Ab initio study of alanine polypeptide chains twisting

We have investigated the potential energy surfaces for alanine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles Phi and Psi, which are widely used for the characterization of the polypeptide chains. These particular degrees of freedom are essential for the characterization of proteins folding process. Calculations have been carried out within ab initio theoretical framework based on the density functional theory and accounting for all the electrons in the system. We have determined stable conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods and with the available experimental data extracted from the Protein Data Base. This comparison demonstrates a reasonable correspondence of the most prominent minima on the calculated potential energy surfaces to the experimentally measured angles Phi and Psi for alanine chains appearing in native proteins. We have also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.Comment: 24 pages, 10 figure

Secondary-Structure Design of Proteins by a Backbone Torsion Energy

We propose a new backbone-torsion-energy term in the force field for protein systems. This torsion-energy term is represented by a double Fourier series in two variables, the backbone dihedral angles phi and psi. It gives a natural representation of the torsion energy in the Ramachandran space in the sense that any two-dimensional energy surface periodic in both phi and psi can be expanded by the double Fourier series. We can then easily control secondary-structure-forming tendencies by modifying the torsion-energy surface. For instance, we can increase/decrease the alpha-helix-forming-tendencies by lowering/raising the torsion-energy surface in the alpha-helix region and likewise increase/decrease the beta-sheet-forming tendencies by lowering/raising the surface in the beta-sheet region in the Ramachandran space. We applied our approach to AMBER parm94 and AMBER parm96 force fields and demonstrated that our modifications of the torsion-energy terms resulted in the expected changes of secondary-structure-forming-tendencies by performing folding simulations of alpha-helical and beta-hairpin peptides.Comment: 13 pages, (Revtex4), 5 figure

Maximum Flux Transition Paths of Conformational Change

Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective variables chosen so that paths cluster in collective variable space. The computational task becomes that of computing the "center" of such a cluster. A good way to define the center employs the concept of a committor, whose value at a point in collective variable space is the probability that a trajectory at that point will reach B before A. The committor "foliates" the transition region into a set of isocommittors. The maximum flux transition path is defined as a path that crosses each isocommittor at a point which (locally) has the highest crossing rate of distinct reactive trajectories. (This path is different from that of the MaxFlux method of Huo and Straub.) It is argued that such a path is nearer to an ideal path than others that have been proposed with the possible exception of the finite-temperature string method path. To make the calculation tractable, three approximations are introduced, yielding a path that is the solution of a nonsingular two-point boundary-value problem. For such a problem, one can construct a simple and robust algorithm. One such algorithm and its performance is discussed.Comment: 7 figure

Excitons in a Photosynthetic Light-Harvesting System: A Combined Molecular Dynamics/Quantum Chemistry and Polaron Model Study

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model, the absorption spectrum of the B850 excitons can be calculated from the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined MD/QC simulations. The obtained result is in good agreement with the experimentally measured absorption spectrum.Comment: REVTeX3.1, 23 pages, 13 (EPS) figures included. A high quality PDF file of the paper is available at http://www.ks.uiuc.edu/Publications/Papers/PDF/DAMJ2001/DAMJ2001.pd

Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation

In this paper, we investigate the conformational dynamics of alanine dipeptide under an external electric field by nonequilibrium molecular dynamics simulation. We consider the case of a constant and of an oscillatory field. In this context we propose a procedure to implement the temperature control, which removes the irrelevant thermal effects of the field. For the constant field different time-scales are identified in the conformational, dipole moment, and orientational dynamics. Moreover, we prove that the solvent structure only marginally changes when the external field is switched on. In the case of oscillatory field, the conformational changes are shown to be as strong as in the previous case, and non-trivial nonequilibrium circular paths in the conformation space are revealed by calculating the integrated net probability fluxes.Comment: 23 pages, 12 figure

CHARMM: The biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2009.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63074/1/21287_ftp.pd

Order through Disorder: Hyper-Mobile C-Terminal Residues Stabilize the Folded State of a Helical Peptide. A Molecular Dynamics Study

Conventional wisdom has it that the presence of disordered regions in the three-dimensional structures of polypeptides not only does not contribute significantly to the thermodynamic stability of their folded state, but, on the contrary, that the presence of disorder leads to a decrease of the corresponding proteins' stability. We have performed extensive 3.4 µs long folding simulations (in explicit solvent and with full electrostatics) of an undecamer peptide of experimentally known helical structure, both with and without its disordered (four residue long) C-terminal tail. Our simulations clearly indicate that the presence of the apparently disordered (in structural terms) C-terminal tail, increases the thermodynamic stability of the peptide's folded (helical) state. These results show that at least for the case of relatively short peptides, the interplay between thermodynamic stability and the apparent structural stability can be rather subtle, with even disordered regions contributing significantly to the stability of the folded state. Our results have clear implications for the understanding of peptide energetics and the design of foldable peptides

Volume-energy correlations in the slow degrees of freedom of computer-simulated phospholipid membranes

Constant-pressure molecular-dynamics simulations of phospholipid membranes in the fluid phase reveal strong correlations between equilibrium fluctuations of volume and energy on the nanosecond time-scale. The existence of strong volume-energy correlations was previously deduced indirectly by Heimburg from experiments focusing on the phase transition between the fluid and the ordered gel phases. The correlations, which are reported here for three different membranes (DMPC, DMPS-Na, and DMPSH), have volume-energy correlation coefficients ranging from 0.81 to 0.89. The DMPC membrane was studied at two temperatures showing that the correlation coefficient increases as the phase transition is approached

Multiple pH Regime Molecular Dynamics Simulation for pK Calculations

Ionisation equilibria in proteins are influenced by conformational flexibility, which can in principle be accounted for by molecular dynamics simulation. One problem in this method is the bias arising from the fixed protonation state during the simulation. Its effect is mostly exhibited when the ionisation behaviour of the titratable groups is extrapolated to pH regions where the predetermined protonation state of the protein may not be statistically relevant, leading to conformational sampling that is not representative of the true state. In this work we consider a simple approach which can essentially reduce this problem. Three molecular dynamics structure sets are generated, each with a different protonation state of the protein molecule expected to be relevant at three pH regions, and pK calculations from the three sets are combined to predict pK over the entire pH range of interest. This multiple pH molecular dynamics approach was tested on the GCN4 leucine zipper, a protein for which a full data set of experimental data is available. The pK values were predicted with a mean deviation from the experimental data of 0.29 pH units, and with a precision of 0.13 pH units, evaluated on the basis of equivalent sites in the dimeric GCN4 leucine zipper