Analysis of stability of different regimes of heart rate dynamics by computer modeling

Computer modeling revealed the following three regimes of heart rate dynamics: linear dynamics, “1st degree chaos,” and “2nd degree chaos.” This study investigated a stability of these regimes with respect to changes in initial conditions. The results show that the greatest stability is notable for the linear regime. For this regime small errors in values of initial conditions can not sharply change the initial dynamics of RR intervals. Both nonlinear regimes of heart rate dynamics are unstable, and a degree of instability of regime “2nd degree chaos” is higher in comparison with regime “1st degree chaos.” The results of computer modeling are in agreement with experimental data pointing to the existence of a relationship between the degree of heart rate irregularity and cardiac electrical stability.     

Richards-like two species population dynamics model

The two-species population dynamics model is the simplest paradigm of inter- and intra-species interaction. Here, we present a generalized Lotka–Volterra model with intraspecific competition, which retrieves as particular cases, some well-known models. The generalization parameter is related to the species habitat dimensionality and their interaction range. Contrary to standard models, the species coupling parameters are general, not restricted to non-negative values. Therefore, they may represent different ecological regimes, which are derived from the asymptotic solution stability analysis and are represented in a phase diagram. In this diagram, we have identified a forbidden region in the mutualism regime, and a survival/extinction transition with dependence on initial conditions for the competition regime. Also, we shed light on two types of predation and competition: weak, if there are species coexistence, or strong, if at least one species is extinguished.     

Increased coupling between subpopulations in a spatially structured environment can lead to population outbreaks

Destruction and fragmentation of habitats is widely considered as a major threat to biological diversity. A theoretical framework aimed at understanding and predicting species responses to these destructive processes is still lacking, however. In this paper, the species dynamics in a spatially structured, two-habitat, patchy environment is considered subject to changes in individual migration intensity, i.e. coupling between the habitats. The subpopulation dynamics inside each habitat is assumed to be bistable but with different parameter values. By using space-discrete/continuous metapopulation dynamic models and computer simulations, we show that there can be two principally different regimes of metapopulation dynamics. With increasing intensity in the interplay between subpopulations, the total abundance can either gradually decrease or experience a sudden burst-like increase. This result is shown to be robust to the choice of mathematical models (discrete or continuous). Particularly, both the "self-excitation" and "self-inhibition" regimes of the metapopulation system are robust to variation in habitat size; however, when one of the habitats is much smaller than the other, the "self-excitation" regime can give way to the "self-inhibition" regime and vice versa.     

Aberrations of cortical and subcortical integration during chronic administration of haloperidol to the dog

The character of evoked potentials (EPs) dynamics to signal light stimulus during elaboration of avoidance reaction, allows to assert that during formation of adaptive activity functional balance is established of sensory and integrative-triggering brain parts or functional balance of "motor" and "sensory" integration regimes. Each of the studied subcortical structures is characterized by simultaneous but specific functioning both in the motor and sensory regimes; such conclusion is based on different dynamics of their EPs parameters: the changes of ones correspond to EPs dynamics in the visual cortical area, of the others--in the motor area. During chronic haloperidol administration, the reorganizations of intercentral relations are observed in 10--12 days after the beginning of drug administration. They may be considered as a succession of disturbances of functional balance between "sensory" and "motor" integration regimes: at first the sensory regime domination appears in which subcortical structures are chiefly and uniformly involved (ncd, pall and n. acc.); "motor" regime is weakened; then, as a result, a distortion of the "motor" regime of integration takes place. In this case a bradykinesia is developed.     

A dynamical model for receptor-mediated cell adhesion to surfaces.

We present a dynamical model for receptor-mediated adhesion of cells in a shear field of viscous fluid to surfaces coated with ligand molecules complementary to receptors in the cell membrane. We refer to this model as the "point attachment model" because it considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis of a system of nonlinear ordinary differential equations which govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low-affinity regime. Many experimental observations can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

Dynamical types of bacteria and bacteriophages interaction: shielding by debris

The dynamics of the bacteria and bacteriophages interaction process was explored in depth, and laid on a firm basis through simulation and analysis. A modified Campbell model of phage-bacteria interaction was used to simulate three interacting species: bacteria, phages and bacterial debris, and their time behavior in terms of three parameters, in selected range values: the phages burst size (β), the dissolution rate of the bacterial debris (q), and the lysing time delay (τ). Six types of dynamical behavior were identified, occupying various zones in the two-dimensional (2D) plane (q, β) for several values of τ, allowing the determination of the region where shielding by bacterial debris is in effect. The problem of the occurrence of stability transitions between stable and unstable dynamical regimes was also addressed analytically, and compared with simulation results.     

Six types of multistability in a neuronal model based on slow calcium current

Background

Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings

Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions

We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.     

Modeling the Spontaneous Activity of the Auditory Cortex

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex. D.H is incumbent to the Hass Russell Career Chair Development.     

Effects of population density and chemical environment on the behavior of Escherichia coli in shallow temperature gradients

In shallow temperature gradients, changes in temperature that bacteria experience occur over long time scales. Therefore, slow processes such as adaptation, metabolism, chemical secretion and even gene expression become important. Since these are cellular processes, the cell density is an important parameter that affects the bacteria's response. We find that there are four density regimes with distinct behaviors. At low cell density, bacteria do not cause changes in their chemical environment; however, their response to the temperature gradient is strongly influenced by it. In the intermediate cell-density regime, the consumption of nutrients becomes significant and induces a gradient of nutrients opposing the temperature gradient due to higher consumption rate at the high temperature. This causes the bacteria to drift toward low temperature. In the high cell-density regime, interactions among bacteria due to secretion of an attractant lead to a strong local accumulation of bacteria. This together with the gradient of nutrients, resulted from the differential consumption rate, creates a fast propagating pulse of bacterial density. These observations are a result of classical nonlinear population dynamics. At extremely high cell density, a change in the physiological state of the bacteria is observed. The bacteria, at the individual level, become cold seeking. This appears initially as a result of a change in the methylation level of the two most abundant sensing receptors, Tsr and Tar. It is further enforced at an even higher cell density by a change in the expression level of these receptors.     

Simulation of oscillatory processes in a beam-plasma system with a virtual cathode in gas-filled interaction space

Physical processes occurring in an intense electron beam with a virtual cathode in an interaction space filled with neutral gas are studied in a two-dimensional model. A mathematical model is proposed for investigating complicated self-consistent processes of neutral gas ionization by the beam electrons and the dynamics of an electron beam and heavy positive ions in the common space charge field with allowance for the two-dimensional motion of charged particles. Three characteristic dynamic regimes of the system are revealed: complete suppression of oscillations of the virtual cathode as a result of neutralizing its space charge by positive ions; the pulsed generation regime, in which the ions dynamics repeatedly suppresses and restores the virtual cathode oscillations; and the continuous generation regime with an anomalously high level of noisy oscillations.     

Actin-mediated bacterial propulsion: comet profile, velocity pulsations

The propulsion of bacteria under the action of an actin gel network is examined in terms of gel concentration dynamics. The model includes the elasticity of the network, the gel-bacterium interaction, the bulk and interface polymerization. A formula for the cruise velocity is obtained where the contributions to bacterial motility arising from elasticity and polymerization are made explicit. Higher velocities correspond to lower concentration peaks and longer tails, in agreement with experimental results. The condition for the onset of motion is explicitly given. The behavior of the system is explored by varying the growth rates and the gel elasticity. At steady state two regimes are found, respectively, of constant and pulsating velocity; in the latter case, the velocity undergoes sudden accelerations and subsequent recoveries. The transition to the pulsating regime is obtained by increasing the elastic response of the gel.     

Properties of bacteria that trigger hemocytopenia in the Atlantic blue crab, Callinectes sapidus

In the blue crab Callinectes sapidus, injection with the bacterial pathogen Vibrio campbellii causes a decrease in oxygen consumption. Histological and physiological evidence suggests that the physical obstruction of hemolymph flow through the gill vasculature, caused by aggregations of bacteria and hemocytes, underlies the decrease in aerobic function associated with bacterial infection. We sought to elucidate the bacterial properties sufficient to induce a decrease in circulating hemocytes (hemocytopenia) as an indicator for the initiation of hemocyte aggregation and subsequent impairment of respiration. Lipopolysaccharide (LPS), the primary component of the gram-negative bacterial cell wall, is known to interact with crustacean hemocytes. Purified LPS was covalently bound to the surfaces of polystyrene beads resembling bacteria in size. Injection of these "LPS beads" caused a decrease in circulating hemocytes comparable to that seen with V. campbellii injection, while beads alone failed to do so. These data suggest that in general, gram-negative bacteria could stimulate hemocytopenia. To test this hypothesis, crabs were injected with different bacteria--seven gram-negative and one gram-positive species--and their effects on circulating hemocytes were assessed. With one exception, all gram-negative strains caused decreases in circulating hemocytes, suggesting an important role for LPS in the induction of this response. However, LPS is not necessary to provoke the immune response given that Bacillus coral, a gram-positive species that lacks LPS, caused a decrease in circulating hemocytes. These results suggest that a wide range of bacteria could impair metabolism in C. sapidus.     

Multiscale analysis for a vector-borne epidemic model

Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an alternative proof of previously known global stability results by using only a Lyapunov approach. In the sequel, we take a different view and we argue that vectors and hosts can have very distinctive intrinsic time-scales, and that such distinctiveness extends to the disease dynamics. Under these hypothesis, we show that two asymptotic regimes naturally appear: the fast host dynamics and the fast vector dynamics. The former regime yields, at leading order, a SIR model for the hosts, but with a rational incidence rate. In this case, the vector disappears from the model, and the dynamics is similar to a directly contagious disease. The latter yields a SI model for the vectors, with the hosts disappearing from the model. Numerical results show the performance of the approximation, and a rigorous proof validates the reduced models.     

Implications of recurrent disturbance for genetic diversity

Exploring interactions between ecological disturbance, species’ abundances and community composition provides critical insights for ecological dynamics. While disturbance is also potentially an important driver of landscape genetic patterns, the mechanisms by which these patterns may arise by selective and neutral processes are not well‐understood. We used simulation to evaluate the relative importance of disturbance regime components, and their interaction with demographic and dispersal processes, on the distribution of genetic diversity across landscapes. We investigated genetic impacts of variation in key components of disturbance regimes and spatial patterns that are likely to respond to climate change and land management, including disturbance size, frequency, and severity. The influence of disturbance was mediated by dispersal distance and, to a limited extent, by birth rate. Nevertheless, all three disturbance regime components strongly influenced spatial and temporal patterns of genetic diversity within subpopulations, and were associated with changes in genetic structure. Furthermore, disturbance‐induced changes in temporal population dynamics and the spatial distribution of populations across the landscape resulted in disrupted isolation by distance patterns among populations. Our results show that forecast changes in disturbance regimes have the potential to cause major changes to the distribution of genetic diversity within and among populations. We highlight likely scenarios under which future changes to disturbance size, severity, or frequency will have the strongest impacts on population genetic patterns. In addition, our results have implications for the inference of biological processes from genetic data, because the effects of dispersal on genetic patterns were strongly mediated by disturbance regimes.     

A dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow

We present a dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow when the surfaces are coated with ligand molecules complementary to receptors in the cell membrane. This model considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis for a system of nonlinear ordinary differential equations that govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low affinity regime. Many experimental observations, including the effects of temperature and receptor mobility on adhesiveness, can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

Continuous-discrete models of the dynamics of an isolated population and of 2 competing species

The paper presents the analysis of various mathematical models for dynamics of isolated population and for competition between two species. It is assumed that mortality is continuous and birth of individuals of new generations takes place in certain fixed moments. Influence of winter upon the population dynamics and conditions of classic discrete model "deduction" of population dynamics (in particular, Moran-Ricker and Hassel's models) are investigated. Dynamic regimes of models under various assumptions about the birth and death rates upon the population states are also examined. Analysis of models of isolated population dynamics with nonoverlapping generations showed the density changes regularly if the birth rate is constant. Moreover, there exists a unique global stable level and population size stabilizes asymptotically at this equilibrium, i.e. cycle and chaotic regimes in various discrete models depend on correlation between individual productivity and population state in previous time. When the correlation is exponential upon mean population size the discrete Hassel model is realized. Modification of basis model, based on the assumption that during winter survival/death changes are constant, showed that population size at global level is stable. Generally, the dependence of population rate upon "winter parameters" has nonlinear character. Nonparametric models of competition between two species does not vary if the individual productivity is constant. In a phase space there are several stable stationary states and population stabilizes at one or other level asymptotically. So, in discrete models of competition between two species oscillation can be explained by dependence of population growth rate on the population size at previous times.     

Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.     

Disturbance regimes and life-history evolution

Disturbance regimes are ecologically important, but many of their evolutionary consequences are poorly understood. A model is developed here that combines the within- and among-season dynamics of disturbances with evolutionary life-history theory. "Disturbance regime" is defined in terms of disturbance timing, frequency, predictability, and severity. The model predicts the optimal body size and time at which organisms should abandon a disturbance-prone growth habitat by maturing and moving to a disturbance-free, nongrowth habitat. The effects of both coarse-grained (those affecting the entire population synchronously) and fine-grained disturbances (those occurring in a patch dynamics setting) are explored. Several predictions are congruent with previous theory. Infrequent or temporally unpredictable disturbances should have little effect on the evolution of life-history strategies, even though they may cause high mortality. Similar to seasonal time constraints on reproduction, disturbance regimes can synchronize metamorphosis within a population, resulting in a seasonal decline in body size at maturity. Other model predictions are novel. When disturbances cause high mortality, coarse-grained disturbances have a much stronger effect on life-history strategies than fine-grained disturbances, suggesting that population structure (relative to the scale of disturbance) plays a critical evolutionary role when disturbances are severe. When within-population variance in juvenile body size is high, two consecutive seasonal declines in body size at maturity can occur, the first associated with disturbance regime and the second associated with seasonal time constraints.     

Unraveling the effects of management regime and plant species on soil organic carbon and microbial phospholipid fatty acid profiles in grassland soils

In a field experiment we have examined the effect of long-term grassland management regimes (viz., intensive versus extensive) and dominant plant species (viz., Arrhenatherum elatius, Holcus lanatus and Dactylis glomerata) on soil organic carbon (SOC) build up, soil microbial communities using biomarker phospholipid fatty acids (PLFA), and the relationship between SOC and PLFAs of major groups of microorganisms (viz., bacteria, fungi, and actinomycetes). The results have revealed that changes in SOC were not significantly affected by the intensity of management or by the plant species composition or by their interaction. The amount of PLFA of each microbial group was affected weakly by management regime and plant species, but the canonical variance analysis (CVA), based on individual PLFA values, demonstrated significant (P<0.05) effects of management regime and plant species on the composition of microbial community. Positive and significant (P<0.01) relationships were observed between PLFA of bacteria (R2=0.47), fungi (R2=0.33), actinomycetes (R2=0.71) and total microbial PLFA (R2=0.53) and SOC content.     

Magnetic resonance of a dextran-coated magnetic fluid intravenously administered in mice

Magnetic resonance was used to investigate the kinetic disposition of magnetite nanoparticles (9.4 nm core diameter) from the blood circulation after intravenous injection of magnetite-based dextran-coated magnetic fluid in female Swiss mice. In the first 60 min the time-decay of the nanoparticle concentration in the blood circulation follows the one-exponential (one-compartment) model with a half-life of (6.9 +/- 0.7) min. The X-band spectra show a broad single line at g approximately 2, typical of nanomagnetic particles suspended in a nonmagnetic matrix. The resonance field shifts toward higher values as the particle concentration reduces, following two distinct regimes. At the higher concentration regime (above 10(14) cm(-3)) the particle-particle interaction responds for the nonlinear behavior, while at the lower concentration regime (below 10(14) cm(-3)) the particle-particle interaction is ruled out and the system recovers the linearity due to the demagnetizing field effect alone.