species and perhaps even individuality itself. We show how this phase ultimately terminated during an event sometimes known as the Darwinian transition, leading to the present epoch of tree-like vertical descent of organismal lineages. These examples illustrate concrete examples of universal biology: the quest for a fundamental understanding of the basic properties of living systems, independent of precise instantiation in chemistry or other media.This article is part of the themed issue 'Reconceptualizing the origins of life'.

Phenomenology of stochastic exponential growth.

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality.

The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Giant Amplification of Noise in Fluctuation-Induced Pattern Formation.

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and nonorthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism shows that fluctuation-induced Turing patterns are observable, and are not strongly limited by the amplitude of demographic stochasticity nor by the value of the diffusion coefficients.

Noise-Induced Mechanism for Biological Homochirality of Early Life Self-Replicators.

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Velocity statistics for interacting edge dislocations in one dimension from Dyson's Coulomb gas model.

The dynamics of edge dislocations with parallel Burgers vectors, moving in the same slip plane, is mapped onto Dyson's model of a two-dimensional Coulomb gas confined in one dimension. We show that the tail distribution of the velocity of dislocations is power law in form, as a consequence of the pair interaction of nearest neighbors in one dimension. In two dimensions, we show the presence of a pairing phase transition in a system of interacting dislocations with parallel Burgers vectors. The scaling exponent of the velocity distribution at effective temperatures well below this pairing transition temperature can be derived from the nearest-neighbor interaction, while near the transition temperature, the distribution deviates from the form predicted by the nearest-neighbor interaction, suggesting the presence of collective effects.