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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. 

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. 

The ability to accurately predict protein–protein interactions is critically important for understanding major cellular processes. However, current experimental and computational approaches for identifying them are technically very challenging and still have limited success. We propose a new computational method for predicting protein–protein interactions using only primary sequence information. It utilizes the concept of physicochemical similarity to determine which interactions will most likely occur. In our approach, the physicochemical features of proteins are extracted using bioinformatics tools for different organisms. Then they are utilized in a machine-learning method to identify successful protein–protein interactions via correlation analysis. It was found that the most important property that correlates most with the protein–protein interactions for all studied organisms is dipeptide amino acid composition (the frequency of specific amino acid pairs in a protein sequence). While current approaches often overlook the specificity of protein–protein interactions with different organisms, our method yields context-specific features that determine protein–protein interactions. The analysis is specifically applied to the bacterial two-component system that includes histidine kinase and transcriptional response regulators, as well as to the barnase–barstar complex, demonstrating the method’s versatility across different biological systems. Our approach can be applied to predict protein–protein interactions in any biological system, providing an important tool for investigating complex biological processes’ mechanisms.