A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes were shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states was derived, which was confirmed by adaptation experiments on bacteria under stress. Next, the theory was extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and environmental adaptation. The link between robustness to noise and mutation, as a result of robustness in developmental dynamics to perturbations, showed proportionality between phenotypic plasticity by genetic changes and by environmental noise. Accordingly, directionality and constraint in phenotypic evolution was quantitatively formulated in terms of phenotypic fluctuation and the response against environmental change. The evolutionary relevance of slow modes in controlling high-dimensional phenotypes is discussed.
We consider the cell population dynamics with $n$ different phenotypes. Both the Markovian branching process model (stochastic model) and the ordinary differential equation (ODE) system model (deterministic model) are presented, and exploited to investigate the dynamics of the phenotypic proportions. We will prove that in both models, these proportions will tend to constants regardless of initial population states ("phenotypic equilibrium") under weak conditions, which explains the experimental phenomenon in Gupta et al.'s paper. We also prove that Gupta et al.'s explanation is the ODE model u…
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 evol…
In microbial communities, each species often has multiple, distinct phenotypes, but studies of ecological stability have largely ignored this subpopulation structure. Here, we show that such implicit averaging over phenotypes leads to incorrect linear stability results. We then analyze the effect of phenotypic switching in detail in an asymptotic limit and partly overturn classical stability paradigms: abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype such as bacterial persisters has a stabilizing effect. Finally, we extend these results by showing how…
Deterministic continuum models formulated in terms of non-local 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 deterministic continuum 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 this paper, we develop a sto…
Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and Segel has proven a popular choice in the modelling of such phenomena, but in its original form restricts to a homogeneous population. To account for the possibility of phenotypic heterogeneity, we extend to the case of a population continuously structured across space, time and phenotype, where the latter determines variation in chemotactic responsiveness, proliferation rate, and the level of chemical environment mo…
Relationship among Phenotypic Plasticity, Genetic and Epigenetic Fluctuations, Robustness, and Evolovability; Waddington's Legacy revisited under the Spirit of Einstein
The evolution and function of imitation have always been placed within the confines of animal learning and associated with its crucial role in cultural transmission and cultural evolution. Can imitation evolve as a form of phenotypic plasticity in the absence of cultural transmission, in phenotypes beyond behavior? We investigate a model in which imitation is unbundled from cultural transmission: an organism's adult phenotype is plastically altered by its experiences as a juvenile of other juveniles' genetically determined traits. The only information transmitted between generations is genetic…
Travelling waves of invasion in microbial communities with phenotypic switching
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）
Earth-Life Science Institute, Tokyo Institute of Technology（东京工业大学地球生命科学研究所）；Department of Earth Sciences, University of Cambridge（剑桥大学地球科学系）
Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of $\textit{Heliconius erato}$ and $\textit{Heliconius melpomene}$. Euclidean phenotypic distances, calculated using a deep convolutional triplet network, demonstrate significant convergence between interspecies co-mimics. This quantitatively validates a key prediction of Müllerian mimicry theory, evolutionary biology's oldest mathematical model. …
In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in response to environmental changes are effectively restricted to a low-dimensional subspace. Thus, uncovering the origin and nature of such a drastic dimension reduction is crucial to understanding the general characteristics of biological adaptation and evolution. Herein, we first formulated the dimension reduction in terms of dynamical systems theory: considering …
Organismal phenotypes emerge from a complex set of genotypic interactions. While technological advances in sequencing provide a quantitative description of an organism's genotype, characterization of an organism's physical phenotype lags far behind. Here, we relate genotype to the complex and multi-dimensional phenotype of an anatomical structure using the Drosophila wing as a model system. We develop a mathematical approach that enables a robust description of biologically salient phenotypic variation. Analysing natural phenotypic variation, and variation generated by weak perturbations in ge…
How adaptive evolution to one environmental stress improves or suppresses adaptation to another is an important problem in evolutionary biology. For instance, in microbiology, the evolution of bacteria to be resistant to different antibiotics is a critical issue that has been investigated as cross-resistance. In fact, recent experiments on bacteria have suggested that the cross-resistance of their evolution to various stressful environments can be predicted by the changes to their transcriptome upon application of stress. However, there are no studies so far that explain a possible theoretical…
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 ch…
Beijing University of Posts and Telecommunications（北京邮电大学）；Beihang University（北京航空航天大学）；Dartmouth College（达特茅斯学院）；Geisel School of Medicine at Dartmouth（达特茅斯盖泽尔医学院）；Yale University（耶鲁大学）
Stochastic gradient descent on the epigenetic landscape: a unified framework for cellular plasticity, tumor heterogeneity, and the asymptotic irrelevance of fitness
Instituto de Matemática e Computação, Universidade Federal de Itajubá（伊塔朱巴联邦大学数学与计算研究所）；Carl Gustav Carus School of Medicine, Technische Universität Dresden（德累斯顿工业大学卡尔·古斯塔夫·卡斯医学院）
