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Inferring underlying microscopic dynamics from low-dimensional experimental signals is a central problem in physics, chemistry, and biology. As a trade-off between molecular complexity and the low-dimensional nature of experimental data, mesoscopic descriptions such as the Markovian master equation are commonly used. The states in such descriptions usually include multiple microscopic states, and the ensuing coarse-grained dynamics are generally non-Markovian. It is frequently assumed that such dynamics can nevertheless be described as a Markov process because of the timescale separation between slow transitions from one observed coarse state to another and the fast interconversion within such states. Here, we use a simple model of a molecular motor with unobserved internal states to highlight that (1) dissipation estimated from the observed coarse dynamics may significantly underestimate microscopic dissipation even in the presence of timescale separation and even when mesoscopic states do not contain dissipative cycles and (2) timescale separation is not necessarily required for the Markov approximation to give the exact entropy production, provided that certain constraints on the microscopic rates are satisfied. When the Markov approximation is inadequate, we discuss whether including memory effects can improve the estimate. Surprisingly, when we do so in a “model-free” way by computing the Kullback–Leibler divergence between the observed probability distributions of forward trajectories and their time reverses, this leads to poorer estimates of entropy production. Finally, we argue that alternative approaches, such as hidden Markov models, may uncover the dissipative nature of the microscopic dynamics even when the observed coarse trajectories are completely time-reversible. 

IntroductionT-cell receptors (TCRs) play a critical role in the immune response by recognizing specific ligand peptides presented by major histocompatibility complex (MHC) molecules. Accurate prediction of peptide binding to TCRs is essential for advancing immunotherapy, vaccine design, and understanding mechanisms of autoimmune disorders. MethodsThis study presents a theoretical approach that explores the impact of feature selection techniques on enhancing the predictive accuracy of peptide binding models tailored for specific TCRs. To evaluate our approach across different TCR systems, we utilized a dataset that includes peptide libraries tested against three distinct murine TCRs. A broad range of physicochemical properties, including amino acid composition, dipeptide composition, and tripeptide features, were integrated into the machine learning-based feature selection framework to identify key properties contributing to binding affinity. ResultsOur analysis reveals that leveraging optimized feature subsets not only simplifies the model complexity but also enhances predictive performance, enabling more precise identification of TCR peptide interactions. The results of our feature selection method are consistent with findings from hybrid approaches that utilize both sequence and structural data as input as well as experimental data. DiscussionOur theoretical approach highlights the role of feature selection in peptide-TCR interactions, providing a quantitative tool for uncovering the molecular mechanisms of the T-cell response and assisting in the design of more advanced targeted therapeutics. 

Recent experiments indicated that nanoparticles (NPs) might efficiently catalyze multiple chemical reactions, frequently exhibiting new phenomena. One of those surprising observations is intra-particle catalytic cooperativity, when the reactions at one active site can stimulate the reactions at spatially distant sites. Theoretical explanations of these phenomena have been presented, pointing out the important role of charged hole dynamics. However, the crucial feature of nanoparticles that can undergo dynamic structural surface rearrangements, potentially affecting the catalytic properties, has not yet been accounted for. We present a theoretical study of the effect of dynamic restructuring in NPs on intra-particle catalytic cooperativity. It is done by extending the original static discrete-state stochastic framework that quantitatively evaluates the catalytic communications. The dynamic restructuring is modeled as stochastic transitions between states with different dynamic properties of charged holes. Our analysis reveals that the communication times always decrease with increasing rates of dynamic restructuring, while the communication lengths exhibit a dynamic behavior that depends on how dynamic fluctuations affect migration and death rates of charged holes. Computer simulations fully support theoretical predictions. These findings provide important insights into the microscopic mechanisms of catalysis on single NPs, suggesting specific routes to rationally design more efficient catalytic systems.