Multiscale Modeling of Biological Macromolecules in Cellular Environments
Established simulation methods limit the time and spatial scales that can be studied in molecular dynamics simulations. Time and spatial scales can be extended by reducing system complexity either through:
We are especially interested in the following directions:
Implicit Models of Aqueous Solvent
The biological environment of most biomolecules is aqueous solvent. The interactions with the surrounding water are very important for the stability and function of proteins and nucleic acids. In molecular modeling studies, the water environment is commonly represented explicitly as in the example shown below in the first picture on the left. Such models can provide a realistic picture of how biomolecules behave in a biological cell, but the large number of water molecules in addition to the biomolecule adds significant computational costs.
By running a computer simulation with explicit solvent, it is possible to determine the average distribution of water molecules around a given molecule as shown in the center picture. The most interesting part is the white surface that encloses the volume occupied by the molecule where water cannot penetrate. It is possible to construct an implicit solvent model by approximating the medium outside the water-excluded volume as a continuum with electrostatic, entropic, and viscous properties that match water.
A continuum electrostatic model of a biomolecule in water commonly involves a low-dielectric (epsilon=1) solute cavity with explicit partial atomic charges of the solute surrounded by a high-dielectric (epsilon=80) continuous medium without any explicit charges. Such a model is described by the Poisson equation. We are particulary interested in an efficient approximation to solutions of the Poisson equation, called the Generalized Born formalism.
Implicit Models of Membrane Environments
Many important proteins are bound to biological membranes. Biological membranes consist of a phospholipid bilayer with a hydrophobic interior surrounded that is surrounded by polar head groups and aqueous solvent on both sides. Therfore, proteins embedded in such lipid bilayers experience a heterogeneous dielectric environment with a dielectric constant that rises from a value between 1 and 2 near the center of the membrane to 80 in bulk aqueous solvent.
Implicit models of membrane environments can be constructed as a system of layers with different dielectric constants. The simplest model shown on the left may include two layers: epsilon=1 for the lipid interior and epsilon=80 for the head group and surrounding water. A more realistic model may include three dielectric layers as shown on the right.
A heterogeneous dielectric environment requires modifications of the canonical Generalized Born formalism. In particular, it is necessary to introduce an effective dielectric constant that is experienced by a spherical probe at different locations within the lipid bilayer as shown in the diagram below:
The effective dielectric constant is then used in a modified generalized Born expression for the electrostatic solvation free energy of a solute in a heterogeneous dielectric environment.
We have applied the implicit membrane model for simulations of membrane-bound proteins and peptides. More details are given here.
Future efforts are directed at improving the description of non-polar interactions within the membrane and allowing dynamic fluctuations of the membrane thickness in response to biomolecular interactions.
Coarse-grained Modeling of Proteins and Nucleic Acids
Most recently we have begun to develop a new coarse-grained model for proteins and nucleic to facilitate the development of multiscale modeling schemes. This model, called PRIMO (PRotein Intermediate MOdel) and PRIMONA for nucleic acids), represents biomolecules at sufficient detail to allow high-resolution reconstruction of fully atomistic representations. This offers the advantage of a one-to-one transformation in both directions which is an essential prerequisite for the development of multiscale methods.
The PRIMO model uses a force-field like interaction potential that can be parameterized by direct comparison with atomistic force fields. It is designed to be fully transferable and can be combined with implicit models of both aqueous solvent and membrane environments. PRIMO allows stable molecular dynamics simulations of proteins and nucleic acids as shown below:
Jing Huang, Sarah Rauscher, Grzegorz Nawrocki, Ting Ran, Michael Feig, Bert L. de Groot, Helmut Grubmüller, Alexander D. MacKerell Jr.: CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins Nature Methods (2016) in press,
Vahid Mirjalili, Michael Feig: Density-biased sampling: A robust computational method for studying pore formation in membranes Journal of Chemical Theory and Computation (2015) 11, 343-350 Abstract PDF
Parimal Kar, Srinivasa Murthy Gopal, Yi-Ming Cheng, Afra Panahi, Michael Feig: Transferring the PRIMO Coarse-Grained Force Field to the Membrane Environment: Simulation of Proteins and Helix-Helix Association Journal of Chemical Theory and Computation (2014) 10, 3459-3472 Abstract PDF
Parimal Kar, Michael Feig: Recent Advances in Transferable Coarse-Grained Modeling of Proteins Advances in Protein Chemistry & Structural Biology: Biomolecular Modelling and Simulations (2014) 10, 3459-3472 Abstract PDF
Afra Panahi, Michael Feig: Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness Journal of Chemical Theory and Computation (2013) 9, 1709-1719 Abstract PDF
Parimal Kar, Srinivasa Murthy Gopal, Yi-Ming Cheng, Alexander Predeus, Michael Feig: PRIMO: A transferable coarse-grained force field for proteins Journal of Chemical Theory and Computation (2013) 9, 3769-3788 Abstract PDF
Yiming Cheng, Srinivasa Gopal, Sean Law, Michael Feig: Molecular dynamics trajectory compression with a coarse-grained model IEEE/ACM Transactions in Computational Biology and Bioinformatics (2012) 6, 476-486 Abstract PDF
Robert Best, Xiao Zhu, Jihyun Shim, Pedro Lopes, Jeetain Mittal, Michael Feig, Alexander MacKerell: Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone phi, psi, and side-chain chi1 and chi2 Dihedral Angles Journal of Chemical Theory and Computation (2012) 8, 3257-3273 Abstract PDF
Robert Best, Jeetain Mittal, Michael Feig, Alexander MacKerell: Inclusion of many-body effects in the additive CHARMM protein CMAP potential results in enhanced cooperativity of alpha-helix and beta-hairpin formation Biophysical Journal (2012) 103, 1045-1051 Abstract PDF
Srinivasa M. Gopal, Shayantani Mukherjee, Yi-Ming Cheng, Michael Feig: PRIMO/PRIMONA: A coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy Proteins (2010) 78, 1266-1281 Abstract PDF
B. R. Brooks, C. L. Brooks III, A. D. MacKerell, Jr., L. Nilsson, R. J. Petrella, B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch, A. Caflisch, L. Caves, Q. Cui, A. R. Dinner, M. Feig, S. Fischer, J. Gao, M. Hodoscek, W. Im, K. Kuczera, T. Lazaridis, J. Ma, V. Ovchinnikov, E. Paci, R. W. Pastor, C. B. Post, J. Z. Pu, M. Schaefer, B. Tidor, R. M. Venable, H. L. Woodcock, X. Wu, W. Yang, D. M. York, M. Karplus: CHARMM: The Biomolecular Simulation Program Journal of Computational Chemistry (2009) 30, 1545-1614 Abstract PDF
Yongcheng Zhou, Michael Feig, Guowei Wei: Highly Accurate Biomolecular Electrostatics in Continuum Dieletric Environments Journal of Computational Chemistry (2008) 29, 87-97 Abstract PDF
Kitiyaporn Wittayanarakul, Supot Hannongbua, Michael Feig: Accurate prediction of protonation state as a prerequisite for reliable MM-PB(GB)SA binding free energy calculations of HIV-1 protease inhibitors Journal of Computational Chemistry (2008) 29, 673-685 Abstract PDF
Michael Feig: Is Alanine Dipeptide a Good Model for Representing the Torsional Preferences of Protein Backbones? Journal of Chemical Theory and Computation (2008) 4, 1555-1564 Abstract PDF
Michael Feig: Implicit Membrane Models for Membrane Protein Simulation Methods in Molecular Biology: Molecular Modeling of Proteins edited by Andreas Kukol, Humana Press (2008) 443, 181-198
Michael Feig: Kinetics from Implicit Solvent Simulations of Biomolecules as a Function of Viscosity Journal of Chemical Theory and Computation (2007) 3, 1734-1748 Abstract PDF
Michael Feig, Jana Chocholousova, Seiichiro Tanizaki: Extending the Horizon: Towards the Efficient Modeling of Large Biomolecular Complexes in Atomic Detail Theoretical Chemistry Accounts (2006) 116, 194-205 Abstract PDF
Yong C. Zhou, Shan Zhao, Michael Feig, Guo W. Wei: High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources Journal of Computational Physics (2006) 213, 1-30 Abstract PDF
Jana Chocholousova, Michael Feig: Balancing an Accurate Representation of the Molecular Surface in Generalized Born Formalisms with Integrator Stability in Molecular Dynamics Simulations Journal of Computational Chemistry (2006) 27, 719-729 Abstract PDF
Seiichiro Tanizaki, Michael Feig: Molecular Dynamics Simulations of Large Integral Membrane Proteins with an Implicit Membrane Model Journal of Physical Chemistry B (2006) 110, 548-556 Abstract PDF
Jana Chocholousova, Michael Feig: Implicit Solvent Simulations of DNA and DNA-Protein Complexes: Agreement with Explicit Solvent vs. Experiment Journal of Physical Chemistry B (2006) 110, 17240-17251 Abstract PDF
Michael Feig, Seiichiro Tanizaki: Development of a Heterogeneous Dielectric Generalized Born Model for the Implicit Modeling of Membrane Environments Modelling Molecular Structure and Reactivity in Biological Systems edited by Kevin J. Naidoo, John Brady, Martin J. Field, Jiali Gao, and Michael Hann, Proceedings of WATOC 2005, Royal Society of Chemistry (2006) , 141-150
Seiichiro Tanizaki, Michael Feig: A generalized Born formalism for heterogeneous dielectric environments: Application to the implicit modeling of biological membranes Journal of Chemical Physics (2005) 122, 124706 Abstract PDF
Michael Feig, Alexey Onufriev, Michael S. Lee, Wonpil Im, David A. Case, Charles L. Brooks III: Performance comparison of generalized Born and Poisson methods in the calculation of electrostatic solvation energies for protein structures Journal of Computational Chemistry (2004) 25, 265-284 Abstract PDF
Michael Feig, Wonpil Im, Charles L. Brooks III: Implicit solvation based on generalized Born theory in different dielectric environments Journal of Chemical Physics (2004) 120, 903-911 Abstract PDF
Michael Feig, John Karanicolas, Charles L. Brooks III: MMTSB Tool Set: Enhanced Sampling and Multiscale Modeling Methods for Applications in Structural Biology Journal of Molecular Graphics and Modeling (2004) 22, 377-395 Abstract PDF
Alexander D. MacKerell jr., Michael Feig, Charles L. Brooks III: Improved treatment of the protein backbone in empiricial force fields Journal of the American Chemical Society (2004) 126, 698-699 Abstract PDF
Michael Feig, Charles L. Brooks III: Recent advances in the development and application of implicit solvent models in biomolecule simulations Current Opinion in Structural Biology (2004) 14, 217-224 Abstract PDF
Alexander D. MacKerell jr., Michael Feig, Charles L. Brooks III: Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations Journal of Computational Chemistry (2004) 25, 1400-1415 Abstract PDF
Michael S. Lee, Michael Feig, Freddie R. Salsbury jr., Charles L. Brooks III: A New Analytical Approximation to the Standard Molecular Volume Definition And Its Application to Generalized Born Calculations Journal of Computational Chemistry (2003) 24, 1348-1356 Abstract PDF
Michael Feig, Alexander D. MacKerell jr., Charles L. Brooks III: The force field influence on the observation of pi-helical protein structures in molecular dynamics simulations Journal of Physical Chemistry B (2003) 107, 2831-2836 Abstract PDF
Michael Feig, Matin Abdullah, Lennart Johnsson, B. Montgomery Pettitt: Large Scale Distributed Data Repository: Design of a Molecular Dynamics Trajectory Database Future Generation Computer Systems (1999) 16, 101-110 Abstract PDF
Grant support: NSF MCB 0447799 (2005-2011), NSF CBET 0941055 (2009-2013), NIH GM084953 (2008-2013), NIH GM092949 (2010-2014)