Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics.

Abstract

We discuss the activation of thin-filament-regulated muscles by calcium ion in terms of a qualitative model based on nearest-neighbor lattice statistics. For the most part, the model takes into account only the essential features of the phenomenon-that there must be an interaction between calcium adsorption to troponin and crossbridge reaction with actin for calcium ion to activate contraction and that the relevant stationary states are nonequilibrium ones. Even so, the model predicts the following features which are seen experimentally but have generally not been considered in previous models: (i) the relative activations of stationary-state isometric force and ATPase are not equal; (ii) in general, neither activation of force nor that of ATPase is proportional to calcium adsorption to the activating sites; and (iii) the slopes of the relations between the activations and the logarithm of the calcium ion concentration generally depend on the necessary interaction between calcium ion adsorption and crossbridge reaction with actin. Thus, these relations show cooperative effects even if there is no interaction between calcium adsorption sites.There is significant understanding ofthe relations between the molecular events and their phenomenological manifestations in the activation of muscle contraction by calcium ion (1-4). Yet this understanding is not complete. Much of it is based on concepts from the theory of equilibrium systems and from other limiting cases, whereas contraction and its activation are distinctly nonequilibrium phenomena, even at the stationary state, and the limiting cases are so particular that they would not seem to obtain in muscle. We have recently begun to develop a model of cooperative systems with nonequilibrium stationary states (5), and in this paper we use this model to offer insights into these facets of the Ca2" activation process. We will attempt to show that some of the previous interpretations of this process have been based on untenable assumptions. We will also offer explanations for some puzzling aspects ofthe phenomenon, but we will not attempt to develop a complete quantitative model; our goal is qualitative rather then quantitative. We will consider only essential aspects of the phenomenon so that the model reflects its basic features. (Derivations of the approximations and details of other points are available upon request.) The model should thus be considered a paradigm for more accurate models. THE MODELWe picture the thin filament as a lattice of two classes of sites: those on troponin that adsorb Ca2" and the actins. Contraction is brought about by a cyclic reaction of projections of myosin from the thick filament, the crossbridges, with the actins and is powered by an ATPase located on the myosins (1-4). It is generally acknowledged that a crossbridge may exist in various states, both when it is reacting with an actin and when it is not reacting. However, because we are concerned with the activation of contraction, not the contraction itself, a two-state cros...

Identification of a Region of Troponin I Important in Signaling Cross-bridge-dependent Activation of Cardiac Myofilaments

“…The strong head to tail interaction between contiguous Tm molecules extends activation along the thin filament. There is also evidence that strongly bound crossbridges are able to increase the affinity of cTnC for Ca 2ϩ (10,11), an effect that is predicted on the basis of detailed balance (46). In view of our finding of an effect of TnI modification on cross-bridge-dependent activation in the absence of Ca 2ϩ and our finding that the Ala/His substitution in cTnI had no effect on Ca 2ϩ off-rate, we favor the hypothesis that modification of the N-terminal region of cTnI alters cross-bridge-dependent activation.…”

Modulation of Cardiac Troponin C Function by the Cardiac-Specific N-Terminus of Troponin I: Influence of PKA Phosphorylation and Involvement in Cardiomyopathies

“…11,42 Theoretical considerations advocate that "neither activation of force nor that of ATPase is proportional to Ca 2+ absorption to the activating sites," which underlines the complexity of Ca 2+ regulation in muscle. 43 At this point, we are unable to provide a mechanistic explanation for the differences in Ca 2+ off rates and filament Ca 2+ sensitivities in phosphorylated and unphosphorylated states and without the N-terminus of cTnI due to the complexity of the system.…”

Cooperative activation in cardiac muscle: impact of sarcomere length

“…The generalization of the Hill equation is an equilibrium formulation (37,38). Because muscle contracts under nonequilibrium conditions, however, the Hill equation may not provide an accurate description of cooperative activation in myocardium.…”

“…In striated muscle, initiation of muscle contraction involves complex cooperative and allosteric interactions along the thin filament (2,14,25,26). Cooperative activation of the myofilaments is manifest by a steeper relationship between activator Ca 2ϩ and developed force than would be predicted solely on the basis of the number of Ca 2ϩ binding sites that are present on the regulatory protein complexes of the thin filament (37,38).…”