Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering

We consider the dynamics of a piecewise affine system of degrade-and-fire oscillators with global repressive interaction, inspired by experiments on synchronization in colonies of bacteria-embedded genetic circuits. Due to global coupling, if any two oscillators happen to be in the same state at some time, they remain in sync at all subsequent times; thus clusters of synchronized oscillators cannot shrink as a result of the dynamics. Assuming that the system is initiated from random initial configurations of fully dispersed populations (no clusters), we estimate asymptotic cluster sizes as a function of the coupling strength. A sharp transition is proved to exist that separates a weak coupling regime of unclustered populations from a strong coupling phase where clusters of extensive size are formed. Each phenomena occurs with full probability in the thermodynamics limit. Moreover, the maximum number of asymptotic clusters is known to diverge linearly in this limit. In contrast, we show that with positive probability, the number of asymptotic clusters remains bounded, provided that the coupling strength is sufficiently large.     

Estimation of molecular averages and equilibrium fluctuations in lipid bilayer systems from the excess heat capacity function

It is demonstrated that the bilayer partition function can be numerically obtained from scanning calorimetric data without assuming a particular model for the gel-liquid crystalline transition. From this partition function, the enthalpy, entropy and volume changes accompanying the transition can be calculated. In the limit of very large systems, the method of the grand partition function allows calculation of cluster model distribution functions from which average sizes of gel and liquid-crystal clusters, cluster densities and equilibrium fluctuations are obtained. These results indicate that the main transition in phospholipid bilayers proceeds through the formation of clusters and that these clusters are not static domains but highly fluctuating entities. These fluctuations in cluster size are approximately equal to the average cluster size and give rise to localized density and volume fluctuations. The magnitude of these fluctuations is affected by the radius of curvature of the bilayer and by the addition of small molecular weight compounds to the system.     

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a non-equilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 2014;118:2599] based on optimised quantum chemical structures.     

Cell cycle dynamics and complement expression distinguishes mature haematopoietic subsets arising from hemogenic endothelium

The emergence of haematopoietic stem and progenitor cells (HSPCs) from hemogenic endothelium results in the formation of sizeable HSPC clusters attached to the vascular wall. We evaluate the cell cycle and proliferation of HSPCs involved in cluster formation, as well as the molecular signatures from their initial appearance to the point when cluster cells are capable of adult engraftment (definitive HSCs). We uncover a non-clonal origin of HSPC clusters with differing cell cycle, migration, and cell signaling attributes. In addition, we find that the complement cascade is highly enriched in mature HSPC clusters, possibly delineating a new role for this pathway in engraftment.     

Ontogenetic Scaling of Foraging Rates and the Dynamics of a Size-Structured Consumer-Resource Model

The ontogenetic scaling of foraging capacity strongly influences the competitive ability of differently sized individuals within a species. We develop a physiologically structured model to investigate the effect of different ontogenetic size scalings of the attack rate on the population dynamics of a consumer-resource system. The resource is assumed to reproduce continuously whereas the consumer only reproduces at discrete time instants. Depending on the ontogenetic size scaling, the model exhibited recruit-driven cycles, stable fixed point dynamics, non-recruit juvenile-driven cycles, quasiperiodic orbits, or chaotic dynamics. The kind of dynamics observed was related to the maintenance resource levels required of differently sized individuals. Stable fixed point dynamics was, besides at the persistence boundary, only observed when the minimum resource levels were similar for newborns and mature individuals. The tendency for large population fluctuations over a wide range of the parameter space was due to the consumer's pulsed reproduction. Background mortality and length of season were major determinants of cycle length. Model dynamics strongly resembled empirically observed dynamics from fish and Daphnia populations with respect to both patterns and mechanisms. The non-recruit juvenile-driven dynamics is suggested to occur in populations with size-dependent interference or preemptive competition like cicada populations.     

Distribution and Dynamics of Rat Basophilic Leukemia Immunoglobulin E Receptors (Fc?RI) on Planar Ligand-Presenting Surfaces

There is considerable interest in the signaling mechanisms of immunoreceptors, especially when triggered with membrane-bound ligands. We have quantified the spatiotemporal dynamics of the redistribution of immunoglobulin E-loaded receptors (IgE-FcɛRI) on rat basophilic leukemia-2H3 mast cells in contact with fluid and gel-phase membranes displaying ligands for immunoglobulin E, using total internal reflection fluorescence microscopy. To clearly separate the kinetics of receptor redistribution from cell spreading, and to precisely define the initial contact time (±50 ms), micropipette cell manipulation was used to bring individual cells into contact with surfaces. On ligand-free surfaces, there are micron-scale heterogeneities in fluorescence that likely reflect regions of the cell that are more closely apposed to the substrate. When ligands are present, receptor clusters form with this same size scale. The initial rate of accumulation of receptors into the clusters is consistent with diffusion-limited trapping with D ∼10⁻¹μm²/s. These results support the hypothesis that clusters form by diffusion to cell-surface contact regions. Over longer timescales (>10 s), individual clusters moved with both diffusive and directed motion components. The dynamics of the cluster motion is similar to the dynamics of membrane fluctuations of cells on ligand-free fluid membranes. Thus, the same cellular machinery may be responsible for both processes.     

An Extended Model for the Evolution of Prebiotic Homochirality: A Bottom-Up Approach to the Origin of Life

A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates epsilon L and epsilon R, respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N = 2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N = 2 model behaves as a control parameter in a chiral symmetry-breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N--> infinity model with symmetric (epsilon L = epsilon R) autogenic formation, showing that it only achieves homochirality for epsilon > epsilon c, where epsilon c is an N-dependent critical value. For epsilon 相似文献   

Critical behaviour of the stochastic Wilson-Cowan model

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.     

Kinetic analysis of local structure formations in protein folding

The protein folding process is described by a cluster model based on the assumption that local structures or clusters are formed at an early stage in different regions of the polypeptide chain. Possible local structural elements in a globular protein are helices, bends, and hydrophobic cores whose formation is presumably determined by the interaction with the environment. Thus the tendency of local structure formation is expressed by a surface free energy of the cluster, which is assigned to the interface between the cluster and its environment. The probability of finding the chain of N residues with k clusters and m residues in the cluster is represented by a cluster distribution map. The cluster model exhibits a distinct two-state-like equilibrium transition, which can be seen on this map as well-separated native and denatured populations at the midpoint of the transition. The native population is localized at k ≈ 1 and m ≈ N, while the position of the denatured population can vary significantly depending on the surface free energy of the cluster. If the surface free energy is strong, the denatured population is localized near k = 0 and m = 0. On the other hand, if the surface free energy is weak, the denatured population is localized at high k and m values. The dynamics of the cluster model are treated as a stochastic process involving the transition from a state (k,m) to one of its six neighbors. The transition probability for each transition is determined by the free energy difference between two states; thus no activation process is assumed. However, the conversion of the two macrostates, native and denatured populations, involves the free energy activation due to the cooperative interaction of the macrosystem. The dynamics are analyzed by following the time evolution of the population profile on the cluster distribution map. Kinetic schemes are proposed to describe the multistep mechanism of protein folding and unfolding.     

A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition

We present a mechanistic hybrid continuum-discrete model to simulate the dynamics of epithelial cell colonies. Collective cell dynamics are modeled using continuum equations that capture plastic, viscoelastic, and elastic deformations in the clusters while providing single-cell resolution. The continuum equations can be viewed as a coarse-grained version of previously developed discrete models that treat epithelial clusters as a two-dimensional network of vertices or stochastic interacting particles and follow the framework of dynamic density functional theory appropriately modified to account for cell size and shape variability. The discrete component of the model implements cell division and thus influences cell size and shape that couple to the continuum component. The model is validated against recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with a constant-thickness rim of growing cells at the cluster edge, as well as the emergence of short-range ordering and solid-like behavior. A detailed analysis of the model reveals a scale invariance of the growth and provides insight into the generation of stresses and their influence on the dynamics of the colonies. Compared to previous models, our approach has several advantages: it is independent of dimension, it can be parameterized using classical elastic properties (Poisson’s ratio and Young’s modulus), and it can easily be extended to incorporate multiple cell types and general substrate geometries.     

Collective detection in escape responses of temporary groups of Iberian green frogs

When confronted with a predator, prey are often in close proximityto conspecifics. This situation has generated several hypothesesregarding antipredator strategies adopted by individuals withingroups of gregarious species, such as the "risk dilution," "earlydetection," or "collective detection" effects. However, whethershort-term temporary aggregations of nongregarious animals arealso influenced in their escape decisions by nearby conspecificsremains little explored. We simulated predator approaches togreen frogs (Rana perezi) in the field while they were foragingat the edge of water, either alone or spatially aggregated intemporary clusters. "Flight initiation distances" of frogs (i.e.,the distance between the simulated predator and the frog atthe time it jumped) that escaped by jumping into the water wereinfluenced by microhabitat variables (vegetation at the edgeand in water and the initial distance of the frog to the closestwater edge) and also by the responses of nearby individuals.In clusters, risk dilution did not influence the first individualto respond to the predator simulation or the average responseof all frogs in the cluster as the frog's responses were independentof group size. Also, flight initiation distances of individualsthat first responded to the predator within clusters did notdiffer from those of solitary individuals, which is contraryto the predictions of the early detection hypothesis. However,the remaining frogs in the cluster had longer flight initiationdistances than expected from the comparison with solitary individuals.We suggest that this pattern originated because the responseof the first frog within a cluster triggered the sequentialresponse of the remaining frogs in the cluster, which agreeswith the expectations from the collective detection hypothesis.Our findings give insight into an early stage in the evolutionof grouping as they suggest that individual frogs may benefitfrom being part of a cluster, even for short periods of time.     

Dynamics of the cluster model of protein folding

The cluster model of protein folding [Kanehisa, M. I. & Tsong, T. Y. (1978) J. Mol. Biol. 124 , 177–194] is further investigated for the thermodynamic and kinetic properties of protein folding–unfolding transitions. A cluster is a locally formed ordered region in the polypeptide chain due to cooperative interactions among residues. In the cluster model a cooperative term is assigned as proportional to the surface area of a globular cluster. This assignment is compared with that for the helix–coil transition of homopolypeptides, where the cooperative term is proportional to the two ends of a linear helical sequence. The dynamics of the cluster model exhibit a slow phase, which is well-separated from other faster phases, because of the cooperative interaction of the macrosystem. This slow phase not only appears within the transition region, but can also persist well below the transition region if the cooperativity depends on the external condition. The amplitudes of certain kinetic phases can vary depending on the choice of physical parameters monitoring the reaction. Thus the same reaction may display different time courses. The qualitative aspects of the folding dynamics are as follows. In one case the rate-limiting formation of a critical-size cluster is followed by its rapid growth, while in the other the rate-limiting step appears in a later stage, where preformed smaller clusters merge into larger ones. The former case is similar to the dynamics of the helix–coil transition, and the latter represents a stepwise mechanism of protein structure formation.     

Propagation of local interactions create global gap structure and dynamics in a tropical rainforest

Gap dynamics in tropical forests are of interest because an understanding of them can help to predict canopy structure and biodiversity. We present a simple cellular automaton model that is capable of capturing many of the trends seen in the canopy gap pattern of a complex tropical rainforest on the Barro Colorado Island (BCI) using a single set of model parameters. We fit the global and local densities, the cluster size distributions, and two correlation functions, for gaps, gap formations, and gap closures determined from a spatial map of the forest (1983-1984). To the best of our knowledge, this is the first report that the cluster size distributions of gap formations and closures in the BCI are both power laws. An important element in the model is that when a transition from gap to non-gap (closure), or vice versa (formation), occurs, this transition is allowed to expand into adjacent cells in order to make different cluster sizes of transitions. Model results are in excellent agreement with reported field data. The propagation of local interactions is necessary in order to obtain the complex dynamics of the gap pattern. We also establish a connection between the global and local densities via the neighborhood-dependent transition rates and the effective global transition rates.     

Inferences of evolutionary history of a widely distributed mangrove species,Bruguiera gymnorrhiza,in the Indo‐West Pacific region

Inference of genetic structure and demographic history is fundamental issue in evolutionary biology. We examined the levels and patterns of genetic variation of a widespread mangrove species in the Indo‐West Pacific region, Bruguiera gymnorrhiza, using ten nuclear gene regions. Genetic variation of individual populations covering its distribution range was low, but as the entire species it was comparable to other plant species. Genetic differentiation among the investigated populations was high. They could be divided into two genetic clusters: the West and East clusters of the Malay Peninsula. Our results indicated that these two genetic clusters derived from their ancestral population whose effective size of which was much larger compared to the two extant clusters. The point estimate of speciation time between B. gymnorrhiza and Bruguiera sexangula was two times older than that of divergence time between the two clusters. Migration from the West cluster to the East cluster was much higher than the opposite direction but both estimated migration rates were low. The past Sundaland and/or the present Malay Peninsula are likely to prevent gene flow between the West and East clusters and function as a geographical or land barrier.     

Quantitative analysis of epithelial cell aggregation in the simple metazoan Hydra reveals a switch from homotypic to heterotypic cell interactions

Hydra, a member of the diploblastic phylum Cnidaria, exhibits the most basic type of organized metazoan tissues. Two unicellular sheets of polarized epithelial cells - ectoderm and endoderm - form a double layer throughout the body column. The double layer can be reestablished from single-cell suspensions by tissue-specific cell-sorting processes. However, the underlying pattern of interactions between ectodermal and endodermal epithelial cells responsible for double-layer formation is unclear. By analyzing cell interactions in a quantitative adhesion assay using mechanically dissociated Hydra epithelial cells, we show that aggregation proceeds in two steps. First, homotypic interactions within ectodermal epithelial cells (ecto-ecto) and within endodermal epithelial cells (endo-endo) form homotypic cell clusters. Second, at an aggregate size of about ten epithelial cells/cluster, ectodermal and endodermal clusters start to form heterotypic aggregates. Homotypic ecto-ecto interactions are inhibited by a polyclonal anti-Hydra membrane antiserum, and under these conditions homotypic endo-endo interactions do not proceed beyond a size of about ten epithelial cells/cluster. These data suggest that homotypic cell clusters reduce their initial homotypic affinity and acquire a new heterotypic affinity. A link between cell adhesion and cell signaling in early Hydra aggregates is discussed.     

Comparative genomic analysis reveals evolutionary characteristics and patterns of microRNA clusters in vertebrates

MicroRNAs (miRNAs) are a class of small non-coding RNAs that can play important regulatory roles in many important biological processes. Although clustering patterns of miRNA clusters have been uncovered in animals, the origin and evolution of miRNA clusters in vertebrates are still poorly understood. Here, we performed comparative genomic analyses to construct 51 sets of orthologous miRNA clusters (SOMCs) across seven test vertebrate species, a collection of miRNA clusters from two or more species that are likely to have evolved from a common ancestral miRNA cluster, and used these to systematically examine the evolutionary characteristics and patterns of miRNA clusters in vertebrates. We found that miRNA clusters are continuously generated, and most of them tend to be conserved and maintained in vertebrate genomes, although some adaptive gains and losses of miRNA cluster have occurred during evolution. Furthermore, miRNA clusters appeared relatively early in the evolutionary history might suffer from more complicated adaptive gain-and-loss than those young miRNA clusters. Detailed analysis showed that genomic duplication events of ancestral miRNAs or miRNA clusters are likely to be major driving force and apparently contribute to origin and evolution of miRNA clusters. Comparison of conserved with lineage-specific miRNA clusters revealed that the contribution of duplication events for the formation of miRNA cluster appears to be more important for conserved miRNA clusters than lineage-specific. Our study provides novel insights for further exploring the origins and evolution of miRNA clusters in vertebrates at a genome scale.     

Lateral lipid distribution and phase transition in phosphatidylethanolamine/phosphatidylserine vesicles: A cross-linking study

To determine the nonideal mixing of two lipid components within the membrane, lipid cross-linking experiments were carried out on dipalmitoylphosphatidylethanolamine (DPPE) vesicles and on dipalmitoylphosphatidylethanolamine/dipalmitoylphosphatidylserine (DPPE/DPPS) vesicles. By comparison of the cross-linking reactions on both types of vesicle the mean neighbourhood relations within the binary lipid mixture can be obtained. To elucidate the relationship between cluster formation and phase transition, the temperature dependences of the lipid arrangement within the vesicle membrane and of the lipid order parameter describing the fluidity of the membrane were measured. Cluster size and phase transition correlate: during the phase transition of the lipid species with the lower phase-transition temperature (DPPS) the nonideality of the mixture increases by phase separation. Above the phase transition temperature of the second lipid species (DPPE) the clusters disappear and a slight alternating lipid arrangement is characteristic of the fluid phase.     

A two-step patterning process increases the robustness of periodic patterning in the fly eye

Complex periodic patterns can self-organize through dynamic interactions between diffusible activators and inhibitors. In the biological context, self-organized patterning is challenged by spatial heterogeneities (‘noise’) inherent to biological systems. How spatial variability impacts the periodic patterning mechanism and how it can be buffered to ensure precise patterning is not well understood. We examine the effect of spatial heterogeneity on the periodic patterning of the fruit fly eye, an organ composed of ～800 miniature eye units (ommatidia) whose periodic arrangement along a hexagonal lattice self-organizes during early stages of fly development. The patterning follows a two-step process, with an initial formation of evenly spaced clusters of ～10 cells followed by a subsequent refinement of each cluster into a single selected cell. Using a probabilistic approach, we calculate the rate of patterning errors resulting from spatial heterogeneities in cell size, position and biosynthetic capacity. Notably, error rates were largely independent of the desired cluster size but followed the distributions of signaling speeds. Pre-formation of large clusters therefore greatly increases the reproducibility of the overall periodic arrangement, suggesting that the two-stage patterning process functions to guard the pattern against errors caused by spatial heterogeneities. Our results emphasize the constraints imposed on self-organized patterning mechanisms by the need to buffer stochastic effects. Author summary Complex periodic patterns are common in nature and are observed in physical, chemical and biological systems. Understanding how these patterns are generated in a precise manner is a key challenge. Biological patterns are especially intriguing, as they are generated in a noisy environment; cell position and cell size, for example, are subject to stochastic variations, as are the strengths of the chemical signals mediating cell-to-cell communication. The need to generate a precise and robust pattern in this ‘noisy’ environment restricts the space of patterning mechanisms that can function in the biological setting. Mathematical modeling is useful in comparing the sensitivity of different mechanisms to such variations, thereby highlighting key aspects of their design.We use mathematical modeling to study the periodic patterning of the fruit fly eye. In this system, a highly ordered lattice of differentiated cells is generated in a two-dimensional cell epithelium. The pattern is first observed by the appearance of evenly spaced clusters of ～10 cells that express specific genes. Each cluster is subsequently refined into a single cell, which initiates the formation and differentiation of a miniature eye unit, the ommatidium. We formulate a mathematical model based on the known molecular properties of the patterning mechanism, and use a probabilistic approach to calculate the errors in cluster formation and refinement resulting from stochastic cell-to-cell variations (‘noise’) in different quantitative parameters. This enables us to define the parameters most influencing noise sensitivity. Notably, we find that this error is roughly independent of the desired cluster size, suggesting that large clusters are beneficial for ensuring the overall reproducibility of the periodic cluster arrangement. For the stage of cluster refinement, we find that rapid communication between cells is critical for reducing error. Our work provides new insights into the constraints imposed on mechanisms generating periodic patterning in a realistic, noisy environment, and in particular, discusses the different considerations in achieving optimal design of the patterning network.     

A Highlights from MBoC Selection: Structurally distinct endocytic pathways for B cell receptors in B lymphocytes

B lymphocytes play a critical role in adaptive immunity. On antigen binding, B cell receptors (BCR) cluster on the plasma membrane and are internalized by endocytosis. In this process, B cells capture diverse antigens in various contexts and concentrations. However, it is unclear whether the mechanism of BCR endocytosis changes in response to these factors. Here, we studied the mechanism of soluble antigen-induced BCR clustering and internalization in a cultured human B cell line using correlative superresolution fluorescence and platinum replica electron microscopy. First, by visualizing nanoscale BCR clusters, we provide direct evidence that BCR cluster size increases with F(ab’)2 concentration. Next, we show that the physical mechanism of internalization switches in response to BCR cluster size. At low concentrations of antigen, B cells internalize small BCR clusters by classical clathrin-mediated endocytosis. At high antigen concentrations, when cluster size increases beyond the size of a single clathrin-coated pit, B cells retrieve receptor clusters using large invaginations of the plasma membrane capped with clathrin. At these sites, we observed early and sustained recruitment of actin and an actin polymerizing protein FCHSD2. We further show that actin recruitment is required for the efficient generation of these novel endocytic carriers and for their capture into the cytosol. We propose that in B cells, the mechanism of endocytosis switches to accommodate large receptor clusters formed when cells encounter high concentrations of soluble antigen. This mechanism is regulated by the organization and dynamics of the cortical actin cytoskeleton.