Nonlinear processes of intracellular calcium signaling as a target for theinfluence of extremely low-frequency fields

Theoretical analysis of peculiarities of reception of weak extremely low-fr equency periodic signals by calcium-dependent intracellular regulatory syst ems was performed on the reduced "minimal" model for calcium oscillations s uggested by Goldbeter et al. (Proc. Natl. Acad. Sci. USA 87, 1461-1465, 199 0). The model considered the following calcium-dependent processes: the ris e in intracellular free calcium concentration ([Ca2+](i)) due to calcium io nophore A23187 action on a cell, activation of the Ca2+ entry through calci um channels in the plasma membrane by the initial rise in [Ca2+](i), and th e Ca2+ release from intracellular stores by the calcium-induced calcium rel ease 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 dem onstrated 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 s timulation of the cell. Such an effect was found only at high strengths of chemical stimulation and with a particular sequence of delivery of the chem ical and electromagnetic stimuli. An increase in noise intensity led to mag nification of the mean level of [Ca2+](i) in a narrow frequency range by th e mechanism of stochastic resonance. Under the influence of a modulating pe riodic signal, the gradual increase in strength of chemical stimulation ind uced a system transition from regular to chaotic behavior, and then to indu ced periodic oscillations. A boundary of the transition from chaotic to per iodic 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 conclu de that the narrow-band response of a system to an external electromagnetic signal is determined purely by nonlinear properties of the system.