Turning the Azimuthal Motions of Adjacent Tropomyosins into a Coupled N-body Problem in a Brownian Model of Cardiac Thin Filament Activation

Abstract

During thin filament activation process, tropomyosin (Tm) oscillates over the surface of actin filament in the azimuthal direction to regulate the access of myosin head to actin binding sites. This motion is characterized by the existence of three distinct equilibrium positions, namely; blocked (B), closed (C), and open (M) regulatory states. The exact dynamics and energy landscape that governs Tm motions between these conformational states is not yet fully understood. In this study, we developed a Brownian flashing ratchet model to mathematically describe Tm motions over the surface of actin filament. The model approximates the Tm flexible chain by a system of discrete and coupled Brownian bodies. In other words, the thin filament regulatory units (RUs) are prescribed by a set of N-body stochastic ODEs that govern the azimuthal motion of adjacent tropomyosins. The model explicitly accounts for spatial interactions among nearest neighbor RUs, which were thought to appear from structural coupling of adjacent tropomyosins. This coupling is achieved by assigning each Brownian Tm-body with a local multi-well potential. The energetic barrier, asymmetry, and bias of each individual energy landscape are hypothesized to be influenced by the Tm status of its neighbors. This coupling approach is anticipated to be sufficient to produce observed cooperativity in both force-Ca2+ relationship and twitch dynamic. The present analysis is expected to perform better than many of current phenomenological myofilament models which were mostly derived based on the classical mean-field approximation. Additionally, this analysis draws a more detailed molecular connection between Tm dynamics and sarcomeric twitch production. Therefore, the Brownian ratchet modeling methodology of Tm motions during thin filament activation may offer an enhanced mechanistic approach to describe cardiac muscle contraction.