Tropomyosin dynamics during cardiac muscle contraction as governed by a multi-well energy landscape

The dynamic oscillations of tropomyosin molecules in the azimuthal direction over the surface of the actin filament during thin filament activation are studied here from an energy landscape perspective. A mathematical model based on principles from nonlinear dynamics and chaos theory is derived to describe these dynamical motions. In particular, an energy potential with three wells is proposed to govern the tropomyosin oscillations between the observed regulatory positions observed during muscle contraction, namely the blocked "B", closed "C" and open "M" states. Based on the variations in both the frequency and amplitude of the environmental (surrounding the thin filament system) driving tractions, such as the electrostatic, hydrophobic, and Ca²⁺-dependent forces, the tropomyosin movements are shown to be complex; they can change from being simple harmonic oscillations to being fully chaotic. Three cases (periodic, period-2, and chaotic patterns) are presented to showcase the different possible dynamic responses of tropomyosin sliding over the actin filament. A probability density function is used as a statistical measure to calculate the average residence time spanned out by the tropomyosin molecule when visiting each (B, C, M) equilibrium state. The results were found to depend strongly on the energy landscape profile and its featured barriers, which normally govern the transitions between the B-C-M states during striated muscle activation.