Isologous diversification: a theory of cell differentiation

Exploring the mechanisms of cell reprogramming and transdifferentiation via intercellular communication

In the past years, the mechanisms of cell reprogramming and transdifferentiation via the way of gene regulation, stochastic fluctuations, or chemical induction to realize cell type transitions from the perspectives of single cells were explored. In multicellular organisms, intercellular communication plays crucial roles in cell fate decisions. However, the importance of intercellular communication to the processes of cell reprogramming and transdifferentiation is often neglected. In this paper, the mechanisms of cell reprogramming and transdifferentiation by intercellular communication are investigated. A two-gene circuit with mutual inhibition and self-activation as a basic model is selected. Then, a coupling mechanism via intercellular communication by introducing a specific signaling molecule into the gene circuit is considered. Finally, the influence of coupling intensity on the dynamics of the coupled system of two cells is analyzed. Moreover, when the coupling intensity changes with respect to the cell number in a discrete way, the effects of coupling intensity on cell reprogramming and transdifferentiation are discussed. Some theoretical analysis of stability and bifurcation of the systems are also given. Our research shows that cells can realize cell reprogramming and transdifferentiation via intercellular interaction at opportune coupling intensity. These results not only further enrich previous studies but also are beneficial to understand the mechanisms of cell reprogramming and transdifferentiation via intercellular communication in the growth and development of multicellular organisms.

Lzts1 controls both neuronal delamination and outer radial glial-like cell generation during mammalian cerebral development

In the developing central nervous system, cell departure from the apical surface is the initial and fundamental step to form the 3D, organized architecture. Both delamination of differentiating cells and repositioning of progenitors to generate outer radial glial cells (oRGs) contribute to mammalian neocortical expansion; however, a comprehensive understanding of their mechanisms is lacking. Here, we demonstrate that Lzts1, a molecule associated with microtubule components, promotes both cell departure events. In neuronally committed cells, Lzts1 functions in apical delamination by altering apical junctional organization. In apical RGs (aRGs), Lzts1 expression is variable, depending on Hes1 expression levels. According to its differential levels, Lzts1 induces diverse RG behaviors: planar division, oblique divisions of aRGs that generate oRGs, and their mitotic somal translocation. Loss-of-function of lzts1 impairs all these cell departure processes. Thus, Lzts1 functions as a master modulator of cellular dynamics, contributing to increasing complexity of the cerebral architecture during evolution.

Outer radial glial cells (oRGs) are undifferentiated cells that divide in the subventricular zone during neurodevelopment, but the underlying mechanisms are not fully understood. Here the authors show that Lzts1 positively controls both neuronal delamination and generation of oRG-like cell types.

Emergence of microbial diversity due to cross-feeding interactions in a spatial model of gut microbial metabolism

Background

The human gut contains approximately 10¹⁴ bacteria, belonging to hundreds of different species. Together, these microbial species form a complex food web that can break down nutrient sources that our own digestive enzymes cannot handle, including complex polysaccharides, producing short chain fatty acids and additional metabolites, e.g., vitamin K. Microbial diversity is important for colonic health: Changes in the composition of the microbiota have been associated with inflammatory bowel disease, diabetes, obesity and Crohn’s disease, and make the microbiota more vulnerable to infestation by harmful species, e.g., Clostridium difficile. To get a grip on the controlling factors of microbial diversity in the gut, we here propose a multi-scale, spatiotemporal dynamic flux-balance analysis model to study the emergence of metabolic diversity in a spatial gut-like, tubular environment. The model features genome-scale metabolic models (GEM) of microbial populations, resource sharing via extracellular metabolites, and spatial population dynamics and evolution.

Results

In this model, cross-feeding interactions emerge readily, despite the species’ ability to metabolize sugars autonomously. Interestingly, the community requires cross-feeding for producing a realistic set of short-chain fatty acids from an input of glucose, If we let the composition of the microbial subpopulations change during invasion of adjacent space, a complex and stratified microbiota evolves, with subspecies specializing on cross-feeding interactions via a mechanism of compensated trait loss. The microbial diversity and stratification collapse if the flux through the gut is enhanced to mimic diarrhea.

Conclusions

In conclusion, this in silico model is a helpful tool in systems biology to predict and explain the controlling factors of microbial diversity in the gut. It can be extended to include, e.g., complex nutrient sources, and host-microbiota interactions via the intestinal wall.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0430-4) contains supplementary material, which is available to authorized users.

Pluripotency, Differentiation, and Reprogramming: A Gene Expression Dynamics Model with Epigenetic Feedback Regulation

Embryonic stem cells exhibit pluripotency: they can differentiate into all types of somatic cells. Pluripotent genes such as Oct4 and Nanog are activated in the pluripotent state, and their expression decreases during cell differentiation. Inversely, expression of differentiation genes such as Gata6 and Gata4 is promoted during differentiation. The gene regulatory network controlling the expression of these genes has been described, and slower-scale epigenetic modifications have been uncovered. Although the differentiation of pluripotent stem cells is normally irreversible, reprogramming of cells can be experimentally manipulated to regain pluripotency via overexpression of certain genes. Despite these experimental advances, the dynamics and mechanisms of differentiation and reprogramming are not yet fully understood. Based on recent experimental findings, we constructed a simple gene regulatory network including pluripotent and differentiation genes, and we demonstrated the existence of pluripotent and differentiated states from the resultant dynamical-systems model. Two differentiation mechanisms, interaction-induced switching from an expression oscillatory state and noise-assisted transition between bistable stationary states, were tested in the model. The former was found to be relevant to the differentiation process. We also introduced variables representing epigenetic modifications, which controlled the threshold for gene expression. By assuming positive feedback between expression levels and the epigenetic variables, we observed differentiation in expression dynamics. Additionally, with numerical reprogramming experiments for differentiated cells, we showed that pluripotency was recovered in cells by imposing overexpression of two pluripotent genes and external factors to control expression of differentiation genes. Interestingly, these factors were consistent with the four Yamanaka factors, Oct4, Sox2, Klf4, and Myc, which were necessary for the establishment of induced pluripotent stem cells. These results, based on a gene regulatory network and expression dynamics, contribute to our wider understanding of pluripotency, differentiation, and reprogramming of cells, and they provide a fresh viewpoint on robustness and control during development.

Characterization of pluripotent states, in which cells can both self-renew and differentiate, and the irreversible loss of pluripotency are important research areas in developmental biology. In particular, an understanding of these processes is essential to the reprogramming of cells for biomedical applications, i.e., the experimental recovery of pluripotency in differentiated cells. Based on recent advances in dynamical-systems theory for gene expression, we propose a gene-regulatory-network model consisting of several pluripotent and differentiation genes. Our results show that cellular-state transition to differentiated cell types occurs as the number of cells increases, beginning with the pluripotent state and oscillatory expression of pluripotent genes. Cell-cell signaling mediates the differentiation process with robustness to noise, while epigenetic modifications affecting gene expression dynamics fix the cellular state. These modifications ensure the cellular state to be protected against external perturbation, but they also work as an epigenetic barrier to recovery of pluripotency. We show that overexpression of several genes leads to the reprogramming of cells, consistent with the methods for establishing induced pluripotent stem cells. Our model, which involves the inter-relationship between gene expression dynamics and epigenetic modifications, improves our basic understanding of cell differentiation and reprogramming.

Minimal model for stem-cell differentiation

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell-cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point-type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent determination of the effective bifurcation parameter as a result of the cell-cell interaction. Complex cell differentiation is designed by combing these simple two-gene networks. The generality of the present differentiation mechanism, as well as its biological relevance, is discussed.

Challenges for complex microbial ecosystems: combination of experimental approaches with mathematical modeling

In the past couple of decades, molecular ecological techniques have been developed to elucidate microbial diversity and distribution in microbial ecosystems. Currently, modern techniques, represented by meta-omics and single cell observations, are revealing the incredible complexity of microbial ecosystems and the large degree of phenotypic variation. These studies propound that microbiological techniques are insufficient to untangle the complex microbial network. This minireview introduces the application of advanced mathematical approaches in combination with microbiological experiments to microbial ecological studies. These combinational approaches have successfully elucidated novel microbial behaviors that had not been recognized previously. Furthermore, the theoretical perspective also provides an understanding of the plasticity, robustness and stability of complex microbial ecosystems in nature.

Kinetic origin of heredity in a replicating system with a catalytic network

The origin of heredity is studied as a recursive state in a replicatingprotocell consisting of many molecule species in mutually catalyzingreaction networks. Protocells divide when the number of molecules, increasing due to replication, exceeds a certain threshold. We study how the chemicals in a catalytic network can form recursive production states in the presence of errors in the replication process. Depending on the balance between the total number of molecules in a cell and the number of molecule species, we have found three phases; a phase without a recursive production state, a phase with itinerancy over a few recursive states, and a phase with fixedrecursive production states. Heredity is realized in the latter two phaseswhere molecule species that are population-wise in the minority are preserved and control the phenotype of the cell. It is shown that evolvability is realized in the itinerancy phase, where a change in the number of minority molecules controls a change of the chemical state.

Oscillatory protein expression dynamics endows stem cells with robust differentiation potential

The lack of understanding of stem cell differentiation and proliferation is a fundamental problem in developmental biology. Although gene regulatory networks (GRNs) for stem cell differentiation have been partially identified, the nature of differentiation dynamics and their regulation leading to robust development remain unclear. Herein, using a dynamical system modeling cell approach, we performed simulations of the developmental process using all possible GRNs with a few genes, and screened GRNs that could generate cell type diversity through cell-cell interactions. We found that model stem cells that both proliferated and differentiated always exhibited oscillatory expression dynamics, and the differentiation frequency of such stem cells was regulated, resulting in a robust number distribution. Moreover, we uncovered the common regulatory motifs for stem cell differentiation, in which a combination of regulatory motifs that generated oscillatory expression dynamics and stabilized distinct cellular states played an essential role. These findings may explain the recently observed heterogeneity and dynamic equilibrium in cellular states of stem cells, and can be used to predict regulatory networks responsible for differentiation in stem cell systems.

Comparative transcriptome analysis reveals vertebrate phylotypic period during organogenesis

One of the central issues in evolutionary developmental biology is how we can formulate the relationships between evolutionary and developmental processes. Two major models have been proposed: the 'funnel-like' model, in which the earliest embryo shows the most conserved morphological pattern, followed by diversifying later stages, and the 'hourglass' model, in which constraints are imposed to conserve organogenesis stages, which is called the phylotypic period. Here we perform a quantitative comparative transcriptome analysis of several model vertebrate embryos and show that the pharyngula stage is most conserved, whereas earlier and later stages are rather divergent. These results allow us to predict approximate developmental timetables between different species, and indicate that pharyngula embryos have the most conserved gene expression profiles, which may be the source of the basic body plan of vertebrates.

The conservation of embryonic development across species is of great interest in evolutionary biology. Here, using transcriptome analysis, the authors show that the pharyngula stage of development—in mid-embryogenesis—is conserved between mice, chickens, frogs and zebrafish.

Cell-cell interaction and diversity of emergent behaviours

Despite myriads of possible gene expression profiles, cells tend to be found in a confined number of expression patterns. The dynamics of Boolean models of gene regulatory networks has proven to be a likely candidate for the description of such self-organisation phenomena. Because cells do not live in isolation, but they constantly shape their functions to adapt to signals from other cells, this raises the question of whether the cooperation among cells entails an expansion or a reduction of their possible steady states. Multi random Boolean networks are introduced here as a model for interaction among cells that might be suitable for the investigation of some generic properties regarding the influence of communication on the diversity of cell behaviours. In spite of its simplicity, the model exhibits a non-obvious phenomenon according to which a moderate exchange of products among adjacent cells fosters the variety of their possible behaviours, which on the other hand are more similar to one another. On the contrary, a more invasive coupling would lead cells towards homogeneity.

Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness: dynamical systems theory of gene expressions under cell-cell interaction explains mutational robustness of differentiated cells and suggests how cancer cells emerge

Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.

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.

Chaotic expression dynamics implies pluripotency: when theory and experiment meet

Background

During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells.

Presentation of the hypothesis

To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic) oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency.

Testing the hypothesis

To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS) analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can examine whether the loss of pluripotency is accompanied by a loss of oscillation.

Implications of the hypothesis

Recovery of pluripotency from determined cells is a long-standing aspiration, from both scientific and clinical perspectives. Our hypothesis suggests a feasible route to recover the potential to differentiate, i.e., by increasing the variety of expressed genes to restore chaotic expression dynamics, as is consistent with the recent generation of induced pluripotent stem (iPS) cells.

Reviewers

This article was reviewed by David Krakauer, Jeroen van Zon (nominated by Rob de Boer), and Williams S. Hlavacek.

Using cell fate attractors to uncover transcriptional regulation of HL60 neutrophil differentiation

BACKGROUND

The process of cellular differentiation is governed by complex dynamical biomolecular networks consisting of a multitude of genes and their products acting in concert to determine a particular cell fate. Thus, a systems level view is necessary for understanding how a cell coordinates this process and for developing effective therapeutic strategies to treat diseases, such as cancer, in which differentiation plays a significant role. Theoretical considerations and recent experimental evidence support the view that cell fates are high dimensional attractor states of the underlying molecular networks. The temporal behavior of the network states progressing toward different cell fate attractors has the potential to elucidate the underlying molecular mechanisms governing differentiation.

RESULTS

Using the HL60 multipotent promyelocytic leukemia cell line, we performed experiments that ultimately led to two different cell fate attractors by two treatments of varying dosage and duration of the differentiation agent all-trans-retinoic acid (ATRA). The dosage and duration combinations of the two treatments were chosen by means of flow cytometric measurements of CD11b, a well-known early differentiation marker, such that they generated two intermediate populations that were poised at the apparently same stage of differentiation. However, the population of one treatment proceeded toward the terminally differentiated neutrophil attractor while that of the other treatment reverted back toward the undifferentiated promyelocytic attractor. We monitored the gene expression changes in the two populations after their respective treatments over a period of five days and identified a set of genes that diverged in their expression, a subset of which promotes neutrophil differentiation while the other represses cell cycle progression. By employing promoter based transcription factor binding site analysis, we found enrichment in the set of divergent genes, of transcription factors functionally linked to tumor progression, cell cycle, and development.

CONCLUSION

Since many of the transcription factors identified by this approach are also known to be implicated in hematopoietic differentiation and leukemia, this study points to the utility of incorporating a dynamical systems level view into a computational analysis framework for elucidating transcriptional mechanisms regulating differentiation.

When does division of labor lead to increased system output?

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models: in the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. The results of our model are consistent with the behavior of the cellular slime mold Dictyostelium discodeum, which switches from a single-celled to a multi-celled state when resources become limited. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stem-cell-based tissue architecture in complex organisms. Finally, the results of this paper may be useful for understanding how, in an economic context, firm productivity is maximized at intermediate firm sizes.

Derivation of rigorous conditions for high cell-type diversity by algebraic approach

The development of a multicellular organism is a dynamic process. Starting with one or a few cells, the organism develops into different types of cells with distinct functions. We have constructed a simple model by considering the cell number increase and the cell-type order conservation, and have assessed conditions for cell-type diversity. This model is based on a stochastic Lindenmayer system with cell-to-cell interactions for three types of cells. In the present model, we have successfully derived complex but rigorous algebraic relations between the proliferation and transition rates for cell-type diversity by using a symbolic method: quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates have emerged for large ratios of the initial cells to the developed cells. The three modes have revealed that the equality between the development rates for the highest cell-type diversity is reduced during the development process of multicellular organisms. Furthermore, we have found that the highest cell-type diversity originates from order conservation.

State differentiation by transient truncation in coupled threshold dynamics

Dynamics with a threshold input-output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. The universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.

Adaptive response of a gene network to environmental changes by fitness-induced attractor selection

Cells switch between various stable genetic programs (attractors) to accommodate environmental conditions. Signal transduction machineries efficiently convey environmental changes to the gene regulation apparatus in order to express the appropriate genetic program. However, since the number of environmental conditions is much larger than that of available genetic programs so that the cell may utilize the same genetic program for a large set of conditions, it may not have evolved a signaling pathway for every environmental condition, notably those that are rarely encountered. Here we show that in the absence of signal transduction, switching to the appropriate attractor state expressing the genes that afford adaptation to the external condition can occur. In a synthetic bistable gene switch in Escherichia coli in which mutually inhibitory operons govern the expression of two genes required in two alternative nutritional environments, cells reliably selected the “adaptive attractor” driven by gene expression noise. A mathematical model suggests that the “non-adaptive attractor” is avoided because in unfavorable conditions, cellular activity is lower, which suppresses mRNA metabolism, leading to larger fluctuations in gene expression. This, in turn, renders the non-adaptive state less stable. Although attractor selection is not as efficient as signal transduction via a dedicated cascade, it is simple and robust, and may represent a primordial mechanism for adaptive responses that preceded the evolution of signaling cascades for the frequently encountered environmental changes.

Inherent characteristics of gene expression for buffering environmental changes without the corresponding transcriptional regulations

Gene expression patterning is crucial for environmental nutritional responses such as the nitrogen response in Escherichia coli. The nitrogen response is primarily regulated by the expression of glutamine synthetase (GS), which catalyzes the sole reaction of glutamine formation, by cis-logic regulatory circuits. Here, by removing the entire corresponding operator and promoter regions required for the control of GS, we constructed an E. coli strain that enables the detection of the basal GS gene expression, which is expressed from a plain promoter unrelated to the nitrogen response, and measured by co-transcribed GFP expression, an indicator of GS expression. Using strain cultures, we found that the GS expression level was able to shift inversely against the change of the environmental glutamine concentration. As a control experiment, we repeated similar experiments with another strain in which the GS regulatory region remained intact and the GFP gene following the plain promoter was introduced into a different chromosomal site. For this strain, we found that the GFP expression level did not shift in accordance with the environmental glutamine concentration. These results showed that GS expression from the plain promoter exhibited a responsive ability to buffer environmental changes, whereas the GS expression shift did not correlate with the specific characteristics of the plain promoter and GFP expression. This study identifies the inherent characteristics of basal gene expression in response to environmental changes, facilitating a deeper understanding of cellular design principles.

Selection of initial conditions for recursive production of multicellular organisms

The development of a multicellular organism is a dynamic process. Starting from one or a few cells, the organism becomes a set of cells with different types that form well-determined patterns. It is rather surprising that differentiation in cell types and formation of controlled patterns are compatible, because the former gives morphogenetic diversification whereas the latter implies recursive production of a cell ensemble, reducing individual differences. We studied this problem by taking a simple cell model with intracellular reaction dynamics of chemical concentrations, cell-cell interactions, and increase in cell numbers. We observed successive differentiation from a cell type with diverse chemicals and chaotic concentration dynamics to cell types with oscillatory or fixed-point dynamics, leading to morphogenetic diversity in a spatial pattern. We further show that, by starting from an initial object consisting of both the former cell type with diverse chemicals and the latter differentiated cell type, the recursive production of a multicellular organism with morphogenetic diversity is possible. By relating the former type to a cell in the vegetal pole and the latter to one in the animal pole, classic experimental results with separation of blastomeres in sea urchin eggs are coherently explained, while some predictions are made for in vitro morphogenesis from embryonic stem cells.

Dynamical systems basis of metamorphosis: diversity and plasticity of cellular states in reaction diffusion network

Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relation to the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics and considering the division and death of cells, the development of cells is studied. Cell differentiation process is found to occur through instability in transient dynamics and cell-cell interaction. In long-term behavior, extinction of multiple cells is repeated, which leads to itinerancy over successive quasi-stable multi-cellular states consisting of different types of cells. By defining the plasticity of a cellular state, it is shown that the plasticity of cells decreases before the extinction of most cell types, from which diversity and plasticity are later recovered. In the following, a decrease of plasticity occurs again, leading to the next extinction. This cycle of diversification and extinction is repeated. Relevance of our results to development and evolution is briefly discussed.

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.

Recursiveness, switching, and fluctuations in a replicating catalytic network

A protocell model consisting of mutually catalyzing molecules is studied, in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the numbers of molecules and species, and the path rate, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.

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.

On a kinetic origin of heredity: minority control in a replicating system with mutually catalytic molecules

As the first step in an investigation of the origin of genetic information, we study how some species of molecules are preserved over cell generations and play an important role in controlling the growth of a cell. We consider a model consisting of protocells. Each protocell contains two mutually catalysing molecule species (X and Y), each of which has catalytically active and inactive types. One of the species Y is assumed to have a slower synthesis speed. Through divisions of the protocells, the system reaches and remains in a state in which there are only a few active Y and almost no inactive Y molecules in most protocells, through the selection of very rare fluctuations. In this state, the active Y molecules are shown to control the behavior of the protocell. The minority molecule species act as the carrier of heredity, due to the relatively discrete nature of its population, in comparison with the majority species which behaves statistically in accordance with the law of large numbers. The minority controlled state may give rise to a selection pressure for mechanisms that ensure the transmission of the minority molecule. Once those mechanisms are in place, the minority molecule becomes the ideal storage device for information to be transmitted across generations, thus giving rise to "genetic information". The relevance of this minority controlled state to evolvability is also discussed.

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.

Sympatric speciation: compliance with phenotype diversification from a single genotype

A novel mechanism for sympatric speciation that takes into account complex bioprocesses within each individual organism is proposed. According to dynamical systems theory, organisms with identical genotypes can possess differentiated physiological states and may coexist 'symbiotically' through appropriate mutual interaction. With mutations, the phenotypically differentiated organisms gradually come to possess distinct genotypes while maintaining their symbiotic relationship. This symbiotic speciation is robust against sexual recombination, because offspring of mixed parentage with intermediate genotypes are less fit than their parents. This leads to sterility of the hybrid. Accordingly, a basis for mating preference also arises.

Self-maintenance and self-reproduction in an abstract cell model

Living cells must maintain their membranes by active metabolism. The membrane is not static but a dynamic structure that has evolved along with its internal reactions. When we reflect on the emergence and evolution of primitive cells, we should not forget the mutual dependency between membranes and metabolic cycles inside the cell. In this paper, we present a simple abstract model of the self-maintaining cell. A metabolic cycle will produce a self-assembling membrane that will enclose the metabolic cycle. We show that a self-maintaining cell has the potential to reproduce itself spontaneously. Further, we have demonstrated two different ways of cellular reproduction depending on the mobility of chemicals. In the first case, a cell releases autocatalytic chemicals that create new cells outside the mother cell. In the second case, a cell grows larger and divides itself into daughter cells by creating a new internal dividing membrane.

Clustering of apoptotic cells via bystander killing by peroxides

Clustering of apoptotic cells is a characteristic of many developing or renewing systems, suggesting that apoptotic cells kill bystanders. Bystander killing can be triggered experimentally by inducing apoptosis in single cells and may be based on the exchange of as yet unidentified chemical cell death signals between nearby cells without the need for cell-to-cell communication via gap junctions. Here we demonstrate that apoptotic cell clusters occurred spontaneously, after serum deprivation or p53 transfection in cell monolayers in vitro. Clustering was apparently induced through bystander killing by primary apoptotic cells. Catalase, a peroxide scavenger, suppressed bystander killing, suggesting that hydrogen peroxide generated by apoptotic cells is the death signal. Although p53 expression increased the number of apoptoses, clustering was found to be similar around apoptotic cells whether or not p53 was expressed, indicating that there is no specific p53 contribution to bystander killing. Bystander killing through peroxides emitted by apoptotic cells may propagate tissue injury in different pathological situations and be relevant in chemo-, gamma-ray, and gene therapy of cancer.

Gene networks capable of pattern formation: from induction to reaction-diffusion

One of the main aims of developmental biology is to understand how a single and apparently homogeneous egg cell achieves the intricate complexity of the adult. Here we present two models to explain the generation of developmental patterns through interactions at the gene level. One model considers direct-contact induction between cells while the other takes into account diffusion of hormones. We show that sets of cells involving identical gene networks and communicating through hormones spontaneously exhibit ordered patterns. We have characterized these patterns and the specific networks responsible for them. The models allow to (i) compare diffusion and direct-contact induction processes as mechanisms of pattern generation; (ii) identify the possible range of behaviour of real gene networks and (iii) suggest causal mechanisms to generate known patterns. The evolutionary implications are discussed.

Origin of complexity in multicellular organisms

Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems can exhibit complex pattern formation with spontaneous cell differentiation. Such systems employ a "cooperative" use of resources and maintain a larger growth speed than simple cell systems, which exist in a homogeneous state and behave "selfishly." The relevance of the diversity of chemicals and reaction dynamics to the growth of a multicellular organism is demonstrated. Chaotic biochemical dynamics are found to provide the multipotency of stem cells.

Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation

Differential cell adhesion, mediated by e.g. integrin and cadherins/catenines, plays an important role in morphogenesis and it has been shown that there is intimate cross-talk between their expression and modification, and inter-cellular signalling, cell differentiation, cell growth and apoptosis. In this paper, we introduce and use a formal model to explore the morphogenetic potential of the interplay between these processes. We demonstrate the formation of interesting morphologies. Initiated by cell differentiation, differential cell adhesion leads to a long transient of cell migrations, e.g. engulfing and intercalation of cells and cell layers. This transient can be sustained dynamically by further cell differentiation, and by cell growth/division and cell death which are triggered by the (also long range) forces (stretching and squeezing) generated by the cell adhesion. We study the interrelation between modes of cell differentiation and modes of morphogenesis. We use an evolutionary process to zoom in on gene-regulation networks which lead to cell differentiation. Morphogenesis is not selected for but appears as a side-effect. The evolutionary dynamics shows the hallmarks of evolution on a rugged landscape, including long neutral paths. We show that a combinatorially large set of morphologies occurs in the vicinity of a neutral path which sustains cell differentiation. Thus, an almost linear molecular phylogeny gives rise to mosaic evolution on the morphological level.

Complex organization in multicellularity as a necessity in evolution

By introducing a dynamical system model of a multicellular system, it is shown that an organism with a variety of differentiated cell types and a complex pattern emerges through cell-cell interactions even without postulating any elaborate control mechanism. Such an organism is found to maintain a larger growth speed as an ensemble, by achieving a cooperative use of resources, than do simple homogeneous cells, which behave "selfishly." This suggests that the emergence of multicellular organisms with complex organization is a necessity in evolution. According to our theoretical model, there initially appear multipotent stem cells, which undergo stochastic differentiation to other cell types. With development and differentiation, both the chemical diversity and the complexity of intra-cellular dynamics are decreased, as a general consequence of our system. Robustness of the developmental process is also confirmed.

Evolution of genetic codes through isologous diversification of cellular states

Evolution of genetic codes is studied as change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states of a cell allows for a choice of enzymes, and this choice is later fixed genetically through evolution. To demonstrate this theory, a dynamical systems model consisting of the concentrations of metabolites, enzymes, amino acyl tRNA synthetase, and tRNA - amino acid complexes in a cell is introduced and studied numerically. It is shown that the biochemical states of cells are differentiated by cell-cell interactions, and each differentiated type starts to use a different synthetase. Through the mutation of genes, this difference in the genetic code is amplified and stabilized. The relevance of this theory to the evolution of non-universal genetic code in mitochondria is suggested. The present theory is based on our recent theory of isologous symbiotic speciation, which is briefly reviewed. According to the theory, phenotypes of organisms are first differentiated into distinct types through the interaction and developmental dynamics, even though they have identical genotypes; later, with mutation in the genotype, the genotype also differentiates into discrete types, while maintaining the "symbiotic" relationship between the types. Relevance of the theory to natural as well as artificial evolution is discussed.

Shapes in the shadow: evolutionary dynamics of morphogenesis

This article investigates the evolutionary dynamics of morphogenesis. In this study, morphogenesis arises as a side-effect of maximization of number of cell types. Thus, it investigates the evolutionary dynamics of side-effects. Morphogenesis is governed by the interplay between differential cell adhesion, gene-regulation, and intercellular signaling. Thus, it investigates the potential to generate complex behavior by entanglement of relatively "boring" processes, and the (automatic) coordination between these processes. The evolutionary dynamics shows all the hallmarks of evolutionary dynamics governed by nonlinear genotype phenotype mapping: for example, punctuated equilibria and diffusion on neutral paths. More striking is the result that interesting, complex morphogenesis occurs mainly in the "shadow" of neutral paths which preserve cell differentiation, that is, the interesting morphologies arise as mutants of the fittest individuals. Characteristics of the evolution of such side-effects in the shadow appear to be the following: (1) The specific complex morphologies are unique (or at least very rare) among the set of de novo initiated evolutionary histories. (2) Similar morphologies are reinvented at large temporal distances during one evolutionary history and also when evolution is restarted after the main cell differentiation pattern has been established. (3) A mosaic-like evolution at the morphological level, where different morphological features occur in many combinations, while at the genotypic level recombination is not implemented and genotypes diverge linearly and at a constant rate.

Isologous diversification for robust development of cell society

Isologous diversification, proposed for cell differentiation, is shown to be stable against molecular and other external fluctuations, where amplification of noise-induced slight difference between cells leads to a noise-tolerant society with differentiated cell types. It is a general consequence of interacting cells with biochemical networks and cell divisions, as is confirmed by several model simulations. According to the theory, differentiation proceeds first by loss of synchrony of intracellular oscillations as the number of cells increases. Then the chemical composition of the cells is differentiated. The differentiated compositions become inherited by the next generation, and lead to determined cell types. As a result of successive occurrence of the cell differentiation, the cell society will be composed of different cell types. The whole developmental process is robust not only against molecular fluctuations but also against the removal of a cluster of cells. This robustness is a remarkable feature of isologous diversification, in contrast to the conventional threshold-type mechanism for development. As a testable consequence of the theory, we also discuss interaction-dependent tumor formation and negative correlation between growth speed and chemical diversity.

Dual interaction producing both territorial and schooling behavior in fish

Fish schools are frequently observed without a leader and an explicit condition forming school. Several models of schooling have been proposed focusing on the influence of neighbors, and introducing probability distributions, while these models are based on the separation of schooling and territorial behavior. We frequently consider the duality of aggregation of animals, in which behavioral patterns involve both attraction and repulsion, antagonistic with each other. The idea of probability does not explain this duality that can provide both schooling and territorial behavior. From these biological facts, we have constructed a behavior model in which the influence of neighbors is formulated by the interface between the states of neighbors and a map of changes in these states. This interface uses a self-similar nowhere differentiable transition map which is temporally constructed, encompassing a crucial duality of repulsive and attractive forces hidden in the interaction among fishes. We tested it with computer simulations against the biological reality of schooling and territorial behavior. Due to the influence neighbors can have on duality, the same model can show both schooling behavior with a high degree of polarization and territorial behavior.

Emergence of multicellular organisms with dynamic differentiation and spatial pattern

The origin of multicellular organisms and the mechanism of development in cell societies are studied by choosing a model with intracellular biochemical dynamics allowing for oscillations, cell-cell interaction through diffusive chemicals on a two-dimensional grid, and state-dependent cell adhesion. Cells differentiate due to a dynamical instability, as described by our "isologous diversification" theory. A fixed spatial pattern of differentiated cells emerges, where spatial information is sustained by cell-cell interactions. This pattern is robust against perturbations. With an adequate cell adhesion force, active cells are release that form the seed of a new generation of multicellular organisms, accompanied by death of the original multicellular unit as a halting state. It is shown that the emergence of multicellular organisms with differentiation, regulation, and life cycle is not an accidental event, but a natural consequence in a system of replicating cells with growth.