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The paper describes a detailed mechanism-based model of a tripartite synapse consisting of P-and R-neurons together with a giant glial cell in the ganglia of the medical leech (Hirudo medicinalis), which is a useful object for experimental studies in situ. We describe the two main pathways of the glial cell activation: (1) via IP 3 production and Ca 2+ release from the endoplasmic reticulum and (2) channels. We suggest that the second pathway is the more significant for establishing the positive feedback in glutamate release that is critical for the self-sustained activity of the postsynaptic neuron. This mechanism differs from the mechanisms of the astrocyte-neuron signaling previously reported.

The paper applies biologically plausible models to investigate how noise input to small ensembles of neurons, coupled via the extracellular potassium concentration, can influence their firing patterns. Using the noise intensity and the volume of the extracellular space as control parameters, we show that potassium induced depolarization underlies the formation of noise-induced patterns such as delayed firing and synchronization. These phenomena are associated with the appearance of new time scales in the distribution of interspike intervals that may be significant for the spatio-temporal oscillations in neuronal ensembles.

Using a relatively simple model we examine how variations of the extracellular potassium concentration can give rise to synchronization of two nearby pacemaker cells. With the volume of the extracellular space and the rate of potassium diffusion as control parameters, the dual nature of this resource-mediated coupling is found to be responsible for the coexistence of competing patterns of in- and anti-phase synchronization between identical cells. Cell heterogeneity produces significant modifications of the dynamical regimes in the control parameter plane. By comparison with conventional gap junctional coupling, potassium signaling gives rise to considerable changes of the cellular response to external stimuli.

The constantly changing labor market requires the formation of specialists with a desire for self-improvement, capable of moving from one type of activity to another, perhaps not related to the previous one. This task can be called a priority in the field of professional education, which dictates its relevance for mathematics education. When setting the formulated problem and solving it, special attention should be paid to recognizing the importance of the formation and development of the educational potential of the creative activity of students. The article presents an analysis of the possibilities of a continuous education system, put forward theoretical provisions and pedagogical conditions for the effective formation of research skills of students within this system. The characteristic of the structural-content model of the formation of the research competence of future teachers (or specialists of other professions requiring the formation of research competencies) in the system of three-level education is given on the example of studying one of the directions of discrete mathematics.