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Biological sensors rely on the temporal dynamics of ligand concentration for signaling. The sensory performance is bounded by the distinguishability between the sensory state transition dynamics under different environmental protocols. This work presents a comprehensive theory to characterize arbitrary transient sensory dynamics of biological sensors. Here the sensory performance is quantified by the Kullback-Leibler (KL) divergence between the probability distributions of the sensor's stochastic paths. We introduce a novel benchmark to assess a sensor's transient sensory performance arbitrarily far from equilibrium. We identify a counterintuitive phenomenon in multistate sensors: while an initial exposure to high ligand concentration may hinder a sensor's sensitivity towards a future concentration up-shift, certain sensors may show a boost in sensitivity if the initial high concentration exposure is followed by a transient resetting at a low concentration environment. The boosted performance exceeds that of a sensor starting from an initially low concentration environment. This effect, reminiscent of a drug withdrawal effect, can be explained by the Markovian dynamics of the multistate sensor, similar to the Markovian Mpemba effect. Moreover, an exhaustive machine learning study of four-state sensors reveals a tight connection between the sensor's performance and the structure of the Markovian graph of its states. Published by the American Physical Society2024 

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system’s dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to time-dependent stochastic systems. Based on this analysis, we revisit several time-dependent kinetic Monte Carlo (KMC) algorithms designed for systems under open-loop-control protocols. Our analysis provides a unified alternative proof to these algorithms, summarized into a pedagogical tutorial. Moreover, with the trajectory probability analysis, we present a novel feedback-controlled KMC algorithm that accurately captures the dynamics systems controlled by an external signal based on the measurements of the system’s state. Our method correctly captures the system dynamics and avoids the artificial Zeno effect that arises from incorrectly applying the direct Gillespie algorithm to feedback-controlled systems. This work provides a unified perspective on existing open-loop-control KMC algorithms and also offers a powerful and accurate tool for simulating stochastic systems with feedback control. 

The ability to distinguish between stochastic systems based on their trajectories is crucial in thermodynamics, chemistry, and biophysics. The Kullback–Leibler (KL) divergence, DKLAB(0,τ), quantifies the distinguishability between the two ensembles of length-τ trajectories from Markov processes A and B. However, evaluating DKLAB(0,τ) from histograms of trajectories faces sufficient sampling difficulties, and no theory explicitly reveals what dynamical features contribute to the distinguishability. This work provides a general formula that decomposes DKLAB(0,τ) in space and time for any Markov processes, arbitrarily far from equilibrium or steady state. It circumvents the sampling difficulty of evaluating DKLAB(0,τ). Furthermore, it explicitly connects trajectory KL divergence with individual transition events and their waiting time statistics. The results provide insights into understanding distinguishability between Markov processes, leading to new theoretical frameworks for designing biological sensors and optimizing signal transduction. 

At stationary environmental conditions, a catalyst’s reaction kinetics may be restricted by its available designs and thermodynamic laws. Thus, its stationary performances may experience practical or theoretical restraints (e.g., catalysts cannot invert the spontaneous direction of a chemical reaction). However, many works have reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric nonequilibrium theory to explain anomalous catalytic behaviors driven by rapidly oscillating environments where stationary-environment restraints are broken. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a single free energy landscape cannot describe catalytic kinetics at various environmental conditions, we propose a novel control-conjugate landscape to encode the reaction kinetics over a range of control parameters λ, inspired by the Arrhenius form. The control-conjugate landscape significantly simplifies the design principle applicable to large-amplitude environmental oscillations. 

Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, nonequilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where preheating a system allows it to cool faster. We present nonequilibrium hasty shortcuts—externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term “hasty” indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using timescale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of nonequilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes. 

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks.