A model for glucose-induced wave propagation in pancreatic islets of Langerhans.

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).

Standing excitation waves in the heart induced by strong alternating electric fields.

We studied the effect of sinusoidal electric fields on cardiac tissue both experimentally and numerically. We found that periodic forcing at 5-20 Hz using voltage applied in the bathing solution could stop the propagation of excitation waves by producing standing waves of membrane depolarization. These patterns were independent of the driving frequency in contrast to classical standing waves. The stimulus strength required for pattern formation was large compared to the excitation threshold. A novel tridomain representation of cardiac tissue was required to reproduce this behavior numerically.

Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans.

In response to glucose application, beta-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of beta-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled beta-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.

Soliton-like regimes and excitation pulse reflection (echo) in homogeneous cardiac purkinje fibers: results of numerical simulations.

On the basis of numerical simulations of the partial McAllister-Noble-Tsien equations quantitatively describing the dynamics of electrical processes in conductive cardiac Purkinje fibers we reveal unusual - soliton-like - regimes of interaction of nonlinear excitation pulses governing the heart contraction rhythm: reflection of colliding pulses instead of their annihilation. The phenomenological mechanism of the reflection effects is that in a narrow (but finite) range of the system parameters the traveling pulse presents a doublet consisting of a high-amplitude leader followed by a low-amplitude subthreshold wave. Upon collisions of pulses the leaders are annihilated, but subthreshold waves summarize becoming superthreshold and initiating two novel echo-pulses traveling in opposite directions. The phenomenon revealed presents an analogy to the effect of reflection of colliding nerve pulses, predicted recently, and can be of use in getting insight into the mechanisms of heart rhythm disturbances.

Analysis of electrical phenomena accompanying the growth of Neurospora crassa hyphae: theory and experiment.

To describe electrical phenomena observed in growth of Neurospora crassa hyphae, a theoretical model was developed considering the hypha as a one-dimensional electric cable with non-uniform longitudinal distribution of current sources reflecting the activity of proton pumps. A profile of the density of the pump current along the hypha is proposed, at which the results of simulation quantitatively coincide with the results of physiological experiments. The model values of energy coupling in the growth zones were estimated. The experimental dependence of the elongation rate of regenerating apical hypha fragments on their lengths was determined. Based on the comparison of these experimental results with the results of analysis of the model, the contribution of the axial metabolite transport, from the distal parts of the hypha to the apical part, to the dynamics of the apical cell growth was estimated. The possibility of evaluating the intensity of high-molecular-weight syntheses and/or accumulation of substances in granules was demonstrated. The growth rate of the regenerating hypha fragments was shown to correlate with the electric current flowing into the apical fragment 0.2-mm in length.

[Splitting of the back edge of a propagating excitation pulse]. / Rasshcheplenie zadnego fronta rasprostraniaiushchegosia impul'sa vozbuzhdeniia.

A new type of unstability of action potential propagating in spatially inhomogeneous electrically excitable media is announced. Numerical experiments with the FitzHugh-Nagumo model show that if the medium contains a region where membrane slow, outward currents are partially depressed then the back front of action potential passing through such a region can split forming a "burning drop"-solitary standing wave of depolarisation with finite "life duration".

[Analytical estimation of the period of reverberator in an arbitrary model of an active medium]. / Analiticheskaia otsenka perioda reverberatora v proizvol'noi modeli aktivnoi sredy.

Reverberators in an active medium with reduction were studied. Analytical estimations were obtained for reverberator period for arbitrary right parts of equations describing non-auto-oscillation active medium satisfying 2 natural conditions (existence of solutions as periodic flat waves, small dependence of the rate of such solutions on the wavelength). It was shown that the reverberator period under such conditions is given only by two parameters of the model: the minimal period of periodic flat waves and the rate of solitary impulse independent of the model of active medium. A comparison with numerical calculation of dimetric model of Fitz Hue Type was carried out.