Forma, Vol. 15 (No. 3), pp. 291-308, 2000
Original Paper

Complex Dynamical Response of Chemical and Biochemical Excitable Systems to Periodic Stimuli

Vladislav Nevoral, Michal Vosla, Igor Schreiber, Pavel Hasal and Milo Marek

Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology, Prague, CZ-166 28 Prague 6, Czech Republic

(Received April 19, 2000; Accepted May 19, 2000)

Keywords: Coupled Cells, Excitability, Chaos, Intercellular Signalling, Electric Field Effects

Abstract. Excitable properties of selected biochemical reactions in one compartment subject to external periodic stimuli, the spreading of signals elicited by periodic stimulation in a linear array of compartments and the spreading of pulse wave trains in a continuous medium are studied. A method of calculating a threshold set and a criterion for its disappearance are formulated. Two kinds of excitability distinguished by either direct or indirect initiation of the activatory process are discussed. The response of the one- and two-compartment systems to periodic perturbations is studied upon varying a bifurcation parameter. Transitions from periodicity to quasiperiodicity and to chaos are observed. The problem of intercellular signalling is addressed by observation of an excitable pulse propagation in reaction-diffusion media with an oscillatory pacemaker entrapped within the excitable domain. The signalling patterns are analysed by proper orthogonal decomposition based techniques and effects of electric field applied to the system are examined.

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