Global Minimum Potential Energy Research Articles

A predictive method for the evaluation of peptide binding in pocket 1 of HLA-DRB1 via global minimization of energy interactions

Human leukocyte antigens (HLA) or histocompatibility molecules are glycoproteins that play a pivotal role in the development of an effective immune response. An important function of the HLA molecules is the ability to bind and present antigen peptides to T lymphocytes. Presently there is no comprehensive way of predicting and energetically evaluating peptide binding on HLA molecules. To quantitatively determine the binding specificity of a class II HLA molecule interacting with peptides, a novel decomposition approach based on deterministic global optimization is proposed that takes advantage of the topography of HLA binding grove, and examined the interactions of the bound peptide with the five different pockets. In particular, the main focus of this paper is the study of pocket 1 of HLADR1 (DRB1*0101 allele). The determination of the minimum energy conformation is based on the ECEPP/3 potential energy model that describes the energetics of the atomic interactions. The minimization of the total potential energy is formulated on the set of peptide dihedral angles, Euler angles, and translation variables to describe the relative position. The deterministic global optimization algorithm, alpha BB, which has been shown to be epsilon-convergent to the global minimum potential energy through the solution of a series of nonlinear convex optimization problems, is utilized. The PACK conformational energy model that utilizes the ECEPP/3 model but also allows the consideration of protein chain interactions is interfaced with alpha BB. MSEED, a program used to calculate the solvation contribution via the area accessible to the solvent, is also interfaced with alpha BB. Results are presented for the entire array of naturally occurring amino acids binding to pocket 1 of the HLA DR1 molecule and very good agreement with experimental binding assays is obtained.

A predictive method for the evaluation of peptide binding in pocket 1 of HLA‐DRB1 via global minimization of energy interactions

Human leukocyte antigens (HLA) or histocompatibility molecules are glycoproteins that play a pivotal role in the development of an effective immune response. An important function of the HLA molecules is the ability to bind and present antigen peptides to T lymphocytes. Presently there is no comprehensive way of predicting and energetically evaluating peptide binding on HLA molecules. To quantitatively determine the binding specificity of a class II HLA molecule interacting with peptides, a novel decomposition approach based on deterministic global optimization is proposed that takes advantage of the topography of HLA binding grove, and examined the interactions of the bound peptide with the five different pockets. In particular, the main focus of this paper is the study of pocket 1 of HLA DR1 (DRB1*0101 allele). The determination of the minimum energy conformation is based on the ECEPP/3 potential energy model that describes the energetics of the atomic interactions. The minimization of the total potential energy is formulated on the set of peptide dihedral angles, Euler angles, and translation variables to describe the relative position. The deterministic global optimization algorithm, αBB, which has been shown to be ϵ-convergent to the global minimum potential energy through the solution of a series of nonlinear convex optimization problems, is utilized. The PACK conformational energy model that utilizes the ECEPP/3 model but also allows the consideration of protein chain interactions is interfaced with αBB. MSEED, a program used to calculate the solvation contribution via the area accessible to the solvent, is also interfaced with αBB. Results are presented for the entire array of naturally occurring amino acids binding to pocket 1 of the HLA DR1 molecule and very good agreement with experimental binding assays is obtained. Proteins 29:87–102, 1997. © 1997 Wiley-Liss, Inc.

Prediction of Oligopeptide Conformations via Deterministic Global Optimization

A deterministic global optimization method is described for identifying the global minimum potential energy conformation of oligopeptides. The ECEPP/3 detailed potential energy model is utilized for describing the energetics of the atomic interactions posed in the space of the peptide dihedral angles. Based on previous work on the microcluster and molecular structure determination [21, 22, 23, 24], a procedure for deriving convex lower bounding functions for the total potential energy function is developed. A procedure that allows the exclusion of domains of the (o, ψ) space based on the analysis of experimentally determined native protein structures is presented. The reduced disjoint sub-domains are appropriately combined thus defining the starting regions for the search. The proposed approach provides valuable information on (i) the global minimum potential energy conformation, (ii) upper and lower bounds of the global minimum energy structure and (iii) low energy conformers close to the global minimum one. The proposed approach is illustrated with Ac-Ala4-Pro-NHMe, Met-enkephalin, Leu-enkephalin, and Decaglycine.

Relaxation of collective excitations in LJ-13 cluster

We have performed classical molecular dynamics simulation of Ar13 cluster to study the behavior of collective excitations. In the solid ‘‘phase’’ of the cluster, the collective oscillation of the monopole mode can be well fitted to a damped harmonic oscillator. The parameters of the equivalent damped harmonic oscillator—the damping coefficient, spring constant, time period of oscillation and the mass of the oscillator—all show a sharp change in behavior at a kinetic temperature of about 7.0 °K. This marks yet another characteristic temperature of the system, a temperature Ts below which collective excitations are very stable, and at higher temperatures the single particle excitations cause the damping of the collective oscillations. We argue that so long as the cluster remains confined within the global potential energy minimum the collective excitations do not decay; and once the cluster comes out of this well, the local potential energy minima pockets act as single particle excitation channels in destroying the collective motion. The effect is manifest in almost all the physical observables of the cluster.

Collective aspects of protein folding illustrated by a toy model.

A simple toy model for polypeptides serves as a testbed to illuminate some nonlocal, or collective, aspects of protein folding phenomena. The model is two dimensional and has only two amino acids, but involves a continuous range of backbone bend angles. Global potential energy minima and their folding structures have been determined for leading members of two special and contrasting polypeptide sequences, center doped and Fibonacci, named descriptively for their primary structures. The results display the presence of spontaneous symmetry breaking, elastic strain, and substantial conformational variation for specific embedded amino acid strings. We conclude that collective variables generated by the primary amino acid structure may be required for fully effective protein folding predictors, including those based on neural networks.

Global minimum potential energy conformations of small molecules

A global optimization algorithm is proposed for finding the global minimum potential energy conformations of small molecules. The minimization of the total potential energy is formulated on an independent set of internal coordinates involving only torsion (dihedral) angles. Analytical expressions for the Euclidean distances between non-bonded atoms, which are required for evaluating the individual pairwise potential terms, are obtained as functions of bond lengths, covalent bond angles, and torsion angles. A novel procedure for deriving convex lower bounding functions for the total potential energy function is also introduced. These underestimating functions satisfy a number of important theoretical properties. A global optimization algorithm is then proposed based on an efficient partitioning strategy which is guaranteed to attain e-convergence to the global minimum potential energy configuration of a molecule through the solution of a series of nonlinear convex optimization problems. Moreover, lower and upper bounds on the total finite number of required iterations are also provided. Finally, this global optimization approach is illustrated with a number of example problems.

A deterministic global optimization approach for molecular structure determination

A deterministic global optimization algorithm is introduced for locating global minimum potential energy molecular conformations. The proposed branch and bound type algorithm attains finite ε-convergence to the global minimum through the successive refinement of converging lower and upper bounds on the solution. These bounds are obtained through a novel convex lowering bounding of the total potential function and the subsequent solution of a series of nonlinear convex optimization problems. The minimization of the total potential energy function is performed on an independent set of internal coordinates involving only dihedral angles. A number of example problems illustrate the proposed approach.

Conformations of disaccharides by empirical force field calculations. Part V: Conformational maps of β-gentiobiose in an optimized consistent force field

A recently optimized set of potential energy functions is used to investigate the conformational flexibility of the beta-(1-->6) glycosidic linkage in beta-gentiobiose. Relaxed Ramachandran maps in vacuo are presented in the torsional angles phi and omega, with torsional angle psi allowed to relax freely, as are all other internal degrees of freedom. The study reveals two almost iso-energetic low energy domains in (phi, psi, omega) space, and cross-sections in the low-energy domains at omega = -60 degrees and omega = 60 degrees show that more than 60% and 70% respectively of the area of the conformational maps are accessible within 40 kJ mol-1. The molecular structure in the crystal, including the exoanomeric effect, is well reproduced. The structure belongs to the potential energy well which includes the global potential energy minimum in vacuo. The most profound structural difference between the crystal structure and the calculated global minimum in vacuo is the 20 degrees deviation of the psi torsional angle (24 degrees from perfect trans). It occurs in the most flexible glucosidic degree of freedom, psi, and is caused by optimization of the hydrogen bonding network and not by the exoanomeric effect.

Monte carlo simulation of the hydration shell of double‐helical amylose: A left‐handed antiparallel double helix fits best into liquid water structure

AbstractThe conformation of double‐helical amylose is influenced by its water environment [A. Imberty, H. Chanzy, S. Perez, A. Buléon, and V. Tran (1988) Journal of Molecular Biology, Vol. 201, pp. 365–378; A. Imberty and S. Perez (1988) Biopolymers, Vol. 27, 1205–1221]. For several low‐energy conformations of left‐handed amylose double helices, we performed Monte Carlo simulations of the (N, V, T)‐ensemble of configurations of water molecules surrounding a single duplex. The crucial point of this simulation is the use of cylindrical periodical boundary conditions with a relatively small asymmetric unit comprising a limited number of water molecules. The output data consists of local maxima of water density in the space near the macromolecule and information on one‐ and two‐membered water bridges between polar groups of amylose as well as energetic characteristics of the system under study.A left‐handed antiparallel‐stranded conformation of the amylose double helix (rise and twist per glucose unit are 0.343 nm and –58.1°) corresponds to the global minimum of intraduplex potential energy W. Schulz and H. Sklenar (1993) Biopolymers, submitted; W. Schulz, H. Sklenar, W. Hinrichs, and W. Saenger (1993) Biopolymers, to be published. We found that this conformation is favored also by its hydration shell characteristics in comparison to parallel‐stranded structures. Three hydration sites per glucose unit in the vicinity of HO6, O6, and O3 could be identified. Regular water bridges forming a network around the duplex were observed. A moderate change of the helical parameters within the family of left‐handed antiparallel structures (to a rise and twist per glucose unit of 0.233 nm and –45°) does not have noteworthy consequences for the characteristics of the hydration shell. The location of the hydration sites with respect to the polar groups of amylose and the observed water bridges are in excellent agreement with the hydration geometry of the heavily hydrated antiparallel‐stranded left‐handed double helix of p‐nitrophenyl α‐maltohexose described in a high‐resolution crystal study [W. Hinrichs, G. Büttner, M. Steifar, Ch. Betzel, V. Zabel, B. Pfannermüller, and W. Saenger (1987) Science, Vol. 238, pp. 205–208; W. Hinrichs and W. Saenger (1990) Journal of the American Chemical Society, Vol. 112, pp. 2789–2796].In the case of parallel‐stranded (nonsymmetric or symmetric) double helices, only one hydration site near the (H) O3 group could be identified. No systematic water bridges with sufficient high probability were observed. The sum of the average potential energies of the amylose–water and water–water interactions is not favourable in comparison with the energy for antiparallel‐stranded double helices. The water‐water interaction is high, i.e., parallel‐stranded amylose breaks the structure of liquid water. This effect would explain the insolubility of natural amylose in cold water and support the occurrence of parallel‐stranded double helices in crystallites of starch granules and in amylose microcrystals having only low water content [see Imberty et al. (1988) and Imberty and Perez ( 1988) above]. Symmetric parallel‐stranded double helices have very well‐exposed polar groups and their conformation should be favored in crystals by the ability to form extensively interduplex hydrogen bonds directly or via single water molecules. Single water molecules incorporated into the crystal would compensate for the shortage of donors of hydrogen bonds on the surface of the symmetric parallel‐stranded double helix. Indeed, in accordance with diffraction data see Imberty and Perez (1988) above; also A. Imberty, H. Chanzy, S. Perez, A. BulBon, V. Tran (1987) Macromolecules, Vol. 20, pp. 2636–26381 a critical amount of water increases the crystallinity of amylose and only symmetric parallel‐stranded double helices would fit into a crystallographic unit cell with c = 1.05 nm. The unfavorable hydration of parallel‐stranded double‐helical amylose would increase the stability of natural starch granules (e.g., in seeds) and, therefore, be biologically sensible. © 1992 John Wiley & Sons, Inc.

Cluster optimization simplified by interaction modification

Even when interactions are known exactly, it is generally very difficult to determine the lowest-energy configuration (a global potential energy minimum) for clusters with more than very few atoms or molecules. In mathematical parlance this is an NP-complete problem. A nonlinear optimization strategy, the ‘‘ant–lion method,’’ has been proposed to accelerate the search for global minima, and works by adroitly deforming the potential surface to produce overwhelming dominance by global minimum potential energy basins. This strategy is illustrated by application to clusters of 13 noble gas atoms. Monte Carlo results demonstrate that reduction of p in the pair potential 4(r−2p−r−p) below the ‘‘physical’’ value 6 produces a dramatic rise to essentially unity in probability of random encounter with the global minimum basins (icosahedral clusters).

Does the global energy minimum always also mean the thermodynamically most stable structure?

A system of the local minima of a potential hypersurface was studied and it is shown that, possibly, the global energy minimum is the most stable species only up to a certain temperature threshold. The situation is exemplified using the isomeric Si 6H 6 system where, above 340 K, the structure corresponding to a local minimum lying about 41 kJ mol −1 above the global potential-energy minimum becomes the most stable species due to the interplay of rotational-vibrational motions. Other examples given are the C 4, C 6 and (CO 2) 2 − systems.