NONLINEAR PROCESSES OF INTRACELLULAR CALCIUM SIGNALING AS A TARGET FOR THE INFLUENCE OF EXTREMELY LOW-FREQUENCY FIELDS

Abstract

Theoretical analysis of peculiarities of reception of weak extremely low-frequency periodic signals by calcium-dependent intracellular regulatory systems was performed on the reduced “minimal” model for calcium oscillations suggested by Goldbeter et al. (Proc. Natl. Acad. Sci. USA 87, 1461–1465, 1990). The model considered the following calcium-dependent processes: the rise in intracellular free calcium concentration ([Ca²⁺]_i) due to calcium ionophore A23187 action on a cell, activation of the Ca²⁺ entry through calcium channels in the plasma membrane by the initial rise in [Ca²⁺]_i, and the Ca²⁺ release from intracellular stores by the calcium-induced calcium release mechanism. Calcium channels of plasma membrane were chosen as a target for the modulating signal and an additive noise influence in the model. An increase in [Ca²⁺]_i under the influence of the modulating signal was demonstrated to depend not only on the amplitude and frequency of this signal, but also on the phase of the signal with respect to a momentary chemical stimulation of the cell. Such an effect was found only at high strengths of chemical stimulation and with a particular sequence of delivery of the chemical and electromagnetic stimuli. An increase in noise intensity led to magnification of the mean level of [Ca²⁺]_i in a narrow frequency range by the mechanism of stochastic resonance. Under the influence of a modulating periodic signal, the gradual increase in strength of chemical stimulation induced a system transition from regular to chaotic behavior, and then to induced periodic oscillations. A boundary of the transition from chaotic to periodic oscillations corresponded to a “threshold” of sensitivity of calcium-dependent intracellular signaling systems on [Ca²⁺]_i to the influence of the modulating signal. Results of the theoretical analysis led us to conclude that the narrow-band response of a system to an external electromagnetic signal is determined purely by nonlinear properties of the system.