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Reproduction of the reactions of biological neurons as a result of modeling structural and functional properties membrane and synaptic structural organization


A.V. Bakhshiev, S.P. Romanov

Modeling of information processes in the nervous system requires matching play as the structure of connections between neurons in the network, and the principles of transformation of information (pulse) flow of each neuron. Known mathematical model of a neuron or did not possess the necessary properties for this task, or require an individual approach for modeling of each individual neuron – compiling equations to describe the dendrite, synapse, preparation of constraint equations, determination of model parameters, etc. The most important is the development of a model neuron function and the set of reactions which will be determined by the structure of its dendritic and synaptic apparatus, the change in the structure should not affect the mathematical description of any modification of the parameters describing its elements. The neural network of these neurons would be an integrated model of the membrane of nerve tissue, interacting through a model of chemical or electrical synapses, or by tonic spread to parts of the membrane potential. The paper proposed a system of differential equations describing the dynamics of transformation of pulsed flows in a natural neuron. The model does not require adjustment of internal parameters in the operation. Properties of the transformation of information a neuron are determined by a modification of the structural organization of the membrane and synaptic apparatus, and formed the current active connections in the network. It was developed by the software implementation of the proposed neuron model and neural networks. The advantage of the model is to describe the interaction of neurons with arbitrary structure of dendritic and synaptic apparatus. It is possible the modification of the models of a neuron's functional elements (membrane, synapse, low-threshold zone) while maintaining the interface agreements on the type and range of input-output data of these elements, or developing of new agreements. A series of numerical experiments showed the possibility and methodology descriptions in terms of the structure of membrane and synaptic apparatus of different classes of reactions of neurons to external stimulation.

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