Conservative Motion Theory – Bio IV Conservative Folding Flows and the Design of Functional Proteins

Abstract

We construct a unified CMT framework for the prediction and design of functional proteins.Protein folding is modeled as a reflection–positive conservative flow on the configurationmanifold, where sequence data define the generator of the flow. A key result is that theFredholm determinant of the folding kernel possesses persistent simple zeros correspondingto stable folded states. We show that any desired catalytic activity or binding geometry canbe realized by constructing kernels that enforce the appropriate zero structure. This yieldsa mathematically rigorous protein design principle based solely on conservative dynamics,independently of heuristics or empirical potentials.