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 nonstationary targets and local control—where only a subset of system states is 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.
- Received 26 June 2021
- Revised 6 March 2022
- Accepted 11 April 2022
DOI:https://doi.org/10.1103/PhysRevX.12.021048
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Many biological systems are inherently stochastic, governed by random microscopic interactions. Trying to precisely control such systems, by manipulating their environmental conditions, is thus quite challenging. But control is nevertheless an essential component of natural regulation mechanisms and many experimental techniques in biophysics. This problem has close mathematical parallels to randomness in quantum systems, where there has been a recent surge of interest to develop quantum control methods, motivated by technologies like quantum computing. Our work shows how one of these methods, called counterdiabatic driving, can be translated into the classical realm of biophysics.
The goal is to calculate a driving protocol—a prescription for how to vary external parameters, such as chemical concentrations or mechanical forces—that will steer the probability distribution of system states along a chosen target trajectory. We present a practical, universal algorithm for calculating these protocols that is based on the graph structure of the network of biochemical reactions that describe the system. The approach can be used at any biological scale, from single proteins to the evolution of whole populations of organisms. We illustrate how control can be achieved in two natural settings: the on-off transitions of a genetic switch and the rapid cellular response to misfolded proteins caused by a sudden temperature rise. We also generalize the approach to the case where the degree of control is limited, and we can drive only a subset of states in the system.
Future directions include testing our theory in biophysical experiments and developing statistical learning methods to generalize this type of control to systems where the underlying parameters are poorly characterized.
