A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator–Prey Systems

Reaction–diffusion theory has played a very important role in the study of pattern formation in biology. However, a group of individuals is described by a single state variable representing population density in reaction–diffusion models, and interaction between individuals can be included only phenomenologically. In this paper, we propose a new scheme that seamlessly combines individual-based models with elements of reaction–diffusion theory and apply it to predator–prey systems as a test of our scheme. In the model, starvation periods and the time to reproductive maturity are modeled for individual predators. Similarly, the life cycle and time to reproductive maturity of an individual prey are modeled. Furthermore, both predators and prey migrate through a two-dimensional space. To include animal migration in the model, we use a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Despite the simplicity of this model, our scheme successfully produces logistic patterns and oscillations in the population size of both predator and prey. The peak for the predator population oscillation lags slightly behind the prey peak. The simplicity of this scheme will aid additional study of spatially distributed negative-feedback systems.     

Reaction–Diffusion Systems and External Morphogen Gradients: The Two-Dimensional Case,with an Application to Skeletal Pattern Formation

We investigate a reaction–diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reaction–diffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first-order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction–diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.     

Vegetation Pattern Formation Due to Interactions Between Water Availability and Toxicity in Plant–Soil Feedback

Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model’s parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.     

Biocomplexity in Coupled Natural–Human Systems: A Multidimensional Framework

As defined by Ascher, biocomplexity results from a “multiplicity of interconnected relationships and levels.” However, no integrative framework yet exists to facilitate the application of this concept to coupled human–natural systems. Indeed, the term “biocomplexity” is still used primarily as a creative and provocative metaphor. To help advance its utility, we present a framework that focuses on linkages among different disciplines that are often used in studies of coupled human–natural systems, including the ecological, physical, and socioeconomic sciences. The framework consists of three dimensions of complexity: spatial, organizational, and temporal. Spatial complexity increases as the focus changes from the type and number of the elements of spatial heterogeneity to an explicit configuration of the elements. Similarly, organizational complexity increases as the focus shifts from unconnected units to connectivity among functional units. Finally, temporal complexity increases as the current state of a system comes to rely more and more on past states, and therefore to reflect echoes, legacies, and evolving indirect effects of those states. This three-dimensional, conceptual volume of biocomplexity enables connections between models that derive from different disciplines to be drawn at an appropriate level of complexity for integration.     

Pattern Formation,Long-Term Transients,and the Turing–Hopf Bifurcation in a Space- and Time-Discrete Predator–Prey System

Understanding of population dynamics in a fragmented habitat is an issue of considerable importance. A natural modelling framework for these systems is spatially discrete. In this paper, we consider a predator–prey system that is discrete both in space and time, and is described by a Coupled Map Lattice (CML). The prey growth is assumed to be affected by a weak Allee effect and the predator dynamics includes intra-specific competition. We first reveal the bifurcation structure of the corresponding non-spatial system. We then obtain the conditions of diffusive instability on the lattice. In order to reveal the properties of the emerging patterns, we perform extensive numerical simulations. We pay a special attention to the system properties in a vicinity of the Turing–Hopf bifurcation, which is widely regarded as a mechanism of pattern formation and spatiotemporal chaos in space-continuous systems. Counter-intuitively, we obtain that the spatial patterns arising in the CML are more typically stationary, even when the local dynamics is oscillatory. We also obtain that, for some parameter values, the system’s dynamics is dominated by long-term transients, so that the asymptotical stationary pattern arises as a sudden transition between two different patterns. Finally, we argue that our findings may have important ecological implications.     

Building Resilience in Lagoon Social–Ecological Systems: A Local-level Perspective

Building resilience in integrated human and nature systems or social–ecological systems (SES) is key for sustainability. Therefore, developing ways of assessing resilience is of practical as well as theoretical significance. We approached the issue by focusing on the local level and using five lagoon systems from various parts of the world for illustration. We used a framework based on four categories of factors for building resilience: (1) learning to live with change and uncertainty; (2) nurturing diversity for reorganization and renewal; (3) combining different kinds of knowledge; and (4) creating opportunity for self-organization. Under each category, the cases generated a number of items for building resilience, and potential surrogates of resilience, that is, variables through which the persistence of SES emerging through change can be assessed. The following factors were robust across all five lagoon SES cases: learning from crisis, responding to change, nurturing ecological memory, monitoring the environment, and building capacity for self-organization and conflict management.     

Strong Emergence in Biological Systems: Is It Open to Mathematical Reasoning?

Acta Biotheoretica - Complex, multigenic biological traits are shaped by the emergent interaction of proteins being the main functional units at the molecular scale. Based on a phenomenological...     

Bioindication and Functional Response in Floodplain Systems: Where to from Here?

We synthesise the results of the papers in this Special Issue, place them within the context of current trends in floodplain research, and outline promising new avenues that emerge from the contributions. The indication system presented complements existing approaches by focussing on a quantitative indication of environmental parameters. A promising research line that emerges is an extension of the systematic comparison of taxonomic groups with contrasting traits in terms of their performance as quantitative indicators for different environmental parameters. The studies show similarities and dissimilarities in the traits explaining the functional response of plants, molluscs, carabids, and syrphids to site conditions but trait databases and studies on additional taxa are required before broad generalisations can be made. The rigorous study design developed for the RIVA project, of which all contributions in this Special Issue are a part, not only was essential for an improvement of the understanding of species environment relationships and the role biological traits play for it, it also provides a baseline for assessing future change as part of long‐term ecological monitoring of floodplains. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neurabin: A Novel Neural Tissue–specific Actin Filament–binding Protein Involved in Neurite Formation

We purified from rat brain a novel actin filament (F-actin)–binding protein of ∼180 kD (p180), which was specifically expressed in neural tissue. We named p180 neurabin (neural tissue–specific F-actin– binding protein). We moreover cloned the cDNA of neurabin from a rat brain cDNA library and characterized native and recombinant proteins. Neurabin was a protein of 1,095 amino acids with a calculated molecular mass of 122,729. Neurabin had one F-actin–binding domain at the NH₂-terminal region, one PSD-95, DlgA, ZO-1–like domain at the middle region, a domain known to interact with transmembrane proteins, and domains predicted to form coiled-coil structures at the COOH-terminal region. Neurabin bound along the sides of F-actin and showed F-actin–cross-linking activity. Immunofluorescence microscopic analysis revealed that neurabin was highly concentrated in the synapse of the developed neurons. Neurabin was also concentrated in the lamellipodia of the growth cone during the development of neurons. Moreover, a study on suppression of endogenous neurabin in primary cultured rat hippocampal neurons by treatment with an antisense oligonucleotide showed that neurabin was involved in the neurite formation. Neurabin is a candidate for key molecules in the synapse formation and function.During the development of the nervous system, the distal tip of the elongating axon—the growth cone—actively migrates toward its target cell in response to the combined actions of attractive and repulsive guidance molecules in the extracellular environment (Garrity and Zipursky, 1995; Keynes and Cook, 1995; Chiba and Keshishian, 1996; Culotti and Kolodkin, 1996; Friedman and O''Leary, 1996; Tessier-Lavigne and Goodman, 1996). When the growth cone contacts with the target cell, it is transformed into the functional presynaptic terminal (Garrity and Zipursky, 1995; Chiba and Kishishian, 1996). The actin cytoskeleton has been shown to play crucial roles in these processes of the synapse formation (Mitchison and Kirschner, 1988; Smith, 1988; Bentley and O''Connor, 1994; Lin et al., 1994; Mackay et al., 1995; Tanaka and Sabry, 1995).In the developing nervous system, the actin cytoskeleton is prominent in two structural domains of the growth cone, filopodia and lamellipodia (Mitchison and Kirschner, 1988; Smith, 1988; Bentley and O''Connor, 1994; Lin et al., 1994; Mackay et al., 1995; Tanaka and Sabry, 1995). In these domains, actin filament (F-actin)¹ assembled at the leading edge are transported into the center of the growth cone and disassembled there. It has been suggested that this retrograde flow of F-actin is crucial for the growth cone motility. Drugs that disrupt F-actin have also been shown to cause the lamellipodial and filopodial collapse and block the ability of neurons to extend the growth cone in the correct direction (Marsh and Letourneau, 1984; Forscher and Smith, 1988; Bentley and Toroian-Raymond, 1986; Chien et al., 1993). These results suggest that the actin cytoskeleton regulates not only the growth cone motility but also the growth cone directionality. Recently, a variety of guidance molecules and their receptors have been identified (Garrity and Zipursky, 1995; Keynes and Cook, 1995; Chiba and Keshishian, 1996; Culotti and Kolodkin, 1996; Friedman and O''Leary, 1996; Tessier-Lavigne and Goodman, 1996). However, which molecules of the actin cytoskeleton are essential for the growth cone motility and directionality is not well understood.When the growth cone contacts with the target cell, the target cell regulates the development of the presynaptic nerve terminal and the formation of the functional synapse (Bowe and Fallon, 1995; Chiba and Keshishian, 1996). In the established nervous system, the presynaptic and postsynaptic membranes get aligned in space and constitute the synaptic junction (Burns and Augustine, 1995; Garner and Kindler, 1996). Electron microscopic studies have revealed the ultrastructural features of the synaptic junction (Burns and Augustine, 1995; Garner and Kindler, 1996). The presynaptic cytoplasm is characterized by synaptic vesicles (SVs). SVs are not distributed uniformly; SVs cluster together in the vicinity of the presynaptic plasma membrane, where F-actin forms a network and is associated with the presynaptic plasma membrane (Hirokawa et al., 1989). Most SVs within the cluster are linked through thin strands to each other, to F-actin, or to both (Hirokawa et al., 1989). A subset of SVs within the cluster are attached by fine filamentous threads to neurotransmitter release zone at the presynaptic plasma membrane (Hirokawa et al., 1989). The presynaptic submembranous cytoskeleton is assumed to be involved in recruiting Ca²⁺ channels and the components of the SV fusion complex, delivering SVs to the neurotransmitter release zone, and keeping them in place (Burns and Augustine, 1995; Garner and Kindler, 1996). At the inner surface of the post-synaptic plasma membrane, there is an electron dense thickening, called postsynaptic density. The postsynaptic density is assumed to be involved in the selective targeting and accumulation of ion channels and receptors (Burns and Augustine, 1995; Garner and Kindler, 1996). It is also assumed that the presynaptic and postsynaptic submembranous cytoskeleton elements are linked to cell adhesion molecules to regulate the synaptic stabilization and plasticity (Fields and Itoh, 1996; Garner and Kindler, 1996). The presynaptic and postsynaptic submembranous cytoskeleton elements are thought to be composed of spectrin/fodrin, ankyrin, α-adducin, and protein 4.1 isoforms and to be linked to F-actin through these cytoskeleton proteins (Garner and Kindler, 1996). However, little is known about which molecules of the submembranous cytoskeleton are essential for the synaptic transmission and/or the synaptic stabilization.To understand the regulation of the actin cytoskeleton during and after the development of the nervous system, it is of crucial importance to identify F-actin–binding proteins implicated in the synapse formation and function. Therefore, we attempted here to isolate neural tissue–specific F-actin–binding proteins. We isolated a novel neural tissue–specific F-actin–binding protein from rat brain, which may be involved in neurite formation, and named it neurabin (neural tissue–specific F-actin–binding protein).     

On the Influence of Observation of the Processes in Quantum Systems: Is it Possible to Determine an Observer Effect in Biological Systems?

Biophysics - Abstract—The issue of how observation of a process in quantum mechanics may influence its outcome is described by case studies of quantum emission by a two-level system and the...     

A Nonlinear Stability Analysis of Vegetative Turing Pattern Formation for an Interaction–Diffusion Plant-Surface Water Model System in an Arid Flat Environment

The development of spontaneous stationary vegetative patterns in an arid flat environment is investigated by means of a weakly nonlinear diffusive instability analysis applied to the appropriate model system for this phenomenon. In particular, that process can be modeled by a partial differential interaction–diffusion equation system for the plant biomass density and the surface water content defined on an unbounded flat spatial domain. The main results of this analysis can be represented by closed-form plots in the rate of precipitation versus the specific rate of plant density loss parameter space. From these plots, regions corresponding to bare ground and vegetative patterns consisting of parallel stripes, labyrinth-like mazes, hexagonal arrays of gaps, irregular mosaics, and homogeneous distributions of vegetation, respectively, may be identified in this parameter space. Then those theoretical predictions are compared with both relevant observational evidence involving tiger and pearled bush patterns and existing numerical simulations of similar model systems as well as placed in the context of the results from some recent nonlinear vegetative pattern formation studies.     

Female Mice Are More Susceptible to Nonalcoholic Fatty Liver Disease: Sex-Specific Regulation of the Hepatic AMP-Activated Protein Kinase–Plasminogen Activator Inhibitor 1 Cascade,but Not the Hepatic Endotoxin Response

As significant differences between sexes were found in the susceptibility to alcoholic liver disease in human and animal models, it was the aim of the present study to investigate whether female mice also are more susceptible to the development of non-alcoholic fatty liver disease (NAFLD). Male and female C57BL/6J mice were fed either water or 30% fructose solution ad libitum for 16 wks. Liver damage was evaluated by histological scoring. Portal endotoxin levels and markers of Kupffer cell activation and insulin resistance, plasminogen activator inhibitor 1 (PAI-1) and phosphorylated adenosine monophosphate–activated protein kinase (pAMPK ) were measured in the liver. Adiponectin mRNA expression was determined in adipose tissue. Hepatic steatosis was almost similar between male and female mice; however, inflammation was markedly more pronounced in livers of female mice. Portal endotoxin levels, hepatic levels of myeloid differentiation primary response gene (88) (MyD88) protein and of 4-hydroxynonenal protein adducts were elevated in animals with NAFLD regardless of sex. Expression of insulin receptor substrate 1 and 2 was decreased to a similar extent in livers of male and female mice with NAFLD. The less pronounced susceptibility to liver damage in male mice was associated with a superinduction of hepatic pAMPK in these mice whereas, in livers of female mice with NAFLD, PAI-1 was markedly induced. Expression of adiponectin in visceral fat was significantly lower in female mice with NAFLD but unchanged in male mice compared with respective controls. In conclusion, our data suggest that the sex-specific differences in the susceptibility to NAFLD are associated with differences in the regulation of the adiponectin–AMPK–PAI-1 signaling cascade.