Origin of complexity in multicellular organisms

Reproductive system, temperature, and genetic background effects in experimentally evolving populations of Caenorhabditis elegans

Experimental evolution (EE) is a powerful research framework for gaining insights into many biological questions, including the evolution of reproductive systems. We designed a long-term and highly replicated EE project using the nematode C. elegans, with the main aim of investigating the impact of reproductive system on adaptation and diversification under environmental challenge. From the laboratory-adapted strain N2, we derived isogenic lines and introgressed the fog-2(q71) mutation, which changes the reproductive system from nearly exclusive selfing to obligatory outcrossing, independently into 3 of them. This way, we obtained 3 pairs of isogenic ancestral populations differing in reproductive system; from these, we derived replicate EE populations and let them evolve in either novel (increased temperature) or control conditions for over 100 generations. Subsequently, fitness of both EE and ancestral populations was assayed under the increased temperature conditions. Importantly, each population was assayed in 2-4 independent blocks, allowing us to gain insight into the reproducibility of fitness scores. We expected to find upward fitness divergence, compared to ancestors, in populations which had evolved in this treatment, particularly in the outcrossing ones due to the benefits of genetic shuffling. However, our data did not support these predictions. The first major finding was very strong effect of replicate block on populations' fitness scores. This indicates that despite standardization procedures, some important environmental effects were varying among blocks, and possibly compounded by epigenetic inheritance. Our second key finding was that patterns of EE populations' divergence from ancestors differed among the ancestral isolines, suggesting that research conclusions derived for any particular genetic background should never be generalized without sampling a wider set of backgrounds. Overall, our results support the calls to pay more attention to biological variability when designing studies and interpreting their results, and to avoid over-generalizations of outcomes obtained for specific genetic and/or environmental conditions.

Scalable Synthesis of Planar Macroscopic Lipid-Based Multi-Compartment Structures

As life evolved, the path from simple single cell organisms to multicellular enabled increasingly complex functionalities. The spatial separation of reactions at the micron scale achieved by cellular structures allowed diverse and scalable implementation in biomolecular systems. Mimicking such spatially separated domains in a scalable approach could open a route to creating synthetic cell-like structured systems. Here, we report a facile and scalable method to create multicellular-like, multi-compartment (MC) structures. Aqueous droplet-based compartments ranging from 50 to 400 μm were stabilized and connected together by hydrophobic layers composed of phospholipids and an emulsifier. Planar centimeter-scale MC structures were formed by droplet deposition on a water interface. Further, the resulting macroscopic shapes were shown to be achieved by spatially controlled deposition. To demonstrate configurability and potential versatility, MC assemblies of both homogeneous and mixed compartment types were shown. Notably, magnetically heterogeneous systems were achieved by the inclusion of magnetic nanoparticles in defined sections. Such structures demonstrated actuated motion with structurally imparted directionality. These novel and functionalized structures exemplify a route toward future applications including compartmentally assembled "multicellular" molecular robots.

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.

Competition for finite resources as coordination mechanism for morphogenesis: An evolutionary algorithm study of digital embryogeny

The standard view of embryogenesis is one of cooperation driven by the cells' shared genetics and evolutionary interests. However, numerous examples from developmental biology and agriculture reveal a surprising amount of competition among body cells, tissues, and organs for both metabolic and informational resources. To explain the existence of such competition we had hypothesized that evolution uses limiting "reservoirs" of resource molecules as a communication medium - a global scratchpad, to enable tissues across the body to coordinate growth. Here, we test this hypothesis via an evolutionary simulation of embryogeny in silico. Genomes encode state transition rules for cells, such as proliferation, differentiation, and resource use, enabling virtual embryos to develop a specific large-scale morphology. An evolutionary algorithm operates over the genomes, with fitness defined as a function of specific morphological requirements for the final embryo shape. We found that not only does such an algorithm rapidly discover rules for cellular behavior that reliably make embryos with specific anatomical properties, but that it discovers the strategy of using finite resources to coordinate development. Given the option of using finite or infinite reservoirs (which determine cells' ability to carry out specific actions), evolution preferentially uses finite reservoirs, which results in higher fitness and increased consistency (without needing direct selection for morphological invariance). We report aspects of anatomical, physiological/transcriptional, and genomic analysis of evolved virtual embryos that help understand how evolution can use competition among genetically identical subunits within a multicellular body to coordinate reliable, complex morphogenesis. Our results suggest that under some conditions, composite multi-scale systems will promote conflict and artificial scarcity for their components.

Symbiotic Cell Differentiation and Cooperative Growth in Multicellular Aggregates

As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as evident in quorum sensing, to achieve mutualism and division of labor. Here, to achieve stable division of labor, three characteristics are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells without interaction and differentiation, by achieving division of labor. Third, this cell aggregate is robust with respect to the number distribution of differentiated cell types. Indeed, theoretical studies have thus far considered how such cooperation is achieved when the ability of cell differentiation is presumed. Here, we address how cells acquire the ability of cell differentiation and division of labor simultaneously, which is also connected with the robustness of a cell society. For this purpose, we developed a dynamical-systems model of cells consisting of chemical components with intracellular catalytic reaction dynamics. The reactions convert external nutrients into internal components for cellular growth, and the divided cells interact through chemical diffusion. We found that cells sharing an identical catalytic network spontaneously differentiate via induction from cell-cell interactions, and then achieve division of labor, enabling a higher growth rate than that in the unicellular case. This symbiotic differentiation emerged for a class of reaction networks under the condition of nutrient limitation and strong cell-cell interactions. Then, robustness in the cell type distribution was achieved, while instability of collective growth could emerge even among the cooperative cells when the internal reserves of products were dominant. The present mechanism is simple and general as a natural consequence of interacting cells with limited resources, and is consistent with the observed behaviors and forms of several aggregates of unicellular organisms.

Unicellular organisms, when aggregated under limited resources, often exhibit behaviors akin to multicellular organisms, possibly without advanced regulation mechanisms, as observed in biofilms and bacterial colonies. Cells in an aggregate have to differentiate into several types that are specialized for different tasks, so that the growth rate should be enhanced by the division of labor among these cell types. To consider how a cell aggregate can acquire these properties, most theoretical studies have thus far assumed the fitness of an aggregate of cells and the ability of cell differentiation a priori. In contrast, we developed a dynamical-systems model consisting of cells without assuming predefined fitness. The model consists of catalytic-reaction networks for cellular growth. By extensive simulations and theoretical analysis of the model, we showed that cells growing under the condition of nutrient limitation and strong cell-cell interactions can differentiate with distinct chemical compositions. They achieve cooperative division of labor by exchanging the produced chemicals to attain a higher growth rate. The conditions for spontaneous cell differentiation and collective growth of cells are presented. The uncovered symbiotic differentiation and collective growth are akin to economic theory on division of labor and comparative advantage.

Using evolutionary computations to understand the design and evolution of gene and cell regulatory networks

This paper surveys modeling approaches for studying the evolution of gene regulatory networks (GRNs). Modeling of the design or 'wiring' of GRNs has become increasingly common in developmental and medical biology, as a means of quantifying gene-gene interactions, the response to perturbations, and the overall dynamic motifs of networks. Drawing from developments in GRN 'design' modeling, a number of groups are now using simulations to study how GRNs evolve, both for comparative genomics and to uncover general principles of evolutionary processes. Such work can generally be termed evolution in silico. Complementary to these biologically-focused approaches, a now well-established field of computer science is Evolutionary Computations (ECs), in which highly efficient optimization techniques are inspired from evolutionary principles. In surveying biological simulation approaches, we discuss the considerations that must be taken with respect to: (a) the precision and completeness of the data (e.g. are the simulations for very close matches to anatomical data, or are they for more general exploration of evolutionary principles); (b) the level of detail to model (we proceed from 'coarse-grained' evolution of simple gene-gene interactions to 'fine-grained' evolution at the DNA sequence level); (c) to what degree is it important to include the genome's cellular context; and (d) the efficiency of computation. With respect to the latter, we argue that developments in computer science EC offer the means to perform more complete simulation searches, and will lead to more comprehensive biological predictions.

Beyond crystals: the dialectic of materials and information

We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The complex structures now being studied in biology and produced in nanotechnology have outstripped the framework of classical crystallography, and a variety of organizing concepts are now taking shape into a more modern and dynamic science of structure, form and function. Absolute stability and equilibrium are replaced by metastable structures existing in a flux of energy-carrying information and moving within an energy landscape of complex topology. Structures give place to processes and processes to systems. The fundamental level is that of atoms. As smaller and smaller groups of atoms are used for their physical properties, quantum effects become important; already we see quantum computation taking shape. Concepts move towards those in life with the emergence of specifically informational structures. We now see the possibility of the artificial construction of a synthetic living system, different from biological life, but having many or all of the same properties. Interactions are essentially nonlinear and collective. Structures begin to have an evolutionary history with episodes of symbiosis. Underlying all the structures are constraints of time and space. Through hierarchization, a more general principle than the periodicity of crystals, structures may be found within structures on different scales. We must integrate unifying concepts from dynamical systems and information theory to form a coherent language and science of shape and structure beyond crystals. To this end, we discuss the idea of categorizing structures based on information according to the algorithmic complexity of their assembly.

Enhancing apoptosis in TRAIL-resistant cancer cells using fundamental response rules

The tumor necrosis factor related apoptosis-inducing ligand (TRAIL) induces apoptosis in malignant cells, while leaving other cells mostly unharmed. However, several carcinomas remain resistant to TRAIL. To investigate the resistance mechanisms in TRAIL-stimulated human fibrosarcoma (HT1080) cells, we developed a computational model to analyze the temporal activation profiles of cell survival (IκB, JNK, p38) and apoptotic (caspase-8 and -3) molecules in wildtype and several (FADD, RIP1, TRAF2 and caspase-8) knock-down conditions. Based on perturbation-response approach utilizing the law of information (signaling flux) conservation, we derived response rules for population-level average cell response. From this approach, i) a FADD-independent pathway to activate p38 and JNK, ii) a crosstalk between RIP1 and p38, and iii) a crosstalk between p62 and JNK are predicted. Notably, subsequent simulations suggest that targeting a novel molecule at p62/sequestosome-1 junction will optimize apoptosis through signaling flux redistribution. This study offers a valuable prospective to sensitive TRAIL-based therapy.

Towards predictive models of stem cell fate

Quantitative approaches are essential for the advancement of strategies to manipulate stem cells or their derivatives for therapeutic applications. Predictive models of stem cell systems would provide the means to pose and validate non-intuitive hypotheses and could thus serve as an important tool for discerning underlying regulatory mechanisms governing stem cell fate decisions. In this paper we review the development of computational models that attempt to describe mammalian adult and embryonic stem (ES) cell responses. Early stochastic models that relied exclusively on statistical distributions to describe the in vitro or in vivo output of stem cells are being revised to incorporate the contributions of exogenous and endogenous parameters on specific stem cell fate processes. Recent models utilize cell specific data (for example, cell-surface receptor distributions, transcription factor half-lives, cell-cycle status, etc.) to provide mechanistic descriptions that are consistent with biologically observed phenomena. Ultimately, the goal of these computational models is to, a priori, predict stem cell output given an initial set of conditions. Our efforts to develop a predictive model of ES cell fate are discussed. The quantitative studies presented in this review represent an important step in developing bioengineering approaches to characterize and predict stem cell behavior. Ongoing efforts to incorporate genetic and signaling network data into computational models should accelerate our understanding of fundamental principles governing stem cell fate decisions.

Computational systems biology of aging

Computational systems biology is expected to make major contributions to unravel the complex molecular mechanisms underlying the progression of aging in cells, tissues, and organisms. The development of computational approaches is, however, challenged by a wide spectrum of aging mechanisms participating on different levels of biological organization. The tight connectivity between the molecular constituents, functions, and cell states requires frameworks and strategies that extend beyond current practice to model, simulate, and predict the progression of aging and the emerging aging phenotypes. We provide a general overview of the specific computational tasks and opportunities in aging research, and discuss some illustrative systems level concepts in more detail. One example provided here is the assembly of a conceptual whole cell model that considers the temporal dynamics of the aging process grounded on molecular mechanisms. Another application is the assembly of interactomes, such as protein networks that allow us to analyze changes in network topology and interaction of proteins that have been implicated in aging with other cellular constituents and processes. We introduce the necessary key steps to build these applications and discuss their merits and future extensions for aging research. WIREs Syst Biol Med 2011 3 414-428 DOI: 10.1002/wsbm.126

Unified description of regeneration by coupled dynamical systems theory: intercalary/segmented regeneration in insect legs

Regeneration phenomena are ubiquitous in nature and are studied in a variety of experiments. Positional information and feedback-loop hierarchy are theories that have been proposed to explain ordering rules in regeneration; however, some regeneration phenomena violate the rules derived from them. In particular, grafted junction stumps with the same value/hierarchy sometimes lead to one extra segmented portion, termed segmented regeneration. To present a unified description of all insect leg regeneration phenomena, we propose a theoretical mechanism for regeneration without postulating positional information, by using a model that consists of intracellular reaction dynamics of chemical concentrations, cell-to-cell interactions, and an increase in cell number. As a normal developmental process, successive differentiation from pluripotent cells appears, as described by transition from cells with intracellular chaotic dynamics to those with oscillatory or fixed-point dynamics. By assigning chaotic and nonchaotic cell types to corresponding positions instead of positional information, intercalary, segmented, and tarsus regeneration are explained coherently. With this assignment of pluripotency to chaotic dynamics, a unified description of regeneration is obtained with some predictive value for new experiments.

Morphogenesis by coupled regulatory networks: reliable control of positional information and proportion regulation

Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multicellular organisms.

Consistency principle in biological dynamical systems

We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are derived and confirmed experimentally. They include a power law distribution of gene expressions, a lognormal distribution of cellular chemical abundances over cells, and embedding of the power law into the network connectivity distribution. Second, given a consistency between genotype and phenotype, a general relationship between phenotype fluctuations by genetic variation and isogenic phenotypic fluctuation by developmental noise is derived. Third, we discuss the chaos mechanism for stem cell differentiation with autonomous regulation, resulting from a consistency between cell reproduction and growth of the cell ensemble.

Evolutionary Conservation of MicroRNA Regulatory Circuits: An Examination of MicroRNA Gene Complexity and Conserved MicroRNA-Target Interactions through Metazoan Phylogeny

During the last decade, a variety of critical biological processes, including early embryo development, cell proliferation, differentiation, apoptosis, and metabolic regularity, have been shown to be genetically regulated by a large gene family encoding a class of tiny RNA molecules termed microRNAs (miRNAs). All miRNAs share a common biosynthetic pathway and reaction mechanisms. The sequence of many miRNAs is found to be conserved, in their mature form, among different organisms. In addition, the evolutionary appearance of multicellular organisms appears to correlate with the appearance of the miRNA pathway for regulating gene expression. The miRNA pathway has the potential to regulate vast networks of gene products in a coordinate manner. Recent evidence has not only implicated the miRNA pathway in regulating a vast array of basic cellular processes but also specialized processes that are required for cellular identity and tissue specificity. A survey of the literature shows that some miRNA pathways are conserved virtually intact throughout phylogeny while miRNA diversity also correlates with speciation. The number of miRNA genes, the expression of miRNAs, and target diversities of miRNAs tend to be positively correlated with morphological complexities observed in animals. Thus, organismal complexity can be estimated by the complexity of the miRNA circuitry. The complexity of the miRNA gene families establishes a link between genotypic complexity and phenotypic complexity in animal evolution. In this paper, we start with the discussion of miRNA conservation. Then we interpret the trends in miRNA conservation to deduce miRNA evolutionary trends in metazoans. Based on these conservation patterns observed in each component of the miRNA regulatory system, we attempt to propose a global insight on the probable consistency between morphological evolution in animals and the molecular evolution of miRNA gene activity in the cell.

Evolution of complexity in signaling pathways

It is not clear how biological pathways evolve to mediate a certain physiological response and why they show a level of complexity that is generally above the minimum required to achieve such a response. One possibility is that pathway complexity increases due to the nature of evolutionary mechanisms. Here, we analyze this possibility by using mathematical models of biological pathways and evolutionary simulations. Starting with a population of small pathways of three proteins, we let the population evolve with mutations that affect pathway structure through duplication or deletion of existing proteins, deletion or creation of interactions among them, or addition of new proteins. Our simulations show that such mutational events, coupled with a selective pressure, leads to growth of pathways. These results indicate that pathways could be driven toward complexity via simple evolutionary mechanisms and that complexity can arise without any specific selective pressure for it. Furthermore, we find that the level of complexity that pathways evolve toward depends on the selection criteria. In general, we find that final pathway size tends to be lower when pathways evolve under stringent selection criteria. This leads to the counterintuitive conclusion that simple response requirements on a pathway would facilitate its evolution toward higher complexity.

Evolutionary origin of power-laws in a biochemical reaction network: embedding the distribution of abundance into topology

The evolutionary origin of general statistics in a biochemical reaction network is studied here to explain the power-law distribution of reaction links and the power-law distribution of chemical abundance. Using cell models with catalytic reaction networks, we have confirmed that the power-law distribution for the abundance of chemicals emerges by the selection of cells with higher growth rates, as suggested in our previous study [Phys. Rev. Lett. 90, 088102 (2003)]. Through further evolution, this inhomogeneity in chemical abundance is shown to be embedded in the distribution of links, leading to the power-law distribution. We analyze the mechanism of this embedding and discuss the generality of the results.

The origin of hematopoietic cell type diversity

The hematopoietic system remains robust with regards to extrinsic perturbations, in sharp contrast with the stochastic behavior of hematopoeitic stem cells (HSCs) at the single cell level, suggesting that stability may be achieved within a stem cell system that undergoes constant self-renewal, commitment to differentiation and generates cell type diversification. Converging evidence at the interface of cellular, molecular and numerical studies suggests that diversity is generated by the chaotic dynamics of transcription factor networks within a cell and of the combination of growth factors and cytokines in the environment, both involving cooperation and competition. Current evidence indicates that HSCs are primed for multilineage gene expression. A subtle shift in transcription factor dosage is sufficient to perturb this equilibrium and to drive lineage commitment that involves a resolution of complexity at the molecular level and a transition towards less chaotic behavior. This dynamical instability establishes a state of responsiveness to extrinsic signals. Evolutionary conserved environmental cues that drive pattern formation or migratory behavior during embryonic development operate in the adult to influence the decision between self-renewal and differentiation in HSCs, as exemplified by the role of Notch1, Wnt proteins, BMPs and VEGF. In contrast, a network of cytokines uniquely present in mammalians influences later developmental stages, from progenitors with more restricted potentials (tri-, bi- or unipotent) to mature functional cells. These cytokines have co-opted the ancient Jak-STAT pathway but also appear to trigger lineage-affiliated transcription factors, thus linking environmental signaling to cell fate decisions.

Robust development as a consequence of generated positional information

The origin and robustness of morphogenesis are studied by dynamical system modeling of a cell society, in which cells possessing internal chemical reaction dynamics interact with each other through their mutual interaction with diffusive chemicals in a two-dimensional medium. It is found that stem-type cells differentiate into various cell types (where a cell 'type' is defined by a type of intra-cellular dynamics) due to a dynamic instability caused by cell-cell interactions in a manner described by the isologous diversification theory. The differentiations are spatially regulated by the concentration of chemicals in the medium, while the chemical concentrations are locally influenced by the intra-cell dynamics. Through this reciprocal relationship, chemical concentrations come to exhibit spatial variation as differentiated cell types begin to emerge, and as a result the regulation exercised by the chemical concentrations become spatially inhomogeneous. This reinforces the process of differentiation, through which spatial patterns of differentiated cells appear. Within this reciprocal relationship, the concentration gradients are read and interpreted by the cell as positional information. A spatial order of cells realized in this process represents a stable state of the system governed by this reciprocal relationship, and that the developmental process through which this state is realized is robust with respect to perturbations. The dependence of the morphogenesis on history and the community effect in cell differentiation are also discussed.

Origin of multicellular organisms as an inevitable consequence of dynamical systems

The origin of multicellular organisms is studied by considering a cell system that satisfies minimal conditions, that is, a system of interacting cells with intracellular biochemical dynamics, and potentiality in reproduction. Three basic features in multicellular organisms-cellular diversification, robust developmental process, and emergence of germ-line cells-are found to be general properties of such a system. Irrespective of the details of the model, such features appear when there are complex oscillatory dynamics of intracellular chemical concentrations. Cells differentiate from totipotent stem cells into other cell types due to instability in the intracellular dynamics with cell-cell interactions, as explained by our isologous diversification theory (Furusawa and Kaneko, 1998a; Kaneko and Yomo, 1997). This developmental process is shown to be stable with respect to perturbations, such as molecular fluctuations and removal of some cells. By further imposing an adequate cell-type-dependent adhesion force, some cells are released, from which the next generation cell colony is formed, and a multicellular organism life-cycle emerges without any finely tuned mechanisms. This recursive production of multicellular units is stabilized if released cells are few in number, implying the separation of germ cell lines. Furthermore, such an organism with a variety of cellular states and robust development is found to maintain a larger growth speed as an ensemble by achieving a cooperative use of resources, compared to simple cells without differentiation. Our results suggest that the emergence of multicellular organisms is not a "difficult problem" in evolution, but rather is a natural consequence of a cell colony that can grow continuously.

Stem cell bioengineering

Tissue engineering and cellular therapies, either on their own or in combination with therapeutic gene delivery, have the potential to significantly impact medicine. Implementation of technologies based on these approaches requires a readily available source of cells for the generation of cells and tissues outside a living body. Because of their unique capacity to regenerate functional tissue for the lifetime of an organism, stem cells are an attractive "raw material" for multiple biotechnological applications. By definition they are self-renewing because on cell division they can generate daughter stem cells. They are also multipotent because they can differentiate into numerous specialized, functional cells. Recent findings have shown that stem cells exist in most, if not all, tissues, and that stem cell tissue specificity may be more flexible than originally thought. Although the potential for producing novel cell-based products from stem cells is large, currently there are no effective technologically relevant methodologies for culturing stem cells outside the body, or for reproducibly stimulating them to differentiate into functional cells. A mechanistic understanding of the parameters important in the control of stem cell self-renewal and lineage commitment is thus necessary to guide the development of bioprocesses for the ex vivo culture of stem cells and their derivates.

Dynamics of coupling functions in globally coupled maps: size, periodicity, and stability of clusters

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the formation of clusters in a globally coupled map system and the resulting periodicity of the global interaction. The allowed distributions of elements among periodic clusters is also found to depend on the functional form of the coupling. Through the analogy between globally coupled maps and a single driven map, the clustering behavior of the former systems can be characterized. By using this analogy, the dynamics of periodic clusters in systems displaying a constant global coupling are predicted; and for a particular family of coupling functions, it is shown that the stability condition of these clustered states can straightforwardly be derived.

Theory of robustness of irreversible differentiation in a stem cell system: chaos hypothesis

Based on an extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the "chaos hypothesis". Two fundamental features of stem cell systems-stochastic differentiation of stem cells and the robustness of a system due to regulation of this differentiation-are found to be general properties of a system of interacting cells exhibiting chaotic intra-cellular reaction dynamics and cell division, whose presence does not depend on the detail of the model. It is found that stem cells differentiate into other cell types stochastically due to a dynamical instability caused by cell-cell interactions, in a manner described by the Isologous Diversification theory. This developmental process is shown to be stable not only with respect to molecular fluctuations but also with respect to the removal of cells. With this developmental process, the irreversible loss of multipotency accompanying the change from a stem cell to a differentiated cell is shown to be characterized by a decrease in the chemical diversity in the cell and of the complexity of the cellular dynamics. The relationship between the division speed and the loss of multipotency is also discussed. Using our model, some predictions that can be tested experimentally are made for a stem cell system.

Transitions induced by the discreteness of molecules in a small autocatalytic system

The autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as an extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with changes of the system size and flow is studied, while a single-molecule switch of the molecule distributions is reported. The relevance of the results to intracellular processes is briefly discussed.

Dynamical clustering in large populations of Rossler oscillators under the action of noise

The effects of noise on the dynamical clustering of globally coupled chaotic Rossler oscillators are numerically investigated. Stable clusters and intermittent clustering regimes are found, depending on the coupling intensity and the noise level. Our results agree with the first experimental observations of dynamical clustering recently reported for globally coupled electrochemical oscillators.