Pattern formation by local self-activation and lateral inhibition

Role of vascular smooth muscle cell clonality in atherosclerosis

Atherosclerotic cardiovascular disease remains the leading cause of death worldwide. While many cell types contribute to the growing atherosclerotic plaque, the vascular smooth muscle cell (SMC) is a major contributor due in part to its remarkable plasticity and ability to undergo phenotype switching in response to injury. SMCs can migrate into the fibrous cap, presumably stabilizing the plaque, or accumulate within the lesional core, possibly accelerating vascular inflammation. How SMCs expand and react to disease stimuli has been a controversial topic for many decades. While early studies relying on X-chromosome inactivation were inconclusive due to low resolution and sensitivity, recent advances in multi-color lineage tracing models have revitalized the concept that SMCs likely expand in an oligoclonal fashion during atherogenesis. Current efforts are focused on determining whether all SMCs have equal capacity for clonal expansion or if a "stem-like" progenitor cell may exist, and to understand how constituents of the clone decide which phenotype they will ultimately adopt as the disease progresses. Mechanistic studies are also beginning to dissect the processes which confer cells with their overall survival advantage, test whether these properties are attributable to intrinsic features of the expanding clone, and define the role of cross-talk between proliferating SMCs and other plaque constituents such as neighboring macrophages. In this review, we aim to summarize the historical perspectives on SMC clonality, highlight unanswered questions, and identify translational issues which may need to be considered as therapeutics directed against SMC clonality are developed as a novel approach to targeting atherosclerosis.

Effects of noise on the critical points of Turing instability in complex ecosystems

Noise is ubiquitous in natural and artificial systems. In a noisy environment, the interactions among nodes may fluctuate randomly, leading to more complicated interactions. In this paper we focus on the effects of noise and network topology on the Turing pattern of ecological networks with activator-inhibitor structure, which may be interpreted as prey-predator interactions. Based on the stability theory of stochastic differential equations, a sufficient condition for the uniform state is derived. The analytical results indicate that noise is beneficial for the uniform state. When the ratio between the diffusion coefficients of the predator and prey increases, the ecosystems can exhibit a transition from a uniform stable state to a Turing pattern, while when the ratio decreases, the ecosystems transit from a Turing pattern to a uniform stable state. There are two crucial critical points in Turing patterns, forward and backward. We find that both forward and backward critical points increase as the noise intensity increases. This means that noise favors a stable homogeneous state compared to a state with a heterogeneous pattern, which is consistent with the analytical results. In addition, noise can weaken the hysteresis phenomenon and even eliminate it in some cases. Furthermore, we report that network topology plays an important role in modulating the uniform state of ecosystems, such as the size of prey-predator systems, the network connectivity, and the strength of interaction.

Stochastic self-assembly of reaction-diffusion patterns in synaptic membranes

Synaptic receptor and scaffold molecules self-assemble into membrane protein domains, which play an important role in signal transmission across chemical synapses. Experiment and theory have shown that the formation of receptor-scaffold domains of the characteristic size observed in nerve cells can be understood from the receptor and scaffold reaction and diffusion processes suggested by experiments. We employ here kinetic Monte Carlo (KMC) simulations to explore the self-assembly of synaptic receptor-scaffold domains in a stochastic lattice model of receptor and scaffold reaction-diffusion dynamics. For reaction and diffusion rates within the ranges of values suggested by experiments we find, in agreement with previous mean-field calculations, self-assembly of receptor-scaffold domains of a size similar to that observed in experiments. Comparisons between the results of our KMC simulations and mean-field solutions suggest that the intrinsic noise associated with receptor and scaffold reaction and diffusion processes accelerates the self-assembly of receptor-scaffold domains, and confers increased robustness to domain formation. In agreement with experimental observations, our KMC simulations yield a prevalence of scaffolds over receptors in receptor-scaffold domains. Our KMC simulations show that receptor and scaffold reaction-diffusion dynamics can inherently give rise to plasticity in the overall properties of receptor-scaffold domains, which may be utilized by nerve cells to regulate the receptor number at chemical synapses.

Nonequilibrium biochemical structures in two space dimensions with local activation and regulation

Integrin receptor (IR) clustering is an example of pattern self-organization in biological systems. This paper describes a model for receptor activation whose content is guided by two major principles in cellular signal transduction: (i) Proteins cycle between different conformational states; (ii) the dynamics of their conformational dynamics is environment dependent. Based on a simple activation pathway where these two hypotheses are formulated in a self-consistent way, this paper focuses mainly on stochastic simulations valid in the limit of a small number of molecules. It is shown that coherent clustering can lead to digital signaling and receptor competition in biochemical systems where the model gives a recruitment mechanism for the reinforcement of the mechanical linkage with the extracellular matrix. Together with previous works, this paper provides a workable model for cell integrin adhesive structures when feedback mediated by membrane diffusing signals is dominant. Consequences are discussed in the framework of published data concerning the local production of a key phospholipid for cell signaling (PIP_{2}).

Turing patterns mediated by network topology in homogeneous active systems

Mechanisms of pattern formation-of which the Turing instability is an archetype-constitute an important class of dynamical processes occurring in biological, ecological, and chemical systems. Recently, it has been shown that the Turing instability can induce pattern formation in discrete media such as complex networks, opening up the intriguing possibility of exploring it as a generative mechanism in a plethora of socioeconomic contexts. Yet much remains to be understood in terms of the precise connection between network topology and its role in inducing the patterns. Here we present a general mathematical description of a two-species reaction-diffusion process occurring on different flavors of network topology. The dynamical equations are of the predator-prey class that, while traditionally used to model species population, has also been used to model competition between antagonistic features in social contexts. We demonstrate that the Turing instability can be induced in any network topology by tuning the diffusion of the competing species or by altering network connectivity. The extent to which the emergent patterns reflect topological properties is determined by a complex interplay between the diffusion coefficients and the localization properties of the eigenvectors of the graph Laplacian. We find that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic.

Similar size of slums caused by a Turing instability of migration behavior

It is a remarkable fact that the size of slums is similar across the globe, regardless of city, country, or culture [Friesen et al., Habitat Int. 73, 79 (2018)0197-397510.1016/j.habitatint.2018.02.002]. The main thesis of this paper is that this universal scale is intrinsic to the slum-city system and is independent from external factors. By interpreting reaction and diffusion as long- and short-distance migration, our paper explains this universal length scale as resulting from a Turing instability of the interaction of two social groups: poor and rich.

Emergence of diversity in homogeneous coupled Boolean networks

The origin of multicellularity in metazoa is one of the fundamental questions of evolutionary biology. We have modeled the generic behaviors of gene regulatory networks in isogenic cells as stochastic nonlinear dynamical systems-coupled Boolean networks with perturbation. Model simulations under a variety of dynamical regimes suggest that the central characteristic of multicellularity, permanent spatial differentiation (diversification), indeed can arise. Additionally, we observe that diversification is more likely to occur near the critical regime of Lyapunov stability.

Co-existence of Ras activation in a chemotactic signal transduction pathway and in an autonomous wave - forming system

The activation of Ras is common to two activities in cells of Dictyostelium discoideum: the directed movement in a gradient of chemoattractant and the autonomous generation of propagating waves of actin polymerization on the substrate-attached cell surface. We produced large cells by electric-pulse induced fusion to simultaneously study both activities in one cell. For imaging, a fluorescent label for activated Ras was combined with labels for filamentous actin, PIP3, or PTEN. Chemotactic responses were elicited in a diffusion gradient of cyclic AMP. Waves initiated at sites separate from the front of the cell propagated in all directions. Nevertheless, the wave-forming cells were capable of recognizing the attractant gradient and managed to migrate in its direction.

How to make a static cytokinetic furrow out of traveling excitable waves

Emergence of the cytokinetic Rho zone that orchestrates formation and ingression of the cleavage furrow had been explained previously via microtubule-dependent cortical concentration of Ect2, a guanine nucleotide exchange factor for Rho. The results of a recent publication now demonstrate that, en route from resting cortex to fully established furrow, there lies a regime of cortical excitability in which Rho activity and F-actin play the roles of the prototypical activator and inhibitor, respectively. This cortical excitability is manifest as dramatic traveling waves on the cortex of oocytes and embryos of frogs and starfish. These waves are initiated by autocatalytic activation of Rho at the wave front and extinguished by F-actin-dependent inhibition at their back. It is still unclear how propagating excitable Rho-actin waves give rise to the stable co-existence of Rho activity and F-actin density in the static cleavage furrow during cytokinesis. It is possible that some central spindle-associated signaling molecule simply turns off the inhibition of Rho activity by F-actin. However, mathematical modeling suggests a distinct scenario in which local “re-wiring” of the Rho-actin coupling in the furrow is no longer necessary. Instead, the model predicts that the continuously rising level of Ect2 produces in the furrow a qualitatively new stable steady state that replaces excitability and brings about the stable co-existence of high Rho activity and dense F-actin despite the continuing inhibition of Rho by F-actin.

Modeling somite scaling in small embryos in the framework of Turing patterns

The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.

Turing-like instabilities from a limit cycle

The Turing instability is a paradigmatic route to pattern formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor. Stable patterns can be also obtained via oscillation quenching of an initially synchronous state of diffusively coupled oscillators. In the literature this is known as the oscillation death phenomenon. Here, we show that oscillation death is nothing but a Turing instability for the first return map of the system in its synchronous periodic state. In particular, we obtain a set of approximated closed conditions for identifying the domain in the parameter space that yields the instability. This is a natural generalization of the original Turing relations, to the case where the homogeneous solution of the examined system is a periodic function of time. The obtained framework applies to systems embedded in continuum space, as well as those defined on a networklike support. The predictive ability of the theory is tested numerically, using different reaction schemes.