Brownian dynamics of diffusion-controlled reactions: the lattice method

Predicting interactions of winged-helix transcription factors with DNA

Determining protein-DNA interactions is important for understanding gene regulation, DNA repair and chromatin structure. Unfortunately, the structures of DNA-bound complexes are often difficult to obtain experimentally, so the development of computational methods that provide good models of these complexes would be valuable. Here, we present a rigid-body docking approach using the computer program DOT. DOT performs a complete, six-dimensional search of all orientations for two rigid molecules and calculates the interaction energy as the sum of electrostatic and van der Waals terms. DOT was applied to three winged-helix transcription factors that share similar DNA-binding structural motifs but bind DNA in different ways. Docking with linear B-form DNA models accomplished several objectives; it (1) distinguished the different ways the transcription factors bind DNA, (2) identified each protein's DNA-binding site and the DNA orientation at the site and (3) gave at least one solution among the three best-ranked that shows the protein side chain-DNA base interactions responsible for recognition. Furthermore, the ensemble of top-ranked, docked linear B-DNA fragments indicated the DNA bending induced upon protein binding. Docking linear B-DNA to structures of the transcription factor FadR suggests that the allosteric, conformational change induced upon effector binding results in loss of the ability to bend DNA as well as loss of sequence-specific interactions with DNA. The electrostatic energy term calculated by DOT is comparable to the electrostatic binding energy calculated by Poisson-Boltzmann methods. Our results show rigid-body docking that includes a rigorous treatment of the electrostatic interaction energy can be effective in predicting protein-DNA interactions.

The protein state of matter

Three ways are generally used to visualize proteins: (1) a static model in which the atomic positions are defined, (2) a dynamic model taking into account fluctuations, and (3) a reactive model that reflects the internal and external electric fields of the molecule. The properties of chromophoric prosthetic groups can be probed by optical spectroscopy, and when high resolution techniques are used, the results reveal information about the local electric fields in proteins, as influenced and determined by atomic positions and dynamics.

Point charge distributions and electrostatic steering in enzyme/substrate encounter: Brownian dynamics of modified copper/zinc superoxide dismutases

The electrostatic steering mechanism of bovine erythrocyte Cu/Zn superoxide dismutase (SOD) was investigated through the use of Brownian dynamics. Simulations of enzyme/substrate encounter were carried out on 14 different SOD models defined by simple changes in the enzyme's point charge distribution. The magnitude and ionic strength dependence of reaction rates, rates for collision anywhere on the enzyme surface, and collision efficiency factors were analyzed to elucidate both the general and specific roles for point charges associated with amino acid residues. Collision rates for the general enzyme surface appear to be solely determined by the net charge on the enzyme. At physiological ionic strength this effect is negligible, with only 6% variation in collision rates observed as the net charge ranges from +2e to -10e. With the exception of a few charged residues in the active-site channel of SOD, point charge modifications had modest effects on reaction rates. For a large region within and surrounding the channel, reaction rates increased or decreased by only 10-15% with the addition or subtraction of a protonic unit of charge, respectively. This effect simply disappeared with increasing distance from the active site. More dramatic effects were seen at only three residues: arginine-141, glutamate-131, and lysine-134. Implications for rate enhancement through site-directed mutagenesis are discussed.

Visualization of molecular flexibility and its effects on electrostatic recognition

To study the effect of protein flexibility on electrostatic recognition, we have devised two novel computer graphic representations of the changes in the electrostatic field of a protein resulting from its internal motions. The atomic structure of Cu, Zn superoxide dismutase was minimized, and the 200 lowest frequency normal modes of the enzyme were determined. Individual and combined normal-mode vibrations were visualized interactively with the program Flex. Normal-mode motions are fast enough (approximately 10(-11) s cycle-1) to evade solvent damping, thus allowing long-range electrostatic interactions to dominate. The changing electrostatic environment of the protein was examined by animating precalculated frames of electrostatic field vectors with GRAMPS. With Vu, changes in electrostatic potential were displayed as variations in the color-coding of dots lying on a consensus surface that maintains the protein's shape. The consensus surface was calculated with the program Sphinx, and was derived from spherical harmonic approximations of expanded molecular surfaces. The ability to view the effects of molecular motions interactively should be useful in understanding the relationships of protein structure to function.

Brownian dynamics of cytochrome c and cytochrome c peroxidase association

Brownian dynamics computer simulations of the diffusional association of electron transport proteins cytochrome c (cyt c) and cytochrome c peroxidase (cyt c per) were performed. A highly detailed and realistic model of the protein structures and their electrostatic interactions was used that was based on an atomic-level spatial description. Several structural features played a role in enhancing and optimizing the electron transfer efficiency of this reaction. Favorable electrostatic interactions facilitated long-lived nonspecific encounters between the proteins that allowed the severe orientational criteria for reaction to be overcome by rotational diffusion during encounters. Thus a "reduction-in-dimensionality" effect operated. The proteins achieved plausible electron transfer orientations in a multitude of electrostatically stable encounter complexes, rather than in a single dominant complex.

Brownian dynamics simulation of protein association

The Brownian Dynamics (BD) method is applied to study the diffusive dynamics and interaction of two proteins, cytochrome c (CYTC) and cytochrome c peroxidase (CYP). We examine the role of protein electrostatic charge distribution in the facilitation of protein-protein docking prior to the electron transfer step, assessing the influence of individual charged amino acid residues. Accurate interaction potentials are computed by iterating the linearized Poisson-Boltzmann (PB) equation around the larger protein CYP. The low dielectric constant inside proteins, electrolyte screening effects and irregular protein surface topography are taken into account. We observe a large ensemble of electrostatically stable encounter complexes seemingly with acceptable geometric requirements for electron transfer rather than a single dominant complex. Stabilities of the large variety of docking complexes are rationalized in terms of generalized charged residue complementarities. However, it is found that the electrostatic interactions giving rise to complex stabilities are somewhat nonspecific in nature. A large series of additional simulations are performed in which individual charged residues on CYTC have been chemically modified. Resulting perturbations of the association rate are significant and qualitatively similar to results observed in comparable kinetics experiments. We therefore demonstrate the potential of the Brownian dynamics method to estimate the effects of site-directed mutagenesis on protein-protein and protein-ligand diffusional association rates.

Computer simulations of the diffusion of a substrate to an active site of an enzyme

Computer simulations of the diffusion of a substrate to an enzyme active site were performed. They included the detailed shape of the protein and an accurate description of its electrostatic potential. Application of the method to the diffusion of the superoxide anion to the protein superoxide dismutase revealed that the electric field of the enzyme enhances the association rate of the anion by a factor of 30 or more. Calculated changes in the association rate as a function of ionic strength and amino acid modification paralleled the observed behavior. Design principles of superoxide dismutase are considered with respect to insights provided by the simulations. A possible means of enhancing the enzyme turnover rate through site-directed mutagenesis is proposed.