Fragment-based modeling of NAD binding to the catalytic subunits of diphtheria and pertussis toxins.

We describe a novel application of a fragment-based ligand docking technique; similar methods are commonly applied to the de novo design of ligands for target protein binding sites. We have used several new flexible docking and superposition tools, as well as a more conventional rigid-body (fragment) docking method, to examine NAD binding to the catalytic subunits of diphtheria (DT) and pertussis (PT) toxins, and to propose a model of the NAD-PT complex. Docking simulations with the rigid NAD fragments adenine and nicotinamide revealed that the low-energy dockings clustered in three distinct sites on the two proteins. Two of the sites were common to both fragments and were related to the structure of NAD bound to DT in an obvious way; however, the adenine subsite of PT was shifted relative to that of DT. We chose adenine/nicotinamide pairs of PT dockings from these clusters and flexibly superimposed NAD onto these pairs. A Monte Carlo-based flexible docking procedure and energy minimization were used to refine the modeled NAD-PT complexes. The modeled complex accounts for the sequence and structural similarities between PT and DT and is consistent with many results that suggest the catalytic importance of certain residues. A possible functional role for the structural difference between the two complexes is discussed.

Critical evaluation of the research docking program for the CASP2 challenge.

The binding positions of six small-molecule ligands in their complexes with target proteins were predicted using our Research docking program for the CASP2 challenge. Research uses a Monte Carlo procedure with pairwise energies and allows for the conformational searching of ligand torsional space. We were able to predict 2 of the 5 noncovalent complexes within 2 A root-mean-square (RMS) of the experimental structures as ranked by interaction energy or by a score calculated using our interaction evaluation program, Out-rank. In addition, for 4 of the 5 noncovalent structures we found a docking within 2 A RMS of the experimental structure within the top 20 dockings as ranked by energy. The main limitation in our approach is in the ability of the energy function and Outrank to discriminate among the lowest energy dockings. On the other hand, our success in exploring the multi-dimensional docking space of position, orientation and conformation is encouraging.

Atomic solvation parameters in the analysis of protein-protein docking results.

Several sets of amino acid surface areas and transfer free energies were used to derive a total of nine sets of atomic solvation parameters (ASPs). We tested the accuracy of each of these sets of parameters in predicting the experimentally determined transfer free energies of the amino acid derivatives from which the parameters were derived. In all cases, the calculated and experimental values correlated well. We then chose three parameter sets and examined the effect of adding an energetic correction for desolvation based on these three parameter sets to the simple potential function used in our multiple start Monte Carlo docking method. A variety of protein-protein interactions and docking results were examined. In the docking simulations studied, the desolvation correction was only applied during the final energy calculation of each simulation. For most of the docking results we analyzed, the use of an octanol-water-based ASP set marginally improved the energetic ranking of the low-energy dockings, whereas the other ASP sets we tested disturbed the ranking of the low-energy dockings in many of the same systems. We also examined the correlation between the experimental free energies of association and our calculated interaction energies for a series of proteinase-inhibitor complexes. Again, the octanol-water-based ASP set was compatible with our standard potential function, whereas ASP sets derived from other solvent systems were not.

Monte Carlo docking with ubiquitin.

The development of general strategies for the performance of docking simulations is prerequisite to the exploitation of this powerful computational method. Comprehensive strategies can only be derived from docking experiences with a diverse array of biological systems, and we have chosen the ubiquitin/diubiquitin system as a learning tool for this process. Using our multiple-start Monte Carlo docking method, we have reconstructed the known structure of diubiquitin from its two halves as well as from two copies of the uncomplexed monomer. For both of these cases, our relatively simple potential function ranked the correct solution among the lowest energy configurations. In the experiments involving the ubiquitin monomer, various structural modifications were made to compensate for the lack of flexibility and for the lack of a covalent bond in the modeled interaction. Potentially flexible regions could be identified using available biochemical and structural information. A systematic conformational search ruled out the possibility that the required covalent bond could be formed in one family of low-energy configurations, which was distant from the observed dimer configuration. A variety of analyses was performed on the low-energy dockings obtained in the experiment involving structurally modified ubiquitin. Characterization of the size and chemical nature of the interface surfaces was a powerful adjunct to our potential function, enabling us to distinguish more accurately between correct and incorrect dockings. Calculations with the structure of tetraubiquitin indicated that the dimer configuration in this molecule is much less favorable than that observed in the diubiquitin structure, for a simple monomer-monomer pair. Based on the analysis of our results, we draw conclusions regarding some of the approximations involved in our simulations, the use of diverse chemical and biochemical information in experimental design and the analysis of docking results, as well as possible modifications to our docking protocol.

A multiple-start Monte Carlo docking method.

We present a method to search for possible binding modes of molecular fragments at a specific site of a potential drug target of known structure. Our method is based on a Monte Carlo (MC) algorithm applied to the translational and rotational degrees of freedom of the probe fragment. Starting from a randomly generated initial configuration, favorable binding modes are generated using a two-step process. An MC run is first performed in which the energy in the Metropolis algorithm is substituted by a score function that measures the average distance of the probe to the target surface. This has the effect of making buried probes move toward the target surface and also allows enhanced sampling of deep pockets. In a second MC run, a pairwise atom potential function is used, and the temperature parameter is slowly lowered during the run (Simulated Annealing). We repeat this procedure starting from a large number of different randomly generated initial configurations in order to find all energetically favorable docking modes in a specified region around the target. We test this method using two inhibitor-receptor systems: Streptomyces griseus proteinase B in complex with the third domain of the ovomucoid inhibitor from turkey, and dihydrofolate reductase from E. coli in complex with methotrexate. The method could consistently reproduce the complex found in the crystal structure searching from random initial positions in cubes ranging from 25 A to 50 A about the binding site. In the case of SGPB, we were also successful in docking to the native structure. In addition, we were successful in docking small probes in a search that included the entire protein surface.

Geometrical aspects of surface morphogenesis.

This paper is concerned with the morphogenesis of structures which form thin deformable sheets. A general formalism is presented for the deformation of a sheet in the presence of an isotropic local body stress. This formalism leads to a set of equations, based on the theory of shells, in which corrections are made in the geometry due to large deformations. Under certain conditions the equations may be solved to give the surface metric tensor as a function of the local tension. A numerical example based on a simple "threshold" model is also presented.

Diffusion effects in calcium-regulated strain fields.

The Goodwin-Trainor equations for cellular morphogenesis, based on calcium ion regulation of the visco-elastic properties of the cellular cortex, are generalized to the situation where the concentration of calcium ions (free plus bound) is allowed to change locally. A stability analysis is presented which shows that the generalized equations are also stable against perturbations at low and high wave lengths and may, for certain parameter values, develop instabilities at intermediate wave lengths.