Global energy minimization by rotational energy embedding

Ligand binding site identification by higher dimension molecular dynamics

We propose a new molecular dynamics (MD) protocol to identify the binding site of a guest within a host. The method utilizes a four spatial (4D) dimension representation of the ligand allowing for rapid and efficient sampling within the receptor. We applied the method to two different model receptors characterized by diverse structural features of the binding site and different ligand binding affinities. The Abl kinase domain is comprised of a deep binding pocket and displays high affinity for the two chosen ligands examined here. The PDZ1 domain of PSD-95 has a shallow binding pocket that accommodates a peptide ligand involving far fewer interactions and a micromolar affinity. To ensure completely unbiased searching, the ligands were placed in the direct center of the protein receptors, away from the binding site, at the start of the 4D MD protocol. In both cases, the ligands were successfully docked into the binding site as identified in the published structures. The 4D MD protocol is able to overcome local energy barriers in locating the lowest energy binding pocket and will aid in the discovery of guest binding pockets in the absence of a priori knowledge of the site of interaction.

A dynamical approach to contact distance based protein structure determination

Protein native structure topology based folding dynamics captures many aspects of protein folding. The fact that folding is driven by a potential derived only from residue pairs in native contact, a sparse distance matrix, lead us to postulate this as a solution method to the molecular distance geometry problem. In the standard Go model non-bonded residues move under the influence of a Lennard-Jones potential and consequently folding is slow. In this study we apply a faster quadratic potential Go model to solving the full-atom distance geometry problem, where distance data is based only on residue atoms within 5 Å in the native structure. We show that the method works well when only atomic contact data is known and when a substantial proportion of this contact data is missing. Also, we show that the method can be applied in conjunction with secondary structure prediction schemes to enhance accuracy in cases of missing contact data.

Biomolecular modeling: Goals, problems, perspectives

Computation based on molecular models is playing an increasingly important role in biology, biological chemistry, and biophysics. Since only a very limited number of properties of biomolecular systems is actually accessible to measurement by experimental means, computer simulation can complement experiment by providing not only averages, but also distributions and time series of any definable quantity, for example, conformational distributions or interactions between parts of systems. Present day biomolecular modeling is limited in its application by four main problems: 1) the force-field problem, 2) the search (sampling) problem, 3) the ensemble (sampling) problem, and 4) the experimental problem. These four problems are discussed and illustrated by practical examples. Perspectives are also outlined for pushing forward the limitations of biomolecular modeling.

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.

Influence of rotational energy barriers to the conformational search of protein loops in molecular dynamics and ranking the conformations

An adjustable-barrier dihedral angle potential was added as an extension to a novel, previously presented soft-core potential to study its contribution to the efficacy of the search of the conformational space in molecular dynamics. As opposed to the conventional soft-core potential functions, the leading principle in the design of the new soft-core potential, as well as of its extension, the soft-core and adjustable-barrier dihedral angle (SCADA) potential (referred as the SCADA potential), was to maintain the main equilibrium properties of the original force field. This qualifies the methods for a variety of a priori modeling problems without need for additional restraints typically required with the conventional soft-core potentials. In the present study, the different potential energy functions are applied to the problem of predicting loop conformations in proteins. Comparison of the performance of the soft-core and SCADA potential showed that the main hurdles for the efficient sampling of the conformational space of (loops in) proteins are related to the high-energy barriers caused by the Lennard-Jones and Coulombic energy terms, and not to the rotational barriers, although the conformational search can be further enhanced by lowering the rotational barriers of the dihedral angles. Finally, different evaluation methods were studied and a few promising criteria found to distinguish the near-native loop conformations from the wrong ones.

Structural characterization of the molecular dimer of the peptide antibiotic vancomycin by distance geometry in four spatial dimensions

The conformation of a dimer of the peptide antibiotic vancomycin is developed from computer simulations based on experimental distance constraints derived from high-resolution NMR measurements. The conformation and topological array of the dimer are determined by a distance geometry based method using the molecules cast into four spatial dimensions. This method was imperative for the refinement of vancomycin given the entwining of the monomers (including hydrogen bonding and interactions between the aromatic ring systems) within the dimer. The development of the high-resolution structure of the monomer and then simple molecular modeling to create the dimer which fulfills all of the experimental observations was not possible. In contrast, the refinement protocol using the dimer cast into four spatial dimensions was able to quickly locate conformations in which both the intra- and intermolecular nuclear Overhauser effects were satisfied. These structures, once converted back to three dimensions, were further refined using standard molecular mechanics energy minimization. The structural characteristics of the dimer with respect to binding to the cell-wall precursor are described.

The measurement of molecular diversity: a three-dimensional approach

This paper describes a method for selecting a small, highly diverse subset from a large pool of molecules. The method has been employed in the design of combinatorial synthetic libraries for use in high-throughput screening for pharmaceutical lead generation. It computes diversity in terms of the main factors relevant to ligand-protein binding, namely the three-dimensional arrangement of steric bulk and of polar functionalities and molecular entropy. The method was used to select a set of 20 carboxylates suitable for use as side-chain precursors in a polyamine-based library. The method depends on estimates of various physical-chemical parameters involved in ligand-protein binding; experiments examined the sensitivity of the method to these parameters. This paper compares the diversity of randomly and rationally selected side-chain sets; the results suggest that careful design of synthetic combinatorial libraries may increase their effectiveness several-fold.

New approaches in molecular structure prediction

In the past years, much effort has been put on the development of new methodologies and algorithms for the prediction of protein secondary and tertiary structures from (sequence) data; this is reviewed in detail. New approaches for these predictions such as neural network methods, genetic algorithms, machine learning, and graph theoretical methods are discussed. Secondary structure prediction algorithms were improved mostly by considering families of related proteins; however, for the reliable tertiary structure modeling of proteins, knowledge-based techniques are still preferred. Methods and examples with more or less successful results are described. Also, programs and parameterizations for energy minimisations, molecular dynamics, and electrostatic interactions have been improved, especially with respect to their former limits of applicability. Other topics discussed in this review include the use of traditional and on-line databases, the docking problem and surface properties of biomolecules, packing of protein cores, de novo design and protein engineering, prediction of membrane protein structures, the verification and reliability of model structures, and progress made with currently available software and computer hardware. In summary, the prediction of the structure, function, and other properties of a protein is still possible only within limits, but these limits continue to be moved.

Local elevation: a method for improving the searching properties of molecular dynamics simulation

The concept of memory has been introduced into a molecular dynamics algorithm. This was done so as to persuade a molecular system to visit new areas of conformational space rather than be confined to a small number of low-energy regions. The method is demonstrated on a simple model system and the 11-residue cyclic peptide cyclosporin A. For comparison, calculations were also performed using simulated temperature annealing and a potential energy annealing scheme. Although the method can only be applied to systems with a small number of degrees of freedom, it offers the chance to generate a multitude of different low-energy structures, where other methods only give a single one or few. This is clearly important in problems such as drug design, where one is interested in the conformational spread of a system.

A novel parameterization scheme for energy equations and its use to calculate the structure of protein molecules

A novel scheme for the parameterization of a type of "potential energy" function for protein molecules is introduced. The function is parameterized based on the known conformations of previously determined protein structures and their sequence similarity to a molecule whose conformation is to be calculated. Once parameterized, minima of the potential energy function can be located using a version of simulated annealing which has been previously shown to locate global and near-global minima with the given functional form. As a test problem, the potential was parameterized based on the known structures of the rubredoxins from Desulfovibrio vulgaris, Desulfovibrio desulfuricans, and Clostridium pasteurianum, which vary from 45 to 54 amino acids in length, and the sequence alignments of these molecules with the rubredoxin sequence from Desulfovibrio gigas. Since the Desulfovibrio gigas rubredeoxin conformation has also been determined, it is possible to check the accuracy of the results. Ten simulated-annealing runs from random starting conformations were performed. Seven of the 10 resultant conformations have an all-C alpha rms deviation from the crystallographically determined conformation of less than 1.7 A. For five of the structures, the rms deviation is less than 0.8 A. Four of the structures have conformations which are virtually identical to each other except for the position of the carboxy-terminal residue. This is also the conformation which is achieved if the determined crystal structure is minimized with the same potential. The all-C alpha rms difference between the crystal and minimized crystal structures is 0.6 A.(ABSTRACT TRUNCATED AT 250 WORDS)

The embedding problem for predistance matrices

A fundamental problem in molecular biology is the determination of the conformation of macromolecules from NMR data. Several successful distance geometry programs have been developed for this purpose, for example DISGEO. A particularly difficult facet of these programs is the embedding problem, that is the problem of determining those conformations whose distances between atoms are nearest those measured by the NMR techniques. The embedding problem is the distance geometry equivalent of the multiple minima problem, which arises in energy minimization approaches to conformation determination. We show that the distance geometry approach has some nice geometry not associated with other methods that allows one to prove detailed results with regard to the location of local minima. We exploit this geometry to develop some algorithms which are faster and find more minima than the algorithms presently used.