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Single-molecule fluorescence resonance energy transfer (FRET) experiments are commonly used to study the dynamics of molecular machines. While in vivo molecular processes often break time-reversal symmetry, the temporal directionality of cyclically operating molecular machines is often not evident from single-molecule FRET trajectories, especially in the most common two-color FRET studies. Solving a more quantitative problem of estimating the energy dissipation/entropy production by a molecular machine from single-molecule data is even more challenging. Here, we present a critical assessment of several practical methods of doing so, including Markov-model-based methods and a model-free approach based on an information-theoretical measure of entropy production that quantifies how (statistically) dissimilar observed photon sequences are from their time reverses. The Markov model approach is computationally feasible and may outperform model free approaches, but its performance strongly depends on how well the assumed model approximates the true microscopic dynamics. Markov models are also not guaranteed to give a lower bound on dissipation. Meanwhile, model-free, information-theoretical methods systematically underestimate entropy production at low photoemission rates, and long memory effects in the photon sequences make these methods demanding computationally. There is no clear winner among the approaches studied here, and all methods deserve to belong to a comprehensive data analysis toolkit.

 

Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such “lumped” observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may—via a process called milestoning—improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations “closer to underlying microscopic dynamics” and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.

 

Whether single-molecule trajectories, observed experimentally or in molecular simulations, can be described using simple models such as biased diffusion is a subject of considerable debate. Memory effects and anomalous diffusion have been reported in a number of studies, but directly inferring such effects from trajectories, especially given limited temporal and/or spatial resolution, has been a challenge. Recently, we proposed that this can be achieved with information-theoretical analysis of trajectories, which is based on the general observation that non-Markov effects make trajectories more predictable and, thus, more “compressible” by lossless compression algorithms. Toy models where discrete molecular states evolve in time were shown to be amenable to such analysis, but its application to continuous trajectories presents a challenge: the trajectories need to be digitized first, and digitization itself introduces non-Markov effects that depend on the specifics of how trajectories are sampled. Here we develop a milestoning-based method for information-theoretical analysis of continuous trajectories and show its utility in application to Markov and non-Markov models and to trajectories obtained from molecular simulations.

 

With the rapid shift to remote learning in the early days of the COVID-19 pandemic, parents, teachers, and students had to quickly adapt to what scholars have called emergency remote learning (ERL). This transition required increased reliance on digital tools, exacerbating privacy and security threats associated with expanded data collection and new vulnerabilities. In this study, we adopt a sociotechnical and infrastructural perspective to understand how these threats emerged through breakdowns and tensions in elementary school ERL. Through interviews with 29 US-based teachers and parents of elementary school students (grades PreK-6), we identify two core findings related to privacy and security. First, we detail three breakdowns in the ERL sociotechnical infrastructure: (1) reduced attention to privacy and security issues as parents and teachers cobbled together a patchwork of tools needed to make ERL work; (2) privacy and security risks that emerged from ambiguous and shifting school policies; and (3) the failure to adapt standard authentication mechanisms (e.g., passwords) to be usable by young children. Second, we identify tensions between parents' and teachers' desire to help children advance in their education and their desire for children's privacy and security in ERL, as well as tensions resulting from the collapse of home and school contexts. These findings collectively suggest that ERL exacerbated existing--and created new--privacy and security challenges for young students, and we argue these challenges will carry beyond the pandemic due to the increasing use of technology to supplement traditional education. In light of these findings, we recommend researchers and educators use a framework of care to develop social and technical approaches to improving remote learning in order to protect children's privacy and security.

 

Single-molecule and single-particle tracking experiments are typically unable to resolve fine details of thermal motion at short timescales where trajectories are continuous. We show that, when a diffusive trajectory [Formula: see text] is sampled at finite time intervals δt, the resulting error in measuring the first passage time to a given domain can exceed the time resolution of the measurement by more than an order of magnitude. Such surprisingly large errors originate from the fact that the trajectory may enter and exit the domain while being unobserved, thereby lengthening the apparent first passage time by an amount that is larger than δt. Such systematic errors are particularly important in single-molecule studies of barrier crossing dynamics. We show that the correct first passage times, as well as other properties of the trajectories such as splitting probabilities, can be recovered via a stochastic algorithm that reintroduces unobserved first passage events probabilistically.