Oren M. Becker

The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics

Topological characteristics of multidimensional potential energy surfaces are explored and the full conformation space is mapped on the set of local minima. This map partitions conformation space into energy-dependent or temperature-dependent “attraction basins’’ and generates a “disconnectivity’’ graph that reflects the basin connectivity and characterizes the shape of the multidimensional surface. The partitioning of the conformation space is used to express the temporal behavior of the system in terms of basin-to-basin kinetics instead of the usual state-to-state transitions. For this purpose the transition matrix of the system is expressed in terms of basin-to-basin transitions and the corresponding master equation is solved. As an example, the approach is applied to the tetrapeptide, isobutyryl-(ala)3-NH-methyl (IAN), which is the shortest peptide that can form a full helical turn. A nearly complete list of minima and barriers is available for this system from the work of Czerminiski and Elber. The m...

Computational Biochemistry and Biophysics

Computational methods: atomistic models and force fields dynamics methods conformational analysis treatment of long-range forces and potential internal co-ordinate simulation method implicit solvent models normal mode analysis of biological molecules free energy calculations reaction rates and transition pathways computer simulation of biochemical reactions with QM-MM methods. Experimental data analysis: X-ray and neutron scattering as probes of the dynamics of biological molecules applications of molecular modelling in NMR structure determination. Modelling and design: comparative protein structure modelling Bayesian statistics in molecular and structural biology. Computer-aided drug design. Advanced applications: protein folding simulations of electron transfer proteins the RISM-SCF/MCSCF approach for the chemical processes in solutions nucleic acids simulations membrane simulations. Appendix: useful Web sites.

Solvent effects on the energy landscapes and folding kinetics of polyalanine

The effect of a solvation on the thermodynamics and kinetics of polyalanine (Ala12) is explored on the basis of its energy landscapes in vacuum and in an aqueous solution. Both energy landscapes are characterized by two basins, one associated with α-helical structures and the other with coil and β-structures of the peptide. In both environments, the basin that corresponds to the α-helical structure is considerably narrower than the basin corresponding to the β-state, reflecting their different contributions to the entropy of the peptide. In vacuum, the α-helical state of Ala12 constitutes the native state, in agreement with common helical propensity scales, whereas in the aqueous medium, the α-helical state is destabilized, and the β-state becomes the native state. Thus solvation has a dramatic effect on the energy landscape of this peptide, resulting in an inverted stability of the two states. Different folding and unfolding time scales for Ala12 in hydrophilic and hydrophobic chemical environments are caused by the higher entropy of the native state in water relative to vacuum. The concept of a helical propensity has to be extended to incorporate environmental solvent effects.

PREDICT modeling and in‐silico screening for G‐protein coupled receptors

G‐protein coupled receptors (GPCRs) are a major group of drug targets for which only one x‐ray structure is known (the nondrugable rhodopsin), limiting the application of structure‐based drug discovery to GPCRs. In this paper we present the details of PREDICT, a new algorithmic approach for modeling the 3D structure of GPCRs without relying on homology to rhodopsin. PREDICT, which focuses on the transmembrane domain of GPCRs, starts from the primary sequence of the receptor, simultaneously optimizing multiple ‘decoy’ conformations of the protein in order to find its most stable structure, culminating in a virtual receptor‐ligand complex. In this paper we present a comprehensive analysis of three PREDICT models for the dopamine D2, neurokinin NK1, and neuropeptide Y Y1 receptors. A shorter discussion of the CCR3 receptor model is also included. All models were found to be in good agreement with a large body of experimental data. The quality of the PREDICT models, at least for drug discovery purposes, was evaluated by their successful utilization in in‐silico screening. Virtual screening using all three PREDICT models yielded enrichment factors 9‐fold to 44‐fold better than random screening. Namely, the PREDICT models can be used to identify active small‐molecule ligands embedded in large compound libraries with an efficiency comparable to that obtained using crystal structures for non‐GPCR targets. Proteins 2004.

MBO(N)D: A multibody method for long-time molecular dynamics simulations

A modeling approach that can significantly speed up the dynamics simulation of large molecular systems is presented herein. A multigranular modeling approach, whereby different parts of the molecule are modeled at different levels of detail, is enabled by substructuring. Substructuring the molecular system is accomplished by collecting groups of atoms into rigid or flexible bodies. Body flexibility is modeled by a truncated set of body‐based modes. This approach allows for the elimination of the high‐frequency harmonic motion while capturing the low‐frequency anharmonic motion of interest. This results in the use of larger integration step sizes, substantially reducing the computational time required for a given dynamic simulation. The method also includes the use of a multiple time scale (MTS) integration scheme. Speed increases of 5‐ to 30‐fold over atomistic simulations have been realized in various applications of the method.

Geometric versus topological clustering: an insight into conformation mapping.

Clustering molecular conformations into “families” is a common procedure in conformational analysis of molecular systems. An implicit assumption which often underlies this clustering approach is that the resulting geometric families reflect the energetic structure of the systems potential energy surface. In a broader context we address the question whether structural similarity is correlated with energy basins, i.e., whether conformations that belong to the same energy basin are also geometrically similar. “Topological mapping” and principal coordinate projections are used here to address this question and to assess the quality of the “family clustering” procedure. Applying the analysis to a small tetrapeptide it was found that the general correlation that exists between energy basins and structural similarity is not absolute. Clusters generated by the geometric “family clustering” procedure do not always reflect the underlying energy basins. In particular it was found that the “family tree” that is generated by the “family clustering” procedure is completely inconsistent with its real topological counterpart, the “disconnectivity” graph of this system. It is also demonstrated that principal coordinate analysis is a powerful visualization technique which, at least for this system, works better when distances are measured in dihedral angle space rather than in cartesian space.

Principal coordinate maps of molecular potential energy surfaces

Obtaining useful representations of molecular conformation spaces and visualizing the associated potential energy surfaces is a complex task, mainly due to the high dimensionality of these spaces. Principal component analysis (PCA), which projects multidimensional data on low‐dimensional subspaces, is thus becoming a common technique for studying such spaces. Three issues, relating to the use of principal component techniques for mapping molecular potential energy surfaces, are discussed in this study: the effectiveness of the projection; its accuracy; and the mapping procedure. The effectiveness of PCA is demonstrated through detailed analyses of principal component projections of several peptides. In these cases PCA projected conformation space into a subspace smaller even than that defined by the peptides backbone dihedral angles. The average accuracy as well as the distribution of errors in the projection (i.e., the errors in reproducing individual distances) are studied as a function of the dimensionality of the projection. The wide variation in accuracy between different systems suggests that it is imperative to indicate the accuracy of the projection whenever PCA projections are used. Furthermore, when projecting potential energy surfaces on the principal two‐dimensional (2D) plane, the projection errors result in artificial roughening of the surface. A new mapping procedure, the “minimal energy envelope” procedure, is introduced to overcome this problem. This procedure yields relatively smooth “energy landscapes,” which highlight the basin structure of the real multidimensional energy surface. It is demonstrated that the projected potential energy maps can be used for charting conformational transitions or dynamic trajectories in the system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1255–1267, 1998

Energy landscapes of conformationally constrained peptides

Conformation constraints are known to affect the flexibility and bioactivity of peptides. In this study we analyzed the effect of conformation constraints on the topography of the energy landscapes of three analogous hexapeptides. The three analogs vary in the degree of constraint imposed on their conformational motion: linear alanine hexapeptide with neutral terminals (Ala6), linear alanine hexapeptide with charged terminals (chrg-Ala6), and cyclic alanine hexapeptide (cyc-Ala6). It was found that significantly different energy landscapes characterize each of the three peptides, leading to different folding behaviors. Since all three analogs would be encoded by the same gene, these results suggest that nongenomic post-translational modifications may play an important role in determining the properties of proteins as well as of their folding pathways. In addition, the present study indicates that the complexity of those energy landscapes that are dominated by funnel topography can be captured by one or two reaction coordinates, such as conformational similarity to the native state. However, for more complex landscapes characterized by multiple basins such a description is insufficient. This study also shows that similar views of the landscape topography were obtained by principal component analysis (based only on local minima) and by topological mapping analysis (based on minima and barrier information). Both methods were able to resolve the complex landscape topographies for all three peptides.

Helix-coil transition of PrP106–126: Molecular dynamic study

A set of 34 molecular dynamic (MD) simulations totaling 305 ns of simulation time of the prion protein‐derived peptide PrP106–126 was performed with both explicit and implicit solvent models. The objective of these simulations is to investigate the relative stability of the α‐helical conformation of the peptide and the mechanism for conversion from the helix to a random‐coil structure. At neutral pH, the wild‐type peptide was found to lose its initial helical structure very fast, within a few nanoseconds (ns) from the beginning of the simulations. The helix breaks up in the middle and then unwinds to the termini. The spontaneous transition into the random coil structure is governed by the hydrophobic interaction between His111 and Val122. The A117V mutation, which is linked to GSS disease, was found to destabilize the helix conformation of the peptide significantly, leading to a complete loss of helicity approximately 1 ns faster than in the wild‐type. Furthermore, the A117V mutant exhibits a different mechanism for helix‐coil conversion, wherein the helix begins to break up at the C‐terminus and then gradually to unwind towards the N‐terminus. In most simulations, the mutation was found to speed up the conversion through an additional hydrophobic interaction between Met112 and the mutated residue Val117, an interaction that did not exist in the wild‐type peptide. Finally, the β‐sheet conformation of the wild‐type peptide was found to be less stable at acidic pH due to a destabilization of the His111–Val122, since at acidic pH this histidine is protonated and is unlikely to participate in hydrophobic interaction. Proteins 2001;45:382–396.

Conformational polymorphism of wild-type and mutant prion proteins: Energy landscape analysis

Conformational transitions are thought to be the prime mechanism of prion diseases. In this study, the energy landscapes of a wild‐type prion protein (PrP) and the D178N and E200K mutant proteins were mapped, enabling the characterization of the normal isoforms (PrPC) and partially unfolded isoforms (PrPPU) of the three prion protein analogs. It was found that the three energy landscapes differ in three respects: (i) the relative stability of the PrPC and the PrPPU states, (ii) the transition pathways from PrPC to PrPPU, and (iii) the relative stability of the three helices in the PrPC state. In particular, it was found that although helix 1 (residues 144‐156) is the most stable helix in wild‐type PrP, its stability is dramatically reduced by both mutations. This destabilization is due to changes in the charge distribution that affects the internal salt bridges responsible for the greater stability of this helix in wild‐type PrP. Although both mutations result in similar destabilization of helix 1, they a have different effect on the overall stability of PrPC and of PrPPU isoforms and on structural properties. The destabilization of helix 1 by mutations provides additional evidences to the role of this helix in the pathogenic transition from the PrPC to the pathogenic isoform PrPSC. Proteins 2002;47:458–468.