Modeling of glutamate-induced dynamical patterns.

Based on established physiological mechanisms, the paper presents a detailed computer model, which supports the hypothesis that temporal lobe epilepsy may be caused by failure of glutamate reuptake from the extracellular space. The elevated glutamate concentration causes an increased activation of NMDA receptors in pyramidal neurons, which in turn leads to neuronal dynamics that is qualitatively identical to epileptiform activity. We identify by chaos analysis a surprising possibility that muscarinergic receptors can help the system out of a chaotic regime.

Spatial periodic forcing of Turing structures.

Spontaneously evolving Turing structures in the chlorine dioxide-iodine-malonic acid reaction-diffusion system typically exhibit many defects that break the symmetry of the pattern. Periodic spatial forcing interacts with the Turing structures and modifies the pattern symmetry and wavelength. We investigate the role of the amplitude and wavelength of spatial periodic forcing on the hexagonal pattern of Turing structures. Experimental results and numerical simulations reveal that forcing at wavelengths slightly larger than the natural wavelength of the pattern is most effective in removing defects and producing ordered symmetric hexagonal patterns.

A model of synaptic memory: a CaMKII/PP1 switch that potentiates transmission by organizing an AMPA receptor anchoring assembly.

Ca2+/calmodulin-dependent protein kinase II (CaMKII) is localized in the postsynaptic density (PSD) and is necessary for LTP induction. Much has been learned about the autophosphorylation of CaMKII and its dephosphorylation by PSD protein phosphatase-1 (PP1). Here, we show how the CaMKII/PP1 system could function as an energy-efficient, bistable switch that could be activated during LTP induction and remain active despite protein turnover. We also suggest how recently discovered binding interactions could provide a structural readout mechanism: the autophosphorylated state of CaMKII binds tightly to the NMDAR and forms, through CaMKII-actinin-actin-(4.1/SAP97) linkages, additional sites for anchoring AMPARs at synapses. The proposed model has substantial experimental support and elucidates principles by which a local protein complex could produce stable information storage and readout.

Turing pattern formation induced by spatially correlated noise.

The effect of spatially correlated noise on Turing structures is analyzed both experimentally and numerically. Using the photosensitive character of the chlorine dioxide-iodine-malonic acid reaction-diffusion system, spatial randomness is introduced in the system. In the presence of noise, Turing patterns appear and are stable at levels of average illumination that would be more than sufficient to suppress pattern formation in the case of homogeneous illumination.

Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities.

We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is inhomogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts finding a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase inside the other. For a one-dimensional front, the function describing the inhomogeneity of the nonlinear term acts as a "potential function" for the motion of the front, i.e., a front initially placed between two of its local maxima asymptotically approaches the intervening minimum. Two-dimensional fronts, with radial symmetry and without dissipation can either shrink to a point in finite time, grow unboundedly, or their radius can oscillate, depending on the initial conditions. When dissipation effects are present, the oscillations either decay spirally or not depending on the value of the damping dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.

Resonant suppression of Turing patterns by periodic illumination.

We study the resonant behavior of Turing pattern suppression in a model of the chlorine dioxide-iodine-malonic acid reaction with periodic illumination. The results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system. The resonance in Turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force. Square wave (on-off) periodic forcing is more effective in suppressing Turing patterns than sinusoidal forcing. We compare the dynamics of periodically forced Turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells. Bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns.

Oscillatory clusters in the periodically illuminated, spatially extended Belousov-Zhabotinsky reaction.

Cluster-cluster transitions in the periodically illuminated photosensitive Belousov-Zhabotinsky (BZ) reaction-diffusion system exhibit the same scenario as in the autonomous BZ system with negative global feedback: two-phase clusters <--> three-phase clusters <--> irregular clusters <--> localized clusters. Transitions induced by changing the dark ( TD) or light ( TL) phases of the periodic external square wave illumination are dependent not only on the frequency of illumination at constant TD/TL, but also on the ratio TD/TL at constant frequency (when TD+TL = const).

A new chemical system for studying pattern formation: bromate-hypophosphite-acetone-dual catalyst.

A modified version of the short-lived BrO3(-)-H2PO2(-)-Mn(II)-N2 oscillator, the BrO3(-)-H2PO2(-)-acetone-dual catalyst system, where the catalyst pair can be Mn(II)-Ru(bpy)3SO4, or Mn(II)-ferroin, or Mn(II)-diphenylamine, shows long-lasting batch oscillations in the potential of a Pt electrode and in colour, accompanying periodic transitions between the oxidised and reduced forms of the catalysts. Experimental conditions for the oscillations are established. The origin of the batch oscillations and the role of the catalyst pair in the oscillatory behaviour are discussed. The new system is ideally suited to the study of waves and patterns in reaction-diffusion systems, since in addition to the longevity of its spatial behaviour in batch, it produces no gaseous or solid products and exhibits significant photosensitivity.

Bistability in the Ca(2+)/calmodulin-dependent protein kinase-phosphatase system.

A mathematical model is presented of autophosphorylation of Ca(2+)/calmodulin-dependent protein kinase (CaMKII) and its dephosphorylation by a phosphatase. If the total concentration of CaMKII subunits is significantly higher than the phosphatase Michaelis constant, two stable steady states of the CaMKII autophosphorylation can exist in a Ca(2+) concentration range from below the resting value of the intracellular [Ca(2+)] to the threshold concentration for induction of long-term potentiation (LTP). Bistability is a robust phenomenon, it occurs over a wide range of parameters of the model. Ca(2+) transients that switch CaMKII from the low-phosphorylated state to the high-phosphorylated one are in the same range of amplitudes and frequencies as the Ca(2+) transients that induce LTP. These results show that the CaMKII-phosphatase bistability may play an important role in long-term synaptic modifications. They also suggest a plausible explanation for the very high concentrations of CaMKII found in postsynaptic densities of cerebral neurons.

Calcium waves in a model with a random spatially discrete distribution of Ca2+ release sites.

We study the propagation of intracellular calcium waves in a model that features Ca2+ release from discrete sites in the endoplasmic reticulum membrane and random spatial distribution of these sites. The results of our simulations qualitatively reproduce the experimentally observed behavior of the waves. When the level of the channel activator inositol trisphosphate is low, the wave undergoes fragmentation and eventually vanishes at a finite distance from the region of initiation, a phenomenon we refer to as an abortive wave. With increasing activator concentration, the mean distance of propagation increases. Above a critical level of activator, the wave becomes stable. We show that the heterogeneous distribution of Ca2+ channels is the cause of this phenomenon.

Transformations of glycolysis control characteristics in human erythrocytes during blood storage.

Changes in glycolysis control characteristics (dependence of glycolysis rate on ATP concentration) in erythrocytes were studied during the storage of donors blood with glucose citrate hemoconservant. During the first two weeks of storage the shape of glycolysis control characteristics in the erythrocytes could be shown to remain practically unchanged, which was represented by a bell-shaped curve such as in fresh erythrocytes. During this period the physiological point of glycolysis will move along the glycolysis control characteristics towards the maximum of the curve. Once the maximum of the physiological point has been reached, the shape of the curve can be seen to change. The maximum on the curve becomes less evident, moving down and to the left from its initial position. These changes will occur after two to four weeks of storage. In some cases the maximum on glycolysis control characteristics will disappear at the latest stages of storage. The changes observed will occur in blood of different donors at different moments of storage. The nature of the changes observed and their influence on erythrocyte viability are discussed.

Dynamic stability of steady states and static stabilization in unbranched metabolic pathways.

The paper is concerned with the conditions of dynamic (asymptotic) stability of steady states in unbranched metabolic pathways. The stationary flux in such pathways is generally determined by the concentration of the end product due to the effector action of this product on the reactions proceeding in its synthetic pathway. The delay in feedback circuits causes violation of dynamic stability at large static stabilization factors. A methods permitting analytic estimation of the critical stabilization factor is suggested. Sufficient and necessary conditions for asymptotic stability of the steady state in the general case of the pathway with a single feedback loop have been established. Mechanisms for maintenance of the steady state asymptotic stability at large static stabilization factors are studied. It has been shown that the range of dynamic stability can be widened greatly, if the pathway contains one or two reactions (but not more) of relatively small effective rate constants. Short strong negative feedback is also found to extend considerably the range of dynamic stability of the pathway. The feedback is more effective if it acts on the reaction with small effective rate constant.

Regulation of glycolysis in human erythrocytes. The mechanism of ATP concentration stabilization.

The mathematical modelling of human erythrocyte energy metabolism has shown that stabilization of ATP concentration can be achieved if the curve representing the relation between glycolysis rate and ATP concentration (glycolysis characteristic) is bell-shaped with steeply descending part at physiologically normal ATP concentration. The glycolysis characteristic of human erythrocytes has been obtained experimentally. In erythrocytes of different donors the glycolysis characteristics are greatly different quantitatively, but have qualitatively similar bel-like shape with steeply descending part at physiologically normal ATP concentration. This characteristics can be made coincident for all donors if they are plotted in relative units taking for 100% the physiologically normal values of glycolysis rate and ATP for every individual donor. The coincidence of the normalized erythrocyte glycolysis characteristics for different donors can be achieved in the mathematical model of erythrocyte energy metabolism under the assumption that the phosphofructokinase rate depends effectively on the relation of ATP to adenylate pool and the total erythrocyte ATPase is strongly inhibited by AMP.

The stoichiometry of ion fluxes during Sr2+-induced oscillations in mitochondria.

A quantitative study of H+, K+, Sr2+ and succinate fluxes in Sr2+-induced oscillatory state of rat liver mitochondria is presented. It was shown that oscillation of succinate content in mitochondria occurs synchronously with oscillations of the cation fluxes. Total charge transferred across the membrane by the registered cations and the succinate-anion is equal to zero. Passive H+-influx has been calculated at all stages of the oscillatory cycle. The conclusion is made that electroneutral 2 H+/Sr2+ exchange is periodically induced in mitochondria. A value of (2 +/- 0.2) . 10(-7) mol Sr2+/min per mg protein has been determined for Sr2+ by this type of exchange.