Cooperativity and switching within the three-state model of muscle regulation

Thin filament regulation is mediated by the presence of tropomyosin (Tm) and troponin (Tn) on the actin filament. Binding of Tm alone induces two states, closed and open (with the equilibrium between them defined by K(T)), which differ in their affinity for myosin subfragment 1 (S1). Cooperative switching between the states results in characteristic sigmoidal myosin S 1 binding curves. In the presence of Tn and absence of Ca²⁺, a third state, blocked, has previously been kinetically shown to be present, leading to the three state model of McKillop and Geeyes [(1993) Biophys. J. 65, 693-701]. We have measured equilibrium binding of S1 to phalloidin-stabilized pyrene - actin filaments by monitoring the pyrene fluorescence at 50 nM, a concentration 10-fold lower than previously possible. In combination with kinetic studies, we show that the data can be fitted to a modified version of the three-state model with an additional term allowing for a varying apparent cooperative unit size (n). Our results show that the apparent cooperative unit size (n) is dependent upon both the presence of Tn and of Ca²⁺. Also in the absence of Ca²⁺, the occupancy of the blocked state (defined by K(B)) is accompanied by a 2-3-fold reduction in K(T). These results are discussed in comparison to the Hill model [(1980) Proc. Natl. Acad. Sci. U.S.A. 77, 3186-3190] and a flexible model of thin filament regulation based upon that of Lehrer et al. [(1997) Biochemistry 36, 13449-13455].