arXiv subjects

Jeremy A. Owen

Publications and source records attributed to Jeremy A. Owen.

5 recordsLinked to original sources

arXiv2022

Thermodynamic bounds on ultrasensitivity in covalent switching

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch, in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants, and thereby reflect fundamental physical constraints on covalent switching.

q-bio.MN↗

arXiv2021

Size limits sensitivity in all kinetic schemes

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. This support bound sheds light on and unifies diverse sensitivity mechanisms, ranging from kinetic proofreading to a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, and represents a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation.

cond-mat.stat-mech↗

arXiv2020

Universal thermodynamic bounds on nonequilibrium response with biochemical applications

Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of response by observing spontaneous equilibrium fluctuations. In this spirit, we derive here a collection of equalities and inequalities valid arbitrarily far from equilibrium that constrain the response of nonequilibrium steady states in terms of the strength of nonequilibrium driving. Our work opens new avenues for characterizing nonequilibrium response. As illustrations, we show how our results rationalize the energetic requirements of two common biochemical motifs.

cond-mat.stat-mech↗

arXiv2019

Number of hidden states needed to physically implement a given conditional distribution

We consider the problem of how to construct a physical process over a finite state space $X$ that applies some desired conditional distribution $P$ to initial states to produce final states. This problem arises often in the thermodynamics of computation and nonequilibrium statistical physics more generally (e.g., when designing processes to implement some desired computation, feedback controller, or Maxwell demon). It was previously known that some conditional distributions cannot be implemented using any master equation that involves just the states in $X$. However, here we show that any conditional distribution $P$ can in fact be implemented---if additional "hidden" states not in $X$ are available. Moreover, we show that it is always possible to implement $P$ in a thermodynamically reversible manner. We then investigate a novel cost of the physical resources needed to implement a given distribution $P$: the minimal number of hidden states needed to do so. We calculate this cost exactly for the special case where $P$ represents a single-valued function, and provide an upper bound for the general case, in terms of the nonnegative rank of $P$. These results show that having access to one extra binary degree of freedom, thus doubling the total number of states, is sufficient to implement any $P$ with a master equation in a thermodynamically reversible way, if there are no constraints on the allowed form of the master equation. (Such constraints can greatly increase the minimal needed number of hidden states.) Our results also imply that for certain $P$ that can be implemented without hidden states, having hidden states permits an implementation that generates less heat.

cond-mat.stat-mech↗

arXiv2019

A space-time tradeoff for implementing a function with master equation dynamics

Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation, even approximately, which raises the question of how they can occur in the real world. Here we show how any function over some "visible" states can be implemented with master equation dynamics--if the dynamics exploits additional, "hidden" states at intermediate times. We also show that any master equation implementing a function can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what state-to-state transitions have nonzero probability. In many real-world situations there is a cost both for more hidden states and for more hidden timesteps. Accordingly, we derive a "space-time" tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given function.

cond-mat.stat-mech↗