Formation of human kinship structures depending on population size and cultural mutation rate.

How does social complexity depend on population size and cultural transmission? Kinship structures in traditional societies provide a fundamental illustration, where cultural rules between clans determine people's marriage possibilities. Here, we propose a simple model of kinship interactions that considers kin and in-law cooperation and sexual rivalry. In this model, multiple societies compete. Societies consist of multiple families with different cultural traits and mating preferences. These values determine interactions and hence the growth rate of families and are transmitted to offspring with mutations. Through a multilevel evolutionary simulation, family traits and preferences are grouped into multiple clans with interclan mating preferences. It illustrates the emergence of kinship structures as the spontaneous formation of interdependent cultural associations. Emergent kinship structures are characterized by the cycle length of marriage exchange and the number of cycles in society. We numerically and analytically clarify their parameter dependence. The relative importance of cooperation versus rivalry determines whether attraction or repulsion exists between families. Different structures evolve as locally stable attractors. The probabilities of formation and collapse of complex structures depend on the number of families and the mutation rate, showing characteristic scaling relationships. It is now possible to explore macroscopic kinship structures based on microscopic interactions, together with their environmental dependence and the historical causality of their evolution. We propose the basic causal mechanism of the formation of typical human social structures by referring to ethnographic observations and concepts from statistical physics and multilevel evolution. Such interdisciplinary collaboration will unveil universal features in human societies.

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.

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.

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.

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.

Evolution of kinship structures driven by marriage tie and competition.

The family unit and kinship structures form the basis of social relationships in indigenous societies. Families constitute a cultural group, a so-called clan, within which marriage is prohibited by the incest taboo. The clan attribution governs the mating preference and descent relationships by certain rules. Such rules form various kinship structures, including generalized exchange, an indirect exchange of brides among more than two clans, and restricted exchange, a direct exchange of brides with the flow of children to different clans. These structures are distributed in different areas and show different cultural consequences. However, it is still unknown how they emerge or what conditions determine different structures. Here, we build a model of communities consisting of lineages and family groups and introduce social cooperation among kin and mates and conflict over mating. Each lineage has parameters characterizing the trait and mate preference, which determines the possibility of marriage and the degree of cooperation and conflict among lineages. Lineages can cooperate with those having similar traits to their own or mates', whereas lineages with similar preferences compete for brides. In addition, we introduce community-level selection by eliminating communities with smaller fitness and follow the so-called hierarchical Moran process. We numerically demonstrate that lineages are clustered in the space of traits and preferences, resulting in the emergence of clans with the incest taboo. Generalized exchange emerges when cooperation is strongly needed, whereas restricted exchange emerges when the mating conflict is strict. This may explain the geographical distribution of kinship structures in indigenous societies.

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.

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.

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.

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.

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.

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.

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.

Horizontal transfer between loose compartments stabilizes replication of fragmented ribozymes.

The emergence of replicases that can replicate themselves is a central issue in the origin of life. Recent experiments suggest that such replicases can be realized if an RNA polymerase ribozyme is divided into fragments short enough to be replicable by the ribozyme and if these fragments self-assemble into a functional ribozyme. However, the continued self-replication of such replicases requires that the production of every essential fragment be balanced and sustained. Here, we use mathematical modeling to investigate whether and under what conditions fragmented replicases achieve continued self-replication. We first show that under a simple batch condition, the replicases fail to display continued self-replication owing to positive feedback inherent in these replicases. This positive feedback inevitably biases replication toward a subset of fragments, so that the replicases eventually fail to sustain the production of all essential fragments. We then show that this inherent instability can be resolved by small rates of random content exchange between loose compartments (i.e., horizontal transfer). In this case, the balanced production of all fragments is achieved through negative frequency-dependent selection operating in the population dynamics of compartments. The horizontal transfer also ensures the presence of all essential fragments in each compartment, sustaining self-replication. Taken together, our results underline compartmentalization and horizontal transfer in the origin of the first self-replicating replicases.

Fold-change detection and scale invariance of cell-cell signaling in social amoeba.

Cell-cell signaling is subject to variability in the extracellular volume, cell number, and dilution that potentially increase uncertainty in the absolute concentrations of the extracellular signaling molecules. To direct cell aggregation, the social amoebae Dictyostelium discoideum collectively give rise to oscillations and waves of cyclic adenosine 3',5'-monophosphate (cAMP) under a wide range of cell density. To date, the systems-level mechanism underlying the robustness is unclear. By using quantitative live-cell imaging, here we show that the magnitude of the cAMP relay response of individual cells is determined by fold change in the extracellular cAMP concentrations. The range of cell density and exogenous cAMP concentrations that support oscillations at the population level agrees well with conditions that support a large fold-change-dependent response at the single-cell level. Mathematical analysis suggests that invariance of the oscillations to density transformation is a natural outcome of combining secrete-and-sense systems with a fold-change detection mechanism.

The origin of the central dogma through conflicting multilevel selection.

The central dogma of molecular biology rests on two kinds of asymmetry between genomes and enzymes: informatic asymmetry, where information flows from genomes to enzymes but not from enzymes to genomes; and catalytic asymmetry, where enzymes provide chemical catalysis but genomes do not. How did these asymmetries originate? Here, we show that these asymmetries can spontaneously arise from conflict between selection at the molecular level and selection at the cellular level. We developed a model consisting of a population of protocells, each containing a population of replicating catalytic molecules. The molecules are assumed to face a trade-off between serving as catalysts and serving as templates. This trade-off causes conflicting multilevel selection: serving as catalysts is favoured by selection between protocells, whereas serving as templates is favoured by selection between molecules within protocells. This conflict induces informatic and catalytic symmetry breaking, whereby the molecules differentiate into genomes and enzymes, establishing the central dogma. We show mathematically that the symmetry breaking is caused by a positive feedback between Fisher's reproductive values and the relative impact of selection at different levels. This feedback induces a division of labour between genomes and enzymes, provided variation at the molecular level is sufficiently large relative to variation at the cellular level, a condition that is expected to hinder the evolution of altruism. Taken together, our results suggest that the central dogma is a logical consequence of conflicting multilevel selection.

Noise-driven growth rate gain in clonal cellular populations.

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.