A thermodynamic optimization analysis of a possible relation between the parameters that determine the energetics of muscle contraction in steady state
M. Santillan, A thermodynamic optimization analysis of a possible relation between the parameters that determine the energetics of muscle contraction in steady state, J THEOR BIO, 199(1), 1999, pp. 105-112
Given the phenomenological relations for muscle's steady-state contraction
and proper definitions of power p and efficiency eta, the behavior of these
quantities is analysed in terms of the parameters that determine the energ
etics of the muscle, here denoted by s(o) and alpha. s(o) is proportional t
o the so-called maintenance heat, while alpha is the parameter that determi
nes the curvature of the Hill's force-velocity curve. The dependence of the
muscle's power and efficiency, averaged over the whole range of force the
muscle can exert, on the parameters s(o) and alpha is studied. The average
power p(avg) is a function only of alpha, and is a growing function that ap
proaches 1/6 asymptotically as alpha goes to infinity. The average efficien
cy eta(avg) is a function of both alpha and s(o). With the value of s(o) fi
xed, the graph of the function eta(avg)(s(o), alpha) is a convex curve with
a single maximum. The value and the position of this maximum point both de
pend on s(o). In the limit alpha --> 0, s(o) --> 0, eta(avg) tends to 1. Th
e points (s(o), alpha(m)(s(o))), with alpha(m)(s(o)) the value of alpha tha
t maximizes eta(avg) for a given s(o), are fitted by the curve alpha = s(o1
/2). This relation was experimentally found by A. V. Hill in his early stud
ies of muscle energetics. Other experimental data are found to qualitativel
y satisfy the same relation. Although some dynamical microscopic models for
muscle contraction, based upon Huxley's cross-bridge model, show that the
same kinetic parameters control both the maintenance heat (s(o)) and the mu
scle's power output (alpha), we suggest that the exact relation between the
m has been reached due to the evolutive stresses that made individuals with
equally powerful and more efficient muscles more suitable to reproduce. (C
) 1999 Academic Press.