Shortcuts in stochastic systems and control of biophysical processes

TL;DR

This paper introduces a graph-theoretic framework for applying counterdiabatic driving to stochastic biological systems, enabling targeted control of biochemical networks with limited control inputs, inspired by quantum control techniques.

Contribution

It adapts counterdiabatic driving from quantum systems to stochastic biological networks, allowing for targeted control with local or global interventions, and provides graphical criteria for control feasibility.

Findings

Control protocols resemble natural heat shock responses.

Framework successfully applied to genetic switches.

Local control is feasible with limited control points.

Abstract

The biochemical reaction networks that regulate living systems are all stochastic to varying degrees. The resulting randomness affects biological outcomes at multiple scales, from the functional states of single proteins in a cell to the evolutionary trajectory of whole populations. Controlling how the distribution of these outcomes changes over time -- via external interventions like time-varying concentrations of chemical species -- is a complex challenge. In this work, we show how counterdiabatic (CD) driving, first developed to control quantum systems, provides a versatile tool for steering biological processes. We develop a practical graph-theoretic framework for CD driving in discrete-state continuous-time Markov networks. Though CD driving is limited to target trajectories that are instantaneous stationary states, we show how to generalize the approach to allow for non-stationary targets and local control -- where only a subset of system states are targeted. The latter is particularly useful for biological implementations where there may be only a small number of available external control knobs, insufficient for global control. We derive simple graphical criteria for when local versus global control is possible. Finally, we illustrate the formalism with global control of a genetic regulatory switch and local control in chaperone-assisted protein folding. The derived control protocols in the chaperone system closely resemble natural control strategies seen in experimental measurements of heat shock response in yeast and E. coli.