# Modal Geometry Governs Proteoform Dynamics

## TL;DR

Modal Geometric Field (MGF) Theory provides a universal framework that links proteoform shape, energy, and entropy through geometric curvature, explaining their dynamic evolution and complex behaviors.

## Contribution

This work introduces MGF Theory, a novel geometric approach that unifies proteoform dynamics with curvature and modal transitions, revealing fundamental governing principles.

## Key findings

- Curvature governs proteoform transitions and energy barriers.
- Entropy emerges from curvature transport and modal interactions.
- The framework explains oscillations between order and chaos in proteoform dynamics.

## Abstract

The fundamental laws governing proteoform dynamics have yet to be formulated. As a result, it is unclear how a specific proteoform, a distinct molecular variant of a protein, dynamically shapes its own future by evolving into new modes that exist only in potential until realised. Here, Modal Geometric Field (MGF) Theory couples real and abstract proteoform transitions through four axioms. Axioms 1 to 3 (invariant) dictate that only first-order transitions occur on the discrete, volume-invariant, non symplectic modal manifold. Axiom 4 (mutable) projects the occupancy and shape of a real, instantiated molecule into the modal manifold, generating occupancy-induced curvature. By coupling what is real to what is abstract, curvature, which is always conserved, governs proteoform dynamics by dictating the least-action modal transition. Because curvature distribution renders activation energy relative, barriers are mutable, and entropy emerges inevitably from curvature transport. This unification of energy, entropy, and curvature yields hysteresis, path dependence, fractal self similarity, and trajectories that oscillate between order and chaos. As a scale invariant and universal framework, MGF Theory reveals how modal geometry governs proteoform dynamics

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Source: https://tomesphere.com/paper/2508.20004