Hysteresis in cross-bridge models of muscle

Abstract

Myosin molecules are involved in a wide range of transport and contractile activities in cells. A single myosin head functions through its ATPase reaction as a force generator and as a mechanosensor, and when two or more myosin heads work together in moving along an actin filament, the interplay between these mechanisms contributes to collective myosin behaviors. For example, the interplay between force-generating and force-sensing mechanisms coordinates the two heads of a myosin V molecule in its hand-over-hand processive stepping along an actin filament. In muscle, it contributes to the Fenn effect and smooth muscle latch. In both examples, a key force-sensing mechanism is the regulation of ADP release via interhead forces that are generated upon actin-myosin binding. Here we present a model describing the mechanism of allosteric regulation of ADP release from myosin heads as a change, DDG ÀD , in the standard free energy for ADP release that results from the work, Dm mech , performed by that myosin head upon ADP release, or DDG ÀD = Dm mech . We show that this model is consistent with previous measurements for strain-dependent kinetics of ADP release in both myosin V and muscle myosin II. The model makes explicit the energetic cost of accelerating ADP release, showing that acceleration of ADP release during myosin V processivity requires B4 kT of energy whereas the energetic cost for accelerating ADP release in a myosin II-based actin motility assay is only B0.4 kT. The model also predicts that the acceleration of ADP release involves a dissipation of interhead forces. To test this prediction, we use an in vitro motility assay to show that the acceleration of ADP release from both smooth and skeletal muscle myosin II correlates with a decrease in interhead force. Our analyses provide clear energetic constraints for models of the allosteric regulation of ADP release and provide novel, testable insights into muscle and myosin V function.

Mechanisms of residual force enhancement in skeletal muscle: insights from experiments and mathematical models

“…The presence of sarcomere length heterogeneity in general (separate from the extreme case of popping) has long been suggested as a contributor to residual force enhancement (Julian and Morgan 1979a), and has been the focus of numerous computational studies (Stoecker et al 2009; Telley and Denoth 2007; Telley et al 2003; Walcott and Sun 2009; Givli 2010), including our own (Campbell et al 2011). While most of the experiments focusing on heterogeneity have considered lengths of sarcomeres, most of these computational models, including our own, have analyzed the behavior of linked half-sarcomeres.…”

“…Several types of half-sarcomere variability are used in the models, including variation in the number of myosin crossbridges (or contractile force) per half-sarcomere (Telley et al 2003; Campbell et al 2011), perturbations to initial velocity (Walcott and Sun 2009), and variation in passive tension (Campbell et al 2011). It is interesting to note that in each case these models exhibit residual force enhancement, regardless of the particular details of their implementation (Telley et al 2003; Walcott and Sun 2009; Givli 2010; Campbell et al 2011). The common thread in each, aside from non-uniform half-sarcomere properties, is the presence of a history-dependent mechanical component in the model.…”

A mechanical model of actin stress fiber formation and substrate elasticity sensing in adherent cells

“…We model these proteins as point masses on zero-length linear springs. Using Kramers' theory, simple expressions for the detachment rate as a function of strain k d ðxÞ and the attachment rate probability density ρ a ðxÞ may be found (see (16,17) and SI Text).…”

Muscle contraction and the elasticity-mediated crosstalk effect

“…In 1971, a widely accepted four-state scheme for the mechanochemical cycle of myosin II was introduced by Lymn and Taylor [11]. More recently, Duke [12], and later others [13][14][15][16][17][18], came up with models that integrated the Lymn-Taylor scheme into the crossbridge model. Duke's model (like Huxley's) treats the motor heads as elastic elements with strain-dependent on and off rates.…”