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.

Explicit Solvent	Average Density	Implicit Solvent

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 solvent models based on the Generalized Born formalism can be accurate enough to allow molecular dynamics simulations of biomolecules that are as realistic as explicit solvent simulations but at much reduced cost. Click the picture on the left to see an implicit solvent molecular dynamics simulation of protein G.

Relevant Publications:

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) in press

Michael Feig, Jana Chocholousova, Seiichiro Tanizaki: Extending the Horizon: Towards the Efficient Modeling of Large Biomolecular Complexes in Atomic Detail. Theoretical Chemistry Accounts (2006) 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 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 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 PDF



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.

Relevant Publications:

Seiichiro Tanizaki, Michael Feig: Molecular Dynamics Simulations of Large Integral Membrane Proteins with an Implicit Membrane Model. Journal of Physical Chemistry B (2006) 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, Special Issue of the Royal Society of Chemistry (UK) (2006) in press

Michael Feig, Jana Chocholousova, Seiichiro Tanizaki: Extending the Horizon: Towards the Efficient Modeling of Large Biomolecular Complexes in Atomic Detail. Theoretical Chemistry Accounts (2006) PDF

Seiichiro Tanizaki, Michael Feig: A new generalized Born formalism for heterogeneous dielectric environments: Application to the implicit modeling of biological membranes. Journal of Chemical Physics (2005) 122, 124706 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 PDF

Wonpil Im, Michael Feig, Charles L. Brooks III: An implicit membrane generalized Born theory for the study of structure, stability, and interactions of membrane proteins. Biophysical Journal (2003) 85, 2900-2918 PDF