Molecular hydrodynamic theory of the velocity autocorrelation function

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by \emph{linear} hydrodynamic equations; the fluid's static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids.Comment: 14 pages, 3 figures; 5 appendices, 2 appendix figures; improved method/results for Fig. 3 w/ appendix 4; added new results w/ procedure in appendix 5. (v2: 11 pages, 3 figures, 3 appendices

Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Fr\'echet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also available from journal site

A communal catalogue reveals Earth’s multiscale microbial diversity

Our growing awareness of the microbial world’s importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth’s microbial diversity

A communal catalogue reveals Earth's multiscale microbial diversity

Our growing awareness of the microbial world's importance and diversity contrasts starkly with our limited understanding of its fundamental structure. Despite recent advances in DNA sequencing, a lack of standardized protocols and common analytical frameworks impedes comparisons among studies, hindering the development of global inferences about microbial life on Earth. Here we present a meta-analysis of microbial community samples collected by hundreds of researchers for the Earth Microbiome Project. Coordinated protocols and new analytical methods, particularly the use of exact sequences instead of clustered operational taxonomic units, enable bacterial and archaeal ribosomal RNA gene sequences to be followed across multiple studies and allow us to explore patterns of diversity at an unprecedented scale. The result is both a reference database giving global context to DNA sequence data and a framework for incorporating data from future studies, fostering increasingly complete characterization of Earth's microbial diversity.Peer reviewe

Supplementary Mathematica notebook for the publication "Molecular hydrodynamic theory of the velocity autocorrelation function"

Supplementary Mathematica notebook for the publication "Molecular hydrodynamic theory of the velocity autocorrelation function" that provides the data and procedures necessary to reproduce VACFs in the corresponding manuscript. If you (re-)use this work and/or find it useful in your own work, we kindly ask that you use the citation provided on this page and include the DOI. Thank you in advance

Hydrodynamic Brownian Motion

This is starting off as a tester project for my work on hydrodynamic Brownian motion and transport efficiency

Molecular hydrodynamic theory of the velocity autocorrelation function

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid’s molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by linear hydrodynamic equations; the fluid’s static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids

Hydrodynamic Brownian motion and nanoscale transport efficiency in liquids (APS March Meeting 2019 presentation slides)

These are the slides for the contributed talk entitled "Hydrodynamic Brownian motion and nanoscale transport efficiency in liquids," which was presented at the 2019 APS March Meeting. The original presentation, which was built with Keynote 8.3, includes a number of animations (mp4 and gif formats) that can be found in the included .zip archive. (Note: for OSX/Keynote users, the .zip extension can be manually changed to .key and the presentation viewed directly in Keynote). For ease of viewing directly on figshare and across different platforms, a PDF export of the keynote is provided with all of the build stages included. If you reuse any part of this work, please cite the corresponding abstract from the 2019 APS March Meeting (http://meetings.aps.org/Meeting/MAR19/Session/S57.5). Thanks in advance