Enzyme Kinetics and Molecular Motors as Action Compatibility: Variational Foundation of Biological Phase Dynamics

This work presents a variational reformulation of biochemical kinetics, in which molecular interactions are described as discrete action compatibility events, rather than continuous processes based solely on stochastic collisions. The construction is based on minimal hypotheses---cumulative action, independent parameterizations, and interferential dependence---without the introduction of new physical postulates.

It is shown that the effective interaction between systems occurs only when the action difference satisfies

$$\Delta S = 2\pi n\hbar,$$

which implies a characteristic temporal scale

$$\Delta t \sim \frac{\hbar}{|\dot{\Delta S}|}.$$

The analysis establishes a general relationship between action, phase, and frequency,

$$\omega = \frac{\dot{S}}{\hbar},$$

valid for massive and massless particles, consistent with special relativity and quantum field theory.

Applied to biology, the formalism allows interpreting enzymatic reactions, molecular motors, and pharmacological effects as action coherence phenomena. The work also presents testable experimental predictions in femtochemistry and single-molecule manipulation systems.

From an epistemological standpoint, this is not a new theory, but a structural consequence of fundamental variational principles when applied to composite systems.