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For a system in thermal equilibrium, described by classical statistical mechanics, we derive an unbiased estimator for the marginal probability distribution of a coordinate of interest, rho( x). This result provides a "binless" method for estimating the potential of mean force, Phi = -beta (-1) ln rho, eliminating the need to construct histograms or perform numerical thermodynamic integration. In our method, the distribution that we seek to compute is expressed as the sum of a reference distribution, rho 0(x)essentially an initial guess or estimate of rho( x)and a correction term. While the method is valid for arbitrary rho 0, we speculate that an accurate choice of the reference distribution improves the convergence of the method. Using a model molecule, simulated both in vacuum and in solvent, we validate our proposed approach and compare its performance with the histogram and thermodynamic integration methods. We also discuss and validate an extension in which our approach is used in combination with a biasing force, meant to improve uniform sampling of the coordinate of interest.
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Development of effective quantitative indicators and methodologies to assess the outcomes of cross-disciplinary collaborative initiatives has the potential to improve scientific program management and scientific output. This article highlights an example of a prospective evaluation that has been developed to monitor and improve progress of the National Cancer Institute Physical Sciences-Oncology Centers (PS-OC) program. Study data, including collaboration information, was captured through progress reports and compiled using the web-based analytic database: Interdisciplinary Team Reporting, Analysis, and Query Resource. Analysis of collaborations was further supported by data from the Thomson Reuters Web of Science database, MEDLINE database, and a web-based survey. Integration of novel and standard data sources was augmented by the development of automated methods to mine investigator pre-award publications, assign investigator disciplines, and distinguish cross-disciplinary publication content. The results highlight increases in cross-disciplinary authorship collaborations from pre- to post-award years among the primary investigators and confirm that a majority of cross-disciplinary collaborations have resulted in publications with cross-disciplinary content that rank in the top third of their field. With these evaluation data, PS-OC Program officials have provided ongoing feedback to participating investigators to improve center productivity and thereby facilitate a more successful initiative. Future analysis will continue to expand these methods and metrics to adapt to new advances in research evaluation and changes in the program.
RESUMO
We have applied the Transition Path Sampling algorithm to the reaction catalyzed by the enzyme Lactate Dehydrogenase. This study demonstrates the ease of scaling Transition Path Sampling for applications on many degree of freedom systems, whose energy surface is a complex terrain of valleys and saddle points. As a Monte Carlo importance sampling method, transition path sampling is capable of surmounting barriers in path phase space and focuses simulation on the rare event of enzyme catalyzed atom transfers. Generation of the transition path ensemble, for this reaction, resolves a paradox in the literature in which some studies exposed the catalytic mechanism of hydride and proton transfer by lactate dehydrogenase to be concerted and others stepwise. Transition path sampling has confirmed both mechanisms as possible paths from reactants to products. With the objective to identify a generalized, reduced reaction coordinate, time series of both donor-acceptor distances and residue distances from the active site have been examined. During the transition from pyruvate to lactate, residues located behind the transferring hydride collectively compress toward the active site causing residues located behind the hydride acceptor to relax away. It is demonstrated that an incomplete compression/relaxation transition across the donor-acceptor axis compromises the reaction.