Minimal model for stem-cell differentiation

Tuning coupling rate to control oscillation quenching in fractional-order coupled oscillators

Introducing the fractional-order derivative into the coupled dynamical systems intrigues gradually the researchers from diverse fields. In this work, taking Stuart-Landau and Van der Pol oscillators as examples, we compare the difference between fractional-order and integer-order derivatives and further analyze their influences on oscillation quenching behaviors. Through tuning the coupling rate, as an asymmetric parameter to achieve the change from scalar coupling to non-scalar coupling, we observe that the onset of fractional-order not only enlarges the range of oscillation death, but attributes to the transition from fake amplitude death to oscillation death for coupled Stuart-Landau oscillators. We go on to show that for a coupled Van der Pol system only in the presence of a fractional-order derivative, oscillation quenching behaviors will occur. The results pave a way for revealing the control mechanism of oscillation quenching, which is critical for further understanding the function of fractional-order in a coupled nonlinear model.

Exploring the mechanisms of cell reprogramming and transdifferentiation via intercellular communication

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

Coexistence of oscillation and quenching states: Effect of low-pass active filtering in coupled oscillators

Effects of a low-pass active filter (LPAF) on the transition processes from oscillation quenching to asymmetrical oscillation are explored for diffusively coupled oscillators. The low-pass filter part and the active part of LPAF exhibit different effects on the dynamics of these coupled oscillators. With the amplifying active part only, LPAF keeps the coupled oscillators staying in a nontrivial amplitude death (NTAD) and oscillation state. However, the additional filter is beneficial to induce a transition from a symmetrical oscillation death to an asymmetrical oscillation death and then to an asymmetrical oscillation state which is oscillating with different amplitudes for two oscillators. Asymmetrical oscillation state is coexisting with a synchronous oscillation state for properly presented parameters. With the attenuating active part only, LPAF keeps the coupled oscillators in rich oscillation quenching states such as amplitude death (AD), symmetrical oscillation death (OD), and NTAD. The additional filter tends to enlarge the AD domains but to shrink the symmetrical OD domains by increasing the areas of the coexistence of the oscillation state and the symmetrical OD state. The stronger filter effects enlarge the basin of the symmetrical OD state which is coexisting with the synchronous oscillation state. Moreover, the effects of the filter are general in globally coupled oscillators. Our results are important for understanding and controlling the multistability of coupled systems.

[In vivo confocal microscopy and optical coherence tomography as innovative tools for the diagnosis of limbal stem cell deficiency (French translation of the article)]

The limbus is the anatomical and functional barrier between corneal and conjunctival epithelia. It is characterized by presence of the limbal stem cell niche which allows corneal homeostasis to be maintained. Limbal stem cell deficiency is characterized by a dual process: insufficient regeneration of corneal epithelium, which cannot therefore assure its function of physiological support, associated with corneal invasion by conjunctival proliferation. Diagnosis is currently made via routine clinical examination, corneal impression cytology and in vivo confocal microscopy (IVCM). Slit lamp examination shows abnormal limbal anatomy, thin and irregular epithelium with late fluorescein staining, and superficial vascularization. With its high resolution, IVCM allows identification of limbal and corneal epithelial changes at a cellular level in en face views, parallel to the corneal surface, but with a restricted viewing field of the corneal surface. It shows a poor transition between the corneal and conjunctival epithelia, associated with a loss of the normal corneal epithelial stratification, low basal cell and sub-basal nerve plexus densities, even with sub-epithelial fibrosis. Optical coherence tomography in central cornea and at the limbus, with scans in different orientations, allows a quick, global and non-invasive analysis of normal eyes and those with limbal stem cell deficiency. It shows a thin limbal epithelium, lacking normal thickening, featuring absence of stromal undulations and limbal crypts in cross-sections and sections parallel to the limbus, lack of visible limbal crypts in en face sections, loss of clear transition between the hyporeflective corneal epithelium and the hyperreflective conjunctival epithelium, and hyperreflective sub-epithelial fibrosis.

The "mechanostat" principle in cell differentiation. The osteochondroprogenitor paradigm

The "mechanostat" principle may be depicted as an oscillating signal of a signaling molecule, in which the amplitude, frequency, cumulative level, delay, and duration of the curve encode the information for concrete cellular responses and biological activities. When the oscillating signal is kept sustained (present delay), cell exit may be performed, whereas when the oscillating signal remains robust, cell proliferation may take place. B-catenin-Wnt signaling pathway has a key role in the differentiation of osteochondroprogenitor cells. Sustained downregulation of the β-catenin-Wnt pathway forces osteochondroprogenitors to a chondrogenic fate instead of an osteoblastic one. Other signaling, for example, bone morphogenetic protein and Notch signaling pathways interact with the Wnt pathway. The crosstalk between biochemical and mechanical stimuli produces the final information that leads to the final cell fate decisions, through the "mechanostat" principle.

Boundary-induced pattern formation from uniform temporal oscillation

Pattern dynamics triggered by fixing a boundary is investigated. By considering a reaction-diffusion 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.

Basis of self-organized proportion regulation resulting from local contacts

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual is aware of the overall situation without a leader. In various species, a specific ratio exists at multiple levels, from the process of cell differentiation in multicellular organisms to the situation of social dilemma in a group of human beings. This study determines a common basis for regulating collective behavior that is realized by a series of local contacts between individuals. In this theory, the most essential behavior of individuals is to change their internal mode by sharing information when in contact with others. Our numerical simulations regulate the proportion of population in two kinds of modes. Furthermore, using theoretical analysis and numerical calculations, we show that asymmetric properties in local contacts are essential for adaptive regulation in response to global information such as group size and overall density. Particle systems are crucial in allowing flexible regulation in no-leader groups, and the critical condition that eliminates overlap with other individuals (the excluded volume effect) also affects the resulting proportion at high densities. The foremost advantage of this strategy is that no global information is required for each individual, and minimal mode switching can regulate the overall proportion. This simple mechanism indicates that proportion regulation in well-organized groups in nature can be realized through and limited to local contacts, and has the potential to explain various phenomena in which microscopic individual behavior results in orderly macroscopic behavior.

The impact of propagation and processing delays on amplitude and oscillation deaths in the presence of symmetry-breaking coupling

We numerically investigate the impacts of both propagation and processing delays on the emergences of amplitude death (AD) and oscillation death (OD) in one system of two Stuart-Landau oscillators with symmetry-breaking coupling. In either the absence of or the presence of propagation delay, the processing delay destabilizes both AD and OD by revoking the stability of the stable homogenous and inhomogenous steady states. In the AD to OD transition, the processing delay destabilizes first OD from large values of coupling strength until its stable regime completely disappears and then AD from both the upper and lower bounds of the stable coupling interval. Our numerical study sheds new insight lights on the understanding of nontrivial effects of time delays on dynamic activity of coupled nonlinear systems.

Symbiotic Cell Differentiation and Cooperative Growth in Multicellular Aggregates

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

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

Evolution-development congruence in pattern formation dynamics: Bifurcations in gene expression and regulation of networks structures

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, they are due to some gene expression that varies slowly and controls the pattern change. The morphogenesis is regulated by combinations of feedback or feedforward regulations, where the upstream feedforward network reads the external morphogen gradient, and generates a pattern used as a boundary condition for the later patterns. The ordering from up to downstream is common in evolution and development, while the successive epochal changes in development and evolution are represented as common bifurcations in dynamical-systems theory, which lead to the evolution-development congruence. Mechanism of exceptional violation of the congruence is also unveiled. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

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

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

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

Emergence of amplitude and oscillation death in identical coupled oscillators

We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly distinguish intrinsic geneses for AD and OD, and further substantially corroborates that AD and OD are indeed two dynamically distinct oscillation quenching phenomena due to distinctly different mechanisms.

Generalizing the transition from amplitude to oscillation death in coupled oscillators

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al., Phys. Rev. Lett. 111, 024103 (2013)]. We identify here the transition from AD to OD in nonlinear oscillators with couplings of distinct natures. It is demonstrated that the presence of time delay in the coupling cannot induce such a transition in identical oscillators, but it can indeed facilitate its occurrence with a low degree of heterogeneity. Moreover, it is further shown that the AD to OD transition is reliably observed in identical oscillators with dynamic and conjugate couplings. The coexistence of AD and OD and rich stable OD configurations after the transition are revealed, which are of great significance for potential applications in physics, biology, and control studies.