A connectionist model of development

BMC Systems Biology, 2012

Background: CD4 + T cells have several subsets of functional phenotypes, which play critical yet diverse roles in the immune system. Pathogen-driven differentiation of these subsets of cells is often heterogeneous in terms of the induced phenotypic diversity. In vitro recapitulation of heterogeneous differentiation under homogeneous experimental conditions indicates some highly regulated mechanisms by which multiple phenotypes of CD4 + T cells can be generated from a single population of naïve CD4 + T cells. Therefore, conceptual understanding of induced heterogeneous differentiation will shed light on the mechanisms controlling the response of populations of CD4 + T cells under physiological conditions. Results: We present a simple theoretical framework to show how heterogeneous differentiation in a two-masterregulator paradigm can be governed by a signaling network motif common to all subsets of CD4 + T cells. With this motif, a population of naïve CD4 + T cells can integrate the signals from their environment to generate a functionally diverse population with robust commitment of individual cells. Notably, two positive feedback loops in this network motif govern three bistable switches, which in turn, give rise to three types of heterogeneous differentiated states, depending upon particular combinations of input signals. We provide three prototype models illustrating how to use this framework to explain experimental observations and make specific testable predictions.

Nature communications, 2015

Here we show that iNOS-deficient mice display enhanced classically activated M1 macrophage polarization without major effects on alternatively activated M2 macrophages. eNOS and nNOS mutant mice show comparable M1 macrophage polarization compared with wild-type control mice. Addition of N6-(1-iminoethyl)-L-lysine dihydrochloride, an iNOS inhibitor, significantly enhances M1 macrophage polarization while S-nitroso-N-acetylpenicillamine, a NO donor, suppresses M1 macrophage polarization. NO derived from iNOS mediates nitration of tyrosine residues in IRF5 protein, leading to the suppression of IRF5-targeted M1 macrophage signature gene activation. Computational analyses corroborate a circuit that fine-tunes the expression of IL-12 by iNOS in macrophages, potentially enabling versatile responses based on changing microenvironments. Finally, studies of an experimental model of endotoxin shock show that iNOS deficiency results in more severe inflammation with an enhanced M1 macrophage ac...

PLoS ONE, 2014

Background: The starlet sea anemone Nematostella vectensis is a diploblastic cnidarian that expresses a set of conserved genes for gut formation during its early development. During the last decade, the spatial distribution of many of these genes has been visualized with RNA hybridization or protein immunolocalization techniques. However, due to N. vectensis' curved and changing morphology, quantification of these spatial data is problematic. A method is developed for twodimensional gene expression quantification, which enables a numerical analysis and dynamic modeling of these spatial patterns.

BMC Systems Biology, 2015

Background: Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions. Results: Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker's yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation. Conclusions: This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/.

Artificial Life, 2006

To increase the evolvability of larger search spaces, several indirect encoding strategies have been proposed. Among these, multicellular developmental systems are believed to offer great potential for the evolution of general, scalable and self-repairing organisms. In this paper we reinforce this view, presenting the results achieved by such a model and comparing it against direct encoding. Extra effort has been made to make this comparison both general and meaningful.

PloS one, 2008

Since synaptic plasticity is regarded as a potential mechanism for memory formation and learning, there is growing interest in the study of its underlying mechanisms. Recently several evolutionary models of cellular development have been presented, but none have been shown to be able to evolve a range of biological synaptic plasticity regimes. In this paper we present a biologically plausible evolutionary cellular development model and test its ability to evolve different biological synaptic plasticity regimes. The core of the model is a genomic and proteomic regulation network which controls cells and their neurites in a 2D environment. The model has previously been shown to successfully evolve behaving organisms, enable gene related phenomena, and produce biological neural mechanisms such as temporal representations. Several experiments are described in which the model evolves different synaptic plasticity regimes using a direct fitness function. Other experiments examine the abil...

Computation

Efficient network inference is one of the challenges of current-day biology. Its application to the study of development has seen noteworthy success, yet a multicellular context, tissue growth, and cellular rearrangements impose additional computational costs and prohibit a wide application of current methods. Therefore, reducing computational cost and providing quick feedback at intermediate stages are desirable features for network inference. Here we propose a hybrid approach composed of two stages: exploration with scatter search and exploitation of intermediate solutions with low temperature simulated annealing. We test the approach on the well-understood process of early body plan development in flies, focusing on the gap gene network. We compare the hybrid approach to simulated annealing, a method of network inference with a proven track record. We find that scatter search performs well at exploring parameter space and that low temperature simulated annealing refines the intermediate results into excellent model fits. From this we conclude that for poorly-studied developmental systems, scatter search is a valuable tool for exploration and accelerates the elucidation of gene regulatory networks.

Physical review. E, 2017

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological...

BMC bioinformatics, 2005

Gene expression programs depend on recognition of cis elements in promoter region of target genes by transcription factors (TFs), but how TFs regulate gene expression via recognition of cis elements is still not clear. To study this issue, we define the cis-regulatory circuit of a gene as a system that consists of its cis elements and the interactions among their recognizing TFs and develop a dynamic model to study the functional architecture and dynamics of the circuit. This is in contrast to traditional approaches where a cis-regulatory circuit is constructed by a mutagenesis or motif-deletion scheme. We estimate the regulatory functions of cis-regulatory circuits using microarray data. A novel cross-gene identification scheme is proposed to infer how multiple TFs coordinate to regulate gene transcription in the yeast cell cycle and to uncover hidden regulatory functions of a cis-regulatory circuit. Some advantages of this approach over most current methods are that it is based on...

Frontiers in Physics

Biological development involves numerous chemical and physical processes which must act in concert to reliably produce a cell, a tissue, or a body. To be successful, the developing organism must be robust to variability at many levels, such as the environment (e.g., temperature, moisture), upstream information (such as long-range positional information gradients), or intrinsic noise due to the stochastic nature of low concentration chemical kinetics. The latter is especially relevant to the regulation of gene expression in cell differentiation. The temporal stochasticity of gene expression has been studied in single celled organisms for nearly two decades, but only recently have techniques become available to gather temporally-resolved data across spatially-distributed gene expression patterns in developing multicellular organisms. These demonstrate temporal noisy "bursting" in the number of gene transcripts per cell, raising the question of how the transcript number defining a particular cell type is produced, such that one cell type can reliably be distinguished from a neighboring cell of different type along a tissue boundary. Stochastic spatio-temporal modeling of tissue-wide expression patterns can identify signatures for specific types of gene regulation, which can be used to extract regulatory mechanism information from experimental time series. This Perspective focuses on using this type of approach to study gene expression noise during the anterior-posterior segmentation of the fruit fly embryo. Advances in experimental and theoretical techniques will lead to an increasing quantification of expression noise that can be used to understand how regulatory mechanisms contribute to embryonic robustness across a range of developmental processes.

PLoS Computational Biology, 2011

The reciprocal differentiation of T helper 17 (T H 17) cells and induced regulatory T (iT reg) cells plays a critical role in both the pathogenesis and resolution of diverse human inflammatory diseases. Although initial studies suggested a stable commitment to either the T H 17 or the iT reg lineage, recent results reveal remarkable plasticity and heterogeneity, reflected in the capacity of differentiated effectors cells to be reprogrammed among T H 17 and iT reg lineages and the intriguing phenomenon that a group of naïve precursor CD4 + T cells can be programmed into phenotypically diverse populations by the same differentiation signal, transforming growth factor beta. To reconcile these observations, we have built a mathematical model of T H 17/iT reg differentiation that exhibits four different stable steady states, governed by pitchfork bifurcations with certain degrees of broken symmetry. According to the model, a group of precursor cells with some small cell-to-cell variability can differentiate into phenotypically distinct subsets of cells, which exhibit distinct levels of the master transcription-factor regulators for the two T cell lineages. A dynamical control system with these properties is flexible enough to be steered down alternative pathways by polarizing signals, such as interleukin-6 and retinoic acid and it may be used by the immune system to generate functionally distinct effector cells in desired fractions in response to a range of differentiation signals. Additionally, the model suggests a quantitative explanation for the phenotype with high expression levels of both master regulators. This phenotype corresponds to a re-stabilized co-expressing state, appearing at a late stage of differentiation, rather than a bipotent precursor state observed under some other circumstances. Our simulations reconcile most published experimental observations and predict novel differentiation states as well as transitions among different phenotypes that have not yet been observed experimentally.

eLife, 2016

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study...

BMC Evolutionary Biology, 2011

Background: Characterization of robustness and plasticity of phenotypes is a basic issue in evolutionary and developmental biology. The robustness and plasticity are concerned with changeability of a biological system against external perturbations. The perturbations are either genetic, i.e., due to mutations in genes in the population, or epigenetic, i.e., due to noise during development or environmental variations. Thus, the variances of phenotypes due to genetic and epigenetic perturbations provide quantitative measures for such changeability during evolution and development, respectively. Results: Using numerical models simulating the evolutionary changes in the gene regulation network required to achieve a particular expression pattern, we first confirmed that gene expression dynamics robust to mutation evolved in the presence of a sufficient level of transcriptional noise. Under such conditions, the two types of variances in the gene expression levels, i.e. those due to mutations to the gene regulation network and those due to noise in gene expression dynamics were found to be proportional over a number of genes. The fraction of such genes with a common proportionality coefficient increased with an increase in the robustness of the evolved network. This proportionality was generally confirmed, also under the presence of environmental fluctuations and sexual recombination in diploids, and was explained from an evolutionary robustness hypothesis, in which an evolved robust system suppresses the so-called error catastrophe -the destabilization of the single-peaked distribution in gene expression levels. Experimental evidences for the proportionality of the variances over genes are also discussed. Conclusions: The proportionality between the genetic and epigenetic variances of phenotypes implies the correlation between the robustness (or plasticity) against genetic changes and against noise in development, and also suggests that phenotypic traits that are more variable epigenetically have a higher evolutionary potential.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008

Biological functions are generated as a result of developmental dynamics that form phenotypes governed by genotypes. The dynamical system for development is shaped through genetic evolution following natural selection based on the fitness of the phenotype. Here we study how this dynamical system is robust to noise during development and to genetic change by mutation. We adopt a simplified transcription regulation network model to govern gene expression, which gives a fitness function. Through simulations of the network that undergoes mutation and selection, we show that a certain level of noise in gene expression is required for the network to acquire both types of robustness. The results reveal how the noise that cells encounter during development shapes any network's robustness, not only to noise but also to mutations. We also establish a relationship between developmental and mutational robustness through phenotypic variances caused by genetic variation and epigenetic noise. A universal relationship between the two variances is derived, akin to the fluctuation-dissipation relationship known in physics. years. We derive a quantitative condition for evolution of robustness which ultimately links robustness to mutation in the evolutionary timescale and robustness to noise in development in the reproductive timescale. Our model simulations predict correlation between the two robustness, which lead to a universal proportionality relationship between variances of genetic and epigenetic phenotype fluctuations, which remind us of fluctuation-dissipation relationship in statistical physics.

Journal of Statistical Physics, 2012

The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic variances of epigenetic and genetic origins is confirmed. The former is given by the variance of the phenotypic fluctuation due to noise in the developmental process; and the latter, by the variance of the phenotypic fluctuation due to genetic mutation. The relationship suggests a link between robustness to noise and to mutation, since robustness can be defined by the sharpness of the distribution of the phenotype. Next, the proportionality between the variances is demonstrated to also hold over expressions of different genes (phenotypic traits) when the system acquires robustness through the evolution. Then, evolution under environmental variation is numerically investigated and it is found that both the adaptability to a novel environment and the robustness are made compatible when a certain degree of phenotypic fluctuations exists due to noise. The highest adaptability is achieved at a certain noise level at which the gene expression dynamics are near the critical state to lose the robustness. Based on our results, we revisit Waddington's canalization and genetic assimilation with regard to the two types of phenotypic fluctuations.

Physica D: Nonlinear Phenomena, 1997

An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by differentiating roles. The former leads to the time sharing of resources, while the latter leads to the separation of roles for the growth. The mechanism of the differentiation of elements is studied. An extension to a model with several internal phase variables is given, which shows differentiation of internal states. The relevance of interacting dynamics with internal states ("intra-inter" dynamics) to biological problems is discussed with an emphasis on heterogeneity by clustering, macroscopic robustness by partial synchronization and recursivity with the selection of initial conditions and digitalization.

Physical Review E, 2007

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. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.

PLoS Computational Biology, 2013

Cells generally adapt to environmental changes by first exhibiting an immediate response and then gradually returning to their original state to achieve homeostasis. Although simple network motifs consisting of a few genes have been shown to exhibit such adaptive dynamics, they do not reflect the complexity of real cells, where the expression of a large number of genes activates or represses other genes, permitting adaptive behaviors. Here, we investigated the responses of gene regulatory networks containing many genes that have undergone numerical evolution to achieve high fitness due to the adaptive response of only a single target gene; this single target gene responds to changes in external inputs and later returns to basal levels. Despite setting a single target, most genes showed adaptive responses after evolution. Such adaptive dynamics were not due to common motifs within a few genes; even without such motifs, almost all genes showed adaptation, albeit sometimes partial adaptation, in the sense that expression levels did not always return to original levels. The genes split into two groups: genes in the first group exhibited an initial increase in expression and then returned to basal levels, while genes in the second group exhibited the opposite changes in expression. From this model, genes in the first group received positive input from other genes within the first group, but negative input from genes in the second group, and vice versa. Thus, the adaptation dynamics of genes from both groups were consolidated. This cooperative adaptive behavior was commonly observed if the number of genes involved was larger than the order of ten. These results have implications in the collective responses of gene expression networks in microarray measurements of yeast Saccharomyces cerevisiae and the significance to the biological homeostasis of systems with many components.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018

Pattern dynamics triggered by fixing a boundary is investigated. By considering a reactiondiffusion equation that has a unique spatially uniform and limit cycle attractor under a periodic or Neumann boundary condition, and then by choosing a fixed boundary condition, we found three novel phases depending on the ratio of diffusion constants of activator to inhibitor: transformation of temporally periodic oscillation into a spatially periodic fixed pattern, travelling wave emitted from the boundary, and aperiodic spatiotemporal dynamics. The transformation into a fixed, periodic pattern is analyzed by crossing of local nullclines at each spatial point, shifted by diffusion terms, as is analyzed by using recursive equations, to obtain the spatial pattern as an attractor. The generality of the boundary-induced pattern formation as well as its relevance to biological morphogenesis is discussed. V

Physical Review Research, 2020

In multicellular organisms, cells differentiate into several distinct types during early development. Determination of each cellular state, along with the ratio of each cell type, as well as the developmental course during cell differentiation are highly regulated processes that are robust to noise and environmental perturbations throughout development. Waddington metaphorically depicted this robustness as the epigenetic landscape in which the robustness of each cellular state is represented by each valley in the landscape. This robustness is now conceptualized as an approach toward an attractor in a gene-expression dynamical system. However, there is still an incomplete understanding of the origin of landscape change, which is accompanied by branching of valleys that corresponds to the differentiation process. Recent progress in developmental biology has unveiled the molecular processes involved in epigenetic modification, which will be a key to understanding the nature of slow landscape change. Nevertheless, the contribution of the interplay between gene expression and epigenetic modification to robust landscape changes, known as homeorhesis, remains elusive. Here, we introduce a theoretical model that combines epigenetic modification with gene expression dynamics driven by a regulatory network. In this model, epigenetic modification changes the feasibility of expression, i.e., the threshold for expression dynamics, and a slow positive-feedback process from expression to the threshold level is introduced. Under such epigenetic feedback, several fixedpoint attractors with distinct expression patterns are generated hierarchically shaping the epigenetic landscape with successive branching of valleys. This theory provides a quantitative framework for explaining homeorhesis in development as postulated by Waddington, based on dynamical-system theory with slow feedback reinforcement.

Physical Review Research

In cellular reprogramming, almost all epigenetic memories of differentiated cells are erased by the overexpression of few genes, regaining pluripotency, potentiality for differentiation. Considering the interplay between oscillatory gene expression and slower epigenetic modifications, such reprogramming is perceived as an unintuitive, global attraction to the unstable manifold of a saddle, which represents pluripotency. The universality of this scheme is confirmed by the repressilator model, and by gene regulatory networks randomly generated and those extracted from embryonic stem cells.

Proceedings of the National Academy of Sciences, 2006

Recent studies show that plant organ positioning may be mediated by localized concentrations of the plant hormone auxin. Auxin patterning in the shoot apical meristem is in turn brought about by the subcellular polar distribution of the putative auxin efflux mediator, PIN1. However, the question of what signals determine PIN1 polarization and how this gives rise to regular patterns of auxin concentration remains unknown. Here we address these questions by using mathematical modeling combined with confocal imaging. We propose a model that is based on the assumption that auxin influences the polarization of its own efflux within the meristem epidermis. We show that such a model is sufficient to create regular spatial patterns of auxin concentration on systems with static and dynamic cellular connectivities, the latter governed by a mechanical model. We also optimize parameter values for the PIN1 dynamics by using a detailed auxin transport model, for which parameter values are taken f...

PLoS Computational Biology, 2008

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Scientific Reports, 2014

Interpreting a morphogen gradient into a single stripe of gene-expression is a fundamental unit of patterning in early embryogenesis. From both experimental data and computational studies the feed-forward motifs stand out as minimal networks capable of this patterning function. Positive feedback within gene networks has been hypothesised to enhance the sharpness and precision of gene-expression borders, however a systematic analysis has not yet been reported. Here we set out to assess this hypothesis, and find an unexpected result. The addition of positive-feedback can have different effects on two different designs of feed-forward motif-it increases the parametric robustness of one design, while being neutral or detrimental to the other. These results shed light on the abundance of the former motif and especially of mutual-inhibition positive feedback in developmental networks. M odularity is a central principle to both systems and synthetic biology 1,2. It implies the reduction of large gene networks to a collection of small, separable subsystems. Milo et al. 3 initiated such a collection by identifying small groups of interacting genes or network motifs that appear statistically overrepresented in complex biological networks. This statistical motif-extraction usually involves the structure-but not the function-of the motif. A proper modularity requires that these motifs always perform a similar function in different biological contexts 4-6. For such an assessment, systems and synthetic biology increasingly aim to explore the biological and dynamical functions of these minimal regulatory motifs. Existing studies mostly addressed the characteristics and requirements of genetic oscillators, biological switches and low-pass filters 7-9. As the list of well-studied motifs is growing, several questions emerge: What happens when simple modules are combined together? Does a given motif perform the same function, whether in isolation or embedded in a large network? (Fig. 1). Here we address these questions by studying the motifs capable of performing a specific biological task. The task chosen is converting a decreasing morphogen gradient into a single stripe of gene expression. The single stripe is a key spatial feature in the early stages of the embryogenesis. It is considered a mechanistic unit in the formation and maintenance of boundaries between future tissues 10. This scenario of an input gradient determining distinct cellular fates is referred to as positional information 11. As a definition, a signalling molecule that generates at least two distinct cell types, or thresholds, at different concentrations is called a morphogen 12. Examples of such threshold-controlling morphogens include Bicoid and Dorsal in Drosophila 13,14 , activin in Xenopus 15 and Sonic Hedgehog in the vertebrate neural tube 16. Initially, it was hypothesised that these thresholds are determined by different responsiveness (i.e. different number and affinity of binding sites) of the genes to the morphogen. However, recent evidence suggests that it is the regulatory logic of the developmental network itself that determines the expression patterns 14,17-20. In other words, the response to morphogen gradients is an emergent property of the regulatory circuit rather than a property of specific genes. Together with the identification of spatiotemporal motifs from developmental gene networks 21 , these observations suggest that general circuit-design principles are responsible for pattern formation at tissue level. Studying simple but essential expression patterns and the genetic circuits that produce them constitutes an approach to uncovering such principles. From the existing studies of gene networks capable of a single-stripe pattern under a morphogen gradient, the 3-gene Incoherent Feed-Forward Motifs (IFFMs) appear as the minimal ones. These studies consisted of general computational explorations 22-24 or specific experimental implementations in synthetic and developmental biology 25-27. More exhaustively, Cotterell & Sharpe 28 computationally analysed all 3-gene configurations and revealed that indeed the networks showing the single-stripe expression include the 3-gene IFFMs.

Physical Review Letters, 2020

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

Physical Review E, 2013

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.

Journal of experimental zoology. Part B, Molecular and developmental evolution, 2016

Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development...

2020

It is acknowledged that embryonic development has tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel’s recapitulation theory, i.e., the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene-expression dynamics with cell-to-cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Both pattern changes consisted of several epochs where stripes are formed in a short time, whereas for other temporal...

PLOS Computational Biology, 2021

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises h...

2017

Much of contemporary systems biology owes its success to the abstraction of anetwork, the idea that diverse kinds of molecular, cellular, and organismal species and interactions can be modeled as relational nodes and edges in a graph of dependencies. Since the advent of high-throughput data acquisition technologies in fields such as genomics, metabolomics, and neuroscience, the automated inference and reconstruction of such interaction networks directly from large sets of activation data, commonly known as reverse-engineering, has become a routine procedure. Whereas early attempts at network reverse-engineering focused predominantly on producing maps of system architectures with minimal predictive modeling, reconstructions now play instrumental roles in answering questions about the statistics and dynamics of the underlying systems they represent. Many of these predictions have clinical relevance, suggesting novel paradigms for drug discovery and disease treatment. While other revie...

Journal of Applied and Industrial Mathematics, 2011

We describe the modeling of the dynamics of renewing zone structure in biological tissues in the formalism of parameterized L-systems on an example of the shoot apical meristem. Under study is the influence of the ratio of the characteristic times of the cell cycle and diffusion of morphogens on the stability of some spatially distributed molecular-genetic control system. We show that cell division is a perturbing factor for the system regulating the renewing zone structure. Some conditions are found for the loss of stability of the regulation.

Physical Review Letters, 2013

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic limit. The dynamics without the limit are found to be represented by stochastic switching over these branches mediated by the collective chaos of the fast elements, while the switching frequency shows a complicated dependence on the ratio of the two timescales with some resonance structure. The ubiquity of the phenomena in the slow-fast dynamics is also discussed.

2021

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. Through the evolution of a given environment, the former, the insensitivity of phenotypes, is expected to increase, whereas the latter, the changeability of phenotypes, tends to diminish. However, in nature, plasticity is preserved to a certain degree. One possible cause for this is environmental variation, with one of the most important “environmental ” factors being inter-species interactions. As a first step toward investigating phenotypic plasticity in response to an ecological interaction, we present the study of a simple two-species system consisting of hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness and increases the robustness of the corresponding phenotype by reducing phenotypic fluctuations. Conversely, plasticity evolves in order to avoid certain phenotypes being attacked by parasites. By simulating ...

2021

Mendelian inheritance is a fundamental law of genetics. Considering two alleles in a diploid, a phenotype of a heterotype is dominated by a particular homotype according to the law of dominance. This picture is usually based on simple genotype-phenotype mapping in which one gene regulates one phenotype. However, in reality, some interactions between genes can result in deviation from Mendelian dominance.Here, by using the numerical evolution of diploid gene regulatory networks (GRNs), we discuss whether Mendelian dominance evolves beyond the classical case of one-to-one genotype-phenotype mapping. We examine whether complex genotype-phenotype mapping can achieve Mendelian dominance through the evolution of the GRN with interacting genes. Specifically, we extend the GRN model to a diploid case, in which two GRN matrices are added to give gene expression dynamics, and simulate evolution with meiosis and recombination. Our results reveal that Mendelian dominance evolves even under comp...

PNAS Nexus

Heterosis describes the phenomenon, whereby a hybrid population has higher fitness than an inbred population, which has previously been explained by either Mendelian dominance or overdominance under the general assumption of a simple genotype–phenotype relationship. However, recent studies have demonstrated that genes interact through a complex gene regulatory network (GRN). Furthermore, phenotypic variance is reportedly lower for heterozygotes, and the origin of such variance-related heterosis remains elusive. Therefore, a theoretical analysis linking heterosis to GRN evolution and stochastic gene expression dynamics is required. Here, we investigated heterosis related to fitness and phenotypic variance in a system with interacting genes by numerically evolving diploid GRNs. According to the results, the heterozygote population exhibited higher fitness than the homozygote population, indicating fitness-related heterosis resulting from evolution. In addition, the heterozygote popula...

Physical Review Research

Living systems adapt to various environmental conditions by changing their internal states through processes such as gene expression and epigenetic modification. In this paper, we propose a generic mechanism for optimization that combines fast oscillatory dynamics with a slower feedback fixation process. Through extensive model simulations, we demonstrate that the fast chaotic dynamics serve as a global search for optimal states, which are then fixed by the slower dynamics. This mechanism becomes more effective as the number of elements is increased. We also discuss the potential relevance of this optimization mechanism to problems in artificial neural networks.

Journal of Chemical Technology & Biotechnology, 2006

Strain improvement and fermentation optimization are two fundamental tasks in industrial fermentation. Multi-scale study on the optimization of industrial fermentation has been proved to be an efficacious method. However, correlations of data used on inter-scale observation and operation are indirect, empirical and there is still much to be improved. Advances in our understanding of complex biological systems are addressed by comprehensive studies that include high-throughput measurements of mRNA, proteins, and low molecular weight metabolites over time and varied conditions during fermentation. Systems biology can be used to relate these omics datasets to the microbial genome and culture conditions in a bioreactor, then identify some new targets for metabolic engineering and elucidate the molecular mechanism of environmental effects. This approach provides a potentially powerful tool for integrating strain improvement and process optimization for industrial biotechnology.

BMC Research Notes, 2012

Background: Spatial gene expression quantification is required for modeling gene regulation in developing organisms. The fruit fly Drosophila melanogaster is the model system most widely applied for spatial gene expression analysis due to its unique embryonic properties: the shape does not change significantly during its early cleavage cycles and most genes are differentially expressed along a straight axis. This system of development is quite exceptional in the animal kingdom. In the sea anemone Nematostella vectensis the embryo changes its shape during early development; there are cell divisions and cell movement, like in most other metazoans. Nematostella is an attractive case study for spatial gene expression since its transparent body wall makes it accessible to various imaging techniques. Findings: Our new quantification method produces standardized gene expression profiles from raw or annotated Nematostella in situ hybridizations by measuring the expression intensity along its cell layer. The procedure is based on digital morphologies derived from high-resolution fluorescence pictures. Additionally, complete descriptions of nonsymmetric expression patterns have been constructed by transforming the gene expression images into a three-dimensional representation. Conclusions: We created a standard format for gene expression data, which enables quantitative analysis of in situ hybridizations from embryos with various shapes in different developmental stages. The obtained expression profiles are suitable as input for optimization of gene regulatory network models, and for correlation analysis of genes from dissimilar Nematostella morphologies. This approach is potentially applicable to many other metazoan model organisms and may also be suitable for processing data from three-dimensional imaging techniques.

PLOS Computational Biology, 2020

There is increased awareness of the possibility of developmental memories resulting from evolutionary learning. Genetic regulatory and neural networks can be modelled by analogous formalism raising the important question of productive analogies in principles, processes and performance. We investigate the formation and persistence of various developmental memories of past phenotypes asking how the number of remembered past phenotypes scales with network size, to what extent memories stored form by Hebbian-like rules, and how robust these developmental "devo-engrams" are against networks perturbations (graceful degradation). The analogy between neural and genetic regulatory networks is not superficial in that it allows knowledge transfer between fields that used to be developed separately from each other. Known examples of spectacular phenotypic radiations could partly be accounted for in such terms.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013

All cells of living organisms contain similar genetic instructions encoded in the organism's DNA. In any particular cell, the control of the expression of each different gene is regulated, in part, by binding of molecular complexes to specific regions of the DNA. The molecular complexes are composed of protein molecules, called transcription factors, combined with various other molecules such as hormones and drugs. Since transcription factors are coded by genes, cellular function is partially determined by genetic networks. Recent research is making large strides to understand both the structure and the function of these networks. Further, the emerging discipline of synthetic biology is engineering novel gene circuits with specific dynamic properties to advance both basic science and potential practical applications. Although there is not yet a universally accepted mathematical framework for studying the properties of genetic networks, the strong analogies between the activation...

Molecular Systems Biology, 2010

The interpretation of morphogen gradients is a pivotal concept in developmental biology, and several mechanisms have been proposed to explain how gene regulatory networks (GRNs) achieve concentration-dependent responses. However, the number of different mechanisms that may exist for cells to interpret morphogens, and the importance of design features such as feedback or local cell-cell communication, is unclear. A complete understanding of such systems will require going beyond a case-by-case analysis of real morphogen interpretation mechanisms and mapping out a complete GRN 'design space.' Here, we generate a first atlas of design space for GRNs capable of patterning a homogeneous field of cells into discrete gene expression domains by interpreting a fixed morphogen gradient. We uncover multiple very distinct mechanisms distributed discretely across the atlas, thereby expanding the repertoire of morphogen interpretation network motifs. Analyzing this diverse collection of mechanisms also allows us to predict that local cell-cell communication will rarely be responsible for the basic dose-dependent response of morphogen interpretation networks.

Journal Of Experimental Zoology Part B: Molecular And Developmental Evolution, 2021

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