Shortcuts in stochastic systems and control of biophysical processes

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 timevarying 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. We illustrate the formalism with examples from gene regulation and chaperone-assisted protein folding, demonstrating the possibility that nature can exploit CD driving to accelerate response to sudden environmental changes. We generalize the method to continuum Fokker-Planck models, and apply it to study AFM single-molecule pulling experiments in regimes where the typical assumption of adiabaticity breaks down, as well as an evolutionary model with competing genetic variants subject to time-varying selective pressures. The AFM analysis shows how CD driving can eliminate non-equilibrium artifacts due to large force ramps in such experiments, allowing accurate estimation of biomolecular properties.

Adaptive Bayesian inference of Markov transition rates

“…These extensions could prove useful for inferring transition rates in stochastic systems with variable rates, as found in chemical kinetic systems modelled by M/G/1 queueing processes [40] and stochastic implementations of Hodgkin–Huxley neuronal dynamics with voltage-dependent transition rates [41,42]. Our adaptive inference algorithm can also be adapted to more complex chain structures, such as those used in age-structured epidemiological models [43] and models for chaperone-assisted protein folding [44]. The only hard constraints to our approach are that the possible transition functions be fully specified and the chain itself be Markovian.…”