Self-regenerating trigger waves can spread rapidly through the crowded cytoplasm without diminishing in amplitude or speed, providing consistent, reliable, long-range communication. The macromolecular concentration of the cytoplasm varies in response to physiological and environmental fluctuations, raising the question of how or if trigger waves can robustly operate in the face of such fluctuations. Using Xenopus extracts, we found that mitotic and apoptotic trigger wave speeds are remarkably invariant. We derived a model that accounts for this robustness and for the eventual slowing at extremely high and low cytoplasmic concentrations. The model implies that the positive and negative effects of cytoplasmic concentration (increased reactant concentration vs. increased viscosity) are nearly precisely balanced. Accordingly, artificially maintaining a constant cytoplasmic viscosity during dilution abrogates this robustness. The robustness in trigger wave speeds may contribute to the reliability of the extremely rapid embryonic cell cycle.

A consumer-resource reaction-diffusion model with a single consumer species was proposed and experimentally studied by Zhang et al.(Ecol Lett 20:1118-1128, 2017). Analytical study on its dynamics was further performed by He et al.(J Math Biol 78:1605-1636, 2019). In this work, we completely settle the conjecture proposed by He et al.(J Math Biol 78:1605-1636, 2019) about the global dynamics of the consumer-resource model for small yield rate. We then study a multi-species consumer-resource model where all the consumer species compete with each other through depression of the limited resources by consumption and there is no direct competition between them. We show that in this case, all consumer species persist uniformly, which implies that \"competition exclusion\" phenomenon will never happen. We also clarify its dynamics in both homogeneous and heterogeneous environments under various circumstances.

We examine the effect of human mobility on disease prevalence by studying the dependence of the total infected population at endemic equilibria with respect to population diffusion rates of a diffusive epidemic model. For small diffusion rates, our results indicate that the total infected population size is strictly decreasing with respect to the ratio of the diffusion rate of the infected population over that of the susceptible population. Moreover, when the disease local reproductive function is spatially heterogeneous, we found that: (i) for large diffusion rate of the infected population, the total infected population size is strictly maximized at large diffusion rate of the susceptible population when the recovery rate is spatially homogeneous, while it is strictly maximized at intermediate diffusion rate of the susceptible population when the difference of the transmission and recovery rates are spatially homogeneous; (ii) for large diffusion rate of the susceptible population, the total infected population size is strictly maximized at intermediate diffusion rate of the infected population when the recovery rate is spatially homogeneous, while it is strictly minimized at large diffusion rate of the infected population when the difference of the transmission and recovery rates is spatially homogeneous. Numerical simulations are provided to complement the theoretical results. Our studies may provide some insight into the impact of human mobility on disease outbreaks and the severity of epidemics.

Room temperature liquid metals (LM) such as gallium (Ga) own the potential to react with specific materials which would incubate new application categories. Here, diverse self-organized ring patterns due to nonequilibrium reaction-diffusion and spreading-limitation of Ga-based LM clusters on gold (Au) film are reported, among which diffusion is the controlling step and the self-limiting oxide layer plays the role of kinetic barrier. Such phenomena, classically known as the Liesegang rings, mainly occur in electrolyte media. Unlike existing systems, the present periodic crystallization mechanism enables highly symmetric spatiotemporal periodic Liesegang rings on a smaller scale under ambient conditions. Typically, the Ga-Au and eutectic gallium-indium alloy (EGaIn)-Au reaction-diffusion-spreading systems are constructed, obtaining the revert type and hybrid type concentric Liesegang patterns, respectively. The competitive patterning behavior of the intermediate phase products AuGa2 and AuIn2 in hybrid Liesegang patterns is further analyzed by altering the initial Ga/In mass ratio, first-principles calculations, and molecular dynamic simulations. When the mass ratio of In in GaIn alloy exceeds 15%, it will preferentially react with Au. The discovery of LM Liesegang phenomenon is expected to be a flashpoint for self-organized reaction-diffusion systems and offers promising rules for diverse areas such as materials synthesis and the jewelry design industry.

In human spermatozoa, calcium dynamics control most of fertilization events. Progesterone, present in the female reproductive system, can trigger several types of calcium responses, such as low-frequency oscillations. Here we aimed to identify the mechanisms of progesterone-induced calcium signaling in human spermatozoa. Progesterone-induced activation of fluorophore-loaded spermatozoa was studied by fluorescent microscopy. Two computational models were developed to describe the spermatozoa calcium responses: a homogeneous one based on a system of ordinary differential equations and a three-dimensional one with added space dimensions and diffusion for the cytosolic species. In response to progesterone, three types of calcium responses were observed in human spermatozoa: a single transient rise of calcium concentration in cytosol, a steady elevation, or low-frequency oscillations. The homogenous model provided qualitative description of the oscillatory and the single spike responses, while the three-dimensional model captured the calcium peak shape and the frequency of calcium oscillations. The model analysis demonstrated that an increase in the calcium diffusion coefficient resulted in the disappearance of the calcium oscillations. Additionally, in silico analysis suggested that the spatial distribution of calcium signaling enzymes governs the appearance of calcium oscillations in progesterone-activated human spermatozoa.

Crohn\'s disease is an inflammatory bowel disease (IBD) that is not well understood. In particular, unlike other IBDs, the inflamed parts of the intestine compromise deep layers of the tissue and are not continuous but separated and distributed through the whole gastrointestinal tract, displaying a patchy inflammatory pattern. In the present paper, we introduce a toy-model which might explain the appearance of such patterns. We consider a reaction-diffusion system involving bacteria and phagocyte and prove that, under certain conditions, this system might reproduce an activator-inhibitor dynamic leading to the occurrence of Turing-type instabilities. In other words, we prove the existence of stable stationary solutions that are spatially periodic and do not vanish in time. We also propose a set of parameters for which the system exhibits such phenomena and compare it with realistic parameters found in the literature. This is the first time, as far as we know, that a Turing pattern is investigated in inflammatory models.

Proteins in cells undergo repeated binding to other molecules, thereby reducing the apparent extent of their intracellular diffusion. While much effort has been made to analytically decouple these combined effects of pure diffusion and chemical binding, it is difficult with conventional approaches to attribute the measured quantities to the nature of specific domains of the proteins. Motivated by the common goal in cell signaling research aimed at identifying the domains responsible for particular intermolecular interactions, here we describe a framework for determining the local physicochemical properties of cellular proteins associated with immobile scaffolds. To validate this new approach, we apply it to transgelin-2, an actin-binding protein whose intracellular dynamics remains elusive. We develop a fluorescence recovery after photobleaching (FRAP)-based framework, in which comprehensive combinations of domain-deletion mutants are created, and the difference among them in FRAP response is analyzed. We demonstrate that transgelin-2 in actin stress fibers (SFs) interacts with F-actin via two separate domains, and the chemical properties are determined for the individual domains. Its pure diffusion properties independent of the association to F-actin is also obtained. Our approach will thus be useful, as presented here for transgelin-2, in addressing the signaling mechanism of cellular proteins associated with SFs.

The formation of large-scale patterns through molecular self-organization is a basic principle of life. Accordingly, the engineering of protein patterns and gradients is of prime relevance for synthetic biology. As a paradigm for such pattern formation, the bacterial MinDE protein system is based on self-organization of the ATPase MinD and ATPase-activating protein MinE on lipid membranes. Min patterns can be tightly regulated by tuning physical or biochemical parameters. Among the biochemically engineerable modules, MinD\'s membrane targeting sequence, despite being a key regulating element, has received little attention. Here we attempt to engineer patterns by modulating the membrane affinity of MinD. Unlike the traveling waves or stationary patterns commonly observed in vitro on flat supported membranes, standing-wave oscillations emerge upon elongating MinD\'s membrane targeting sequence via rationally guided mutagenesis. These patterns are capable of forming gradients and thereby spatially target co-reconstituted downstream proteins, highlighting their functional potential in designing new life-like systems.

It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. The line and the domain interact by constant exchanges of populations. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced Berestycki et al. (J Math Biol 66:743-766, 2013) to describe the enhancement of biological invasions by lines of fast diffusion. We establish the existence of a minimal spreading speed, and we show that it may be quite large, even when the basic reproduction number [Formula: see text] is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line.

Local cell contraction pulses play important roles in tissue and cell morphogenesis. Here, we improve a chemo-optogenetic approach and apply it to investigate the signal network that generates these pulses. We use these measurements to derive and parameterize a system of ordinary differential equations describing temporal signal network dynamics. Bifurcation analysis and numerical simulations predict a strong dependence of oscillatory system dynamics on the concentration of GEF-H1, an Lbc-type RhoGEF, which mediates the positive feedback amplification of Rho activity. This prediction is confirmed experimentally via optogenetic tuning of the effective GEF-H1 concentration in individual living cells. Numerical simulations show that pulse amplitude is most sensitive to external inputs into the myosin component at low GEF-H1 concentrations and that the spatial pulse width is dependent on GEF-H1 diffusion. Our study offers a theoretical framework to explain the emergence of local cell contraction pulses and their modulation by biochemical and mechanical signals.