Forced oscillations in a windkessel model

Volume elasticity of the arterial system and its component parts is developed starting from a Windkessel^*-model, which is defined in 4 points. Emphasis is laid on the simplicity of the derived equations and accessibility to experimental verification. The theory is an extension of earlier work achieved by Wetterer and Pieper (1953), who introduced an essentially physical method for the indirect determination of volume elasticity in situ, by creating forced sinusoidal oscillations in the arterial system, using a special pump operated at a considerably lower frequency than the mean heart frequency. The elegance of both experimental technique and the derived equations incited us to investigate the mathematical foundation and possible generalization of the method.     

Limited emigration from an outbreak of a forest pest insect

Population density and individual dispersal behaviour affect species' distribution dynamics. Population densities vary over time, and some species occasionally increase to very high numbers, for example during outbreaks. In such situations, populations are expected to expand into new areas as a result of density-dependent dispersal which sometimes even results in range expansion. A local population of the northern pine processionary moth Thaumetopoea pinivora has recently reached outbreak densities at the edge of its northern range at the southern tip of Gotland Island in the Baltic Sea. We first investigated whether the outbreak had resulted in establishment of populations in suitable habitats on Gotland Island outside the outbreak area. Six small populations were found that could potentially have originated from the outbreak area. However, data from 12 microsatellite markers strongly suggest that these populations did not originate from the recent outbreak. Genetic variability was not reduced in these small, isolated populations, and there were several unique alleles, indicating instead a different population history and that there has been no recent range expansion. In addition, there was apparent genetic isolation by geographic distance, implying that despite the high density of the outbreak population, significant gene flow has not occurred.     

Canards for a reduction of the Hodgkin-Huxley equations

This paper shows that canards, which are periodic orbits for which the trajectory follows both the attracting and repelling part of a slow manifold, can exist for a two-dimensional reduction of the Hodgkin-Huxley equations. Such canards are associated with a dramatic change in the properties of the periodic orbit within a very narrow interval of a control parameter. By smoothly connecting stable and unstable manifolds in an asymptotic limit, we predict with great accuracy the parameter value at which the canards exist for this system. This illustrates the power of using singular perturbation theory to understand the dynamical properties of realistic biological systems.     

Chaotic oscillations in a simple collapsible-tube model.

A steady flow through a segment of externally pressurized, collapsible tube can become unstable to a wide variety of self-excited oscillations of the internal flow and tube walls. A simple, one-dimensional model of the conventional laboratory apparatus, which has been shown previously to predict steady flows and multiple modes of oscillation, is investigated numerically here. Large amplitude oscillations are shown to have a relaxation structure, and the nonlinear interaction between different modes is shown to give rise to quasiperiodic and apparently aperiodic behavior. These predictions are shown to compare favorably with experimental observations.     

Travelling waves of resistance in a bi-trophic pest adaptation model

We consider a reaction-diffusion system for spatial spread of pest resistance to host plant resistance genes which is based on the Lotka-Volterra predator-prey equations, with logistic growth of the resource level and a diffusion term added to account for spatial spread of the pest. The model is phenotype specific, in which a pest subpopulation's fitness comes down to a balance between its resource assimilation rate and its respiration rate. We derive an expression for the rate of spatial spread of the resistant pest types from an initial point source, and discuss its relevance for adaptive pest resistance management strategies. Using results for an analogous single-species reaction-diffusion model in heterogeneous media, we consider the likely impact of pest-susceptible plant refugia on the speed of the travelling wave of resistant pests, and simultaneously the expected trade-off, in terms of crop yield decrease, when refugia are included. We also explore the possibility that resistance breaking by the pest population is not an inevitable phenomenon, particularly when refugia of the appropriate size are used.     

Stomatal oscillations in adult forest trees in natural environment

Conductance of abaxial epidermis was measured in leaves ofAcer campeatre, Carpinus betulus, Quercus cerris andQ. petraea sample trees growing in an oak-hornbeam forest. Measurements were performed on several summer days during morning and midday hours. Stomata tended to oscillations only inQ. cerris. The occurrence of stomatal oscillations was controlled by environmental conditions,e.g. weather.     

Self-sustained oscillations of electric potential in a model membrane

A model membrane constructed from a Millipore filter, whose pores are filled with dioleyl phosphate molecules, exhibits a self-oscillation of the electric potential with a period of about a few seconds in the presence of a salt-concentration difference, pressure difference and/or electric current across the filter. In this paper, the effects of chemicals such as KCl, CaCl2, pH and sucrose on the self-oscillation are investigated experimentally. These chemical substances are shown to alter the characteristic properties as the frequency of oscillation. Theoretical consideration of electrochemical interaction between these substances and DOPH molecules gives a fairly good explanation of the observed results.     

Organizing centres and symbolic dynamic in the study of mixed-mode oscillations generated by models of biological autocatalytic processes

The organization of the complex mixed-mode oscillations generated, in a three-dimensional variable space, by an autocatalytic process formalized as a cubic monomial is analyzed. The generation of the temporal patterns is elucidated by complementary approaches dealing with the three-variable differential continuous system itself and with successive discrete applications modelling its first return map. The extent to which the underlying bifurcation structures could constitute a fingerprint of autocatalytic processes is discussed in connection with the modelling of biological systems.     

Bi-trophic mathematical model for pest adaptation to a resistant crop

A version of the Lotka-Volterra predator-prey model with logistic crop growth is modified to explore the rate of adaptation of a herbivore to a pest-resistant crop. This provides a phenotypic model for the evolution of resistance in a population comprising three different pest types each defined by differing parameter values for respiration rate and crop palatability. Expressions estimating the rates of increase of the fitter pest types are obtained as a function of the food qualities, and respiration and mortality rates. Potential strategies for delaying the rate of adaptation with regard to the expressions derived above, via the use of pest-susceptible refugia and natural enemies, are discussed. Although the model is formulated as one in which a single gene is the factor conferring resistance it can be interpreted and used independently of this.     

Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

Theta oscillations by synaptic excitation in a neocortical circuit model

Neocortical theta-band oscillatory activity is associated with cognitive tasks involving learning and memory. This oscillatory activity is proposed to originate from the synchronization of interconnected layer V intrinsic bursting (IB) neurons by recurrent excitation. To test this hypothesis, a sparsely connected spiking circuit model based on empirical data was simulated using Hodgkin-Huxley-type bursting neurons and use-dependent depressing synaptic connections. In response to a heterogeneous tonic current stimulus, the model generated coherent and robust oscillatory activity throughout the theta-band (4-12 Hz). These oscillations were not, however, self-sustaining without a driving current, and not dependent on N-methyl-D-aspartate receptor synaptic currents. At realistic connection strengths, synaptic depression was necessary to avoid instability and expanded the basin of attraction for theta oscillations by controlling the gain of recurrent excitation. These results support the hypothesis that IB neuron networks can generate robust and coherent theta-band oscillations in neocortex.     

Linking flickering to waves and whole-cell oscillations in a mitochondrial network model

It has been shown that transient single mitochondrial depolarizations, known as flickers, tend to occur randomly in space and time. On the other hand, many studies have shown that mitochondrial depolarization waves and whole-cell oscillations occur under oxidative stress. How single mitochondrial flickering events and whole-cell oscillations are mechanistically linked remains unclear. In this study, we developed a Markov model of the inner membrane anion channel in which reactive-oxidative-species (ROS)-induced opening of the inner membrane anion channel causes transient mitochondrial depolarizations in a single mitochondrion that occur in a nonperiodic manner, simulating flickering. We then coupled the individual mitochondria into a network, in which flickers occur randomly and sparsely when a small number of mitochondria are in the state of high superoxide production. As the number of mitochondria in the high-superoxide-production state increases, short-lived or abortive waves due to ROS-induced ROS release coexist with flickers. When the number of mitochondria in the high-superoxide-production state reaches a critical number, recurring propagating waves are observed. The origins of the waves occur randomly in space and are self-organized as a consequence of random flickering and local synchronization. We show that at this critical state, the depolarization clusters exhibit a power-law distribution, a signature of self-organized criticality. In addition, the whole-cell mitochondrial membrane potential changes from exhibiting small random fluctuations to more periodic oscillations as the superoxide production rate increases. These simulation results may provide mechanistic insight into the transition from random mitochondrial flickering to the waves and whole-cell oscillations observed in many experimental studies.     

Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations

Temperature sensitivities and conditions for temperature compensation have been investigated in a model for yeast glycolytic oscillations. The model can quantitatively simulate the experimental observation that the period length of glycolytic oscillations decreases with increasing temperature. Temperature compensation is studied by using control coefficients describing the effect of rate constants on oscillatory frequencies. Temperature compensation of the oscillatory period is observed when the positive contributions to the sum of products between control coefficients and activation energies balance the corresponding sum of the negative contributions. The calculations suggest that by changing the activation energies for one or several of the processes, i.e. by mutations, it could be possible to obtain temperature compensation in the yeast glycolytic oscillator.     

Vertical signal flow and oscillations in a three-layer model of the cortex

A model of vertical signal flow across a layered cortical structure is presented and analyzed. Neurons communicate through spikes, which evoke an excitatory or inhibitory postsynaptic potential (spike response model). The layers incorporate two anatomical features - dendritic and axonal arborization patterns and distance-dependent time delays. The vertical signal flow through the network is discussed for various stimulus conditions using two different, but typical, axonal arborization patterns. We find stationary as well as oscillatory response, but the oscillatory response may be restricted to a single layer. Confronted with conflicting stimuli the network separates the patterns through phase-shifted oscillations. We also discuss two hypothetical animals, to be called cat and mouse. These have different axonal arborizations, which give rise to a different oscillatory response (if any) of the various layers.     

Role of latency period in viral infection: a pest control model

The interrelationship of latency period in viral infection and overall infection process in host community are of critical importance in context of pest control programme. Both of them regulate the overall system stability as they are dynamically linked to predation by natural enemies in the system. The present paper deals with the role of latency period in viral infection through mathematical modeling and analysis. We propose a four dimensional mathematical model with delayed infection in pest community. It is shown that there exists a certain value of delay, say T( *) such that for T>T( *) the system exhibits global stability towards disease-free equilibrium. But for T相似文献   

Analysis of a minimal model for p53 oscillations

Oscillatory behaviours in genetic networks are important examples for studying the principles underlying the dynamics of cellular regulation. Recently the team of Alon has reported a surprisingly rich oscillatory response of the p53 tumor suppressor to irradiation stress et al. [Lahav, G., Rosenfeld, N., Sigal, A., Geva-Zatorsky, N., Levine, A.J., Elowitz, M.B., Alon, U., 2004. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat. Genet. 36 (2), 147-150; Geva-Zatorsky, N., Rosenfeld, N., Itzkovitz, S., Milo, R., Sigal, A., Dekel, E., Yarnitzky, T., Liron, Y., Polak, P., Lahav, G., Alon, U., 2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033]. Several models for this system have been proposed by different groups, based essentially on negative feedback loops. In this paper we investigate in detail oscillations and stability in a deterministic time delayed differential model of the core circuit for p53 expression. This model is representative of a class of modelling approaches of this system, based on a minimal set of well-established biomolecular regulations. Depending on the protein degradation rates we show the existence of bifurcations between a stable steady state and oscillations both in presence and absence of stress.     

A model of microtubule oscillations

Simulations of microtubule oscillations have been obtained by a kinetic model including nucleation of microtubules, elongation by addition of GTP-loaded tubulin dimers, disassembly into oligomers, and dissolution of oligomers followed by nucleotide exchange at the free dimers. Dynamic instability is described by the on and off rates for dimer association in the growth phase, the rate of rapid shortening, and the transition rates for catastrophe and rescue. The latter are assumed to be completely determined by the current state of the system (short cap hypothesis). Microtubule oscillations and normal polymerizations measured by time-resolved X-ray scattering were used to test the model. The model is able to produce oscillations without further assumptions. However, in order to obtain good fits to the experimental data one requires an additional mechanism which prevents rapid desynchronization of the microtubules. One of several possible mechanisms that will be discussed is the destabilization of microtubules by the products of disassembly.Abbreviations MT(s) microtubule(s) - G-MT/S-MT microtubule in the state of growth/shortening - GTP guanosine 5-triphosphate - GDP guanosine 5-diphosphate - TU · GDP/TU · GTP tubulin dimer with GDP/GTP bound to the exchangeable nucleotide binding site - MAP(s) microtubule-associated protein(s) - PC tubulin phosphocellulose-purified tubulin - PIPES piperazine-1,4-bis(2-ethane sulfonic acid) - DDT dithiothreitol - EGTA ethylene glycol-O,O-bis(2-amino ethyl ether)-N,N,N,N-tetraacetic acid     

Landscape diversity slows the spread of an invasive forest pest species

According to the associational resistance hypothesis, diverse habitats provide better resistance to biological invasions than monocultures. Host‐plant abundance has been shown to affect the range expansion of invasive pests, but the effect of landscape diversity (i.e. density of host/non‐host patches and diversity of forest habitat patches) on invasions remains largely untested. We used boundary displacement models and boosted regression tree analyses to investigate the effects of landscape diversity on the invasion of Corsica by the maritime pine bast scale Matsucoccus feytaudi over an 18‐yr period. Taking the passive wind dispersal of the scale into account, we showed that open habitats and connectivity between host patches accelerated spread by up to 13%, whereas landscapes with high tree diversity and a high density of non‐host trees decreased scale spread by up to 14%. We suggest a new mechanism for such associational resistance to pest invasion at the landscape level, which we term ‘the pitfall effect’.