Coupling between contraction rhythm and calcium oscillation in a cultured cardiac myocyte: Fluctuation behaviour and its modelling

Abstract

Isolated and cultured neonatal cardiac myocytes show self-sustaining cyclic contraction, and have the properties of a nonlinear oscillator. We study the dynamics of mechanical contraction and cellular free Ca²⁺ in a single myocyte for the purposes of gaining an insight into the way in which excitation and contraction processes are inter-related. The concentration of intracellular Ca²⁺ in the myocyte is also found to vary periodically associated with its rhythmic contraction. The Ca²⁺ dynamics maintains its self-oscillatory nature when the spontaneous contraction is abolished by pharmacological treatment using 2,3-butanedione monoxime. However, fluctuation analysis of the Ca²⁺ oscillation intervals reveals that there occurs a characteristic change in the fluctuation behaviour due to the suppression of contraction; the mean value and fluctuation magnitude of the oscillation intervals and the persistency of the fluctuation correlations at short timescales all increase after pharmacological treatment. We develop a new nonlinear model based on Bonhoeffer – van der Pol oscillators to elucidate the mechanisms behind the observed effects of cardiac contraction on the Ca²⁺ oscillation. The model is composed of three coupled nonlinear differential equations that can describe the dynamics of both excitation (cellular free Ca²⁺) and contraction. Almost all the experimental findings are successfully reproduced by adjusting a parameter in the model responsible for excitation – contraction coupling.

Keywords:

• Contraction rhythm
• calcium oscillation
• cardiac myocyte
• fluctuation
• Bonhoeffer – van der Pol model