Theories of continuum media have proven useful in understanding physical properties of liquids and solids under a broad range of conditions. Similar approaches are desirable for computer simulations of biomolecules. However, the mesoscopic nature of these systems makes it difficult to capture the main physical effects of the solvent on their structure, dynamics, and interactions. The mean field approximation embedded in this continuum model must capture the effects of the bulk medium, and of solvent induced forces (SIF) originating in the microscopic nature of the solvent around the solute. Bulk effects originate in the polarization and orientation of water molecules in the bulk liquid and may be described by classical theory of polar/polarizable liquids; SIF originates in the rearrangement of water molecules around the biomolecule due to their exclusion from the region occupied by the biomolecule itself. Part of our efforts focuses on the development of a continuum model that incorporates these solvent effects incrementally and systematically, thus avoiding the introduction of arbitrary parameters (see below, and discussion in references).

A minimal model must describe the effects of the bulk liquid. Because of the size scale of a biomolecule a statistical mechanics approach to the dielectric properties of the medium is the most natural way to attempt such description. We are developing a general formalism to calculate the inhomogeneous dielectric function in the solvated systems, which in turn can be used to calculate the electrostatic component of the total energy and the hydration energy of a macromolecule. We have used the Debye theory, with further approximations/corrections, in combination with a screened Coulomb potentials superposition approximation to derive a basic model for protein solvation. With further corrections (e.g., to account for hydrogen-bonding competition with water, which is a minimum correction for SIF) this continuum model has been implemented into the CHARMM software to carry out dynamics simulations of proteins and peptides (theory and practical implementation can be downloaded).

To describe protein-ligand interactions in solution furher refinements are needed that are currently being pursued:

1) a connection between the electron structure and the dielectric properties of the medium; this is done by combining quantum chemical calculations with the classical theory of polar liquids described above. This effort is important because it will allow us to use the same description of solvent effects in two size domains, i.e., small molecules, such as drugs and neurotransmitters, and macromolecules, such as enzymes and other proteins. It will also permit a unique descriptions of solvent effects in QM, QM/MM, and MM type of calculations. Another fundamental reason for this development is that it minimizes empiricism (and the usual arbitrariness in the definition of parameters) in models of solvent effects, which is the most serious limitation for reliable application of these methods to problems in molecular and chemical biology. We are using GAMESS as the software environment for our development and methodological implementation. GAMESS is interfaced with CHARMM to carry out QM/MM calculations

2) the dielectric response of the medium is only part of the effects to be accounted for in a continuum formulation of biomolecules in aqueous solution. We are trying to develop a more basic description of solvent induced forces, which are essential in molecular interactions, particularly, in protein-ligand interactions at a protein/solvent interface. This development is important to quantify the forces and torques mediated by the solvent, what determine the docking modes of a ligand to a protein binding site and its binding free energy. We are trying to understand the molecular origin of these SIF in complex solutes using molecular dynamics simulations. From a theoretical view point these developments will benefit from integral equation formalisms (such as the three dimensional extension of the reference interaction sites model, RISM) to characterize the solvent density profiles around ligands and protein cavities. At any rate, a proper description of these forces requires to move beyond simple pairwise additive potentials, thus introducing a semi-microscopic approach that accounts for the granularity of the liquid.
 

S A Hassan, PhD (main page)