All-atom level direct folding simulation of a betabetaalpha miniprotein

We performed ab initio folding simulation for a betabetaalpha peptide BBA5 (PDB code 1T8J) with a modified param99 force field using the generalized Born solvation model (param99MOD5/GBSA). For efficient conformational sampling, we extended a previously developed novel Q-replica exchange molecular dynamics (Q-REMD) into a multiplexed Q-REMD. Starting from a fully extended conformation, we were able to locate the nativelike structure in the global free minimum region at 280 K. The current approach, which combines the more balanced force field with the efficient sampling scheme, demonstrates a clear advantage in direct folding simulation at all-atom level.     

Calibration of force-field dependency in free energy landscapes of peptide conformations by quantum chemical calculations

The free energy landscapes of peptide conformations were calibrated by ab initio quantum chemical calculations, after the enhanced conformational diversity search using the multicanonical molecular dynamics simulations. Three different potentials of mean force for an isolated dipeptide were individually obtained by the multicanonical molecular dynamics simulations using the conventional force fields, AMBER parm94, AMBER parm96, and CHARMm22. Each potential of mean force was then calibrated based upon the umbrella sampling algorithm from the adiabatic energy map that was calculated separately by the ab initio molecular orbital method, and all of the calibrated potentials of mean force coincided well. The calibration method was also applied to the simulations of a peptide dimer in explicit water models, and it was shown that the calibrated free energy landscapes did not depend on the force field used in the classical simulations, as far as the conformational space was sampled well. The current calibration method fuses the classical free energy calculation with the quantum chemical calculation, and it should generally make simulations for biomolecular systems much more reliable when combining with enhanced conformational sampling.     

Free energy perturbation study of water dimer dissociation kinetics

An efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABC-FEP (ab initio/classical free energy perturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energy perturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmann-weighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energy perturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energy perturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and TIP4PFQ) are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT-5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.     

Comparative study of generalized born models: Born radii and peptide folding

In this study, we have implemented four analytical generalized Born (GB) models and investigated their performance in conjunction with the GROMOS96 force field. The four models include that of Still and co-workers, the HCT model of Cramer, Truhlar, and co-workers, a modified form of the AGB model of Levy and co-workers, and the GBMV2 model of Brooks and co-workers. The models were coded independently and implemented in the GROMOS software package and in TINKER. They were compared in terms of their ability to reproduce the results of Poisson-Boltzmann (PB) calculations and in their performance in the ab initio peptide folding of two peptides, one that forms a beta-hairpin in solution and one that forms an alpha-helix. In agreement with previous work, the GBMV2 model is most successful in reproducing PB results while the other models tend to underestimate the effective Born radii of buried atoms. In contrast, stochastic dynamics simulations on the folding of the two peptides, the C-terminus beta-hairpin of the B1 domain of protein G and the alanine-based alpha-helical peptide 3K(I), suggest that the simpler GB models are more effective in sampling conformational space. Indeed, the Still model used in conjunction with the GROMOS96 force field is able to fold the hairpin peptide to a native-like structure without the benefit of enhanced sampling techniques. This is due in part to the properties of the united-atom GROMOS96 force field which appears to be more flexible, and hence to sample more efficiently, than force fields such as OPLSAA. Our results suggest a general strategy which involves using different combinations of force fields and solvent models in different applications, for example, using GROMOS96 and a simple GB model in sampling and OPLSAA and a more accurate GB model in refinement. The fact that various methods have been implemented in a unified way should facilitate the testing and subsequent use of different methods to evaluate conformational free energies in different applications. Our results also bear on some general issues involved in peptide folding and structure prediction which are addressed in the Discussion.     

Challenges of crystal structure prediction of diastereomeric salt pairs

A methodology for the computational prediction of the crystal structures and resolution efficiency for diastereomeric salt pairs is developed by considering the polymorphic system of the diastereomeric salt pair (R)-1-phenylethylammonium (R/S)-2-phenylpropanoate. To alleviate the mathematical complexity of the search for minima in the lattice energy due to the presence of two flexible entities in the asymmetric unit, the range of rigid-body lattice energy global optimizations was guided by a statistical analysis of the Cambridge Structural Database for common ion-pair geometries and ion conformations. A distributed multipole model for the dominant electrostatic interactions and high-level ab initio calculations for the intramolecular energy penalty for conformational distortions are used to quantify the relative stabilities of the p- and n-salt forms. While the ab initio prediction of the known structure of the p-salt as the most stable structure was insensitive to minor changes in the rigid-ion conformations considered, the relative stabilities of the known polymorphs and hypothetical structures of the n-salt were very sensitive. Although this paper provides a significant advance over traditional search algorithms and empirical force fields in determining the structures and relative stabilities of diastereomeric salt pairs, the sensitivity of the computed lattice energies to the fine details of the ion conformations overtaxes current computational models and renders the design of diastereomeric resolution processes by computational chemistry a challenging problem.     

Many-body optimization using an ab initio monte carlo method

Advances in computing power have made it possible to study solvated molecules using ab initio quantum chemistry. Inclusion of discrete solvent molecules is required to determine geometric information about solute/solvent clusters. Monte Carlo methods are well suited to finding minima in many-body systems, and ab initio methods are applicable to the widest range of systems. A first principles Monte Carlo (FPMC) method was developed to find minima in many-body systems, and emphasis was placed on implementing moves that increase the likelihood of finding minimum energy structures. Partial optimization and molecular interchange moves aid in finding minima and overcome the incomplete sampling that is unavoidable when using ab initio methods. FPMC was validated by studying the boron trifluoride-water system, and then the method was used to examine the methyl carbenium ion in water to demonstrate its application to solvation problems.     

Dominant folding pathways of a peptide chain from ab initio quantum-mechanical simulations

Using the dominant reaction pathways method, we perform an ab initio quantum-mechanical simulation of a conformational transition of a peptide chain. The method we propose makes it possible to investigate the out-of-equilibrium dynamics of these systems, without resorting to an empirical representation of the molecular force field. It also allows to study rare transitions involving rearrangements in the electronic structure. By comparing the results of the ab initio simulation with those obtained by employing a standard force field, we discuss its capability to describe the nonequilibrium dynamics of conformational transitions.     

A study of density of states and ground states in hydrophobic-hydrophilic protein folding models by equi-energy sampling

We propose an equi-energy (EE) sampling approach to study protein folding in the two-dimensional hydrophobic-hydrophilic (HP) lattice model. This approach enables efficient exploration of the global energy landscape and provides accurate estimates of the density of states, which then allows us to conduct a detailed study of the thermodynamics of HP protein folding, in particular, on the temperature dependence of the transition from folding to unfolding and on how sequence composition affects this phenomenon. With no extra cost, this approach also provides estimates on global energy minima and ground states. Without using any prior structural information of the protein the EE sampler is able to find the ground states that match the best known results in most benchmark cases. The numerical results demonstrate it as a powerful method to study lattice protein folding models.     

Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent

Replica exchange methods (REMs) are increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. However, despite having been shown to be very effective on model systems, the application of REM in complex systems such as for the simulation of protein and peptide folding in explicit solvent has not been objectively tested in detail. Here we present a comparison of conventional MD and temperature replica exchange MD (T-REMD) simulations of a beta-heptapeptide in explicit solvent. This system has previously been shown to undergo reversible folding on the time scales accessible to MD simulation and thus allows a direct one-to-one comparison of efficiency. The primary properties compared are the free energy of folding and the relative populations of different conformers as a function of temperature. It is found that to achieve a similar degree of precision T-REMD simulations starting from a random set of initial configurations were approximately an order of magnitude more computationally efficient than a single 800 ns conventional MD simulation for this system at the lowest temperature investigated (275 K). However, whereas it was found that T-REMD simulations are more than four times more efficient than multiple independent MD simulations at one temperature (300 K) the actual increase in conformation sampling was only twofold. The overall gain in efficiency using REMD resulted primarily from the ordering of different conformational states over temperature, as opposed to a large increase of conformational sampling. It is also shown that in this system exchanges are accepted primarily based on (random) fluctuations within the solvent and are not strongly correlated with the instantaneous peptide conformation raising questions in regard to the efficiency of T-REMD in larger systems.     

Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver

An alternative strategy to find the minimal energy structure of nanoclusters is presented and implemented. We use it to determine the structure of metallic clusters. It consists in an unbiased search, with a global minimum algorithm: conformational space annealing. First, we find the minima of a many-body phenomenological potential to create a data bank of putative minima. This procedure assures us the generation of a set of cluster configurations of large diversity. Next, the clusters in this data bank are relaxed by ab initio techniques to obtain their energies and geometrical structures. The scheme is successfully applied to magic number 13 atom clusters of rhodium, palladium, and silver. We obtained minimal energy cluster structures not previously reported, which are different from the phenomenological minima. Moreover, they are not always highly symmetric, thus casting some doubt on the customary biased search scheme, which consists in relaxing with density functional theory global minima chosen among high symmetry structures obtained by means of phenomenological potentials.     

Theoretical investigations on the geometric and electronic structures of phenylene-acetylene macrocycles.

The geometric and electronic structures of a series of conjugated macrocycles (phenylene-acetylene macrocycles, PAMs) have been studied theoretically with ab initio and semiempirical molecular orbital methods. The ab initio calculations at the HF/6-31G* level demonstrate that the model molecules may have a planar conformation. Bigger macrocycles, for example, 7PAM, 8PAM, and 9PAM, result in several energy minima. The boatlike conformation is the most energetically favored form. Based on the conformational analysis, a novel method for analyzing the ring-strain energy was proposed and used. In view of their potential applications as electronic materials, the electronic structures of a series of PAMs are also investigated. The LUMO-HOMO gaps of the planar PAMs show an odd-even difference behavior. In addition, the HOMOs of the planar species 3PAM, 5PAM, 7PAM, and 9PAM are doubly degenerated.     

Achieving fast convergence of ab initio free energy perturbation calculations with the adaptive force-matching method

This paper studies the possibility of improving the convergence of ab initio free energy perturbation (FEP) calculations by developing customized force fields with the adaptive force-matching (AFM) method. The ab initio FEP method relies on a molecular mechanics (MM) potential to sample configuration space. If the Boltzmann weight of the MM sampling is close to that of the ab initio method, the efficiency of ab initio FEP will be optimal. The difference in the Boltzmann weights can be quantified by the relative energy difference distribution (REDD). The force field developed through AFM significantly improves the REDD when compared with standard MM models, thus improving the convergence of the ab initio FEP calculation. The static dielectric constant ε_s of ice-Ih was studied with PW-91 through ab initio FEP. With a customized force field developed through AFM, we were able to converge ε_s to 80 ± 4 with 3,600 configurations. A similar ab initio FEP calculation with the TIP4P model would require 220 times more configurations to achieve the same accuracy. Our study indicates that the PW-91 functional underestimates ice-Ih ε_s by about 20%.     

Ab initio studies of conformational properties of dimethyl diphosphate dianion and its complex with magnesium

The conformational properties of the diphosphate linkage have been studied with ab initio methods using the dimethyl diphosphate dianion (1) and magnesium dimethyl diphosphate (2) as models. The ab initio energy and geometry of the conformers around the P-O bonds have been determined at the self-consistent-field (SCF) using the 6-31G* and the tzp basis sets; whereas, the 6-31G* basis set alone has been used for 2. In addition, the adiabatic connection method (ACM) of density functional theory (DFT) using the dzvp basis set has been employed for 1. The optimization of all possible staggered conformers assumed for the four P-O bonds, led to nine minima for 1. In agreement with the general anomeric effect, the sc conformation about the P-O bonds is clearly preferred over the ap one. Vibrational frequencies were calculated at the SCF level using the 6-31G* basis set and used to evaluate zero-point energies, thermal energies, and entropies for all minima of 1. The effect of zero-point energies and thermal energies is quite small. However, the effect of entropies, mainly resulting from a multiplicity contribution, changes the stability of the conformers. For each minimum of 1, up to six different arrangements of the Mg²⁺ were used to determine minima of 2. This procedure led to 21 distinct minima. The presence of the magnesium counter-ion appeared to completely change the structure and relative energy of the conformers. The preferred structures of the complex exhibit the (sc, ap) orientation around the two central P–O bonds and an arrangement in which the magnesium cation is coordinated by three phosphoryl oxygen atoms. The results of this work clearly demonstrate that interactions with the metal counter-ion can induce conformational changes in the overall 3D-shape adopted by molecules containing diphosphate linkages. The PM3 and MNDO quantum semi-empirical methods and molecular mechanics methods using the CVFF force field were tested and large differences in the minimum structures, as well as in the conformational energies between these and ab initio methods, are discussed.     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

Global exploration of the energy landscape of solids on the ab initio level

Predicting which crystalline modifications can be present in a chemical system requires the global exploration of its energy landscape. Due to the large computational effort involved, in the past this search for sufficiently stable minima has been performed employing a variety of empirical potentials and cost functions followed by a local optimization on the ab initio level. However, this entails the risk of overlooking important modifications that are not modeled accurately using empirical potentials. In order to overcome this critical limitation, we develop an approach to employ ab initio energy functions during the global optimization phase of the structure prediction. As an example, we perform a global exploration of the landscape of LiF on the ab initio level and show that the relevant crystalline modifications are found during the search.     

Ab initio conformational maps in the gas phase and aqueous solution for a prototype of the glycosidic linkage

Ab initio conformational maps for methoxyethoxymethane (MEM) in both the gas phase and aqueous solution have been constructed using two different approaches. The results obtained allow us to conclude that a rigid conformational map is able to predict the regions of the minima, in the potential energy surface of MEM, in full agreement with those found in the relaxed conformational map, in both phases studied. This is a good indication that ab initio rigid conformational maps may be reliably used to sort the stablest conformers of disaccharides in aqueous solution. Besides that, in the MEM case, the solvation effects do not give rise to any new local minimum in its potential energy surface, but just change the relative energies of the stablest conformers found in the gas phase. This may be an indication that even in aqueous solution the anomeric effect is still the determinant effect defining the conformation of the molecule.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail