1
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Berges AJ, Vedula SS, Chara A, Hager GD, Ishii M, Malpani A. Eye Tracking and Motion Data Predict Endoscopic Sinus Surgery Skill. Laryngoscope 2023; 133:500-505. [PMID: 35357011 PMCID: PMC9825109 DOI: 10.1002/lary.30121] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Revised: 03/10/2022] [Accepted: 03/14/2022] [Indexed: 01/11/2023]
Abstract
OBJECTIVE Endoscopic surgery has a considerable learning curve due to dissociation of the visual-motor axes, coupled with decreased tactile feedback and mobility. In particular, endoscopic sinus surgery (ESS) lacks objective skill assessment metrics to provide specific feedback to trainees. This study aims to identify summary metrics from eye tracking, endoscope motion, and tool motion to objectively assess surgeons' ESS skill. METHODS In this cross-sectional study, expert and novice surgeons performed ESS tasks of inserting an endoscope and tool into a cadaveric nose, touching an anatomical landmark, and withdrawing the endoscope and tool out of the nose. Tool and endoscope motion were collected using an electromagnetic tracker, and eye gaze was tracked using an infrared camera. Three expert surgeons provided binary assessments of low/high skill. 20 summary statistics were calculated for eye, tool, and endoscope motion and used in logistic regression models to predict surgical skill. RESULTS 14 metrics (10 eye gaze, 2 tool motion, and 2 endoscope motion) were significantly different between surgeons with low and high skill. Models to predict skill for 6/9 ESS tasks had an AUC >0.95. A combined model of all tasks (AUC 0.95, PPV 0.93, NPV 0.89) included metrics from eye tracking data and endoscope motion, indicating that these metrics are transferable across tasks. CONCLUSIONS Eye gaze, endoscope, and tool motion data can provide an objective and accurate measurement of ESS surgical performance. Incorporation of these algorithmic techniques intraoperatively could allow for automated skill assessment for trainees learning endoscopic surgery. LEVEL OF EVIDENCE N/A Laryngoscope, 133:500-505, 2023.
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Affiliation(s)
| | | | | | | | - Masaru Ishii
- Johns Hopkins Department of Otolaryngology–Head and Neck Surgery
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2
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Workman RJ, Pettitt BM. Thermodynamic Compensation in Peptides Following Liquid-Liquid Phase Separation. J Phys Chem B 2021; 125:6431-6439. [PMID: 34110175 DOI: 10.1021/acs.jpcb.1c02093] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Liquid-liquid phase separation of proteins often incorporates intrinsically disordered proteins or those with disordered regions. Examining these processes via the entropy change is desirable for establishing a quantitative foundation with which to probe and understand these phase transitions. Of interest is the effect of residue sequence on the entropy of the peptide backbone. In this work we model these systems via all atom simulations of liquid-liquid phase separation of peptides. Systems of supersaturated pentapeptides separate into a peptide-dense liquid droplet phase as well as a dilute (saturated) aqueous phase. An analysis of the change in backbone conformational entropy associated with the phase transition was performed. We examined systems of four different pentapeptides (GGGGG, GGQGG, GGNGG, and GGVGG) in order to explore the effect of sequence variation on the conformational entropy, as well as the effect of side chain variation on the physical characteristics of the droplet phases. We find that the loss of conformational entropy that accompanies aqueous → droplet transitions is more than compensated by a decrease in interaction enthalpy as contributions to the free energy change for the process.
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Affiliation(s)
- Riley J Workman
- Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, Texas 77555, United States
| | - B Montgomery Pettitt
- Sealy Center for Structural Biology and Molecular Biophysics, University of Texas Medical Branch, Galveston, Texas 77555, United States
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3
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Fogolari F, Esposito G, Tidor B. Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method. J Chem Theory Comput 2021; 17:3039-3051. [PMID: 33856225 DOI: 10.1021/acs.jctc.1c00016] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The entropy associated with rotations, translations, and their coupled motions provides an important contribution to the free energy of many physicochemical processes such as association and solvation. The kth nearest neighbor method, which offers a convenient way to estimate the entropy in high-dimensional spaces, has been previously applied for translational-rotational entropy estimation. Here, we explore the possibility of extending the kth nearest neighbor method to the computation of the entropy of correlated translation-rotations of two molecules, i.e., in the product space of two translation-rotations, both referred to the same independent reference system, which is relevant for all cases in which the correlated translational-rotational motion of more than two molecules is involved. Numerical tests show that, albeit the relatively high dimensionality (12) of the space, the kth nearest neighbor approach provides an accurate estimate for the entropy of two correlated translational-rotational motions, even when computed from a limited number of samples.
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Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Matematiche, Informatiche e Fisiche (DMIF), University of Udine, Via delle Scienze 206, 33100 Udine, Italy.,Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d'Oro 305, 00136 Roma, Italy
| | - Gennaro Esposito
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d'Oro 305, 00136 Roma, Italy.,Science and Math Division, New York University at Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates
| | - Bruce Tidor
- Department of Biological Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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4
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Song C, Xu Z, Zhang Y. The optimized evidence k-Nearest Neighbor based on FOA under the hesitant fuzzy environment and its application in classification. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-192026] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Chenyang Song
- Command & Control Engineering College, Army Engineering University of PLA, Nanjing, China
| | - Zeshui Xu
- Business School, State Key Laboratory of Hydraulics and Mountain River Engineering, Chengdu, China
| | - Yixin Zhang
- Business School, State Key Laboratory of Hydraulics and Mountain River Engineering, Chengdu, China
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5
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Hanson AJ. The quaternion-based spatial-coordinate and orientation-frame alignment problems. Acta Crystallogr A Found Adv 2020; 76:432-457. [PMID: 32608360 PMCID: PMC7330932 DOI: 10.1107/s2053273320002648] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2018] [Accepted: 02/25/2020] [Indexed: 12/02/2022] Open
Abstract
The general problem of finding a global rotation that transforms a given set of spatial coordinates and/or orientation frames (the `test' data) into the best possible alignment with a corresponding set (the `reference' data) is reviewed. For 3D point data, this `orthogonal Procrustes problem' is often phrased in terms of minimizing a root-mean-square deviation (RMSD) corresponding to a Euclidean distance measure relating the two sets of matched coordinates. This article focuses on quaternion eigensystem methods that have been exploited to solve this problem for at least five decades in several different bodies of scientific literature, where they were discovered independently. While numerical methods for the eigenvalue solutions dominate much of this literature, it has long been realized that the quaternion-based RMSD optimization problem can also be solved using exact algebraic expressions based on the form of the quartic equation solution published by Cardano in 1545; focusing on these exact solutions exposes the structure of the entire eigensystem for the traditional 3D spatial-alignment problem. The structure of the less-studied orientation-data context is then explored, investigating how quaternion methods can be extended to solve the corresponding 3D quaternion orientation-frame alignment (QFA) problem, noting the interesting equivalence of this problem to the rotation-averaging problem, which also has been the subject of independent literature threads. The article concludes with a brief discussion of the combined 3D translation-orientation data alignment problem. Appendices are devoted to a tutorial on quaternion frames, a related quaternion technique for extracting quaternions from rotation matrices and a review of quaternion rotation-averaging methods relevant to the orientation-frame alignment problem. The supporting information covers novel extensions of quaternion methods to the 4D Euclidean spatial-coordinate alignment and 4D orientation-frame alignment problems, some miscellaneous topics, and additional details of the quartic algebraic eigenvalue problem.
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Affiliation(s)
- Andrew J. Hanson
- Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana, USA
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6
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Heinz LP, Grubmüller H. Computing Spatially Resolved Rotational Hydration Entropies from Atomistic Simulations. J Chem Theory Comput 2019; 16:108-118. [DOI: 10.1021/acs.jctc.9b00926] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Leonard P. Heinz
- Department of Theoretical and Computational Biophysics, Max-Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | - Helmut Grubmüller
- Department of Theoretical and Computational Biophysics, Max-Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany
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7
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Fogolari F, Maloku O, Dongmo Foumthuim CJ, Corazza A, Esposito G. PDB2ENTROPY and PDB2TRENT: Conformational and Translational–Rotational Entropy from Molecular Ensembles. J Chem Inf Model 2018; 58:1319-1324. [DOI: 10.1021/acs.jcim.8b00143] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Matematiche, Informatiche e Fisiche (DIMF), University of Udine, Via delle Scienze 206, 33100 Udine, Italy
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
| | - Ornela Maloku
- Dipartimento di Scienze Matematiche, Informatiche e Fisiche (DIMF), University of Udine, Via delle Scienze 206, 33100 Udine, Italy
| | | | - Alessandra Corazza
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
- Dipartimento di Area Medica (DAME), University of Udine, Piazzale Kolbe 4, 33100 Udine, Italy
| | - Gennaro Esposito
- Dipartimento di Scienze Matematiche, Informatiche e Fisiche (DIMF), University of Udine, Via delle Scienze 206, 33100 Udine, Italy
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
- Science and Math Division, New York University at Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates
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8
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Dynamics and Thermodynamics of Transthyretin Association from Molecular Dynamics Simulations. BIOMED RESEARCH INTERNATIONAL 2018; 2018:7480749. [PMID: 29967786 PMCID: PMC6008865 DOI: 10.1155/2018/7480749] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 05/06/2018] [Indexed: 12/15/2022]
Abstract
Molecular dynamics simulations are used in this work to probe the structural stability and the dynamics of engineered mutants of transthyretin (TTR), i.e., the double mutant F87M/L110M (MT-TTR) and the triple mutant F87M/L110M/S117E (3M-TTR), in relation to wild-type. Free energy analysis from end-point simulations and statistical effective energy functions are used to analyze trajectories, revealing that mutations do not have major impact on protein structure but rather on protein association, shifting the equilibria towards dissociated species. The result is confirmed by the analysis of 3M-TTR which shows dissociation within the first 10 ns of the simulation, indicating that contacts are lost at the dimer-dimer interface, whereas dimers (formed by monomers which pair to form two extended β-sheets) appear fairly stable. Overall the simulations provide a detailed view of the dynamics and thermodynamics of wild-type and mutant transthyretins and a rationale of the observed effects.
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9
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Alberstein R, Suzuki Y, Paesani F, Tezcan FA. Engineering the entropy-driven free-energy landscape of a dynamic nanoporous protein assembly. Nat Chem 2018; 10:732-739. [PMID: 29713036 DOI: 10.1038/s41557-018-0053-4] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Accepted: 03/29/2018] [Indexed: 12/27/2022]
Abstract
De novo design and construction of stimuli-responsive protein assemblies that predictably switch between discrete conformational states remains an essential but highly challenging goal in biomolecular design. We previously reported synthetic, two-dimensional protein lattices self-assembled via disulfide bonding interactions, which endows them with a unique capacity to undergo coherent conformational changes without losing crystalline order. Here, we carried out all-atom molecular dynamics simulations to map the free-energy landscape of these lattices, validated this landscape through extensive structural characterization by electron microscopy and established that it is predominantly governed by solvent reorganization entropy. Subsequent redesign of the protein surface with conditionally repulsive electrostatic interactions enabled us to predictably perturb the free-energy landscape and obtain a new protein lattice whose conformational dynamics can be chemically and mechanically toggled between three different states with varying porosities and molecular densities.
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Affiliation(s)
- Robert Alberstein
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA
| | - Yuta Suzuki
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA. .,Materials Science and Engineering, University of California, San Diego, La Jolla, CA, USA.
| | - F Akif Tezcan
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA. .,Materials Science and Engineering, University of California, San Diego, La Jolla, CA, USA.
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10
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Kim J, Seo O, Song C, Chen Y, Hiroi S, Irokawa Y, Nabatame T, Koide Y, Sakata O. Characterization of a 4-inch GaN wafer by X-ray diffraction topography. CrystEngComm 2018. [DOI: 10.1039/c8ce01440j] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
We have investigated the crystal quality of a 4-inch GaN wafer by X-ray diffraction topography.
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Affiliation(s)
- Jaemyung Kim
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
| | - Okkyun Seo
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
| | - Chulho Song
- Synchrotron X-ray Station at SPring-8
- RNFS
- NIMS
- Sayo
- 679-5148 Japan
| | - Yanna Chen
- Synchrotron X-ray Station at SPring-8
- RNFS
- NIMS
- Sayo
- 679-5148 Japan
| | - Satoshi Hiroi
- Synchrotron X-ray Station at SPring-8
- RNFS
- NIMS
- Sayo
- 679-5148 Japan
| | - Yoshihiro Irokawa
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
| | - Toshihide Nabatame
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
| | - Yasuo Koide
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
| | - Osami Sakata
- Center for GaN Characterization
- Research Network and Facility Services Division (RNFS)
- National Institute for Materials Science (NIMS)
- Tsukuba
- 305-0047 Japan
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11
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Ahmad M, Helms V, Kalinina OV, Lengauer T. Elucidating the energetic contributions to the binding free energy. J Chem Phys 2017; 146:014105. [PMID: 28063433 DOI: 10.1063/1.4973349] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
New exact equations are derived for the terms contributing to the binding free energy (ΔG0) of a ligand-receptor pair using our recently introduced formalism which we here call perturbation-divergence formalism (PDF). Specifically, ΔG0 equals the sum of the average of the perturbation (pertaining to new interactions) and additional dissipative terms. The average of the perturbation includes the sum of the average receptor-ligand interactions and the average of the change of solvation energies upon association. The Kullback-Leibler (KL) divergence quantifies the energetically dissipative terms, which are due to the configurational changes and, using the chain rule of KL divergence, can be decomposed into (i) dissipation due to limiting the external liberation (translation and rotation) of the ligand relative to the receptor and (ii) dissipation due to conformational (internal) changes inside the receptor and the ligand. We also identify all exactly canceling energetic terms which do not contribute to ΔG0. Furthermore, the PDF provides a new approach towards dimensionality reduction in the representation of the association process and towards relating the dynamic (high dimensional) with the thermodynamic (one-dimensional) changes.
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Affiliation(s)
- Mazen Ahmad
- Department for Computational Biology and Applied Algorithmics, Max Planck Institute for Informatics, Saarland Informatics Campus E1 4, 66123 Saarbrücken, Germany
| | - Volkhard Helms
- Center for Bioinformatics, Saarland University, 66123 Saarbrücken, Germany
| | - Olga V Kalinina
- Department for Computational Biology and Applied Algorithmics, Max Planck Institute for Informatics, Saarland Informatics Campus E1 4, 66123 Saarbrücken, Germany
| | - Thomas Lengauer
- Department for Computational Biology and Applied Algorithmics, Max Planck Institute for Informatics, Saarland Informatics Campus E1 4, 66123 Saarbrücken, Germany
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12
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Huggins DJ. Studying the role of cooperative hydration in stabilizing folded protein states. J Struct Biol 2016; 196:394-406. [PMID: 27633532 PMCID: PMC5131609 DOI: 10.1016/j.jsb.2016.09.003] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2016] [Revised: 09/03/2016] [Accepted: 09/07/2016] [Indexed: 01/19/2023]
Abstract
Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.
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Affiliation(s)
- David J Huggins
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, 19 J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom; Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, United Kingdom.
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13
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Ramsey S, Nguyen C, Salomon-Ferrer R, Walker RC, Gilson MK, Kurtzman T. Solvation thermodynamic mapping of molecular surfaces in AmberTools: GIST. J Comput Chem 2016; 37:2029-37. [PMID: 27317094 DOI: 10.1002/jcc.24417] [Citation(s) in RCA: 87] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2016] [Revised: 04/19/2016] [Accepted: 05/17/2016] [Indexed: 02/06/2023]
Abstract
The expulsion of water from surfaces upon molecular recognition and nonspecific association makes a major contribution to the free energy changes of these processes. In order to facilitate the characterization of water structure and thermodynamics on surfaces, we have incorporated Grid Inhomogeneous Solvation Theory (GIST) into the CPPTRAJ toolset of AmberTools. GIST is a grid-based implementation of Inhomogeneous Fluid Solvation Theory, which analyzes the output from molecular dynamics simulations to map out solvation thermodynamic and structural properties on a high-resolution, three-dimensional grid. The CPPTRAJ implementation, called GIST-cpptraj, has a simple, easy-to-use command line interface, and is open source and freely distributed. We have also developed a set of open-source tools, called GISTPP, which facilitate the analysis of GIST output grids. Tutorials for both GIST-cpptraj and GISTPP can be found at ambermd.org. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Steven Ramsey
- Department of Chemistry, Lehman College, 205 W Bedford Pk Blvd, Bronx, New York, 10468.,Ph.D. Program in Biochemistry, The Graduate Center of the City University of New York, 365 5th Avenue, New York, New York, 10016
| | - Crystal Nguyen
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0736
| | - Romelia Salomon-Ferrer
- San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California, 92093-0505
| | - Ross C Walker
- San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive MC0505, La Jolla, California, 92093-0505.,Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0505
| | - Michael K Gilson
- Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0736
| | - Tom Kurtzman
- Department of Chemistry, Lehman College, 205 W Bedford Pk Blvd, Bronx, New York, 10468.,Ph.D. Program in Biochemistry, The Graduate Center of the City University of New York, 365 5th Avenue, New York, New York, 10016.,Ph. D. Program in Chemistry, The Graduate Center of the City University of New York, 365 5th Avenue, New York, New York, 10016
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14
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Chong SH, Ham S. New Computational Approach for External Entropy in Protein-Protein Binding. J Chem Theory Comput 2016; 12:2509-16. [PMID: 27153451 DOI: 10.1021/acs.jctc.6b00174] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Molecular recognition through the noncovalent association of biomolecules is of central importance in biology and pharmacology. Developing reliable computational methods for estimating binding thermodynamic parameters is therefore of great practical value. However, considerable uncertainty remains regarding the external entropy that is associated with the reduction in the external (positional and orientational) degrees of freedom upon complex formation. Here, we present a novel statistical mechanical method for computing the external entropy by extending the energetic approach we have developed for unimolecular processes to association processes. We find that, in contrary to what is postulated in most of the previous methods, intrinsic couplings between the internal and external degrees of freedom of bound complex cannot in general be neglected in the determination of the external entropy. Nevertheless, there exists the best choice of the external coordinates with which those couplings are minimized. With such a choice of the external coordinates, the lowest upper bound of the external entropy is obtained from a tractable expression, which serves as an estimate of the external entropy. Our method can be implemented in a straightforward manner with molecular dynamics simulations, and its applicability is demonstrated through the application to the barnase-barstar complex.
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Affiliation(s)
- Song-Ho Chong
- Department of Chemistry, Sookmyung Women's University , Cheongpa-ro 47-gil 100, Yongsan-Ku, Seoul 04310, Korea
| | - Sihyun Ham
- Department of Chemistry, Sookmyung Women's University , Cheongpa-ro 47-gil 100, Yongsan-Ku, Seoul 04310, Korea
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15
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Huggins DJ. Estimating Translational and Orientational Entropies Using the k-Nearest Neighbors Algorithm. J Chem Theory Comput 2015; 10:3617-25. [PMID: 26588506 DOI: 10.1021/ct500415g] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Inhomogeneous fluid solvation theory (IFST) and free energy perturbation (FEP) calculations were performed for a set of 20 solutes to compute the hydration free energies. We identify the weakness of histogram methods in computing the IFST hydration entropy by showing that previously employed histogram methods overestimate the translational and orientational entropies and thus underestimate their contribution to the free energy by a significant amount. Conversely, we demonstrate the accuracy of the k-nearest neighbors (KNN) algorithm in computing these translational and orientational entropies. Implementing the KNN algorithm within the IFST framework produces a powerful method that can be used to calculate free-energy changes for large perturbations. We introduce a new KNN approach to compute the total solute-water entropy with six degrees of freedom, as well as the translational and orientational contributions. However, results suggest that both the solute-water and water-water entropy terms are significant and must be included. When they are combined, the IFST and FEP hydration free energies are highly correlated, with an R(2) of 0.999 and a mean unsigned difference of 0.9 kcal/mol. IFST predictions are also highly correlated with experimental hydration free energies, with an R(2) of 0.997 and a mean unsigned error of 1.2 kcal/mol. In summary, the KNN algorithm is shown to yield accurate estimates of the combined translational-orientational entropy and the novel approach of combining distance metrics that is developed here could be extended to provide a powerful method for entropy estimation in numerous contexts.
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Affiliation(s)
- David J Huggins
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge , 19 J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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16
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Fogolari F, Dongmo Foumthuim CJ, Fortuna S, Soler MA, Corazza A, Esposito G. Accurate Estimation of the Entropy of Rotation-Translation Probability Distributions. J Chem Theory Comput 2015; 12:1-8. [PMID: 26605696 DOI: 10.1021/acs.jctc.5b00731] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The estimation of rotational and translational entropies in the context of ligand binding has been the subject of long-time investigations. The high dimensionality (six) of the problem and the limited amount of sampling often prevent the required resolution to provide accurate estimates by the histogram method. Recently, the nearest-neighbor distance method has been applied to the problem, but the solutions provided either address rotation and translation separately, therefore lacking correlations, or use a heuristic approach. Here we address rotational-translational entropy estimation in the context of nearest-neighbor-based entropy estimation, solve the problem numerically, and provide an exact and an approximate method to estimate the full rotational-translational entropy.
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Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Mediche e Biologiche (DSMB), University of Udine , Piazzale Kolbe 4, 33100 Udine, Italy.,Istituto Nazionale Biostrutture e Biosistemi, Viale Medaglie d'Oro 305, 00136 Roma, Italy
| | | | - Sara Fortuna
- Dipartimento di Scienze Mediche e Biologiche (DSMB), University of Udine , Piazzale Kolbe 4, 33100 Udine, Italy
| | - Miguel Angel Soler
- Dipartimento di Scienze Mediche e Biologiche (DSMB), University of Udine , Piazzale Kolbe 4, 33100 Udine, Italy
| | - Alessandra Corazza
- Dipartimento di Scienze Mediche e Biologiche (DSMB), University of Udine , Piazzale Kolbe 4, 33100 Udine, Italy.,Istituto Nazionale Biostrutture e Biosistemi, Viale Medaglie d'Oro 305, 00136 Roma, Italy
| | - Gennaro Esposito
- Dipartimento di Scienze Mediche e Biologiche (DSMB), University of Udine , Piazzale Kolbe 4, 33100 Udine, Italy.,Istituto Nazionale Biostrutture e Biosistemi, Viale Medaglie d'Oro 305, 00136 Roma, Italy
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17
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Quantifying the entropy of binding for water molecules in protein cavities by computing correlations. Biophys J 2015; 108:928-936. [PMID: 25692597 PMCID: PMC4336375 DOI: 10.1016/j.bpj.2014.12.035] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2014] [Revised: 12/16/2014] [Accepted: 12/17/2014] [Indexed: 11/20/2022] Open
Abstract
Protein structural analysis demonstrates that water molecules are commonly found in the internal cavities of proteins. Analysis of experimental data on the entropies of inorganic crystals suggests that the entropic cost of transferring such a water molecule to a protein cavity will not typically be greater than 7.0 cal/mol/K per water molecule, corresponding to a contribution of approximately +2.0 kcal/mol to the free energy. In this study, we employ the statistical mechanical method of inhomogeneous fluid solvation theory to quantify the enthalpic and entropic contributions of individual water molecules in 19 protein cavities across five different proteins. We utilize information theory to develop a rigorous estimate of the total two-particle entropy, yielding a complete framework to calculate hydration free energies. We show that predictions from inhomogeneous fluid solvation theory are in excellent agreement with predictions from free energy perturbation (FEP) and that these predictions are consistent with experimental estimates. However, the results suggest that water molecules in protein cavities containing charged residues may be subject to entropy changes that contribute more than +2.0 kcal/mol to the free energy. In all cases, these unfavorable entropy changes are predicted to be dominated by highly favorable enthalpy changes. These findings are relevant to the study of bridging water molecules at protein-protein interfaces as well as in complexes with cognate ligands and small-molecule inhibitors.
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18
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Fogolari F, Corazza A, Fortuna S, Soler MA, VanSchouwen B, Brancolini G, Corni S, Melacini G, Esposito G. Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations. PLoS One 2015; 10:e0132356. [PMID: 26177039 PMCID: PMC4503633 DOI: 10.1371/journal.pone.0132356] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2015] [Accepted: 06/13/2015] [Indexed: 12/29/2022] Open
Abstract
Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.
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Affiliation(s)
- Federico Fogolari
- Dipartimento di Scienze Mediche e Biologiche, Universita’ di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
- * E-mail:
| | - Alessandra Corazza
- Dipartimento di Scienze Mediche e Biologiche, Universita’ di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
| | - Sara Fortuna
- Dipartimento di Scienze Mediche e Biologiche, Universita’ di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
| | - Miguel Angel Soler
- Dipartimento di Scienze Mediche e Biologiche, Universita’ di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
| | - Bryan VanSchouwen
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main St. W. Hamilton, ON L8S 4M1, Canada
| | - Giorgia Brancolini
- Center S3, CNR Institute Nanoscience, Via Campi 213/A, 41125 Modena, Italy
| | - Stefano Corni
- Center S3, CNR Institute Nanoscience, Via Campi 213/A, 41125 Modena, Italy
| | - Giuseppe Melacini
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main St. W. Hamilton, ON L8S 4M1, Canada
| | - Gennaro Esposito
- Dipartimento di Scienze Mediche e Biologiche, Universita’ di Udine, Piazzale Kolbe 4, 33100 Udine, Italy
- Istituto Nazionale Biostrutture e Biosistemi, Viale medaglie d’Oro 305, 00136 Roma, Italy
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19
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Raman EP, MacKerell AD. Spatial analysis and quantification of the thermodynamic driving forces in protein-ligand binding: binding site variability. J Am Chem Soc 2015; 137:2608-21. [PMID: 25625202 DOI: 10.1021/ja512054f] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The thermodynamic driving forces behind small molecule-protein binding are still not well-understood, including the variability of those forces associated with different types of ligands in different binding pockets. To better understand these phenomena we calculate spatially resolved thermodynamic contributions of the different molecular degrees of freedom for the binding of propane and methanol to multiple pockets on the proteins Factor Xa and p38 MAP kinase. Binding thermodynamics are computed using a statistical thermodynamics based end-point method applied on a canonical ensemble comprising the protein-ligand complexes and the corresponding free states in an explicit solvent environment. Energetic and entropic contributions of water and ligand degrees of freedom computed from the configurational ensemble provide an unprecedented level of detail into the mechanisms of binding. Direct protein-ligand interaction energies play a significant role in both nonpolar and polar binding, which is comparable to water reorganization energy. Loss of interactions with water upon binding strongly compensates these contributions leading to relatively small binding enthalpies. For both solutes, the entropy of water reorganization is found to favor binding in agreement with the classical view of the "hydrophobic effect". Depending on the specifics of the binding pocket, both energy-entropy compensation and reinforcement mechanisms are observed. It is notable to have the ability to visualize the spatial distribution of the thermodynamic contributions to binding at atomic resolution showing significant differences in the thermodynamic contributions of water to the binding of propane versus methanol.
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Affiliation(s)
- E Prabhu Raman
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy , 20 Penn Street HSF II, Baltimore, Maryland 21201, United States
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