Ligand binding to protein-binding pockets with wet and dry regions.

Biological processes often depend on protein-ligand binding events, yet accurate calculation of the associated energetics remains as a significant challenge of central importance to structure-based drug design. Recently, we have proposed that the displacement of unfavorable waters by the ligand, replacing them with groups complementary to the protein surface, is the principal driving force for protein-ligand binding, and we have introduced the WaterMap method to account this effect. However, in spite of the adage "nature abhors vacuum," one can occasionally observe situations in which a portion of the receptor active site is so unfavorable for water molecules that a void is formed there. In this paper, we demonstrate that the presence of dry regions in the receptor has a nontrivial effect on ligand binding affinity, and suggest that such regions may represent a general motif for molecular recognition between the dry region in the receptor and the hydrophobic groups in the ligands. With the introduction of a term attributable to the occupation of the dry regions by ligand atoms, combined with the WaterMap calculation, we obtain excellent agreement with experiment for the prediction of relative binding affinities for a number of congeneric ligand series binding to the major urinary protein receptor. In addition, WaterMap when combined with the cavity contribution is more predictive than at least one specific implementation [Abel R, Young T, Farid R, Berne BJ, Friesner RA (2008) J Am Chem Soc 130:2817-2831] of the popular MM-GBSA approach to binding affinity calculation.

Large-scale ab initio quantum chemical calculations on biological systems.

In this Account we describe recent advances in two ab initio electronic structure methods, localized perturbation approaches and density functional theory, that allow accurate calculations including electron correlation to be carried out for systems with hundreds of atoms. Application of these methods to large-scale modeling of biological systems is discussed. Localized perturbation methods are best suited to computation of conformational energetics and nonbonded interactions: determination of the relative energetics of various conformations of the alanine tetrapetide is presented. Density functional theory is the method of choice for studying reactive chemistry; investigations of the catalytic cycle of the enzyme methane monooxygenase are reviewed.

Protein structure prediction using a combination of sequence-based alignment, constrained energy minimization, and structural alignment.

We present a novel approach to protein structure prediction in which fold recognition techniques are combined with ab initio folding methods. Based on the predicted secondary structure, one of two different protocols is followed. For mostly alpha proteins, global optimization and sampling of a statistical energy function is used to generate many low-energy structures; these structures are then screened against a fold library. Any structural matches are then selected for further refinement. For proteins predicted to have significant beta-content, sequence and secondary structure-based alignment is used to identify candidate templates; spatial constraints are then extracted from these templates and used, along with the statistical energy function, in the global sampling and optimization program. Successes and failures of both protocols are discussed.

Prediction of protein tertiary structure to low resolution: performance for a large and structurally diverse test set.

We report the tertiary structure predictions for 95 proteins ranging in size from 17 to 160 residues starting from known secondary structure. Predictions are obtained from global minimization of an empirical potential function followed by the application of a refined atomic overlap potential. The minimization strategy employed represents a variant of the Monte Carlo plus minimization scheme of Li and Scheraga applied to a reduced model of the protein chain. For all of the cases except beta-proteins larger than 75 residues, a native-like structure, usually 4-6 A root-mean-square deviation from the native, is located. For beta-proteins larger than 75 residues, the energy gap between native-like structures and the lowest energy structures produced in the simulation is large, so that low RMSD structures are not generated starting from an unfolded state. This is attributed to the lack of an explicit hydrogen bond term in the potential function, which we hypothesize is necessary to stabilize large assemblies of beta-strands.

Prediction of loop geometries using a generalized born model of solvation effects.

We have carried out an extensive exploration of the possibility of predicting the structure of long loops in proteins, using an 8- and a 12-residue loop in ribonuclease A as models. The native X-ray structure is used as a template while allowing for template flexibility; this makes our work relevant to the problem of homology modeling in which the template is not precisely known. Energies are calculated with the AMBER* and AMBER94 molecular mechanics potentials and the generalized Born continuum solvation model; and conformational space is sampled by means of a combination of Monte Carlo and molecular dynamics methods. Our AMBER94 results demonstrate that we can successfully generate loops with low root-mean-square deviations from the native as well as excellent energetic rankings.

Protein tertiary structure prediction using a branch and bound algorithm.

We report a new method for predicting protein tertiary structure from sequence and secondary structure information. The predictions result from global optimization of a potential energy function, including van der Waals, hydrophobic, and excluded volume terms. The optimization algorithm, which is based on the alphaBB method developed by Floudas and coworkers (Costas and Floudas, J Chem Phys 1994;100:1247-1261), uses a reduced model of the protein and is implemented in both distance and dihedral angle space, enabling a side-by-side comparison of methodologies. For a set of eight small proteins, representing the three basic types--all alpha, all beta, and mixed alpha/beta--the algorithm locates low-energy native-like structures (less than 6A root mean square deviation from the native coordinates) starting from an unfolded state. Serial and parallel implementations of this methodology are discussed.

A branch and bound algorithm for protein structure refinement from sparse NMR data sets.

We describe new methods for predicting protein tertiary structures to low resolution given the specification of secondary structure and a limited set of long-range NMR distance constraints. The NMR data sets are derived from a realistic protocol involving completely deuterated 15N and 13C-labeled samples. A global optimization method, based upon a modification of the alphaBB (branch and bound) algorithm of Floudas and co-workers, is employed to minimize an objective function combining the NMR distance restraints with a residue-based protein folding potential containing hydrophobicity, excluded volume, and van der Waals interactions. To assess the efficacy of the new methodology, results are compared with benchmark calculations performed via the X-PLOR program of Brünger and co-workers using standard distance geometry/molecular dynamics (DGMD) calculations. Seven mixed alpha/beta proteins are examined, up to a size of 183 residues, which our methods are able to treat with a relatively modest computational effort, considering the size of the conformational space. In all cases, our new approach provides substantial improvement in root-mean-square deviation from the native structure over the DGMD results; in many cases, the DGMD results are qualitatively in error, whereas the new method uniformly produces high quality low-resolution structures. The DGMD structures, for example, are systematically non-compact, which probably results from the lack of a hydrophobic term in the X-PLOR energy function. These results are highly encouraging as to the possibility of developing computational/NMR protocols for accelerating structure determination in larger proteins, where data sets are often underconstrained.

Ab initio calculation of electronic coupling in the photosynthetic reaction center.

We have carried out an ab initio electronic structure calculations of electron transfer couplings between chromophores in the bacterial photosynthetic reaction center. The couplings agree remarkably well with parameters obtained from recent quantum dynamical modeling of experimental data assuming an explicit intermediate mechanism. We also have computed couplings on the M-side of the reaction center and have found that the interaction of the primary donor to the M-side intermediate bacteriochlorophyll is quite small because of destructive interference of the two localized coupling matrix elements. This may explain the slow rate of electron transfer down the M-side of the reaction center.

Tertiary structure prediction of mixed alpha/beta proteins via energy minimization.

We describe an improved algorithm for protein structure prediction, assuming that the location of secondary structural elements is known, with particular focus on prediction for proteins containing beta-strands. Hydrogen bonding terms are incorporated into the potential function, supplementing our previously developed residue-residue potential which is based on a combination of database statistics and an excluded volume term. Two small mixed alpha/beta proteins, 1-CTF and BPTI, are studied. In order to obtain native-like structures, it is necessary to allow the beta-strands in BPTI to distort substantially from an ideal geometry, and an automated algorithm to carry this out efficiently is presented. Simulated annealing Monte Carlo methods, which contain a genetic algorithm component as well, are used to produce an ensemble of low-energy structures. For both proteins, a cluster of structures with low RMS deviation from the native structure is generated and the energetic ranking of this cluster is in the top 2 or 3 clusters obtained from simulations. These results are encouraging with regard to the possibility of constructing a robust procedure for tertiary folding which is applicable to beta-strand containing proteins.

Quantum mechanical calculations on biological systems.

Improvements in quantum chemical methods have led to increased applications to biological problems, including the development of potential energy functions for molecular mechanics and modeling of the reactive chemistry in enzyme active sites, with particularly interesting progress being made for metal-containing systems. An important direction is the development and application of hybrid quantum chemical-molecular mechanics methods.

Computational studies of protein folding.

This review describes computational approaches to the determination of protein structure from sequence. The emphasis is on reduced protein models that are sufficiently accurate to represent protein structure at low resolution, yet are computationally efficient enough to allow the extensive search of phase space required to locate the global minimum from an unfolded state. A discussion of both potential functions and algorithmic simulation strategies for such models are presented, along with a number of specific models that have been developed and successfully applied to proteins as large as myoglobin. The results indicate that significant progress is being made in understanding the requirements for computational prediction of protein structure.

Computer modeling of protein folding: conformational and energetic analysis of reduced and detailed protein models.

Recently we developed methods to generate low-resolution protein tertiary structures using a reduced model of the protein where secondary structure is specified and a simple potential based on a statistical analysis of the Protein Data Bank is employed. Here we present the results of an extensive analysis of a large number of detailed, all-atom structures generated from these reduced model structures. Following side-chain addition, minimization and simulated annealing simulations are carried out with a molecular mechanics potential including an approximate continuum solvent treatment. By combining reduced model simulations with molecular modeling calculations we generate energetically competitive, plausible misfolded structures which provide a more significant test of the potential function than current misfolded models based on superimposing the native sequence on the folded structures of completely different proteins. The various contributions to the total energy and their interdependence are analyzed in detail for many conformations of three proteins (myoglobin, the C-terminal fragment of the L7/L12 ribosomal protein, and the N-terminal domain of phage 434 repressor). Our analysis indicates that the all-atom potential performs reasonably well in distinguishing the native structure. It also reveals inadequacies in the reduced model potential, which suggests how this potential can be improved to yield greater accuracy. Preliminary results with an improved potential are presented.

An algorithm to generate low-resolution protein tertiary structures from knowledge of secondary structure.

An algorithm is described to assemble the three-dimensional fold of a protein starting from its secondary structure. A reduced representation of the polypeptide chain is used together with a crude potential based on pair hydrophobicities. The method is shown to be successful in locating the native topology for two 4-alpha-helix bundles, myohemerythrin and cytochrome b-562.

Comparison of theory and experiment for electron transfers in proteins: where's the beef?

The correct way to describe the transfer of electrons across proteins has been the subject of some controversy. Recent advances in theoretical methods and an increase in the amount of experimental data may resolve this dispute.

Scanning electrochemical microscopy: theory and application of the transient (chronoamperometric) SECM response.

A study of the transient (chronoamperometric) response of the scanning electrochemical microscope (SECM) is presented. SECM transients were simulated digitally with a novel integrator based on a Krylov algorithm. The transients observed with planar electrodes (PE), microdisks (MD), and thin-layer cells (TLC) are shown to be limiting cases that fit the simulated SECM transients at very short, intermediate, and long times, respectively. A procedure is established that, provided the tip radius is known, allows the determination of the diffusion coefficient of the species in solution independent of its concentration and the number of electrons transferred in the electrode reaction. Experimental SECM transients are reported for the electrochemical oxidation of Fe(CN)6(4-) in KCl; the diffusion coefficient of Fe(CN)6(4-) was found to agree very well with the literature value.