Elasticity tunes mechanical stress localization around active topological defects.

Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized mechanical stress. It is therefore important to ask how mechanical stress localization around topological defects is controlled. Here, we use continuum simulations of nonequilibrium, fluctuating and active nematics to explore the patterns of stress localization, as well as their extent and intensity around topological defects. We find that by increasing the orientational elasticity of the material, the isotropic stress pattern around topological defects is changed substantially, from a stress dipole characterized by symmetric compression-tension regions around the core of the defect, to a localized stress monopole at the defect position. Moreover, we show that elastic anisotropy alters the extent and intensity of the stresses, and can result in the dominance of tension or compression around defects. Finally, including both nonequilibrium fluctuations and active stress generation, we find that the elastic constant tunes the relative effect of each, leading to the flipping of tension and compression regions around topological defects. This flipping of the tension-compression regions only by changing the elastic constant presents an interesting, simple, way of switching the dynamic behavior in active matter by changing a passive material property. We expect these findings to motivate further exploration tuning stresses in active biological materials by varying material properties of the constituent units.

Bridging microscopic cell dynamics to nematohydrodynamics of cell monolayers.

It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects cell-cell interactions specified at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the instability threshold in terms of activity and elasticity of the cells. Furthermore, we provide a quantitative characterisation and comparison of flows and topological defects for extensile and contractile stress generation mechanisms, and demonstrate activity-induced heterogeneity and spontaneous formation of gaps within a confluent monolayer. Together, these results contribute to bridging the gap between cell-scale dynamics and tissue-scale collective cellular organisation.

Ribozyme Mutagenic Evolution: Mechanisms of Survival.

Primeval populations replicating at high error rates required a mechanism to overcome the accumulation of mutations and information deterioration. Known strategies to overcome mutation pressures include RNA processivity, epistasis, selection, and quasispecies. We investigated the mechanism by which small molecular ribozyme populations can survive under high error rates by propagating several lineages under different mutagen concentrations. We found that every population that evolved without mutagen went extinct, while those subjected to mutagenic evolution survived. To understand how they survived, we characterized the evolved genotypic diversity, the formation of genotype-genotype interaction networks, the fitness of the most common mutants for each enzymatic step, and changes in population size along the course of evolution. We found that the elevated mutation rate was necessary for the populations to survive in the novel environment, in which all the steps of the metabolism worked to promote the survival of even less catalytically efficient ligases. Besides, an increase in population size and the mutational coupling of genotypes in close-knit networks, which helped maintain or recover lost genotypes making their disappearance transient, prevented Muller's ratchet and extinction.

A Mathematical Dissection of the Adaptation of Cell Populations to Fluctuating Oxygen Levels.

The disordered network of blood vessels that arises from tumour angiogenesis results in variations in the delivery of oxygen into the tumour tissue. This brings about regions of chronic hypoxia (i.e. sustained low oxygen levels) and regions with alternating periods of low and relatively higher oxygen levels, and makes it necessary for cancer cells to adapt to fluctuating environmental conditions. We use a phenotype-structured model to dissect the evolutionary dynamics of cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continuous variable that provides a simple representation of its metabolic phenotype, ranging from fully oxidative to fully glycolytic, and cells are grouped into two competing populations that undergo heritable, spontaneous phenotypic variations at different rates. Model simulations indicate that, depending on the rate at which oxygen is consumed by the cells, dynamic nonlinear interactions between cells and oxygen can stimulate chronic hypoxia and cycling hypoxia. Moreover, the model supports the idea that under chronic-hypoxic conditions lower rates of phenotypic variation lead to a competitive advantage, whereas higher rates of phenotypic variation can confer a competitive advantage under cycling-hypoxic conditions. In the latter case, the numerical results obtained show that bet-hedging evolutionary strategies, whereby cells switch between oxidative and glycolytic phenotypes, can spontaneously emerge. We explain how these results can shed light on the evolutionary process that may underpin the emergence of phenotypic heterogeneity in vascularised tumours.

Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments.

Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in ecology, which is used to explain how species may survive when faced with the evolutionary risks associated with temporally varying environments. In order to support a deeper understanding of the adaptive role of spontaneous phenotypic variations in fluctuating environments, we consider a system of non-local partial differential equations modelling the evolutionary dynamics of two competing phenotype-structured populations in the presence of periodically oscillating nutrient levels. The two populations undergo heritable, spontaneous phenotypic variations at different rates. The phenotypic state of each individual is represented by a continuous variable, and the phenotypic landscape of the populations evolves in time due to variations in the nutrient level. Exploiting the analytical tractability of our model, we study the long-time behaviour of the solutions to obtain a detailed mathematical depiction of the evolutionary dynamics. The results suggest that when nutrient levels undergo small and slow oscillations, it is evolutionarily more convenient to rarely undergo spontaneous phenotypic variations. Conversely, under relatively large and fast periodic oscillations in the nutrient levels, which bring about alternating cycles of starvation and nutrient abundance, higher rates of spontaneous phenotypic variations confer a competitive advantage. We discuss the implications of our results in the context of cancer metabolism.

Fluctuation-induced dynamics of nematic topological defects.

Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.

Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments.

Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.