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PubMed1990

A model study of stability and oscillations in the myocardial cell membrane.

As a step towards an improved understanding of cardiac arrhythmias caused by abnormal automaticity, we perform a stability analysis of a Hodgkin-Huxley model of the myocardial cell membrane (modified Beeler-Reuter, MBR). The bifurcation structure of the model is obtained as a function of three parameters: the intensity of an applied constant current; the potassium equilibrium potential representing the accumulation of K+ ions in the external medium; and the maximum conductance of the slow inward current mimicking the local application of catecholamines on the membrane. For a range of parameter values, the model exhibits either stable automaticity or bistability between two quiescent states or between a quiescent state and an oscillatory state. These transformations of the bifurcation structure are shown to depend on the interrelationship between three elements: the activation of the slow inward current, the region of high slope conductance of the time-independent potassium current functions, and the slow variables controlling the activation of the potassium current and the inactivation of the slow inward current. Reduced two- and three-dimensional models are shown to reproduce the main stability properties of the full MBR model and to facilitate the understanding of its dynamic behavior. The onset of instability and the oscillatory features of the MBR model are in good agreement with relevant experimental results, and possible sources of disagreement on certain points are discussed.

Arrhythmias, Cardiac↗
PubMed1987

Model of pattern formation in epithelial morphogenesis.

One of the most universal events in morphogenesis is the formation of domains of morphologically polarized cells in the initially homogeneous epithelial sheets. We investigate the possibility of considering this process as a phenomenon of self-organization which is based upon the following experimentally proven mechanochemical cell properties: (1) a capacity of individual cells for morphological polarization considered as a bistable "all-or-none" transition of a cell from a non-polarized to a polarized state; (2) transmission of this capacity from one cell to another on their contacts; (3) feedback relations between co-operative cell polarization and tangential elastic tensions in a cell sheet: cell polarization increases tangential tensions whereas the latter inhibit further cell polarization. We have constructed a phenomenological model which formally expresses the above properties. Its mathematical description includes but few macroscopic parameters available to experimental investigation and controlled changes. The analysis of the collective dynamic regimes of cell polarization demonstrates that variations of some non-specific parameters leads to spontaneous transition in the morphology of cell layers accompanied by symmetry breaking (Turing's instability). Under these conditions either long-range ordered patterns of cell polarization (including hexagonal cell nets) or non-regular spotted structures can emerge. In the particular case of a sheet having fixed complete dimensions and lacking any external elastic bonds a stable macrostate is created; it corresponds to the sheet's binary subdivision into polarized and non-polarized cell domains of size-invariant proportions. The model conclusions are compared with the morphogenetical processes in sea-urchin development, the morphogenesis of skin derivates and artificially induced budding in hydrozoa.

Animals↗
PubMed1987

The frequency of shifts between alternative equilibria.

We derive a formula giving the frequency with which random drift shifts a population between alternative equilibria. This formula is valid when such shifts are rare (Ns much greater than 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4 N mu much less than 1), the rate of stochastic shifts reduces to the product of the mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4 N mu much greater than 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for the frequency of stochastic shifts, which depends only on the equilibrium probability distribution near the saddle point separating the alternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.

Adaptation, Biological↗
PubMed1988

Computer simulations of the effect of non-inactivating sodium channels on the electric behavior of excitable cells.

Non-inactivating sodium channels have been discovered in various cell types. Additionally, normal voltage-gated sodium channels can be induced to lose their ability to inactivate by treatment with proteolytic enzymes, with certain chemical reagents, or with toxins. The presence of non-inactivating sodium channels in the outer membrane of a cell is expected to profoundly modify the electrical properties of the cell, because the electrical depolarization of the cell and the opening of these channels reciprocally reinforce each other without intrinsic control. The normal resting state may thus be destabilized and a new resting state at depolarized resting potentials may become possible. In this study, computer simulations were carried out to systematically explore the patterns of behavior of excitable cells which have non-inactivating sodium channels in their plasma membrane. The cells were assumed to be space clamped and the relevant Hodgkin and Huxley equations were assumed to describe the electrical behavior of the cells, except that some or all of the sodium channels could not inactivate. The sodium currents were thus represented by the sum of two terms: FI.gNa.m3.h.(V-ENa) + (1-FI).gNa.m3(V-ENa), where FI(0 less than or equal to FI less than or equal to 1) is the fraction of sodium channels which inactivate normally, and the other symbols have their usual significance. The behavior of non-inactivating sodium channels created by pronase treatment or reaction with chemical reagents was found to conform with that predicted by the second term in this expression. The simulations thus quantitatively apply to excitable cells thus treated, but may serve additionally to qualitatively illustrate patterns of electrical activity induced by non-inactivating sodium channels also in other cases. A variety of possible types of electrical behavior was obtained: Normal behavior, including capability of firing action potentials, requires values of FI which are not far from unity, the permissible range depending on the fully activated potassium ion conductance, gK. Bistability, at which the cell may exist in one of two stable states of different resting potential, occurs when the value of FI is lowered. Transitions from the polarized to the depolarized resting states, and vice versa, may be brought about by depolarizing and hyperpolarizing triggers, respectively. Such behavior is like that of memory storage devices. Monostability at depolarized potentials is favored by low FI values and can occur if gK is less than the Hodgkin and Huxley value.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗
PubMed1988

Complex behaviour of the repressible operon.

The repressor-mediated repression process in bacteria is modelled using a gene-enzyme-endproduct control unit. A combined analytical-numerical study shows that the system, though stable normally, becomes unstable for super-repressing strains even at low values of the cooperativity of repression, provided demand for the endproduct saturates at large endproduct concentrations. In addition the system also shows bistability, i.e., the co-existence of a stable steady-state and a stable limit cycle. The tryptophan operon is used as a model system and the results are discussed in the light of differential regulation of gene expression in lower organisms, especially in mutant strains.

Gene Expression Regulation↗
PubMed2000

Dynamical analysis of density-dependent selection in a discrete one-island migration model.

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The birth of an unusual chaotic attractor is also illustrated. This attractor is produced when migration causes chaotic dynamics on a boundary of phase space to bifurcate into the interior of phase space, resulting in bistable genetic polymorphic behavior.

Alleles↗
PubMed2001

A competition model with dynamically allocated inhibitor production.

The chemostat is a basic model for competition in an open system and a model for the laboratory bio-reactor (CSTR). Inhibitors in open systems are studied with a view of detoxification in natural systems and of control in bio-reactors. This study allows the amount of resource devoted to inhibitor production to depend on the state of the system. The feasibility of one dependence is provided by quorum sensing. In contrast to the constant allocation case, a much wider set of outcomes is possible including interior, stable rest points and stable limit cycles. These outcomes are important contrasts to competitive exclusion or bistable attractors that are often the outcomes for competitive systems. The model consists of four non-linear ordinary differential equations and computer software is used for most of the stability calculations.

Bioreactors↗
PubMed2003

Simulation of waves in calcium models with 3D spherical geometry.

Waves of calcium ions are present in fertilized eggs of many species. Models for pulse and tidal wave propagation have usually been studied in one or two spatial coordinates only. We examine in three spatial coordinates some established models, based on Ca(2+)-induced Ca(2+)-release from both (assumed) continuously or heterogeneously distributed stores of endoplasmic reticulum (ER) through channels activated by inositol triphosphate (IP(3)). With continuous IP(3) distribution decreasing radially towards the interior, we obtain concave pulse shapes for waves penetrating the interior. Concave waves are also recorded in systems with ER confined to distributions of small spheres (microdomains) inside the cell, which we simulate for front waves (tides) in bistable systems.

Animals↗
PubMed2003

Allee effects, extinctions, and chaotic transients in simple population models.

Discrete time single species models with overcompensating density dependence and an Allee effect due to predator satiation and mating limitation are investigated. The models exhibit four behaviors: persistence for all initial population densities, bistability in which a population persists for intermediate initial densities and otherwise goes extinct, extinction for all initial densities, and essential extinction in which "almost every" initial density leads to extinction. For fast-growing populations, these models show populations can persist at high levels of predation even though lower levels of predation lead to essential extinction. Alternatively, increasing the predator's handling time, the population's carrying capacity, or the likelihood of mating success may lead to essential extinction. In each of these cases, the mechanism behind these disappearances are chaotic dynamics driving populations below a critical threshold determined by the Allee effect. These disappearances are proceeded by chaotic transients that are proven to be approximately exponentially distributed in length and highly sensitive to initial population densities.

Alleles↗
PubMed2002

Computing relief structure from motion with a distributed velocity and disparity representation.

Recent psychophysical experiments suggest that humans can recover only relief structure from motion (SFM); i.e., an object's 3D shape can only be determined up to a stretching transformation along the line of sight. Here we propose a physiologically plausible model for the computation of relief SFM, which is also applicable to the related problem of motion parallax. We assume that the perception of depth from motion is related to the firing of a subset of MT neurons tuned to both velocity and disparity. The model MT neurons are connected to each other laterally to form modulatory interactions. The overall connectivity is such that when a zero-disparity velocity pattern is fed into the system, the most responsive neurons are not those tuned to zero disparity, but instead are those having preferred disparities consistent with the relief structure of the velocity pattern. The model computes the correct relief structure under a wide range of parameters and can also reproduce the SFM illusions involving coaxial cylinders. It is consistent with the psychophysical observation that subjects with stereo impairment are also deficient in perceiving motion parallax, and with the physiological data that the responses of direction- and disparity-tuned MT cells covary with the perceived surface order of bistable SFM stimuli.

Cues↗
PubMed1998

A rotational stereoscopic 3-dimensional movement aftereffect.

A stereoscopic rotational movement aftereffect (MAE) and a stereoscopic bi-directional MAE were generated by rotation of a cyclopean random dot cylinder in depth and by movement of two cyclopean random dot planes in opposite directions, respectively. Cross-adaptational MAEs were also generated on each other, but not with stimuli lacking any disparity. Cross-adaptation MAEs were generated between stereoscopic and non-stereoscopic random dot stimuli moving in the one X/Y plane. Spontaneous reversals in direction of movement were observed with bistable stimuli lacking disparity. Two models of the middle temporal area were considered which might explain both the stereoscopic MAEs and the spontaneous reversals.

Adaptation, Ocular↗
PubMed2002

Spinal plasticity mediated by postsynaptic L-type Ca2+ channels.

In the spinal cord, motoneurons and specific subgroups of interneurons express L-type Ca(2+) channels. As elsewhere, these dihydropyridine-sensitive channels mediate a slowly activating inward current in response to depolarisation and show little or no inactivation. The slow kinetics for activation and deactivation provide voltage-sensitive properties in a time range from hundreds of milliseconds to tens of seconds and lead to plateau potentials, bistability and wind-up in neurons in both sensory and motor networks. This slow dynamics is in part due to facilitation of L-type Ca(2+) channels by depolarisation. The voltage sensitivity of L-type Ca(2+) channels is also regulated by a range of metabotropic transmitter receptors. Up-regulation is mediated by receptors for glutamate, acetylcholine, noradrenaline and serotonin in motoneurons and by receptors for glutamate and substance P in plateau-generating dorsal horn interneurons. In both cell types, L-type Ca(2+) channels are down-regulated by activation of GABA(B) receptors. In this way, metabotropic regulation in cells expressing L-type Ca(2+) channels provides mechanisms for flexible adjustment of excitability and of the contribution of plateau currents to the intrinsic properties. This type of regulation also steers the magnitude and compartmental distribution of Ca(2+) influx during depolarisation, thus providing a signal for local synaptic plasticity.

Animals↗
PubMed2001

Biochemical networks in nervous systems: expanding neuronal information capacity beyond voltage signals.

In addition to synaptically mediated signals that are based on changes in membrane potential, neurons also generate and receive many types of signals that involve biochemical pathways, some of which are independent of voltage. Although networks of biochemical pathways have often been thought of as being only neuromodulatory, recent computational and experimental studies have highlighted how these pathways can also integrate and transfer information themselves. Interactions between biochemical pathways involving positive and negative feedback loops allow biochemical signals to exhibit emergent properties, most notably bistability and oscillations. New and evolving techniques, including real-time imaging of second messengers, hold the promise of illuminating information processing that cannot be detected using microelectrodes, and revealing how 'biochemical integration' might contribute to the computational abilities of the nervous system.

Animals↗
PubMed2001

Radiation dosimetry using three-dimensional optical random access memories.

Three-dimensional optical random access memories (3D ORAMs) are a new generation of high-density data storage devices. Binary information is stored and retrieved via a light induced reversible transformation of an ensemble of bistable photochromic molecules embedded in a polymer matrix. This paper describes the application of 3D ORAM materials to radiation dosimetry. It is shown both theoretically and experimentally, that ionizing radiation in the form of heavy charged particles is capable of changing the information originally stored on the ORAM material. The magnitude and spatial distribution of these changes are used as a measure of the absorbed dose, particle type and energy. The effects of exposure on 3D ORAM materials have been investigated for a variety of particle types and energies, including protons, alpha particles and 12C ions. The exposed materials are observed to fluoresce when exposed to laser light. The intensity and the depth of the fluorescence is dependent on the type and energy of the particle to which the materials were exposed. It is shown that these effects can be modeled using Monte Carlo calculations. The model provides a better understanding of the properties of these materials. which should prove useful for developing systems for charged particle and neutron dosimetry/detector applications.

Alpha Particles↗
PubMed1997

Complex dynamics of mass-closed coupled autocatalytic systems in response to minute asymmetric perturbations.

The role of kinetic coupling in catering to a remote-control mechanism for the onset and regulation of self-organization phenomena in a multicompartmental biochemical system has been examined. Using two cyclic autocatalytic reaction networks operating in two chambers separated by a membrane and coupled through a common cofactor, it has been demonstrated that (i) in response to asymmetric perturbations, the coupled reaction networks exhibit a variety of temporal self-organization phenomena such as bistability, multiple periodicity, hard excitation and coexistence of aperiodic oscillation with limit cycle even in mass-closed conditions; (ii) without disturbing a network directly, its dynamic behaviour can be regulated by perturbing some other network kinetically coupled to it and (iii) the dynamics of two coupled networks can be made to flip-flop between oscillatory and steady-states simply by modulating the time of application of external perturbations. The extreme sensitivity of this model to minute asymmetric fluctuations in the environment can predict how the impact of local changes in physico-chemical conditions can be transmitted from one compartment to another through coupled biochemical pathways in a living cell.

Journal Article↗
PubMed1998

Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes.

Using a modular approach, in which kinetic models of various mechanisms of calcium handling in cells are fine-tuned to in vivo and in vitro measurements before combining them into whole-cell models, three distinct modes of transmission of calcium waves in mature and immature frog eggs have been defined. Two modes of transmission are found in immature eggs, where the inositol 1,4,5-trisphosphate receptor (IP3R) controls release of calcium from the endoplasmic reticulum (ER). The first mode corresponds to an excitable physiological state of the cytoplasm and results in solitary waves that can appear as circular or spiral waves in two dimensions with the wave speed proportional to the square root of the diffusion constant of calcium. A second mode occurs when the state of the cytoplasm is oscillatory and because of the small size of the buffered diffusion constant for calcium, the wave speed can appear to be weakly dependent on diffusion. In the mature frog egg, where the sperm-induced Ca2+ fertilization wave is a propagating front, the cytoplasm appears to be bistable and in this mode the wave speed is also proportional to the square root of the diffusion constant. Here we investigate a fourth mode of propagation for cardiac myocytes, in which calcium release from the sarcoplasmic reticulum (SR) is dominated by clusters of ryanodine receptors spaced at regular intervals. In myocytes a stochastically excitable myoplasm leads to the spontaneous production of calcium 'sparks' that under certain conditions can merge into saltatory waves with a speed proportional to the diffusion constant.

Animals↗
PubMed1998

Multiple attractors in immunology: theory and experiment.

This selective survey discusses the relative merits of various modeling approaches in immunology that exhibit multiple attractors, and also assesses the ability of the different models to contribute to deeper biological understanding. The first topic is global anti-idiotypic network models, which, like Hopfield neural network models, exhibit a large number of steady states that are identified with memory. It is shown that a 'reverse engineering approach' to T-cell vaccination for autoimmunity, featuring steady states corresponding respectively to 'normality', 'vaccination' and 'disease', is able to spur new experiments, in spite of the model's deliberate neglect of almost all biological detail. Mention is made of several other T-cell models that feature bistability for Th1 or Th2 dominance, or for activation and unresponsiveness.

Autoimmunity↗
PubMedDate not supplied

Alternans and 2:1 rhythms in an ionic model of heart cells.

ECG alternans is commonly held to be an indicator of electrical instability of the heart, but the development of alternans has not yet been fully understood theoretically. We investigate the onset of alternans and 2:1 rhythms for stimulation at increasing frequencies in the Beeler-Reuter model, a simple ionic model of cardiac tissue. We find hysteresis and bistability at the onset of alternans; well-timed stimuli can switch between the two limit cycles. We determine quantitatively the effect of blocking specific ionic currents. Moreover, we find that calcium buffers generally promote alternans.

Action Potentials↗