  With the formal construction of a thermodynamic spring, I describe the
mechanics, energetics, entropy, and kinetics of a binary mechanical model
system. A protein that transitions between two metastable structural states
behaves as a molecular switch, and an ensemble of molecular switches that
displace compliant elements equilibrated with a system force constitutes a
binary mechanical model system. In biological systems, many protein switches
equilibrate with cellular forces, yet the statistical mechanical problem
relevant to this system has remained unsolved. A binary mechanical model system
establishes a limited number of macroscopic parameters into which structural
and mechanistic details must be fit. Novel advances include a non-equilibrium
kinetic and energetic equivalence; scalable limits on kinetics and energetics;
and entropic effects on kinetics and mechanics. The model unifies disparate
models of molecular motor mechanochemistry, accounts for the mechanical
performance of muscle in both transient and steady states, and provides a new
perspective on biomechanics with a focus here on how muscle and molecular motor
ensembles work.
