Controlling stiffness & dynamics: insights into muscle behavior from nonlinear springs and confined semiflexible polymers

We present findings from our theoretical studies on the behavior of simple mechanical oscillators with nonlinear stiffness, in conjunction with our investigation of semiflexible polymer chains, to obtain potential insights into the behavior of biological tissue-like muscles. We try to understand the very complicated problem of describing living tissue in physiological conditions by modelling the system analogously to wormlike, semiflexible polyelectrolyte chains under confinement and then correlating the effects of various parameters with the rich, dynamical behaviour shown in our mechanical system. By employing a double-screening field-theoretical approach alongside a Kratky-Porod wormlike chain model, we model the behavior of a semiflexible polyelectrolyte chain. The impact of confinement on the chain's flexibility is examined, with the Odijk deflection length introduced as an additional length scale governing its behavior. Molecular weight, salt, and monomer concentrations are critical parameters that influence chain behavior, impacting both conformational and dynamic properties. We consider how these factors affect persistence length and chain flexibility, aiming to develop a broader understanding within biologically relevant contexts, wherein one may naturally tune system behaviour to preferred dynamical regimes and desired responses.