To address the possibility that proliferative disorders may originate from interactions between multiple populations of proliferating and maturing cells, we formulate a model for this process as a set of coupled nonlinear first order partial differential equations. Using recent results for the asymptotic behaviour of the solutions to this model, we demonstrate that there exists a region of coupling coefficients, maturation rates, and proliferation rates that will guarantee the stable coexistence of coupled cellular populations. The analysis shows that (...) increases in the coupling between populations may ultimately lead to a loss of stability. Furthermore, the analysis indicates that increases (decreases) in the maturation and/or proliferation rates above (below) critical levels will lead either to instability in the populations or the destruction of one population and the persistence of the other. (shrink)

We present an age-structured model for erythropoiesis in which the mortality of mature cells is described empirically by a physiologically realistic probability distribution of survival times. Under some assumptions, the model can be transformed into a system of delay differential equations with both constant and distributed delays. The stability of the equilibrium of this system and possible Hopf bifurcations are described for a number of probability distributions. Physiological motivation and interpretation of our results are provided.

Pluripotency can be considered a functional characteristic of pluripotent stem cells (PSCs) populations and their niches, rather than a property of individual cells. In this view, individual cells within the population independently adopt a variety of different expression states, maintained by different signaling, transcriptional, and epigenetics regulatory networks. In this review, we propose that generation of integrative network models from single cell data will be essential for getting a better understanding of the regulation of self‐renewal and differentiation. In (...) particular, we suggest that the identification of network stability determinants in these integrative models will provide important insights into the mechanisms mediating the transduction of signals from the niche, and how these signals can trigger differentiation. In this regard, the differential use of these stability determinants in subpopulation‐specific regulatory networks would mediate differentiation into different cell fates. We suggest that this approach could offer a promising avenue for the development of novel strategies for increasing the efficiency and fidelity of differentiation, which could have a strong impact on regenerative medicine. (shrink)

In this paper, we propose two HIV infection models with specific nonlinear incidence rate by including a class of infected cells in the eclipse phase. The first model is described by ordinary differential equations and generalizes a set of previously existing models and their results. The second model extends our ODE model by taking into account the diffusion of virus. Furthermore, the global stability of both models is investigated by constructing suitable Lyapunov functionals. Finally, we check our (...) theoretical results with numerical simulations. (shrink)

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 suchaberrantgene 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, otheraberrantcellular states lacking such high robustness are expected to remain, which would correspond to cancer cells. (shrink)

The paper is devoted to modelling of cell differentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell differentiation is initiated locally in space in the population of undifferentiated cells, it can propagate as a travelling wave converting undifferentiated cells into differentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular (...) regulation and different cell types. They include undifferentiated cells and two types of differentiated cells. When a cell differentiates, its choice between two types of differentiated cells is determined by the concentrations of intracellular proteins. Differentiated cells can either stimulate differentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of differentiated cells will finally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave. (shrink)

Graphical AbstractCurrent differentiation therapies for cancer may not be effective because it might not be enough to only use molecules targeting chromatin remodelers. It may also be necessary to stabilize the re-expressed genes to convert malignant cells into benign ones.

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ( $$IP_{3}$$ ) and adenosine triphosphate (ATP) in various cells including pancreatic $$\beta$$ -cells. The calcium signaling mechanisms regulating $$IP_{3}$$, ATP and insulin responsible for various functions of $$\beta$$ -cells are still not well understood. Any disturbance in these mechanisms can alter the functions of $$\beta$$ -cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for (...) calcium dynamics and a system of first-order differential equations for $$IP_{3}$$, ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of $$IP_{3}$$ -production and degradation, ATP production and insulin secretion on calcium dynamics in a $$\beta$$ -cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of $$IP_{3}$$, ATP and insulin levels in a $$\beta$$ -cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of $$IP_{3}$$, ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in $$IP_3$$, ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases. (shrink)

Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the (...) class='Hi'>model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested. (shrink)

Solvency assessment is the core content of insurance supervision. In this paper, from the perspective of capital flow, the insurance company’s capital flow is regarded as a dynamic system, the stochastic differential equations model is established to describe its flow characteristics, and the existence of positive equilibrium point of the system is proved, as well as the conditions of stability at equilibrium point, that is, the requirements of the insurance company’s solvency. Furthermore, by using the numerical simulation method, we (...) get the strategy of insurance companies to deal with the solvency shortage when facing the change of external environment, and the strategy of insurance company to deal with solvency shortage is obtained. (shrink)

A model is given of the development of a radialised larval head pattern inLimnaea stagnalis, as it occurs under certain experimental conditions. It is assumed that the differentiation of the pattern is entirely based on cell-internal factors, and that the internal state of each cell is dependent on that of its progenitor and on the direction of the division by which it is produced. This internal state determines the direction of the subsequent division or the nature (...) of the cell's differentiation. Cell interactions, which are during this period of minor importance, are left out of consideration. (shrink)

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue $$\mathcal{R}_\sigma$$ (...) of the basic reproduction number $$\mathcal{R}_0$$ of the underlying deterministic model, with $$\mathcal{R}_\sigma \le \mathcal{R}_0$$. We prove that the disease-free equilibrium is almost sure exponentially stable if $$\mathcal{R}_\sigma <1$$. (shrink)

Mitochondrial shape change, brought about by molecules that promote either fission or fusion between individual mitochondria, has been documented in several model systems. However, the deeper significance of mitochondrial shape change has only recently begun to emerge: among others, it appears to play a role in the regulation of cell proliferation. Here, I review the emerging interplay between mitochondrial fission‐fusion components with cell cycle regulatory machineries and how that may impact cell differentiation. Regulation of mitochondrial (...) shape may modulate mitochondrial metabolism and/or energetics to promote crosstalk between signaling components and the cell cycle machinery. Focused research in this area will reveal the exact role of mitochondria in development and disease, specifically in stem cell regulation and tumorigenesis. Such research may also reveal whether and how the endosymbiotic event that gave rise to the mitochondrion was crucial for the evolution of cell cycle regulatory mechanisms in eukaryotes that are absent in prokaryotes. (shrink)

This article concerns the elaboration of epigenetic models for differentiation. I discuss how results and conclusions arising from studies of prokaryotes were extrapolated to explain differentiation during metazoan development. In this respect, I focus on the presentation of a multi-stable biochemical model by Delbrück in 1949, and on a series of works dealing with enzyme adaptation in Escherichia coli that culminated in Jacob and Monod's operon model. These influential contributions are discussed in the context of debates (...) on nuclear versus cytoplasmic heredity, on the regulation of gene expression, as well as on the mechanisms at the basis of cell differentiation. (shrink)

Cellular pattern formations of some epithelia are believed to be governed by the direct lateral inhibition rule of cell differentiation. That is, initially equivalent cells are all competent to differentiate, but once a cell has differentiated, the cell inhibits its immediate neighbors from following this pathway. Such a differentiation repeats until all non-inhibited cells have differentiated. The cellular polygonal patterns can be characterized by the numbers of undifferentiated cells and differentiated ones. When the differentiated cells (...) become large in size, the polygonal pattern is deformed since more cells are needed to enclose the large cell. An actual example of such a cellular pattern was examined. The pupal wing epidermis of a butterfly Pieris rapae shows a transition of the equivalent-size cell pattern to the pattern involving large cells. The process of the transition was analyzed by using the method of weighted Voronoi tessellation that is useful for treatment of irregularly sized polygons. The analysis supported that the pattern transition of the early stage of the pupal wing epidermis is governed by the lateral inhibition rule. The differentiation takes place in order of largeness, but not smallness, of the apical polygonal area in the differentiating region of the pupal wing. (shrink)

Classical embryological studies have provided a great deal of information on the autonomy and stability of cell fate determination in early sea urchin embryos. However, these studies were limited by the tools available at the time, and the interpretation of the results of these experiments was limited by the lack of information available at the molecular level. Recent studies which have re‐examined classical experiments at the molecular level have provided important new insights into the mechanism of determination in sea (...) urchins, and require us to re‐evaluate some long standing theories on the process of differentiation. (shrink)

T‐bet and Eomes are two related transcription factors (TFs) that regulate the differentiation of cytotoxic lymphocytes such as Natural Killer (NK) cells and CD8 T cells. Recent genome‐wide analyses suggest they have complementary roles in instructing the transcriptional program of NK cells, although their DNA binding sites appear to be very similar. In this essay, we discuss the mechanisms that could specify their action, addressing their expression profile, the cofactors they interact with, as well as their roles in the (...) epigenetic regulation of chromatin accessibility. Based on the recent literature on these TFs, we propose different models to describe how they regulate gene expression in NK cells at steady state, or in the context of activation or exhaustion. We also discuss recent findings in the field of CD8 T cell differentiation and residency, where Eomes and T‐bet appear to be major regulators, and the parallels that can be drawn between mechanisms of NK and CD8 T cell differentiation and trafficking. (shrink)

Heterocyst spacing in blue -green bacteria is widely assumed to be due to a diffusible inhibitor. The inhibitor, a nitrogen-rich compound, probably glutamine, is produced via the N2-fixing enzymes of the heterocyst and in turn serves to suppress the induction of these enzymes and of the differentiation of vegetative cells to heterocysts. This simple morphogenetic mechanism operating in growing cellular filaments ofAnabaena species is investigated on the basis of a continuous and a discrete cellular model, as well as (...) by cell-by-cell simulation of the inhibitor transport. The resulting distances between heterocysts and kinetics of their production are compared with observations, and the values of physical parameters are estimated from the models. (shrink)

From stem cells to oocyte, Drosophila germ cells undergo a short, defined lineage. Molecular genetic analyses of a collection of female sterile mutations have indicated that a germ cell‐specific organelle called the fusome has a central role at several steps in this lineage. The fusome grows from a prominent spherical organelle to an elongated and branched structure that connects all mitotic sisters in a germ cell syncytium. The organelle is assembled from proteins normally found in the membrane skeleton (...) and, additionally, contains an extensive membranous reticulum, the probable product of differentiation‐dependent vesicle trafficking. This review briefly summarizes a current view of the processes that drive germ cell differentiation, particularly the various roles that the fusome might play in regulating the developmental events. Future efforts will consider to what extent an organelle assembly‐dependent model for differentiation is heuristic and whether the Drosophila fusome represents a homolog of a similar organelle in vertebrate lymphocytes. (shrink)

The paper is devoted to a conceptual model of cell patterning, based on a generalized notion of the epigenetic code of a cell determining its state. We introduce the concept of signaling depending both upon the spatial distance between cells and the distance between their cell states (s-distance); signaling can repel cells in the space of cell states (s-space) or attract them. The influence of different types of repelling signaling on the evolution of cells is (...) considered. Stabilizing signaling, namely a signaling monotonically decreasing with s-distance, causes the restoring of cell states after perturbations; destabilizing signaling, i.e., the one in which the signaling monotonically increases with s-distance, causes the appearance of pairs of cells with alternating cell states (one close to the state conventionally called “head”, and another close to the “tail” state). Non-monotonic (in s-space) signaling splits the cells into groups. The model shows that different types of signaling may provide different types of cellular patterns. General principles for applying this model to complex cellular structures are discussed. (shrink)

Alternative splicing (AS) greatly expands the coding capacities of genomes by allowing the generation of multiple mature mRNAs from a limited number of genes. Although the massive switch in AS profiles that often accompanies variations in gene expression patterns occurring during cell differentiation has been characterized for a variety of models, their causes and mechanisms remain largely unknown. Here, we integrate foundational and recent studies indicating the AS switches that govern the processes of cell fate determination. We (...) include some distinct AS events in pluripotent cells and somatic reprogramming and discuss new progresses on alternative isoform expression in adipogenesis, myogenic differentiation and stimulation of immune cells. Finally, we cover novel insights on AS mechanisms during neuronal differentiation, paying special attention to the role of chromatin structure. (shrink)

Central to the differentiation and patterning of the Drosophila oocyte is the asymmetric intracellular localization of numerous mRNA and protein molecules involved in developmental signalling. Recent advances have identified some of the molecules mediating oocyte differentiation, specification of the anterior pole of the embryo, and determination of the embryonic germ line. This work is considered in the context of the classical model of the germ plasm as a cytoplasmic determinant for germ cell formation.

This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}$$\end{document} is obtained. We investigate the equilibrium stability of the system, and the (...) COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate (α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\alpha )$$\end{document}, the rate of first vaccine dose (ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\phi )$$\end{document}, the second dose vaccination rate (σ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\sigma )$$\end{document} and the recovery rate due to the second dose of vaccination (η)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\eta )$$\end{document} are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population. (shrink)

Abstract.Since the gene splicing debates of the 1980s, the public has been exposed to an ongoing sequence of genetic and reproductive technologies. Many issue areas have outcomes that lose track of people's inner values or engender opposing religious viewpoints defying final resolution. This essay relocates the discussion of what is an acceptable application from the individual to the societal level, examining technologies that stand to address large numbers of people and thus call for policy resolution, rather than individual fiat, in (...) their application. A major source of guidance is the “Genetic Frontiers” series of professional dialogues and conferences held by the National Conference for Community and Justice from 2002 to 2004. Genetic testing, human gene therapy, genetic engineering of plants and animals, and stem cell technology are examined. While differences in perspective on the beginning of life persist, a stepwise approach to the examination of genetic testing reveals areas of general agreement. Stewardship of life, human co‐creativity with the divine, and social justice help define the bounds of application of genetic engineering and therapy; compassionate care plays a major role in establishing stem cell policy. Active, sustained dialogue is a useful resource for enabling sharing of religious values and crystallization of policies. (shrink)

The estrangement between genetic scientists and theologians originating in the 1960s is reflected in novel combinations of human thought (subject) and genes (investigational object), paralleling each other through the universal process known in chaos theory as self-similarity. The clash and recombination of genes and knowledge captures what Philip Hefner refers to as irony, one of four voices he suggests transmit the knowledge and arguments of the religion-and-science debate. When viewed along a tangent connecting irony to leadership, journal dissemination, and the (...) activities of the "public intellectual" and the public at large, the sequence of voices is shown to resemble the passage of genetic information from DNA to mRNA, tRNA, and protein, and from cell nucleus to surrounding environment. In this light, Hefner's inquiry into the voices of Zygon is bound up with the very subject matter Zygon covers. (shrink)

Many lymphokine genes have now been cloned from activated T cells and their products have been expressed in mammalian cells. Use of these recombinant lymphokines has provided the opportunity to evaluate both the spectrum of their biological activities and the mechanisms of their action in promoting proliferation and differentiation of hemopoietic and lymphoid cells. Characterization of the structure of lymphokine genes will provide information about their regulated expression in T‐cell activation.

Fractional calculus is nowadays an efficient tool in modelling many interesting nonlinear phenomena. This study investigates, in a novel way, the Ulam–Hyers and Ulam–Hyers–Rassias stability of differential equations with general conformable derivative. In our analysis, we employ some version of Banach fixed-point theory. In this way, we generalize several earlier interesting results. Two examples are given at the end to illustrate our results.

Self‐renewal and differentiation of stem cells are tightly regulated processes subject to intrinsic and extrinsic signals. Molecular chaperones and co‐chaperones, especially heat shock proteins (Hsp), are ubiquitous molecules involved in the modulation of protein conformational and complexation states. The function of Hsp, which are typically associated with stress response and tolerance, is well characterized in differentiated cells, while their role in stem cells remains unclear. It appears that embryonic stem cells exhibit increased stress tolerance and concomitant high levels of (...) chaperone expression. This review critically evaluates stem cell research from a molecular chaperone perspective. Furthermore, we propose a model of chaperone‐modulated self‐renewal in mouse embryonic stem cells. (shrink)

Recent studies support a model in which the progeny of SOX9+ epithelial progenitors at the distal tip of lung branches undergo cell allocation and differentiation sequentially along the distal‐to‐proximal axis. Concomitant with the elongation and ramification of lung branches, the descendants of the distal SOX9+ progenitors are distributed proximally, express SOX2, and differentiate into cell types in the conducting airways. Amid subsequent sacculation, the distal SOX9+ progenitors generate alveolar epithelial cells to form alveoli. Sequential cell (...) allocation and differentiation are integrated with the branching process to generate a functional branching organ. This review focuses on the roles of SOX9+ cells as precursors for new branches, as the source of various cell types in the conducting airways, and as progenitors of the alveolar epithelium. All of these processes are controlled by multiple signaling pathways. Many mouse mutants with defective lung branching contain underlying defects in one or more steps of cell allocation and differentiation of SOX9+ progenitors. This model provides a framework to understand the molecular basis of lung phenotypes and to elucidate the molecular mechanisms of lung patterning. It builds a foundation on which comparing and contrasting the mechanisms employed by different branching organs in diverse species can be made. (shrink)

Understanding the evolutionary role of environmentally induced phenotypic variation (i.e., plasticity) is an important issue in developmental evolution. A major physiological response to environmental change is cellular stress, which is counteracted by generic stress reactions detoxifying the cell. A model, stress‐induced evolutionary innovation (SIEI), whereby ancestral stress reactions and their corresponding pathways can be transformed into novel structural components of body plans, such as new cell types, is described. Previous findings suggest that the cell differentiation (...) cascade of a cell type critical to pregnancy in humans, the decidual stromal cell, evolved from a cellular stress reaction. It is hypothesized that the stress reaction in these cells was elicited ancestrally via inflammation caused by embryo attachment. The present study proposes that SIEI is a distinct form of plasticity‐based evolutionary change leading to the origin of novel structures rather than adaptive transformation of pre‐existing characters. (shrink)

The mechanism(s) by which the thymidine analogue 5‐bromodeoxyuridine (BUdR) specifically inhibits the expression of differentiated functions is poorly understood, as are the ways in which cells regulate processes exhibiting probabilistic aspects. I have developed a theoretical model for the regulation of the decision of myogenic cells to differentiate that can explain both of the above phenomena. This model provided a strategy for isolating myoblast variants that had amplified the expression of the factors regulating the decision to differentiate. These (...) myoblasts served as the source of mRNA for making and screening a cDNA library in order to isolate these factors. The successful cloning of these genes should represent a major advance in our understanding of the molecular basis for the major coordinated changes in gene expression that accompany cell differentiation. (shrink)

Cadherins are a large family of single‐pass transmembrane proteins principally involved in Ca2+‐dependent homotypic cell adhesion. The cadherin molecules comprise three domains, the intracellular domain, the transmembrane domain and the extracellular domain, and form large complexes with a vast array of binding partners (including cadherin molecules of the same type in homophilic interactions and cellular protein catenins), orchestrating biologically essential extracellular and intracellular signalling processes. While current, contrasting models for classic cadherin homophilic interaction involve varying numbers of specific repeats (...) found in the extracellular domain, the structure of the domain itself clearly remains the main determinant of cell stability and binding specificity. Through intracellular interactions, cadherin enhances its adhesive properties binding the cytoskeleton via cytoplasmic associated factors α‐ catenin, β‐catenin and p120ctn. Recent structural studies on classic cadherins and these catenin molecules have provided new insight into the essential mechanisms underlying cadherin‐mediated cell interaction and catenin‐mediated cellular signalling. Remarkable structural diversity has been observed in β‐catenin recognition of other cellular factors including APC, Tcf and ICAT, proteins that contribute to or compete with cadherin/catenin functioning. BioEssays 26:497–511, 2004. © 2004 Wiley Periodicals, Inc. (shrink)

Dimorphism in the yeast Candida albicans provides an unusually simple model system for investigating the mechanisms which regulate cellular differentiation, or cell divergence. Under the regime of pH‐regulated dimorphism, it has been demonstrated that the programs of protein synthesis accompanying bud and hypha formation are strikingly similar. Instead of dramatic differences in the repertoire of gene products possessed by bud‐ and hypha‐forming cells, subtle temporal, spatial and quantitative differences in the same architectural events appear to be basic (...) to the genesis of alternative phenotypes. This emerging story of phenotypic regulation does not exclude differential gene expression, but rather de‐emphasizes its role and underscores other mechanisms which are not generally considered. (shrink)

How cell commitment and differentiation are controlled in the early stages of embryogenesis is a problem that has long fascinated developmental biologists. Retinoic acidinduced differentiation of embryonal carcinoma cells in culture provides a model in which these questions can be explored. Recent work has yielded exciting insights into the central series of molecular changes which drives the commitment of these cells to formation of a new phenotype. Interacting with the key molecules in this central pathway is (...) a variety of transcription factors, many of which show changes in availability and/or activity during differentiation. In various combinations, these modulate the activities of genes involved in both cell proliferation and in the production of extracellular matrix and other proteins characteristic of differentiated cells. (shrink)

This review explores the hypothesis that regulation of nucleocytoplasmic shuttling is a means of driving differentiation, using spermatogenesis as a model. The transition from undifferentiated spermatogonial stem cell to terminally differentiated spermatozoon is, at its most basic, a change in the repertoire of expressed genes. To effect this, the complement of nuclear proteins, such as transcription factors and chromatin remodelling components must change. Current knowledge of the nuclear proteins and nucleocytoplasmic transport machinery relevant to spermatogenesis is consolidated (...) in this review, and their functional linkages are highlighted not only as a means of regulating nuclear protein composition, but also as a key mechanism regulating gene transcription and hence cell fate. Through this, we hypothesize that male germ cell differentiation is mediated through regulation of nuclear transport machinery components, and thereby of the access of critical factors to the nucleus. The importance of nucleocytoplasmic trafficking to male germ cell differentiation is discussed, using the sex-determining factors Sry and SOX9, cell cycle regulators, CREM and cofactors and the Smads as specific examples, together with the roles in gametogenesis for particular nuclear transport factors in Caenorhabditis elegans and Drosophila. BioEssays 27:1011–1025, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold $$\mathcal{R}_0$$ is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission $$\mathcal{R}_0$$ and the endemic equilibrium (...) are determined. Both $$\mathcal{R}_0$$ and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d m . The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, $$\Uppi_l$$ and $$\Uppi_h$$, respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level. (shrink)

The Continuous Parameter Estimation Model is applied to develop individual genomic-level heritabilities for the latent hierarchical structure and developmental dynamics of Life History (LH) strategy LH strategies relate to the allocations of bioenergetic resources into different domains of fitness. LH has moderate to high population-level heritability in humans, both at the level of the high-order Super-K Factor and the lower-order factors, the K-Factor, Covitality Factor, and General Factor of Personality (GFP). Several important questions remain unexplored. We developed measures of (...) genome-level heritabilities employing an American sample of 316 monozygotic (MZ) and 274 dizygotic (DZ) twin dyads and a Swedish sample of 863 MZ and 475 DZ twin dyads. This novel heritability index measures individual genetic transmissibility, therefore opening new avenues for analyzing complex interactions among heritable traits inaccessible to standard structural equations methods. For these samples: (1) moderate to high heritability of factor loadings of Super-K on its lower-order factors is demonstrated, evidencing biological preparedness, genetic accommodation, and the gene-culture coevolution of biased epigenetic rules of development; (2) moderate to high heritability of the magnitudes of the effect of the higher-order factors upon their loadings on their constituent factors, evidencing genetic constraints upon phenotypic plasticity; and (3) that heritability of the LH factors, of factor loadings, and of the magnitudes of the correlations among factors are weaker among those with slower LH speeds, demonstrating that inter-individual variation in transmissibility is a function of individual socioecological selection pressures. (shrink)

The differentiation of T Lymphocytes within the thymus is an important biological phenomenon during wich these cell acquire their functions to further control the immune system. Numerous experiments under various conditions have been devised to understand the different mechanisms involved in this complex process. Nevertheless, interpretation of these experiments lead to still contradictory debatable hypotheses. Modelisation of this process through classical simulation methods cannot be envisaged because they are not adapted to modifications of the model structure, which (...) is the point of interest. For these reasons, we proposed a new approach of automatic search for model. The program consists of four independent connected modules : The generator produces model, based on the rationale of formal grammars. Protocol and experimental data are stored in a set of experiments. The simulator using a protocol and a model provides simulated results. Finally, the supervisor by comparing simulated results and experimental data, adapts the model parameters to increase their fit and either chooses a new experiment to explore, or modifies the model structure. Change of the model structure is performed among still unexplored models according to their promise level, which is iteratively evaluated relatively to previously explored models through a proposed model distance. The generator is written in Prolog and the other modules in C++. The architecture of the program allows us to modify or complete a module without changing anything in the other modules. As a consequence, the proposed modeling approach conceived to study T lymphocyte differentiation within the thymus remains independent of this biological phenomenon and can be applied to other biological problems. (shrink)

This paper presents an integrated model describing the control of Saccharomyces cerevisiae yeast cells bioenergetics. This model describes the oxidative and respirofermentative metabolism. The model assumes that the mitochondria of the Saccharomyces cerevisiae cells are charged with NADH during the tricarboxylic acid cycle, and NADH is discharged from mitochondria later in the electron transport system. Selected effects observed in the Saccharomyces cerevisiae eucaryotic cells, including the Pasteur's and Crabtree effects, are also modeled.

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium , using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium with respect to concentrations of enzymes. We give some conclusions (...) concerning the dynamical behavior of coupled genetic/metabolic systems. (shrink)

From the 1930s through the 1970s, C. H. Waddington attempted to reunite genetics, embryology, and evolution. One of the means to effect this synthesis was his model of the epigenetic landscape. This image originally recast genetic data in terms of embryological diagrams and was used to show the identity of genes and inducers and to suggest the similarities between embryological and genetic approaches to development. Later, the image became more complex and integrated gene activity and mutations. These revised epigenetic (...) landscapes presented an image of how mutations could alter developmental pathways to yield larger phenotypic changes. These diagrams became less important as the operon became used to model differential gene regulation. (shrink)

Balancing self‐renewal and differentiation of stem cells is an important issue in stem cell and cancer biology. Recently, the Drosophila neuroblast (NB), neural stem cell has emerged as an excellent model for stem cell self‐renewal and tumorigenesis. It is of great interest to understand how defects in the asymmetric division of neural stem cells lead to tumor formation. Here, we review recent advances in asymmetric division and the self‐renewal control of Drosophila NBs. We summarize molecular (...) mechanisms of asymmetric cell division and discuss how the defects in asymmetric division lead to tumor formation. Gain‐of‐function or loss‐of‐function of various proteins in the asymmetric machinery can drive NB overgrowth and tumor formation. These proteins control either the asymmetric protein localization or mitotic spindle orientation of NBs. We also discuss other mechanisms of brain tumor suppression that are beyond the control of asymmetric division. (shrink)

differential from bottom to top, depth of fluid, and the coefficients of expansion, viscosity and thermal Bénard convection, is one of the more intensely conductivity of the fluid. Even though it is a simple studied dissipative systems, both theoretically and..

Sickle cell haemoglobin polymerization reduces erythrocyte deformability, causing deleterous vaso-occlusions. The double-nucleation model states that polymers grow from HbS aggregates, the nuclei, in solution , onto existing polymers . When linearized at initial HbS concentration, this model predicts early polymerization and its characteristic delay-time :591–610, 611–631, 1985). Addressing its relevance for describing complete polymerization, we constructed the full, non-linearized model . Here, we compare the simulated outputs to experimental progress curves . Within 10% from start, average (...) root mean square deviation between simulated and experimental curves is 0.04 ± 0.01 . Conversely, for complete progress curves, averaged rms is 0.48 ± 0.04. This figure is improved to 0.13 ± 0.01 by adjusting heterogeneous pathway parameters : the nucleus stability , and the fraction of polymer surface available for nucleation , from 5e−7, to 13 . Similar results are obtained at 37°C. We conclude that the physico-chemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process. (shrink)

The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine (...) the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear. (shrink)

This review discusses the possible role of α‐tubulin detyrosination, a reversible post‐translational modification that occurs at the protein's C‐terminus, in cellular morphogenesis. Higher eukaryotic cells possess a cyclic post‐translational mechanism by which dynamic microtubules are differentiated from their more stable counterparts; a tubulin‐specific carboxypeptidase detyrosinates tubulin protomers within microtubules, while the reverse reaction, tyrosination, is performed on the soluble protomer by a second tubulin‐specific enzyme, tubulin tyrosine ligase. In general, the turnover of microtubules in undifferentiated, proliferating cells is so rapid (...) that the microtubules accumulate very little detyrosinated tubulin; that is, they are enriched in tyrosinated tubulin. However, an early event common to at least three well‐studied morphogenetic events myogenesis, neuritogenesis, and directed cell motility is the elaboration of a polarized array of stable microtubules that become enriched in detyrosinated tubulin. The formation of this specialized array of microtubules in specific locations in cells undergoing morphogenesis suggests that it plays an important role in generating cellular asymmetries. (shrink)

Let us start by some general definitions of the concept of complexity. We take a complex system to be one composed by a large number of parts, and whose properties are not fully explained by an understanding of its components parts. Studies of complex systems recognized the importance of “wholeness”, defined as problems of organization (and of regulation), phenomena non resolvable into local events, dynamics interactions in the difference of behaviour of parts when isolated or in higher configuration, etc., in (...) short, systems of various orders (or levels) not understandable by investigation of their respective parts in isolation. In a complex system it is essential to distinguish between ‘global’ and ‘local’ properties. Theoretical physicists in the last two decades have discovered that the collective behaviour of a macro-system, i.e. a system composed of many objects, does not change qualitatively when the behaviour of single components are modified slightly. Conversely, it has been also found that the behaviour of single components does change when the overall behaviour of the system is modified. There are many universal classes which describe the collective behaviour of the system, and each class has its own characteristics; the universal classes do not change when we perturb the system. The most interesting and rewarding work consists in finding these universal classes and in spelling out their properties. This conception has been followed in studies done in the last twenty years on second order phase transitions. The objective, which has been mostly achieved, was to classify all possible types of phase transitions in different universality classes and to compute the parameters that control the behaviour of the system near the transition (or critical or bifurcation) point as a function of the universality class. This point of view is not very different from the one expressed by Thom in the introduction of Structural Stability and Morphogenesis (1975). It differs from Thom’s program because there is no a priori idea of the mathematical framework which should be used. Indeed Thom considers only a restricted class of models (ordinary differential equations in low dimensional spaces) while we do not have any prejudice regarding which models should be accepted. One of the most interesting and surprising results obtained by studying complex systems is the possibility of classifying the configurations of the system taxonomically. It is well-known that a well founded taxonomy is possible only if the objects we want to classify have some unique properties, i.e. species may be introduced in an objective way only if it is impossible to go continuously from one specie to another; in a more mathematical language, we say that objects must have the property of ultrametricity. More precisely, it was discovered that there are conditions under which a class of complex systems may only exist in configurations that have the ultrametricity property and consequently they can be classified in a hierarchical way. Indeed, it has been found that only this ultrametricity property is shared by the near-optimal solutions of many optimization problems of complex functions, i.e. corrugated landscapes in Kauffman’s language. These results are derived from the study of spin glass model, but they have wider implications. It is possible that the kind of structures that arise in these cases is present in many other apparently unrelated problems. Before to go on with our considerations, we have to pick in mind two main complementary ideas about complexity. (i) According to the prevalent and usual point of view, the essence of complex systems lies in the emergence of complex structures from the non-linear interaction of many simple elements that obey simple rules. Typically, these rules consist of 0–1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. Quite intricate patterns and structures can occur in such systems. However, what can be also said is that these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. (ii) So, this bring a new aspect that seems essential and indispensable to the emergence and functioning of complex systems, namely the coordination of individual agents or elements that themselves are complex at their own scale of operation. This coordination dramatically reduces the degree of freedom of those participating agents. Even the constituents of molecules, i.e. the atoms, are rather complicated conglomerations of subatomic particles, perhaps ultimately excitations of patterns of superstrings. Genes, the elementary biochemical coding units, are very complex macromolecular strings, as are the metabolic units, the proteins. Neurons, the basic elements of cognitive networks, themselves are cells. In those mentioned and in other complex systems, it is an important feature that the potential complexity of the behaviour of the individual agents gets dramatically simplified through the global interactions within the system. The individual degrees of freedom are drastically reduced, or, in a more formal terminology, the factual space of the system is much smaller than the product of the state space of the individual elements. That is one key aspect. The other one is that on this basis, that is utilizing the coordination between the activities of its members, the system then becomes able to develop and express a coherent structure at a higher level, that is, an emergent behaviour (and emergent properties) that transcends what each element is individually capable of. (shrink)

Why do humans menstruate while most mammals do not? Here, we present our answer to this long‐debated question, arguing that (i) menstruation occurs as a mechanistic consequence of hormone‐induced differentiation of the endometrium (referred to as spontaneous decidualization, or SD); (ii) SD evolved because of maternal–fetal conflict; and (iii) SD evolved by genetic assimilation of the decidualization reaction, which is induced by the fetus in non‐menstruating species. The idea that menstruation occurs as a consequence of SD has been proposed (...) in the past, but here we present a novel hypothesis on how SD evolved. We argue that decidualization became genetically stabilized in menstruating lineages, allowing females to prepare for pregnancy without any signal from the fetus. We present three models for the evolution of SD by genetic assimilation, based on recent advances in our understanding of the mechanisms of endometrial differentiation and implantation. Testing these models will ultimately shed light on the evolutionary significance of menstruation, as well as on the etiology of human reproductive disorders like endometriosis and recurrent pregnancy loss. (shrink)

When two populations of cells within a tissue mass differ from one another in magnitude or type of intercellular adhesions, a boundary can form within the tissue, across which cells will fail to mix. This phenomenon may occur regardless of the identity of the molecules that mediate cell adhesion. If, in addition, a choice between the two adhesive states is regulated by a molecule the concentration of which is periodic in space, or in time, then alternating bands of non‐mixing (...) tissue, or segments, can form. But temporal or spatial periodicities in concentration will tend to arise for any molecule that is positively autoregu‐latory. It is therefore proposed that segmentation is a ‘generic’ property of metazoan organisms, and that metamerism would be expected to have emerged numerous times during evolution. A simple model of segmentation, based solely on differential adhesion and periodic regulation of adhesion, can account for segment properties as disparate as those seen in long and short germ band insects, and for diverse experimental results on boundary regeneration in the chick hind brain and the insect cuticle. It is suggested that the complex, multicom‐ponent segment‐forming systems found in contemporary organisms (e.g., Drosophila) are the products of evolutionary recruitment of molecular cues such as homeobox gene products, that increase the reliability and stability of metameric patterns originally templated by generic self‐organizing properties of tissues. (shrink)