Robust trigger wave speed in Xenopus cytoplasmic extracts

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.

Liesegang Phenomenon of Liquid Metals on Au Film

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.

Occurrence of Calcium Oscillations in Human Spermatozoa Is Based on Spatial Signaling Enzymes Distribution

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.

Increasing MinD's Membrane Affinity Yields Standing Wave Oscillations and Functional Gradients on Flat Membranes

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.

Optogenetic Tuning Reveals Rho Amplification-Dependent Dynamics of a Cell Contraction Signal Network

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.

Existence of pulses for a reaction-diffusion system of blood coagulation in flow

A reaction-diffusion system describing blood coagulation in flow is studied. We prove the existence of stationary solutions provided that the speed of the travelling wave problem for the limiting value of the velocity is positive. The implications to the problem of clot growth are discussed.

The proneural wave in the Drosophila optic lobe is driven by an excitable reaction-diffusion mechanism

In living organisms, self-organised waves of signalling activity propagate spatiotemporal information within tissues. During the development of the largest component of the visual processing centre of the Drosophila brain, a travelling wave of proneural gene expression initiates neurogenesis in the larval optic lobe primordium and drives the sequential transition of neuroepithelial cells into neuroblasts. Here, we propose that this 'proneural wave' is driven by an excitable reaction-diffusion system involving epidermal growth factor receptor (EGFR) signalling interacting with the proneural gene l'sc. Within this framework, a propagating transition zone emerges from molecular feedback and diffusion. Ectopic activation of EGFR signalling in clones within the neuroepithelium demonstrates that a transition wave can be excited anywhere in the tissue by inducing signalling activity, consistent with a key prediction of the model. Our model illuminates the physical and molecular underpinnings of proneural wave progression and suggests a generic mechanism for regulating the sequential differentiation of tissues.

Stationary Patterns in a Two-Protein Reaction-Diffusion System

Patterns formed by reaction-diffusion mechanisms are crucial for the development or sustenance of most organisms in nature. Patterns include dynamic waves, but are more often found as static distributions, such as animal skin patterns. Yet, a simplistic biological model system to reproduce and quantitatively investigate static reaction-diffusion patterns has been missing so far. Here, we demonstrate that the Escherichia coli Min system, known for its oscillatory behavior between the cell poles, is under certain conditions capable of transitioning to quasi-stationary protein distributions on membranes closely resembling Turing patterns. We systematically titrated both proteins, MinD and MinE, and found that removing all purification tags and linkers from the N-terminus of MinE was critical for static patterns to occur. At small bulk heights, dynamic patterns dominate, such as in rod-shaped microcompartments. We see implications of this work for studying pattern formation in general, but also for creating artificial gradients as downstream cues in synthetic biology applications.

Mathematical approach to unpinning of spiral waves anchored to an obstacle with high-frequency pacing

Spiral waves are observed in wide variety of reaction-diffusion systems. Those observed in cardiac tissues are important since they are related to serious disease that threatens human lives, such as atrial or ventricular fibrillation. We consider the unpinning of spiral waves anchored to a circular obstacle on excitable media using high-frequency pacing. Here, we consider two types of the obstacle; i.e., that without any diffusive interaction with the environment, and that with diffusive interaction. We found that the threshold frequency for success in unpinning is lower for the obstacle with diffusive interaction than for the one without it. We discuss the threshold frequency based on the angular velocity of a chemical wave anchoring the obstacle.

Possibility of Controlling Self-Organized Patterns with Totalistic Cellular Automata Consisting of Both Rules like Game of Life and Rules Producing Turing Patterns

The basic rules of self-organization using a totalistic cellular automaton (CA) were investigated, for which the cell state was determined by summing the states of neighboring cells, like in Conway's Game of Life. This study used a short-range and long-range summation of the cell states around the focal cell. These resemble reaction-diffusion (RD) equations, in which self-organizing behavior emerges from interactions between an activating factor and an inhibiting factor. In addition, Game-of-Life-type rules, in which a cell cannot survive when adjoined by too many or too few living cells, were applied. Our model was able to mimic patterns characteristic of biological cells, including movement, growth, and reproduction. This result suggests the possibility of controlling self-organized patterns. Our model can also be applied to the control of engineering systems, such as multirobot swarms and self-assembling microrobots.

Signal Transmission of Biological Reaction-Diffusion System by Using Synchronization

Molecular signal transmission in cell is very crucial for information exchange. How to understand its transmission mechanism has attracted many researchers. In this paper, we prove that signal transmission problem between neural tumor molecules and drug molecules can be achieved by synchronous control. To achieve our purpose, we derive the Fokker-Plank equation by using the Langevin equation and theory of random walk, this is a model which can express the concentration change of neural tumor molecules. Second, according to the biological character that vesicles in cell can be combined with cell membrane to release the cargo which plays a role of signal transmission, we preliminarily analyzed the mechanism of tumor-drug molecular interaction. Third, we propose the view of synchronous control which means the process of vesicle docking with their target membrane is a synchronization process, and we can achieve the precise treatment of disease by using synchronous control. We believe this synchronous control mechanism is reasonable and two examples are given to illustrate the correctness of our results obtained in this paper.

Mesoscopic and continuum modelling of angiogenesis

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.

The spreading frontiers of avian-human influenza described by the free boundary

In this paper, a reaction-diffusion system is proposed to investigate avian-human influenza. Two free boundaries are introduced to describe the spreading frontiers of the avian influenza. The basic reproduction numbers r ₀ ^F (t) and R ₀ ^F (t) are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem, respectively. Properties of these two time-dependent basic reproduction numbers are obtained. Sufficient conditions both for spreading and for vanishing of the avian influenza are given. It is shown that if r ₀ ^F (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if r ₀ ^F (0) < 1 and R ₀ ^F (0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that r ₀ ^F (0) < 1 and R ₀ ^F (0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if r ₀ ^F (t ₀) ⩾ 1 for any t ₀ ⩾ 0, the avian influenza spreads in the bird world.