Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness.

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

[1]  M S Sansom,et al.  Membrane simulations: bigger and better? , 2000, Current opinion in structural biology.

[2]  J. Salgado,et al.  Orientational landscapes of peptides in membranes: prediction of (2)H NMR couplings in a dynamic context. , 2009, Biochemistry.

[3]  G. Heijne,et al.  Genome‐wide analysis of integral membrane proteins from eubacterial, archaean, and eukaryotic organisms , 1998, Protein science : a publication of the Protein Society.

[4]  R. S. Spolar,et al.  Hydrophobic effect in protein folding and other noncovalent processes involving proteins. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[5]  C. Brooks,et al.  An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins. , 2003, Biophysical journal.

[6]  W F Drew Bennett,et al.  Statistical Convergence of Equilibrium Properties in Simulations of Molecular Solutes Embedded in Lipid Bilayers. , 2011, Journal of chemical theory and computation.

[7]  V. Cherezov,et al.  Transmembrane peptides stabilize inverted cubic phases in a biphasic length-dependent manner: implications for protein-induced membrane fusion. , 2006, Biophysical journal.

[8]  T. Ramasami,et al.  Molecular dynamic simulation studies on the effect of one residue chain staggering on the structure and stability of heterotrimeric collagen-like peptides with interruption. , 2012, Biopolymers.

[9]  Charles L. Brooks,et al.  New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations , 2003, J. Comput. Chem..

[10]  Ronald M. Levy,et al.  AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling , 2004, J. Comput. Chem..

[11]  J. Killian,et al.  On the orientation of a designed transmembrane peptide: toward the right tilt angle? , 2007, Journal of the American Chemical Society.

[12]  Michael Feig,et al.  MMTSB Tool Set: enhanced sampling and multiscale modeling methods for applications in structural biology. , 2004, Journal of molecular graphics & modelling.

[13]  Velin Z. Spassov,et al.  Introducing an Implicit Membrane in Generalized Born/Solvent Accessibility Continuum Solvent Models , 2002 .

[14]  Jakob P Ulmschneider,et al.  Sampling efficiency in explicit and implicit membrane environments studied by peptide folding simulations , 2009, Proteins.

[15]  Toby W Allen,et al.  On the thermodynamic stability of a charged arginine side chain in a transmembrane helix , 2007, Proceedings of the National Academy of Sciences.

[16]  Luís M. S. Loura,et al.  Is there a preferential interaction between cholesterol and tryptophan residues in membrane proteins? , 2008, Biochemistry.

[17]  M. Goulian,et al.  Energetics of inclusion-induced bilayer deformations. , 1998, Biophysical journal.

[18]  A. Ulrich,et al.  Orientation and dynamics of peptides in membranes calculated from 2H-NMR data. , 2009, Biophysical journal.

[19]  D. Frenkel,et al.  Molecular dynamics simulations. , 2002, Current opinion in structural biology.

[20]  Syma Khalid,et al.  Coarse-grained molecular dynamics simulations of membrane proteins and peptides. , 2007, Journal of structural biology.

[21]  J. Killian,et al.  Self-association of transmembrane alpha-helices in model membranes: importance of helix orientation and role of hydrophobic mismatch. , 2005, The Journal of biological chemistry.

[22]  B. Bengtsson,et al.  Structure of the Natural Transgene PgiC2 in the Common Grass Festuca ovina , 2010, PloS one.

[23]  Nathan A. Baker,et al.  Improving implicit solvent simulations: a Poisson-centric view. , 2005, Current opinion in structural biology.

[24]  R. Larson,et al.  Molecular dynamics simulations of model trans-membrane peptides in lipid bilayers: a systematic investigation of hydrophobic mismatch. , 2006, Biophysical journal.

[25]  Erik Strandberg,et al.  Tilt angles of transmembrane model peptides in oriented and non-oriented lipid bilayers as determined by 2H solid-state NMR. , 2004, Biophysical journal.

[26]  G. Heijne,et al.  The membrane protein universe: what's out there and why bother? , 2007 .

[27]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[28]  J. Killian,et al.  Interfacial anchor properties of tryptophan residues in transmembrane peptides can dominate over hydrophobic matching effects in peptide-lipid interactions. , 2003, Biochemistry.

[29]  Naomi R. Latorraca,et al.  Membrane bending is critical for the stability of voltage sensor segments in the membrane , 2012, The Journal of general physiology.

[30]  J. A. Lundbæk,et al.  Spring constants for channel-induced lipid bilayer deformations. Estimates using gramicidin channels. , 1999, Biophysical journal.

[31]  Jianpeng Ma,et al.  CHARMM: The biomolecular simulation program , 2009, J. Comput. Chem..

[32]  Charles L. Brooks,et al.  Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures , 2004, J. Comput. Chem..

[33]  C. Brooks,et al.  Novel generalized Born methods , 2002 .

[34]  Justin L. MacCallum,et al.  Partitioning of Amino Acid Side Chains into Lipid Bilayers: Results from Computer Simulations and Comparison to Experiment , 2007, The Journal of general physiology.

[35]  Sunhwan Jo,et al.  Transmembrane helix orientation and dynamics: insights from ensemble dynamics with solid-state NMR observables. , 2011, Biophysical journal.

[36]  H. Huang,et al.  Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime. , 1986, Biophysical journal.

[37]  M. Feig,et al.  A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes. , 2005, The Journal of chemical physics.

[38]  G. von Heijne,et al.  Interface connections of a transmembrane voltage sensor. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Wonpil Im,et al.  Revisiting hydrophobic mismatch with free energy simulation studies of transmembrane helix tilt and rotation. , 2010, Biophysical journal.

[40]  Harry A. Stern,et al.  Calculation of the dielectric permittivity profile for a nonuniform system: Application to a lipid bilayer simulation , 2003 .

[41]  Olaf S Andersen,et al.  Bilayer thickness and membrane protein function: an energetic perspective. , 2007, Annual review of biophysics and biomolecular structure.

[42]  J. Chocholousová,et al.  Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment. , 2006, The journal of physical chemistry. B.

[43]  H Luecke,et al.  Structure of bacteriorhodopsin at 1.55 A resolution. , 1999, Journal of molecular biology.

[44]  M. Feig,et al.  Role of conformational sampling of Ser16 and Thr17-phosphorylated phospholamban in interactions with SERCA. , 2013, Biochimica et biophysica acta.

[45]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[46]  O. Andersen,et al.  Inclusion-induced bilayer deformations: effects of monolayer equilibrium curvature. , 2000, Biophysical journal.

[47]  Alexander D. MacKerell,et al.  All‐atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data , 2000 .

[48]  Nathan A. Baker,et al.  APBSmem: A Graphical Interface for Electrostatic Calculations at the Membrane , 2010, PloS one.

[49]  S. Safran,et al.  Interaction between inclusions embedded in membranes. , 1996, Biophysical journal.

[50]  C. Brooks,et al.  Interfacial folding and membrane insertion of designed peptides studied by molecular dynamics simulations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Alexander D. MacKerell,et al.  Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles. , 2012, Journal of chemical theory and computation.

[52]  Michael Grabe,et al.  A Continuum Method for Determining Membrane Protein Insertion Energies and the Problem of Charged Residues , 2008, The Journal of general physiology.

[53]  H. Robert Guy,et al.  A large iris-like expansion of a mechanosensitive channel protein induced by membrane tension , 2002, Nature Structural Biology.

[54]  E. Lindahl,et al.  Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. , 2000, Biophysical journal.

[55]  Martin Zacharias,et al.  Continuum Solvent Modeling of Nonpolar Solvation: Improvement by Separating Surface Area Dependent Cavity and Dispersion Contributions , 2003 .

[56]  Alexander D. MacKerell,et al.  Improved treatment of the protein backbone in empirical force fields. , 2004, Journal of the American Chemical Society.

[57]  A. Holt,et al.  Tilt and rotation angles of a transmembrane model peptide as studied by fluorescence spectroscopy. , 2009, Biophysical journal.

[58]  Zhenfeng Liu,et al.  Structure of a tetrameric MscL in an expanded intermediate state , 2009, Nature.

[59]  J. Killian,et al.  Sensitivity of single membrane-spanning alpha-helical peptides to hydrophobic mismatch with a lipid bilayer: effects on backbone structure, orientation, and extent of membrane incorporation. , 2001, Biochemistry.

[60]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[61]  Sunhwan Jo,et al.  Solid-state NMR ensemble dynamics as a mediator between experiment and simulation. , 2011, Biophysical journal.

[62]  W. Im,et al.  Influence of hydrophobic mismatch on structures and dynamics of gramicidin a and lipid bilayers. , 2012, Biophysical journal.

[63]  Ray Luo,et al.  Accelerated Poisson–Boltzmann calculations for static and dynamic systems , 2002, J. Comput. Chem..

[64]  Federico Fogolari,et al.  Protocol for MM/PBSA molecular dynamics simulations of proteins. , 2003, Biophysical journal.

[65]  E. Jakobsson,et al.  Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels. , 1990, Biophysical journal.

[66]  A. Libchaber,et al.  Gramicidin channel kinetics under tension. , 1998, Biophysical journal.

[67]  M. Feig,et al.  Effect of membrane thickness on conformational sampling of phospholamban from computer simulations. , 2010, Biophysical journal.

[68]  J. F. Hinton,et al.  Structures of gramicidins A, B, and C incorporated into sodium dodecyl sulfate micelles. , 2001, Biochemistry.

[69]  Michael Feig,et al.  Implicit solvation based on generalized Born theory in different dielectric environments. , 2004, The Journal of chemical physics.

[70]  M. Karplus,et al.  A Comprehensive Analytical Treatment of Continuum Electrostatics , 1996 .

[71]  M Karplus,et al.  Solvent effects on protein motion and protein effects on solvent motion. Dynamics of the active site region of lysozyme. , 1989, Journal of molecular biology.

[72]  Ahmed Hassanein,et al.  Electroelastic coupling between membrane surface fluctuations and membrane-embedded charges: continuum multidielectric treatment. , 2010, The Journal of chemical physics.

[73]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[74]  Yun-Dong Wu,et al.  Parameterization of PACE Force Field for Membrane Environment and Simulation of Helical Peptides and Helix-Helix Association. , 2012, Journal of chemical theory and computation.

[75]  A. Parsegian,et al.  Energy of an Ion crossing a Low Dielectric Membrane: Solutions to Four Relevant Electrostatic Problems , 1969, Nature.

[76]  Peter C. Jordan,et al.  Membrane deformation and the elastic energy of insertion: Perturbation of membrane elastic constants due to peptide insertion , 2002 .

[77]  Anesthetic molecules embedded in a lipid membrane: a computer simulation study. , 2012, Physical chemistry chemical physics : PCCP.

[78]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

[79]  J. Beckwith,et al.  How many membrane proteins are there? , 1998, Protein science : a publication of the Protein Society.

[80]  J. Killian,et al.  Hydrophobic mismatch between helices and lipid bilayers. , 2003, Biophysical journal.

[81]  C. Brooks,et al.  Recent advances in the development and application of implicit solvent models in biomolecule simulations. , 2004, Current opinion in structural biology.

[82]  Nathan A. Baker,et al.  Electrostatics of nanosystems: Application to microtubules and the ribosome , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[83]  T. Woolf,et al.  Coarse-grained simulations of transitions in the E2-to-E1 conformations for Ca ATPase (SERCA) show entropy-enthalpy compensation. , 2012, Journal of molecular biology.

[84]  Barry Honig,et al.  Calculation of Alkane to Water Solvation Free Energies Using Continuum Solvent Models , 1996 .

[85]  A. D. McLachlan,et al.  Solvation energy in protein folding and binding , 1986, Nature.

[86]  M. Feig,et al.  Conformational sampling of influenza fusion peptide in membrane bilayers as a function of termini and protonation states. , 2010, The journal of physical chemistry. B.

[87]  M. Feig,et al.  Effect of flanking residues on the conformational sampling of the internal fusion peptide from Ebola virus , 2011, Proteins.

[88]  J. Killian,et al.  Phospholipid flop induced by transmembrane peptides in model membranes is modulated by lipid composition. , 2003, Biochemistry.