A semi-stochastic model for Salmonella infection in a multi-group herd

A multi-group semi-stochastic model is formulated to identify possible causes of why different strains of Salmonella develop so much variation in their infection dynamics in UK dairy herds. The model includes demography (managed populations) and various types of transmission: direct, pseudovertical and indirect (via free-living infectious units in the environment). The effects of herd size and epidemiological parameters on mean prevalence of infection and mean time until fade out are investigated. Numerical simulation shows that higher pathogen-induced mortality, shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower mean prevalence of infection, a shorter mean time until fade out, and a greater probability of fade out of infection within 600 days. Combining these results and those for the deterministic counterpart could explain differences in observed epidemiological patterns and help to identify the factors inducing the decline in reported cases of epidemic strains such as DT104 in cattle. We further investigate the effect of group structure on the probability of a major outbreak by using the stochastic threshold theory in homogeneous populations and that in heterogeneous populations. Numerical studies suggest that group structure makes major outbreaks less likely than would be the case in a homogeneous population with the same basic reproduction number. Moreover, some control strategies are suggested by investigating the effect of epidemiological parameters on the probability of an epidemic.     

A cellular automaton model for the migration of glioma cells

We present a study of in vitro cell migration in two dimensions as a first step towards understanding the mechanisms governing the motility of glioma cells. Our study is based on a cellular automaton model which aims at reproducing the kinetics of a lump of glioma cells deposited on a substrate of collagen. The dynamical effects of cell attraction and motion inertia are introduced through adequate automaton rules. We compare the density profiles given by the model to those obtained experimentally. The result of the best fit indicates a substantial cell-cell attraction due to cell-cell communication through gap junctions (or chemotaxis) and negligible inertia effects during migration. Tracking of individual migrating cells indicates highly convoluted cell trajectories.     

A semi-stochastic model of the transmission of Escherichia coli O157 in a typical UK dairy herd: dynamics, sensitivity analysis and intervention/prevention strategies

When modelling the transmission of infection within small populations, it is necessary to consider the possibility of stochastic fade-out of infection. We present a semi-stochastic model for the transmission of a microparasite, in this case Escherichia coli O157, within a multigroup system, namely a typical UK dairy herd. The model includes birth, death, maturation, the dry/lactating cycle and various types of transmission (i.e. direct, pseudovertical (representing direct faecal-oral transmission between dam and calf within the first 48 h) and indirect (via free-living infectious units in the environment)). We present the results of our simulation study alongside data from empirical studies and also compare simulation results with those for the corresponding deterministic model. We then examine the effects of reducing shedding in the food-producing groups on outbreak size and prevalence of infection. A sensitivity analysis of herd prevalence reveals that, for both the deterministic and the semi-stochastic model, the prevalence within the herd is most sensitive to two parameters relating to the weaned group. This supports our previously reported conclusions for the deterministic model, which were based on an analysis of the next-generation matrix. The sensitivity analysis also indicates that herd prevalence is greatly affected by two other parameters relating to the lactating group. We conclude by discussing the possible efficacy of suggested intervention strategies.     

The coalescent in two colonies with symmetric migration

Kingman's coalescent process is extended to two colonies with symmetric migration. The mean waiting time until a sample of genes taken from two colonies coalesces to a common ancestor is obtained. The final step in the waiting time before the process is absorbed at 1 is observed to have an intriguing behaviour. The distribution of this final waiting time converges to the known distribution of the corresponding waiting time in the case of a single population as the migration rate tends to zero. The mean, however, does not converge. The waiting time until a sample has two common ancestors is modeled as a function of the migration rate. Finally bounds for the expected waiting time for the two colonies to have j > 1 ancestors are derived.     

A simple formalism on dynamics of proteins on potential energy landscapes

We present a simple formalism for the dynamics of proteins on a potential energy landscape, using connectedness of configurational domains as an order parameter. This formalism clearly shows that the energy bias required to form a unit correct contact toward the native configuration of a two-state folder, to overcome Levinthal's paradox, is E(bias) congruent with RT ln 2. This result agrees well with earlier studies and indicates that the bias is mainly due to hydrophobic interaction. Further investigations have shown that the landscape funnel could be experimentally mapped onto a two-dimensional space formed by denaturant concentration and the connectedness of configurational domains. The theoretical value of the depth-of-folding funnel in terms of denaturant concentration has been calculated for a model protein (P450cam), which agrees well with the experimental value. Using our model, it is also possible to explain the turnover nature of heat-capacity change upon unfolding of proteins and the existence of enthalpy and entropy convergence temperatures during unfolding without any strict assumptions as proposed in earlier studies.     

A novel model to study the dorsolateral migration of melanoblasts

Melanocytes derived from pluripotent neural crest cells migrate initially in the dorsolateral pathway between the ectoderm and dermomyotome. To understand the role of specific proteins involved in this cell migration, we looked for a cellular model that mimics the in vivo behavior of melanoblasts, and that allows functional studies of their migration. We report here that wild-type embryonic stem (ES) cells are able to follow the ventral and dorsolateral neural crest pathways after being grafted into chicken embryos. By contrast, a mutant ES cell line deficient for beta1 integrin subunits, proteins involved in cell-extracellular interactions, had a severely impaired migratory behavior. Interestingly, ES cells deficient for Kit, the tyrosine kinase receptor for the stem cell factor (SCF), behaved similarly to wild-type ES cells. Thus, grafting mouse ES cells into chicken embryos provides a new cellular system that allows both in vitro and in vivo studies of the molecular mechanisms controlling dorsolateral migration.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell–cell interfacial tensions γ are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell-cell interfacial tensions gamma are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

Rhythmical sporogenesis in Streptomyces colonies. A one-dimensional model

A one-dimensional model imitating the growth and zone formation of a colony of the radiant fungus streptomycete on a synthetic agar nutrient medium with pyruvate, glucose, or succinate as a limiting source of energy and carbon was considered. The key parameters were determined whose values depend on the composition of nutrient medium and environmental conditions.     

A monte carlo approach to population dynamics of cells in a HIV immune response model

Summary Using a direct Monte Carlo simulation, population growth of helper T-cells (N _H) and viral cells (N _v) is studied for an immune response model with an enhanced spatial inter-cellular interaction relevant to HIV as a function of viral mutation. In the absence of cellular mobility (P _mob=0), the helper T-cells grow nonmonotonically before reaching saturation and the viral population grows monotonically before reaching a constant equilibrium. Cellular mobility (P _mob=1) enhances the viral growth and reduces the stimulative T-cell growth. Below a mutation threshold (P _c), the steady-state density of helper T-cell (p _H) is larger than that of the Virus (p _v); the density difference Δp _o(=pV−pH) remains a constant at P _mob=1 while −Δp _o→0 as P _mut→P _c at P _mob=0. Above the mutation threshold, the difference Δp _o in cell density, grows with ΔP=P _mut−P _c monotonically: ΔP _o ∞ (ΔP)^β ≃ with β≈0.574±0.016 in absence of mobility, while Δp _o≈6(ΔP) with P _mob=1.     

Contacts between the cells in bacterial colonies

The interaction of cells in microbial colonies has been studied by electron-microscopic techniques. Two types of contacts between cells have been found to exist in the colonies of Gram-negative bacteria of the genera Escherichia, Shigella and Salmonella: close cell adhesion due to the fusion of cell-wall outer membranes and the formation of intersections consisting of membranous tubules. At the sites of close adhesion the fusion of cytoplasmic and outer membranes have been found to occur in Bayer's zones. In the colonies of Gram-positive bacteria of the genera Staphylococcus and Brevibacterium only one type of contacts has been revealed: the fusion of the peptidoglycan layers of the cell walls. The results of this study indicate that in colonies bacteria are not completely isolated; their interaction leads to the formation of a three-dimensional structure denoted as a cooperative cell system.     

Adhesion dynamics and cytoskeletal structure of gliding human fibrosarcoma cells: a hypothetical model of cell migration

During motility of fibroblast type cells on planar surfaces, adhesions are formed at the anterior of the protruding lamella, which remain stationary relative to the substrate and undergo a maturation process as the cell passes over them. Through these adhesions force is exerted, the orientation of which is parallel to the direction of the movement. Here we show that, during gliding-type motility of human tumor cells, characterized by a semicircular shape, adhesions were found at the outer rim of the cells, along the semicircle. Time-lapse microscopy of GFP-vinculin-expressing cells showed that these adhesions were constantly renewed at the cell edge and followed a curved trajectory according to the graded radial extension model. Eventually, the adhesions reached the long axis of the cell where they were retracted into the cell body. Actin cables formed arcs, with the concave face at the anterior of the lamella found to be oriented in the direction of movement. Since adhesions moved backward with respect to the cell, actin cables connected to these adhesions must continuously grow, reaching maximal size at the long axis of the cell. Contraction of the arcs is responsible for the forward movement of the cell body.     

A model for the formation of ring-shaped structures in colonies of mycelial fungi

Mathematical model of the development of the pattern of colonies is considered. The model represents the systems of differential equations of the first order. It includes non-dimensional parameters characterizing the following features: concentration of substrate, concentration of metabolic products--growth inhibitor, mycelium and spores, radial and specific rate of mycelium growth, rate of substrate consumption and production of metabolic products, coefficients of diffusion of substrate and metabolic products, initial concentration of mycelium and substrate, time of delay of mycelium reaction on metabolic products and spore formation, threshold concentration of metabolic products. The model is adequate to the experiments with cultivation of Penicillium chrysogenum. It was shown that necessary condition for the formation of the circle periodical structures (zoning) in the colonies is an ability for the production of growth inhibitors (antibiotics, etc.). It was proved that formation of colonies of "continuous lawn" type is caused by restrictions on growth because of mycelium satiation or exhaustion of substrate. Such growth scenario is realized in experiments either on reach substrate or on hungry agar. For the appearance of regulating of "zone structure" type limitation on critical level of metabolic product concentration is very important. The number of periodical zone structures and their widths are determined by the above parameters.     

A model of migration modification

Two subpopulations whose different sizes are in a constant ratio interact via migration. The fitness of the diploid organisms is determined by two alleles at a single locus and by the niche the organism is in. The rates of migration depend upon two neutral modifier genes at a second locus. The second modifying allele is introduced into an equilibrium where the first modifying allele is fixed, and where the other two alleles are already polymorphic. It is shown that the new migration modifier is selected for when it reduces migration. The similarity between this result and some recombination modifier models is noted.     

Thermoregulation dynamics in commercially reared colonies of the bumblebee Bombus terrestris

Thermoregulation, that is, the active control of temperature, is key to ensure proper brood development in both wild and captive bumblebee nests. In this study, thermoregulation dynamics were assessed relative to colony age and ambient temperature using commercially reared Bombus terrestris L. (Hymenoptera, Apidae, Bombus) colonies. We observed a positive relationship between brood and nest temperatures in response to ambient temperature. Thermoregulation investment (by either brooding or fanning) was lowest at brood surface temperatures between 33 and 34 °C and ambient temperatures between 28 and 32 °C. Brood temperature was less stable and thermoregulation investment higher in younger colonies, especially at lower ambient temperatures. Furthermore, queens initiated colonies sooner and colonies developed faster when kept at an ambient temperature of 29 °C as compared to 24 °C. Our results suggest that ambient temperatures are ideally kept between 29 and 31 °C.     

Characterization of contracting cardiomyocyte colonies in the primary culture of neonatal rat myocardial cells: A model of in vitro cardiomyogenesis

The unmet clinical need for myocardial repair after irreversible ischemic injury requires a better understanding of the biological properties of cardiac stem cells (CSCs). Using a primary culture of neonatal rat myocardial cells, we describe the formation and maturation of contracting cardiomyocyte colonies stemming from c-kit⁺, Sca⁺, or Isl1⁺ CSCs, which occurs in parallel to the hypertrophy of the major cardiac myocyte population. The contracting cardiomyocyte colonies (~1–2 colonies per 1 × 10⁵ of myocardial cells) were identified starting from eighth day of culturing. At first, spontaneous weak, asynchronous, and arrhythmic contractions of the colonies at a rate of 2–3 beats/min were registered. Over time, the contractions of the colonies became more synchronous and frequent, with a contraction rate of 58–60 beats/min by the 30th day of culturing. The colonies were characterized by the CSCs subtype-specific pattern of growth and structure. The cells of the colonies were capable of spontaneous cardiomyogenic differentiation, demonstrating expression of both sarcomeric α-actinin and α-sarcomeric actin as well as the maturation of contractile machinery and typical Ca²⁺ responses to caffeine (5 mМ) and K⁺ (120 mМ). Electromechanical coupling, characterized by cardiac muscle-specific Ca²⁺-induced Ca²⁺ release, was evident at 3 weeks of culturing. Thus, the co-cultivation of CSCs with mature cardiac cells resulted in the formation of contracting cardiomyocyte colonies, resembling the characteristics of in vivo cardiomyogenesis. The proposed model can be used for the investigation of fundamental mechanisms underlying cardiomyogenic differentiation of CSCs as well as for drug testing and/or other applications.     

A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis

This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis.