Universal Transitions between Growth and Dormancy via Intermediate Complex Formation.

A simple cell model consisting of a catalytic reaction network with intermediate complex formation is numerically studied. As nutrients are depleted, the transition from the exponential growth phase to the growth-arrested dormant phase occurs along with hysteresis and a lag time for growth recovery. This transition is caused by the accumulation of intermediate complexes, leading to the jamming of reactions and the diversification of components. These properties are generic in random reaction networks, as supported by dynamical systems analyses of corresponding mean-field models.

Bayesian inference is facilitated by modular neural networks with different time scales.

Various animals, including humans, have been suggested to perform Bayesian inferences to handle noisy, time-varying external information. In performing Bayesian inference by the brain, the prior distribution must be acquired and represented by sampling noisy external inputs. However, the mechanism by which neural activities represent such distributions has not yet been elucidated. Our findings reveal that networks with modular structures, composed of fast and slow modules, are adept at representing this prior distribution, enabling more accurate Bayesian inferences. Specifically, the modular network that consists of a main module connected with input and output layers and a sub-module with slower neural activity connected only with the main module outperformed networks with uniform time scales. Prior information was represented specifically by the slow sub-module, which could integrate observed signals over an appropriate period and represent input means and variances. Accordingly, the neural network could effectively predict the time-varying inputs. Furthermore, by training the time scales of neurons starting from networks with uniform time scales and without modular structure, the above slow-fast modular network structure and the division of roles in which prior knowledge is selectively represented in the slow sub-modules spontaneously emerged. These results explain how the prior distribution for Bayesian inference is represented in the brain, provide insight into the relevance of modular structure with time scale hierarchy to information processing, and elucidate the significance of brain areas with slower time scales.

Developmental hourglass: Verification by numerical evolution and elucidation by dynamical-systems theory.

Determining the general laws between evolution and development is a fundamental biological challenge. Developmental hourglasses have attracted increased attention as candidates for such laws, but the necessity of their emergence remains elusive. We conducted evolutionary simulations of developmental processes to confirm the emergence of the developmental hourglass and unveiled its establishment. We considered organisms consisting of cells containing identical gene networks that control morphogenesis and evolved them under selection pressure to induce more cell types. By computing the similarity between the spatial patterns of gene expression of two species that evolved from a common ancestor, a developmental hourglass was observed, that is, there was a correlation peak in the intermediate stage of development. The fraction of pleiotropic genes increased, whereas the variance in individuals decreased, consistent with previous experimental reports. Reduction of the unavoidable variance by initial or developmental noise, essential for survival, was achieved up to the hourglass bottleneck stage, followed by diversification in developmental processes, whose timing is controlled by the slow expression dynamics conserved among organisms sharing the hourglass. This study suggests why developmental hourglasses are observed within a certain phylogenetic range of species.

A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks.

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks.

Autotoxin-mediated latecomer killing in yeast communities.

Cellular adaptation to stressful environments such as starvation is essential to the survival of microbial communities, but the uniform response of the cell community may lead to entire cell death or severe damage to their fitness. Here, we demonstrate an elaborate response of the yeast community against glucose depletion, in which the first adapted cells kill the latecomer cells. During glucose depletion, yeast cells release autotoxins, such as leucic acid and L-2keto-3methylvalerate, which can even kill the clonal cells of the ones producing them. Although these autotoxins were likely to induce mass suicide, some cells differentiated to adapt to the autotoxins without genetic changes. If nondifferentiated latecomers tried to invade the habitat, autotoxins damaged or killed the latecomers, but the differentiated cells could selectively survive. Phylogenetically distant fission and budding yeast shared this behavior using the same autotoxins, suggesting that latecomer killing may be the universal system of intercellular communication, which may be relevant to the evolutional transition from unicellular to multicellular organisms.

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database.

The recent development of artificial intelligence provides us with new and powerful tools for studying the mysterious relationship between organism evolution and protein evolution. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the proteins of different organisms. The statistics of AlphaFold-predicted structures show that, for organisms with higher complexity, their constituent proteins will have larger radii of gyration, higher coil fractions, and slower vibrations, statistically. By conducting normal mode analysis and scaling analyses, we demonstrate that higher organismal complexity correlates with lower fractal dimensions in both the structure and dynamics of the constituent proteins, suggesting that higher functional specialization is associated with higher organismal complexity. We also uncover the topology and sequence bases of these correlations. As the organismal complexity increases, the residue contact networks of the constituent proteins will be more assortative, and these proteins will have a higher degree of hydrophilic-hydrophobic segregation in the sequences. Furthermore, by comparing the statistical structural proximity across the proteomes with the phylogenetic tree of homologous proteins, we show that, statistical structural proximity across the proteomes may indirectly reflect the phylogenetic proximity, indicating a statistical trend of protein evolution in parallel with organism evolution. This study provides new insights into how the diversity in the functionality of proteins increases and how the dimensionality of the manifold of protein dynamics reduces during evolution, contributing to the understanding of the origin and evolution of lives.

Chemophoresis engine: A general mechanism of ATPase-driven cargo transport.

Cell polarity regulates the orientation of the cytoskeleton members that directs intracellular transport for cargo-like organelles, using chemical gradients sustained by ATP or GTP hydrolysis. However, how cargo transports are directly mediated by chemical gradients remains unknown. We previously proposed a physical mechanism that enables directed movement of cargos, referred to as chemophoresis. According to the mechanism, a cargo with reaction sites is subjected to a chemophoresis force in the direction of the increased concentration. Based on this, we introduce an extended model, the chemophoresis engine, as a general mechanism of cargo motion, which transforms chemical free energy into directed motion through the catalytic ATP hydrolysis. We applied the engine to plasmid motion in a ParABS system to demonstrate the self-organization system for directed plasmid movement and pattern dynamics of ParA-ATP concentration, thereby explaining plasmid equi-positioning and pole-to-pole oscillation observed in bacterial cells and in vitro experiments. We mathematically show the existence and stability of the plasmid-surfing pattern, which allows the cargo-directed motion through the symmetry-breaking transition of the ParA-ATP spatiotemporal pattern. We also quantitatively demonstrate that the chemophoresis engine can work even under in vivo conditions. Finally, we discuss the chemophoresis engine as one of the general mechanisms of hydrolysis-driven intracellular transport.

Emergence of kinship structures and descent systems: multi-level evolutionary simulation and empirical data analysis.

In many indigenous societies, people are categorized into several cultural groups, or clans, within which they believe they share ancestors. Clan attributions provide certain rules for marriage and descent. Such rules between clans constitute kinship structures. Anthropologists have revealed several kinship structures. Here, we propose an agent-based model of indigenous societies to reveal the evolution of kinship structures. In the model, several societies compete. Societies themselves comprise multiple families with parameters for cultural traits and mate preferences. These values determine with whom each family cooperates and competes, and they are transmitted to a new generation with mutation. The growth rate of each family is determined by the number of cooperators and competitors. Through this multi-level evolution, family traits and preferences diverge to form clusters that can be regarded as clans. Subsequently, kinship structures emerge, including dual organization and generalized or restricted exchange, as well as patrilineal, matrilineal and double descent systems. These structures emerge depending on the necessity of cooperation and the strength of mating competition. Their dependence is also estimated analytically. Finally, statistical analysis using the Standard Cross-Cultural Sample, a global ethnographic database, empirically verified the theoretical results. Such collaboration between theoretical and empirical approaches will unveil universal features in anthropology.

Dynamical systems approach to evolution-development congruence: Revisiting Haeckel's recapitulation theory.

It is acknowledged that embryonic development has a tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel's recapitulation theory, that is, the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene expression dynamics with cell-to-cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Changes in both patterns consisted of several epochs where stripes are formed in a short time, whereas for other temporal regimes, the pattern hardly changes. In evolution, these quasi-stationary generations are needed to achieve relevant mutations, whereas, in development, they are due to some gene expressions that vary slowly and control the pattern change. These successive epochal changes in development and evolution are represented as common bifurcations in dynamical systems theory, regulating working network structure from feedforward subnetwork to those containing feedback loops. The congruence is the correspondence between successive acquisitions of subnetworks through evolution and changes in working subnetworks in development. Consistency of the theory with the segmentation gene-expression dynamics is discussed. Novel outlook on recapitulation and heterochrony are provided, testable experimentally by the transcriptome and network analysis.

A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined.

Numerous living systems are hierarchically organized, whereby replicating components are grouped into reproducing collectives-e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by N) and the mutation rate of components (m) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing N or m accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: Nmα is a constant, where scaling exponent α depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although N and m have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if m is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically organized replicating systems.

Heterosis of fitness and phenotypic variance in the evolution of a diploid gene regulatory network.

Heterosis describes the phenomenon, whereby a hybrid population has higher fitness than an inbred population, which has previously been explained by either Mendelian dominance or overdominance under the general assumption of a simple genotype-phenotype relationship. However, recent studies have demonstrated that genes interact through a complex gene regulatory network (GRN). Furthermore, phenotypic variance is reportedly lower for heterozygotes, and the origin of such variance-related heterosis remains elusive. Therefore, a theoretical analysis linking heterosis to GRN evolution and stochastic gene expression dynamics is required. Here, we investigated heterosis related to fitness and phenotypic variance in a system with interacting genes by numerically evolving diploid GRNs. According to the results, the heterozygote population exhibited higher fitness than the homozygote population, indicating fitness-related heterosis resulting from evolution. In addition, the heterozygote population exhibited lower noise-related phenotypic variance in expression levels than the homozygous population, implying that the heterozygote population is more robust to noise. Furthermore, the distribution of the ratio of heterozygote phenotypic variance to homozygote phenotypic variance exhibited quantitative similarity with previous experimental results. By applying dominance and differential gene expression rather than only a single gene expression model, we confirmed the correlation between heterosis and differential gene expression. We explain our results by proposing that the convex high-fitness region is evolutionarily shaped in the genetic space to gain noise robustness under genetic mixing through sexual reproduction. These results provide new insights into the effects of GRNs on variance-related heterosis and differential gene expression.

Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations.

Sequential transitions between metastable states are ubiquitously observed in the neural system and underlying various cognitive functions such as perception and decision making. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, fine recurrent neural networks trained with supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations and such learning methods are biologically implausible. How stable and complex sequences are generated in the neural system still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the hierarchy of timescales on neural activities in the cortex. The slow dynamics store the history of inputs and outputs and affect the fast dynamics depending on the stored history. We show that the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized depending on the previous patterns. This co-existence period leads to the stable transition between the current and the next pattern in the non-Markov sequence. We further find that timescale balance is critical to the co-existence period. Our study provides a novel mechanism generating robust complex sequences with multiple timescales. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.

Evolution of phenotypic fluctuation under host-parasite interactions.

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important "environmental" factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host-parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host-parasite interactions.

Dynamics-Evolution Correspondence in Protein Structures.

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

Adaptation of metabolite leakiness leads to symbiotic chemical exchange and to a resilient microbial ecosystem.

Microbial communities display remarkable diversity, facilitated by the secretion of chemicals that can create new niches. However, it is unclear why cells often secrete even essential metabolites after evolution. Based on theoretical results indicating that cells can enhance their own growth rate by leaking even essential metabolites, we show that such "leaker" cells can establish an asymmetric form of mutualism with "consumer" cells that consume the leaked chemicals: the consumer cells benefit from the uptake of the secreted metabolites, while the leaker cells also benefit from such consumption, as it reduces the metabolite accumulation in the environment and thereby enables further secretion, resulting in frequency-dependent coexistence of multiple microbial species. As supported by extensive simulations, such symbiotic relationships generally evolve when each species has a complex reaction network and adapts its leakiness to optimize its own growth rate under crowded conditions and nutrient limitations. Accordingly, symbiotic ecosystems with diverse cell species that leak and exchange many metabolites with each other are shaped by cell-level adaptation of leakiness of metabolites. Moreover, the resultant ecosystems with entangled metabolite exchange are resilient against structural and environmental perturbations. Thus, we present a theory for the origin of resilient ecosystems with diverse microbes mediated by secretion and exchange of essential chemicals.

Evolution of dominance in gene expression pattern associated with phenotypic robustness.

BACKGROUND: Mendelian inheritance is a fundamental law of genetics. When we consider two genomes in a diploid cell, a heterozygote's phenotype is dominated by a particular homozygote according to the law of dominance. Classical Mendelian dominance is concerned with which proteins are dominant, and is usually based on simple genotype-phenotype relationship in which one gene regulates one phenotype. However, in reality, some interactions between genes can exist, resulting in deviations from Mendelian dominance. Whether and how Mendelian dominance is generalized to the phenotypes of gene expression determined by gene regulatory networks (GRNs) remains elusive. RESULTS: Here, by using the numerical evolution of diploid GRNs, we discuss whether the dominance of phenotype evolves beyond the classical Mendelian case of one-to-one genotype-phenotype relationship. We examine whether complex genotype-phenotype relationship can achieve Mendelian dominance at the expression level by a pair of haplotypes through the evolution of the GRN with interacting genes. This dominance is defined via a pair of haplotypes that differ from each other but have a common phenotype given by the expression of target genes. We numerically evolve the GRN model for a diploid case, in which two GRN matrices are added to give gene expression dynamics and simulate evolution with meiosis and recombination. Our results reveal that group Mendelian dominance evolves even under complex genotype-phenotype relationship. Calculating the degree of dominance shows that it increases through the evolution, correlating closely with the decrease in phenotypic fluctuations and the increase in robustness to initial noise. We also demonstrate that the dominance of gene expression patterns evolves concurrently. This evolution of group Mendelian dominance and pattern dominance is associated with phenotypic robustness against meiosis-induced genome mixing, whereas sexual recombination arising from the mixing of genomes from the parents further enhances dominance and robustness. Due to this dominance, the robustness to genetic differences increases, while optimal fitness is sustained to a significant difference between the two genomes. CONCLUSION: Group Mendelian dominance and gene-expression pattern dominance are achieved associated with the increase in phenotypic robustness to noise.

Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes.

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis.

Proteins in cellular environments are highly susceptible. Local perturbations to any residue can be sensed by other spatially distal residues in the protein molecule, showing long-range correlations in the native dynamics of proteins. The long-range correlations of proteins contribute to many biological processes such as allostery, catalysis, and transportation. Revealing the structural origin of such long-range correlations is of great significance in understanding the design principle of biologically functional proteins. In this work, based on a large set of globular proteins determined by X-ray crystallography, by conducting normal mode analysis with the elastic network models, we demonstrate that such long-range correlations are encoded in the native topology of the proteins. To understand how native topology defines the structure and the dynamics of the proteins, we conduct scaling analysis on the size dependence of the slowest vibration mode, average path length, and modularity. Our results quantitatively describe how native proteins balance between order and disorder, showing both dense packing and fractal topology. It is suggested that the balance between stability and flexibility acts as an evolutionary constraint for proteins at different sizes. Overall, our result not only gives a new perspective bridging the protein structure and its dynamics but also reveals a universal principle in the evolution of proteins at all different sizes.

Advantage of Leakage of Essential Metabolites for Cells.

Microbial cells generally leak various metabolites including those necessary to grow. Why cells secrete even essential chemicals so often is, however, still unclear. Based on analytical and numerical calculations, we show that if the intracellular metabolism includes multibody (e.g., catalytic) reactions, leakage of essential metabolites can promote the leaking cell's growth. This advantage is typical for most metabolic networks via "flux control" and "growth-dilution" mechanisms, as a general consequence of the balance between synthesis and growth-induced dilution with autocatalytic reactions. We further argue that this advantage may lead to a novel form of symbiosis among diverse cells.