Tropomyosin Dynamics during Cardiac Thin Filament Activation as Governed by a Multi-Well Energy Landscape

Abstract

The thin filament of cardiac muscle is composed of multi-subunits of machinery proteins, namely; actin, myosin, tropomyosin (Tm), and the troponin complex. Contraction depends upon highly nonlinear dynamical processes that rely on interactions between these components. During the thin filament activation process, Tm slides over the surface of actin filament. Its dynamics governs access of myosin head (S1) to binding sites on actin and, hence, it plays an important role in muscle contraction.Currently, there are two debating hypothetical mechanisms (sliding vs. rolling) proposed to describe Tm motions on actin's surface. In both scenarios, Tm undergoes distinct movements to uncover the S1-binding sites. These motions are characterized by three equilibrium positions, namely; the blocked position “B” (binding sites are blocked), closed position “C” (weak binding is permissible), and the open position “M” (strong binding of S1). Although, the three-state-model describes the final Tm's regulatory states, however, still the actual intrinsic mechanism by which Tm oscillates between these states are not yet fully understood.In this study, we propose a novel mathematical model that can explain Tm motions on actin's surface using principles from nonlinear dynamical systems, energy landscape, and chaotic theory. Tm oscillations between the three observed equilibrium states (B-C-M) are modelled using an energy potential with multiple wells. Each well is hypothesized to mimic one of the regulatory positions proposed by the three-state-model. The Jacobian and Lyapunov methods are then used to study the system's local and global stability. A bifurcation analysis using Melinkov function is used to find conditions (parameter values) that signify Tm transitions from simple harmonic oscillation to chaotic behaviors. Results demonstrate that Tm's dynamical motions on the surface of actin filament may exhibit periodic, aperiodic, and chaotic behaviors during muscle contraction.