Two elementary models for the regulation of skeletal muscle contraction by calcium

It is shown by use of an extremely simple explicit two-state model that two basic ideas may be sufficient to understand at least qualitatively the sensitive activation of isometric muscle contraction by Ca2+. (a) Ca2+ binds much more strongly on troponin if myosin is already attached to actin. The steady state analogue of this is that the single rate constant (in the two-state model) for myosin attachment plus Pi release is much larger if Ca2+ is bound to troponin. (b) End-to-end tropomyosin interactions are responsible for positive cooperativity. Although these ideas seem to be sufficient, this of course does not mean that they are necessary. These same ingredients were used in two previous, more elaborate models for the cooperative equilibrium binding of myosin subfragment-1 on actin-tropomyosin-troponin, with and without Ca2+, and for a study of the steady state ATPase activity of the same system. Essentially as an appendix, the above-mentioned simple treatment is extended to a somewhat more realistic and complicated model of isometric contraction.