A White Noise Approach To System Analysis In Demembranated Muscle Mechanics

Abstract

Measuring the force response to sinusoidal length perturbations in muscle enables calculating the viscoelastic properties of the tissue over a wide range of frequencies. Coupling these empirical results with complementary mathematical and computational models describes the kinetics of force-generating actomyosin cross-bridges. This sinusoidal analysis requires system linearity, a constraint confining length stimuli to very small amplitudes in demembranated (skinned) muscle preparations because larger length perturbations produce a non-linear force response. Therefore, it becomes difficult to examine cross-bridge cycling kinetics during length transients that are comparable with sarcomeric strains experienced during contraction in living muscles. Here we introduce a white noise method of system analysis that facilitates extracting the linear and non-linear components of the system response. Building upon Wiener theory, this method estimates the system response to a band-limited Gaussian white noise length stimulus through cross-correlation techniques (Lee-Schetzen approach). To examine and develop this approach, we computer simulated the response of a pre-defined system consisting of both linear and non-linear components and were able to estimate the expected linear response of the system. These simulations demonstrate the powerful utility of this technique to separate the linear and non-linear system responses in both the time or frequency domains. We also examined the experimental applicability of these methods using small strips of skinned muscle tissue, from which we estimated the linear and non-linear components of the system response in calcium-activated muscle. This linear component is consistent with the linear system response calculated from comparable measurements using sinusoidal length perturbation analysis. These computational and experimental methods provide a platform for characterizing cross-bridge cycling behavior, and permits distinguishing between linear and non-linear components of the complicated force responses following length transients associated with normal muscle contraction.