Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding

TL;DR

This paper introduces a Chetaev instability framework to analyze and synthesize control strategies for protein unfolding, leveraging kinetostatic compliance models and nonlinear control theory, with applications to optical tweezer experiments.

Contribution

It formulates protein unfolding as a destabilizing control problem and develops Chetaev functions for analysis and control synthesis within this context.

Findings

Chetaev functions effectively analyze unfolding dynamics.

Control inputs derived from the Chetaev framework can elongate proteins.

Results align with optical tweezer unfolding experiments.

Abstract

Understanding the process of protein unfolding plays a crucial role in various applications such as design of folding-based protein engines. Using the well-established kinetostatic compliance (KCM)-based method for modeling of protein conformation dynamics and a recent nonlinear control theoretic approach to KCM-based protein folding, this paper formulates protein unfolding as a destabilizing control analysis/synthesis problem. In light of this formulation, it is shown that the Chetaev instability framework can be used to investigate the KCM-based unfolding dynamics. In particular, a Chetaev function for analysis of unfolding dynamics under the effect of optical tweezers and a class of control Chetaev functions for synthesizing control inputs that elongate protein strands from their folded conformations are presented. Based on the presented control Chetaev function, an unfolding input is derived from the Artstein-Sontag universal formula and the results are compared against optical tweezer-based unfolding.