A mathematical model of agonist-induced propagation of calcium waves in astrocytes.

In astrocytes, calcium signals evoked by neurotransmitters appear as waves within single cells, which spread to other cells in the network. Recent analysis has shown that waves are initiated at a single invariant site in the cell and propagated within the cell in a nonlinear and saltatory manner by regenerative amplification at specific predestined cellular sites. In order to gain insight into local cellular waves and wave collisions we have developed a mathematical model of cellular wave amplification loci. This model is in good agreement with experimental data which includes: ambient calcium gradients in resting cells, wave origination and local amplification and generation of local waves. As observed in experiments, the model also predicts that different locations in the cell can have different frequencies of oscillation. The amplification loci are thought to be specialized areas of the endoplasmic reticulum membrane containing a higher density or higher sensitivity of IP3 receptors. Our analysis suggests that the cellular loci act as weakly coupled oscillators each with its intrinsic latency and frequency of oscillation. Thus the appearance of the propagated calcium wave may be a reflection of these differences rather than an actual diffusional wave propagation.

Nonlinear propagation of agonist-induced cytoplasmic calcium waves in single astrocytes.

In astrocytes in primary culture, activation of neurotransmitter receptors results in intracellular calcium signals that propagate as waves across the cell. Similar agonist-induced calcium waves have been observed in astrocytes in organotypic cultures in response to synaptic activation. By using primary cultured astrocytes grown on glass coverslips, in conjunction with fluorescence microscopy we have analyzed agonist-induced Ca2+ wave initiation and propagation in individual cells. Both norepinephrine and glutamate elicited Ca2+ signals which were initiated focally and discretely in one region of the cell, from where the signals spread as waves along the entire length of the cell. Analysis of the wave propagation and the waveform revealed that the propagation was nonlinear with one or more focal loci in the cytoplasm where the wave was regeneratively amplified. These individual loci appear as discrete focal areas 7-15 microns in diameter and having intrinsic oscillatory properties that differ from each other. The wave initiation locus and the different amplification loci remained invariant in space during the course of the experiment and supported an identical spatiotemporal pattern of signalling in any given cell in response to multiple agonist applications and when stimulated with different agonists which are coupled via InsP3. Cytoplasmic Ca2+ concentration at rest was consistently higher (17 +/- 4 nM, mean +/- S.E.M.) in the wave initiation locus compared with the rest of the cytoplasm. The nonlinear propagation results from significant changes in signal rise times, amplitudes, and wave velocity in cellular regions of active loci. Analysis of serial slices across the cell revealed that the rise times and amplitudes of local signals were as much as three- to fourfold higher in the loci of amplification. A phenomenon of hierarchy in local amplitudes of the signal in the amplification loci was observed with the wave initiation locus having the smallest and the most distal locus having the largest amplitude. By this mechanism locally very high concentrations of Ca2+ are achieved in strategic locations in the cell in response to receptor activation. While the average wave velocity calculated over the length of the cell was 10-15 microns/s, in the active loci rates as high as 40 microns/s were measured. Wave velocity was fivefold lower in regions of the cell separating active loci. The differences in the intrinsic oscillatory periods give rise to local Ca2+ waves that show the properties of collision and annihilation. It is hypothesized that the wave front provokes regenerative Ca2+ release from specialized areas in the cell where the endoplasmic reticulum is endowed with higher density of InsP3 receptor channels.(ABSTRACT TRUNCATED AT 400 WORDS)

Principles of signal coding by the discharge pattern of a neuron population.

The principles of information coding by "rings" of stochastic dependence, formed by neuron populations, are described. Such a population was shown to be capable of existing only in strictly definite stochastic states, determined by a certain number of "rings" of stochastic dependence. A system consisting of a fixed number of neurons was shown to be able to code and transmit a number of different messages equal to the square of the number of stochastic states permitted for that system. The number of messages differing from each other either in the number of letters or their order in the word was equal to the number of permitted stochastic states, whereas the number of messages containing the same number of letters in the word was equal to the difference between the number of permitted stochastic states and the number of neurons in the system. The alphabet consists of two letters: A for assembling of the ring of stochastic dependence, and B for breaking of this ring, together with punctuation signs indicating neither assembling nor breaking (compared with the initial state) of stochastic dependence rings.