Meeting Abstract
During muscle force production, each discrete neural spike results in a large fast efflux of calcium ions from the sarcoplasmic reticulum (SR) into the myoflibrillar space, which is then more slowly pumped back into the SR by a Calcium pump. A sequence of neural spikes results in an oscillatory calcium concentration in the myobrillar space. Why are muscles are excited by an oscillatory calcium signal when a more gradually changing calcium signal would likely do as well (and even might provide more constant muscle forces)? Here, I provide an adaptationist argument, suggesting that an oscillatory calcium signal is better because it reduces the energy expenditure of the calcium pump in the sarcoplasmic reticulum. We construct a simple mathematical model of the dynamics and energetics of calcium pumping, consisting of two `chambers’: (1) the SR with an initially high concentration of Ca2+ and (2) the myofibrillar space with a lower initial calcium concentration. Calcium in the myofibrillar space eventually leads to actomyosin interaction, modeled here through some low order dynamics, a simplified reaction network — the key necessary feature being that the dynamics are such that the force fluctuations are much smoother than the calcium fluctuations. Energy is needed for calcium pump and myofibrillar interaction. Using numerical optimization, we compute the energy optimal strategy to maintain an average muscle force and find that this optimal strategy is to use a sequence of large effluxes (neural spikes) combined with longer periods where the calcium is pumped back more slowly – similar to what is observed in nature. In addition, this model predicts, as observed, that a higher average force requires a higher frequency sequence of calcium effluxes from the SR (increased spike rate).
