arXiv subjects

John D. Chodera

Publications and source records attributed to John D. Chodera.

24 records · Page 2Linked to original sources

arXiv2011

A robust approach to estimating rates from time-correlation functions

While seemingly straightforward in principle, the reliable estimation of rate constants is seldom easy in practice. Numerous issues, such as the complication of poor reaction coordinates, cause obvious approaches to yield unreliable estimates. When a reliable order parameter is available, the reactive flux theory of Chandler allows the rate constant to be extracted from the plateau region of an appropriate reactive flux function. However, when applied to real data from single-molecule experiments or molecular dynamics simulations, the rate can sometimes be difficult to extract due to the numerical differentiation of a noisy empirical correlation function or difficulty in locating the plateau region at low sampling frequencies. We present a modified version of this theory which does not require numerical derivatives, allowing rate constants to be robustly estimated from the time-correlation function directly. We compare these approaches using single-molecule force spectroscopy measurements of an RNA hairpin.

cond-mat.stat-mech↗

arXiv2011

Bayesian hidden Markov model analysis of single-molecule force spectroscopy: Characterizing kinetics under measurement uncertainty

Single-molecule force spectroscopy has proven to be a powerful tool for studying the kinetic behavior of biomolecules. Through application of an external force, conformational states with small or transient populations can be stabilized, allowing them to be characterized and the statistics of individual trajectories studied to provide insight into biomolecular folding and function. Because the observed quantity (force or extension) is not necessarily an ideal reaction coordinate, individual observations cannot be uniquely associated with kinetically distinct conformations. While maximum-likelihood schemes such as hidden Markov models have solved this problem for other classes of single-molecule experiments by using temporal information to aid in the inference of a sequence of distinct conformational states, these methods do not give a clear picture of how precisely the model parameters are determined by the data due to instrument noise and finite-sample statistics, both significant problems in force spectroscopy. We solve this problem through a Bayesian extension that allows the experimental uncertainties to be directly quantified, and build in detailed balance to further reduce uncertainty through physical constraints. We illustrate the utility of this approach in characterizing the three-state kinetic behavior of an RNA hairpin in a stationary optical trap.

cond-mat.stat-mech↗

arXiv2011

Splitting probabilities as a test of reaction coordinate choice in single-molecule experiments

To explain the observed dynamics in equilibrium single-molecule measurements of biomolecules, the experimental observable is often chosen as a putative reaction coordinate along which kinetic behavior is presumed to be governed by diffusive dynamics. Here, we invoke the splitting probability as a test of the suitability of such a proposed reaction coordinate. Comparison of the observed splitting probability with that computed from the kinetic model provides a simple test to reject poor reaction coordinates. We demonstrate this test for a force spectroscopy measurement of a DNA hairpin.

cond-mat.stat-mech↗

arXiv2010

Estimating equilibrium ensemble averages using multiple time slices from driven nonequilibrium processes: theory and application to free energies, moments, and thermodynamic length in single-molecule pulling experiments

Recently discovered identities in statistical mechanics have enabled the calculation of equilibrium ensemble averages from realizations of driven nonequilibrium processes, including single-molecule pulling experiments and analogous computer simulations. Challenges in collecting large data sets motivate the pursuit of efficient statistical estimators that maximize use of available information. Along these lines, Hummer and Szabo developed an estimator that combines data from multiple time slices along a driven nonequilibrium process to compute the potential of mean force. Here, we generalize their approach, pooling information from multiple time slices to estimate arbitrary equilibrium expectations. Our expression may be combined with estimators of path-ensemble averages, including existing optimal estimators that use data collected by unidirectional and bidirectional protocols. We demonstrate the estimator by calculating free energies, moments of the polymer extension, and the metric tensor for thermodynamic length in a model single-molecule pulling experiment. Compared to estimators that only use individual time slices, our multiple time-slice estimators yield substantially smoother estimates and achieve lower variance for higher-order moments.

cond-mat.stat-mech↗

arXiv2009

Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages

Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtaining asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. Lastly, they are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, it does not work well for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.

cond-mat.stat-mech↗

arXiv2008

Statistically optimal analysis of samples from multiple equilibrium states

We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we term the multistate Bennett acceptance ratio (MBAR) estimator because it reduces to the Bennett acceptance ratio when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

physics.comp-ph↗