Many Will Enter, Few Will Win: Cost and Sensitivity of Exploratory Dynamics

TL;DR

This paper explores how biomolecular systems use exploratory dynamics and resetting cycles to achieve high sensitivity to parameter changes, balancing energetic costs with functional benefits in processes like translation and microtubule regulation.

Contribution

It introduces minimalist models and analytical approaches to quantify the trade-offs between energy expenditure and sensitivity in biomolecular exploratory processes.

Findings

Enhanced sensitivity achieved with limited thermodynamic driving.

Resetting cycles improve substrate discrimination and length control.

Modest energy costs enable qualitative transitions to sensitive states.

Abstract

A variety of biomolecular systems rely on exploratory dynamics to reach target locations or states within a cell. Without a mechanism to remotely sense and move directly towards a target, the system must sample over many paths, often including resetting transitions back to the origin. We investigate how exploratory dynamics can confer an important functional benefit: the ability to respond to small changes in parameters with large shifts in the steady-state behavior. However, such enhanced sensitivity comes at a cost: resetting cycles require energy dissipation in order to push the system out of its equilibrium steady state. We focus on minimalist models for two concrete examples: translational proofreading in the ribosome and microtubule length control via dynamic instability to illustrate the trade-offs between energetic cost and sensitivity. In the former, a driven hydrolysis step enhances the ability to distinguish between substrates and decoys with small binding energy differences. In the latter, resetting cycles enable catalytic control, with the steady-state length distribution modulated by sub-stoichiometric concentrations of a reusable catalyst. Synthesizing past models of these well-studied systems, we show how path-counting and circuit mapping approaches can be used to address fundamental questions such as the number of futile cycles inherent in translation and the steady-state length distribution of a dynamically unstable polymer. In both cases, a limited amount of thermodynamic driving is sufficient to yield a qualitative transition to a system with enhanced sensitivity, enabling accurate discrimination and catalytic control at a modest energetic cost.