Geometric and electrostatic modeling using molecular rigidity functions

Mu, Lin; Xia, Kelin; Wei, Guowei

doi:10.1016/j.cam.2016.08.019

Title: Geometric and electrostatic modeling using molecular rigidity functions

Abstract

Geometric and electrostatic modeling is an essential component in computational biophysics and molecular biology. Commonly used geometric representations admit geometric singularities such as cusps, tips and self-intersecting facets that lead to computational instabilities in the molecular modeling. Our present work explores the use of flexibility and rigidity index (FRI), which has a proved superiority in protein B-factor prediction, for biomolecular geometric representation and associated electrostatic analysis. FRI rigidity surfaces are free of geometric singularities. We propose a rigidity based Poisson–Boltzmann equation for biomolecular electrostatic analysis. These approaches to surface and electrostatic modeling are validated by a set of 21 proteins. Our results are compared with those of established methods. Finally, being smooth and analytically differentiable, FRI rigidity functions offer excellent curvature analysis, which characterizes concave and convex regions on protein surfaces. Polarized curvatures constructed by using the product of minimum curvature and electrostatic potential is shown to predict potential protein–ligand binding sites.

Authors:

; Xia, Kelin; Wei, Guowei

Publication Date:: Wed Mar 01 00:00:00 EST 2017

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1771195

Alternate Identifier(s):: OSTI ID: 1329763; OSTI ID: 1358866

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Published Article

Journal Name:: Journal of Computational and Applied Mathematics

Additional Journal Information:: Journal Name: Journal of Computational and Applied Mathematics Journal Volume: 313 Journal Issue: C; Journal ID: ISSN 0377-0427

Publisher:: Elsevier

Country of Publication:: Belgium

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; Flexibility rigidity index; Rigidity function; Molecular surface; Curvature

Citation Formats


                    Mu, Lin, Xia, Kelin, and Wei, Guowei. Geometric and electrostatic modeling using molecular rigidity functions.  Belgium: N. p., 2017. 
Web.  doi:10.1016/j.cam.2016.08.019.

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                    Mu, Lin, Xia, Kelin, & Wei, Guowei. Geometric and electrostatic modeling using molecular rigidity functions.  Belgium.  https://doi.org/10.1016/j.cam.2016.08.019

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                    Mu, Lin, Xia, Kelin, and Wei, Guowei. Wed .  
"Geometric and electrostatic modeling using molecular rigidity functions".  Belgium.  https://doi.org/10.1016/j.cam.2016.08.019.

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@article{osti_1771195,

  title        = {Geometric and electrostatic modeling using molecular rigidity functions},

  author       = {Mu, Lin and Xia, Kelin and Wei, Guowei},

  abstractNote = {Geometric and electrostatic modeling is an essential component in computational biophysics and molecular biology. Commonly used geometric representations admit geometric singularities such as cusps, tips and self-intersecting facets that lead to computational instabilities in the molecular modeling. Our present work explores the use of flexibility and rigidity index (FRI), which has a proved superiority in protein B-factor prediction, for biomolecular geometric representation and associated electrostatic analysis. FRI rigidity surfaces are free of geometric singularities. We propose a rigidity based Poisson–Boltzmann equation for biomolecular electrostatic analysis. These approaches to surface and electrostatic modeling are validated by a set of 21 proteins. Our results are compared with those of established methods. Finally, being smooth and analytically differentiable, FRI rigidity functions offer excellent curvature analysis, which characterizes concave and convex regions on protein surfaces. Polarized curvatures constructed by using the product of minimum curvature and electrostatic potential is shown to predict potential protein–ligand binding sites.},

  doi          = {10.1016/j.cam.2016.08.019},

  journal      = {Journal of Computational and Applied Mathematics},

  number       = C,

  volume       = 313,

  place        = {Belgium},

  year         = {Wed Mar 01 00:00:00 EST 2017},

  month        = {Wed Mar 01 00:00:00 EST 2017}

}

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Journal of Computer-Aided Molecular Design, Vol. 34, Issue 2
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Title: Geometric and electrostatic modeling using molecular rigidity functions

Abstract

Citation Formats

Multiscale molecular dynamics using the matched interface and boundary method journal, January 2011

Kernel modeling for molecular surfaces using a uniform solution journal, April 2010

Spherical harmonic molecular surfaces journal, July 1988

Precision space-filling atomic models journal, December 1965

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM) journal, November 2015

A general and Robust Ray-Casting-Based Algorithm for Triangulating Surfaces at the Nanoscale journal, April 2013

Investigation of the molecular surface area and volume: Defined and calculated by the molecular face theory journal, March 2010

Multiresolution Topological Simplification journal, September 2015

Multiscale geometric modeling of macromolecules I: Cartesian representation journal, January 2014

Differential Geometry Based Multiscale Models journal, February 2010

Cation-π interactions in protein-protein interfaces journal, February 2005

A Continuum Model for Protein–Protein Interactions: Application to the Docking Problem journal, July 1995

Vibrational Dynamics of Folded Proteins: Significance of Slow and Fast Motions in Relation to Function and Stability journal, March 1998

Differential geometry based solvation model II: Lagrangian formulation journal, January 2011

Functionally Linked Hydration Changes in Escherichia coli Aspartate Transcarbamylase and Its Catalytic Subunit † journal, August 1997

GRASP2: Visualization, Surface Properties, and Electrostatics of Macromolecular Structures and Sequences book, January 2003

MIBPB: A software package for electrostatic analysis journal, September 2010

Molecular Models of Amino Acids, Peptides, and Proteins journal, August 1953

A Gaussian Description of Molecular Shape journal, March 1995

Second-order Poisson–Nernst–Planck solver for ion transport journal, June 2011

Minimal molecular surfaces and their applications journal, January 2007

Variational Multiscale Models for Charge Transport journal, January 2012

Multiscale multiphysics and multidomain models—Flexibility and rigidity journal, November 2013

Reduced surface: An efficient way to compute molecular surfaces journal, March 1996

A new approach to analysis and display of local lipophilicity/hydrophilicity mapped on molecular surfaces journal, October 1993

Multiscale, Multiphysics and Multidomain Models i: Basic Theory journal, December 2013

Differential geometry based solvation model I: Eulerian formulation journal, November 2010

Geometric modeling of subcellular structures, organelles, and multiprotein complexes: GEOMETRIC MODELING OF SUBCELLULAR STRUCTURES journal, November 2012

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation journal, June 2008

DNA Binding and Bending by HMG Boxes: Energetic Determinants of Specificity journal, October 2004

Differential geometry based solvation model. III. Quantum formulation journal, November 2011

Molecular surface-volume and property matching to superpose flexible dissimilar molecules journal, December 1995

Quality mesh generation for molecular skin surfaces using restricted union of balls journal, April 2009

Multiresolution persistent homology for excessively large biomolecular datasets journal, October 2015

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources journal, March 2006

SIMS: computation of a smooth invariant molecular surface journal, August 1997

Areas, Volumes, Packing, and Protein Structure journal, June 1977

The interdependence of protein surface topography and bound water molecules revealed by surface accessibility and fractal density measures journal, November 1992

TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique journal, November 2010

Coupling of local folding to site-specific binding of proteins to DNA journal, February 1994

Wavelets generated by using discrete singular convolution kernels journal, November 2000

Surface shape and curvature scales journal, October 1992

Poisson–Boltzmann–Nernst–Planck model journal, May 2011

Multi-Scale Surface Descriptors journal, November 2009

Macromolecule backbone models book, January 1985

Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential journal, June 1997

The interpretation of protein structures: Estimation of static accessibility journal, February 1971

Molecular surface generation using marching tetrahedra journal, August 1998

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis journal, June 2014

Depth-buffer algorithms for molecular modelling journal, March 1985

Multiscale geometric modeling of macromolecules II: Lagrangian representation journal, June 2013

Biomolecular surface construction by PDE transform: BIOMOLECULAR SURFACE CONSTRUCTION BY PDE TRANSFORM journal, September 2011

Improving implicit solvent simulations: a Poisson-centric view journal, April 2005

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects journal, November 2001

Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities journal, November 2007

Treatment of geometric singularities in implicit solvent models journal, June 2007

Treatment of charge singularities in implicit solvent models journal, September 2007

Absorption Classification of Oral Drugs Based on Molecular Surface Properties journal, February 2003

DG-GL: Differential geometry-based geometric learning of molecular datasets journal, February 2019

MathDL: mathematical deep learning for D3R Grand Challenge 4 journal, November 2019

Multiscale molecular dynamics using the matched interface and boundary method
journal, January 2011

Kernel modeling for molecular surfaces using a uniform solution
journal, April 2010

Spherical harmonic molecular surfaces
journal, July 1988

Precision space-filling atomic models
journal, December 1965

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)
journal, November 2015

A general and Robust Ray-Casting-Based Algorithm for Triangulating Surfaces at the Nanoscale
journal, April 2013

Investigation of the molecular surface area and volume: Defined and calculated by the molecular face theory
journal, March 2010

Multiresolution Topological Simplification
journal, September 2015

Multiscale geometric modeling of macromolecules I: Cartesian representation
journal, January 2014

Differential Geometry Based Multiscale Models
journal, February 2010

Cation-π interactions in protein-protein interfaces
journal, February 2005

A Continuum Model for Protein–Protein Interactions: Application to the Docking Problem
journal, July 1995

Vibrational Dynamics of Folded Proteins: Significance of Slow and Fast Motions in Relation to Function and Stability
journal, March 1998

Differential geometry based solvation model II: Lagrangian formulation
journal, January 2011

Functionally Linked Hydration Changes in Escherichia coli Aspartate Transcarbamylase and Its Catalytic Subunit ^†
journal, August 1997

GRASP2: Visualization, Surface Properties, and Electrostatics of Macromolecular Structures and Sequences
book, January 2003

MIBPB: A software package for electrostatic analysis
journal, September 2010

Molecular Models of Amino Acids, Peptides, and Proteins
journal, August 1953

A Gaussian Description of Molecular Shape
journal, March 1995

Second-order Poisson–Nernst–Planck solver for ion transport
journal, June 2011

Minimal molecular surfaces and their applications
journal, January 2007

Variational Multiscale Models for Charge Transport
journal, January 2012

Multiscale multiphysics and multidomain models—Flexibility and rigidity
journal, November 2013

Reduced surface: An efficient way to compute molecular surfaces
journal, March 1996

A new approach to analysis and display of local lipophilicity/hydrophilicity mapped on molecular surfaces
journal, October 1993

Multiscale, Multiphysics and Multidomain Models i: Basic Theory
journal, December 2013

Differential geometry based solvation model I: Eulerian formulation
journal, November 2010

Geometric modeling of subcellular structures, organelles, and multiprotein complexes: GEOMETRIC MODELING OF SUBCELLULAR STRUCTURES
journal, November 2012

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation
journal, June 2008

DNA Binding and Bending by HMG Boxes: Energetic Determinants of Specificity
journal, October 2004

Differential geometry based solvation model. III. Quantum formulation
journal, November 2011

Molecular surface-volume and property matching to superpose flexible dissimilar molecules
journal, December 1995

Quality mesh generation for molecular skin surfaces using restricted union of balls
journal, April 2009

Multiresolution persistent homology for excessively large biomolecular datasets
journal, October 2015

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
journal, March 2006

SIMS: computation of a smooth invariant molecular surface
journal, August 1997

Areas, Volumes, Packing, and Protein Structure
journal, June 1977

The interdependence of protein surface topography and bound water molecules revealed by surface accessibility and fractal density measures
journal, November 1992

TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique
journal, November 2010

Coupling of local folding to site-specific binding of proteins to DNA
journal, February 1994

Wavelets generated by using discrete singular convolution kernels
journal, November 2000

Surface shape and curvature scales
journal, October 1992

Poisson–Boltzmann–Nernst–Planck model
journal, May 2011

Multi-Scale Surface Descriptors
journal, November 2009

Macromolecule backbone models
book, January 1985

Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential
journal, June 1997

The interpretation of protein structures: Estimation of static accessibility
journal, February 1971

Molecular surface generation using marching tetrahedra
journal, August 1998

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis
journal, June 2014

Depth-buffer algorithms for molecular modelling
journal, March 1985

Multiscale geometric modeling of macromolecules II: Lagrangian representation
journal, June 2013

Biomolecular surface construction by PDE transform: BIOMOLECULAR SURFACE CONSTRUCTION BY PDE TRANSFORM
journal, September 2011

Improving implicit solvent simulations: a Poisson-centric view
journal, April 2005

Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects
journal, November 2001

Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
journal, November 2007

Treatment of geometric singularities in implicit solvent models
journal, June 2007

Treatment of charge singularities in implicit solvent models
journal, September 2007

Absorption Classification of Oral Drugs Based on Molecular Surface Properties
journal, February 2003

DG-GL: Differential geometry-based geometric learning of molecular datasets
journal, February 2019

MathDL: mathematical deep learning for D3R Grand Challenge 4
journal, November 2019