  Key insights in molecular biology, such as enzyme kinetics, protein allostery
and gene regulation emerged from quantitative analysis based on time-scale
separation, allowing internal complexity to be eliminated and resulting in the
well-known formulas of Michaelis-Menten, Monod-Wyman-Changeux and
Ackers-Johnson-Shea. In systems biology, steady-state analysis has yielded
eliminations that reveal emergent properties of multi-component networks. Here
we show that these analyses of nonlinear biochemical systems are consequences
of the same linear framework, consisting of a labelled, directed graph on which
a Laplacian dynamics is defined, whose steady states can be algorithmically
calculated. Analyses previously considered distinct are revealed as identical,
while new methods of analysis become feasible.
