Models for ion channel gating with compliant states.

In a previous letter to the editor, Sachs and Lecar (1991) described a model for gating of mechanosensitive ion channels. This treatment draws on our "gating-spring" model for gating, which involves an elastic element that conveys force to the channel (Corey and Hudspeth, 1983; Howard and Hudspeth, 1988) and extends it to deal with the elasticity of the channel protein itself. The gating-spring model predicts that the difference in energy between the open and closed states of the channel depends linearly on applied force, whereas quadratic terms arise if the open and closed states of the channel do not have the same elasticity. Their letter provides a valuable reconciliation of divergent theories (Corey and Hudspeth, 1983; Howard and Hudspeth, 1988; Guhary and Sachs, 1984; Morris, 1990), but it stops short of estimating the relative importance of the linear and quadratic terms. In this letter, we show that the theoretical assumptions made by Sachs and Lecar imply that the quadratic term is small and probably negligible. An even more general model has recently been published by Lecar and Morris (1993), in which large quadratic terms are at least theoretically possible. Here we point out published experimental evidence that indicates that the quadratic term is small. We conclude that the simple gating-spring model remains an adequate description of the gating of mechanically sensitive ion channels. To reiterate the two theories, we refer to Figs. 1 and 2 (cf. also Fig. 1 of Sachs and Lecar). In a simple two-state theory, we suppose that there is a closed state and an open state (Fig. 1 A). If a constant force f is applied along the reaction coordinate (Fig. 2), then the energy Uof the channel in a state i is equal to the integral of the force, from an arbitrary zero to the position xi of that state on the reaction coordinate