Replica-exchange molecular dynamics simulations for a small-sized protein folding with implicit solvent

Modulation of phase transition of thermosensitive liposomes with leucine zipper-structured lipopeptides

Targeted therapy for cancer requires thermosensitive components in drug carriers for controlled drug release against viral cells. The conformational transition characteristic of leucine zipper-structured lipopeptides is utilized in our lab to modulate the phase transition temperature of liposomes, thus achieving temperature-responsive control. In this study, we computationally examined the conformational transition behaviors of leucine zipper-structured lipopeptides that were modified at the N-terminus by distinct functional groups. The conformational transition temperatures of these lipopeptides were determined by structural analysis of the implicit-solvent replica exchange molecular dynamics simulation trajectories using the dihedral angle principal component analysis and the dictionary of protein secondary structure method. Our calculations revealed that the computed transition temperatures of the lipopeptides are in good agreement with the experimental measurements. The effect of hydrogen bonds on the conformational stability of the lipopeptide dimers was examined in conventional explicit-solvent molecular dynamics simulations. A quantitative correlation of the degree of structural dissociation of the dimers and their binding strength is well described by an exponential fit of the binding free energies to the conformation transition temperatures of the lipopeptides.

Kinetics from Implicit Solvent Simulations of Biomolecules as a Function of Viscosity

Kinetic properties of alanine dipeptide, the B1 domain of streptococcal protein G, and ubiquitin are compared between explicit solvent and implicit solvent simulations with the generalized Born molecular volume (GBMV) method. The results indicate that kinetics from explicit solvent simulations and experiments can be matched closely when the implicit solvent simulations are combined with Langevin dynamics and a friction coefficient near 10 ps(-1). Smaller and larger friction coefficients accelerate and slow down conformational sampling. It is found that local conformational exploration without the crossing of significant barriers can be accelerated by a factor of 4-5; however, the acceleration of barrier crossings is limited to about a factor of 2. The use of a Nosé-Hoover thermostat instead of Langevin dynamics greatly enhances local conformational sampling but slows down the crossing of barriers by at least an order of magnitude because of the lack of solute-solvent stochastic collisions.

REMD and umbrella sampling simulations to probe the energy barrier of the folding pathways of engrailed homeodomain

Proteins fold by diverse pathways which depend on the energy barriers involved in reaching different intermediates. There has been a lot of development in the theoretical aspects of protein folding, from force-field to simulation techniques. One such simulation approach is replica exchange molecular dynamics simulation (REMD), which provides an efficient conformational sampling method to understand the events involved in protein folding. In this study, an attempt is made to explore the folding funnel of engrailed homeodomain protein (EnHD) using REMD simulations. EnHD is a 54 residue long helix bundle protein which has a folding time of about 15 μs. The protein was represented using the Amber United atom model in order to reduce the system size which helped to speed up the simulation. Individual replicas were simulated for 1.4-2 μs making cumulative time of more than 100 μs of REMD simulations. Free energy analysis was carried out to understand the folding behavior of EnHD protein. Effects of temperature range and exchange frequency in REMD simulations have been explored. In addition to this, multiple umbrella sampling (US) simulations of a total of 320 ns were also carried out, followed by weighted histogram analysis method (WHAM) to investigate the energy barriers involved during the folding of various intermediates. US studies were also carried on mutational variants of EnHD protein to see effect of the mutations on the folding pathway of the protein. The use of US technique may be helpful for predicting fast folding mutants or protein engineering. The combination of REMD with US may help in understanding the energetics between multiple pathways of fast folding proteins and their mutant counterparts.

Microsecond scale replica exchange molecular dynamic simulation of villin headpiece: an insight into the folding landscape

Reaching the experimental time scale of millisecond is a grand challenge for protein folding simulations. The development of advanced Molecular Dynamics techniques like Replica Exchange Molecular Dynamics (REMD) makes it possible to reach these experimental timescales. In this study, an attempt has been made to reach the multi microsecond simulation time scale by carrying out folding simulations on a three helix bundle protein, Villin, by combining REMD and Amber United Atom model. Twenty replicas having different temperatures ranging from 295 K to 390 K were simulated for 1.5 µs each. The lowest Root Mean Square Deviation (RMSD) structure of 2.5 Å was obtained with respect to native structure (PDB code 1VII), with all the helices formed. The folding population landscapes were built using segment-wise RMSD and Principal Components as reaction coordinates. These analyses suggest the two-stage folding for Villin. The combination of REMD and Amber United Atom model may be useful to understand the folding mechanism of various fast folding proteins.

All-atom ab initio native structure prediction of a mixed fold (1FME): a comparison of structural and folding characteristics of various beta beta alpha miniproteins

We performed an all-atom ab initio native structure prediction of 1FME, which is one of the computationally challenging mixed fold beta beta alpha miniproteins, by combining a novel conformational search algorithm (multiplexed Q-replica exchange molecular dynamics scheme) with a well-balanced all-atom force field employing a generalized Born implicit solvation model (param99MOD5/GBSA). The nativelike structure of 1FME was identified from the lowest free energy minimum state and in excellent agreement with the NMR structure. Based on the interpretation of the free energy landscape, the structural properties as well as the folding behaviors of 1FME were compared with other beta beta alpha miniproteins (1FSD, 1PSV, and BBA5) that we have previously studied with the same force field. Our simulation showed that the 28-residue beta beta alpha miniproteins (1FME, 1FSD, and 1PSV) share a common feature of the free energy topography and exhibit the three local minimum states on each computed free energy map, but the 23-residue miniprotein (BBA5) follows a downhill folding with a single minimum state. Also, the structure and stability changes resulting from the two point mutation (Gln1-->Glu1 and Ile7-->Tyr7) of 1FSD were investigated in details for direct comparison with the experiment. The comparison shows that upon mutation, the experimentally observed turn type switch from an irregular turn (1FSD) to type I(') turn (1FME) was well reproduced with the present simulation.

Combination of molecular dynamics method and 3D-RISM theory for conformational sampling of large flexible molecules in solution

We have developed an algorithm for sampling the conformational space of large flexible molecules in solution, which combines the molecular dynamics (MD) method and the three-dimensional reference interaction site model (3D-RISM) theory. The solvent-induced force acting on solute atoms was evaluated as the gradient of the solvation free energy with respect to the solute-atom coordinates. To enhance the computation speed, we have applied a multiple timestep algorithm based on the RESPA (Reversible System Propagator Algorithm) to the combined MD/3D-RISM method. By virtue of the algorithm, one can choose a longer timestep for renewing the solvent-induced force compared with that of the conformational update. To illustrate the present MD/3D-RISM simulation, we applied the method to a model of acetylacetone in aqueous solution. The multiple timestep algorithm succeeded in enhancing the computation speed by 3.4 times for this model case. Acetylacetone possesses an intramolecular hydrogen-bonding capability between the hydroxyl group and the carbonyl oxygen atom, and the molecule is significantly stabilized due to this hydrogen bond, especially in gas phase. The intramolecular hydrogen bond was kept intact during almost entire course of the MD simulation in gas phase, while in the aqueous solutions the bond is disrupted in a significant number of conformations. This result qualitatively agrees with the behavior on a free energy barrier lying upon the process for rotating a torsional degree of freedom of the hydroxyl group, where it is significantly reduced in aqueous solution by a cancellation between the electrostatic interaction and the solvation free energy.

Accurate prediction of protonation state as a prerequisite for reliable MM-PB(GB)SA binding free energy calculations of HIV-1 protease inhibitors

Binding free energies were calculated for the inhibitors lopinavir, ritonavir, saquinavir, indinavir, amprenavir, and nelfinavir bound to HIV-1 protease. An MMPB/SA-type analysis was applied to conformational samples from 3 ns explicit solvent molecular dynamics simulations of the enzyme-inhibitor complexes. Binding affinities and the sampled conformations of the inhibitor and enzyme were compared between different HIV-1 protease protonation states to find the most likely protonation state of the enzyme in the complex with each of the inhibitors. The resulting set of protonation states leads to good agreement between calculated and experimental binding affinities. Results from the MMPB/SA analysis are compared with an explicit/implicit hybrid scheme and with MMGB/SA methods. It is found that the inclusion of explicit water molecules may offer a slight advantage in reproducing absolute binding free energies while the use of the Generalized Born approximation significantly affects the accuracy of the calculated binding affinities.

A study of local effect and global effect on the microthermal bio-flows by molecular dynamics

This study develops a hybrid numerical scheme based on a molecular dynamics (MD) algorithm and the GROMACS protein data bank to analyze the thermal bio-flow of alanine molecules in a microchannel. The numerical results show that the velocity profiles in the microchannel are highly dependent on both global effects, i.e. the effective channel width and local effects, i.e. the thermal boundary conditions. Specifically, the magnitude of the fluctuations observed in the velocity profiles increase as the channel width decreases or as the thermal boundary temperature increases. The results presented in this study provide useful information regarding suitable microchannel widths and operational temperatures for bio-chip devices and contribute a further understanding of basic human thermal bio-flow phenomena, particularly, regarding the correlation between the rate of local metabolism, burn and frostbite events, respectively.

Are solvation free energies of homogeneous helical peptides additive?

We investigated the additivity of the solvation free energy of amino acids in homogeneous helices of different length in water and in chloroform. Solvation free energies were computed by multiconfiguration thermodynamic integration involving extended molecular dynamics simulations and by applying the generalized-born surface area solvation model to static helix geometries. The investigation focused on homogeneous peptides composed of uncharged amino acids, where the backbone atoms are kept fixed in an ideal helical conformation. We found nonlinearity especially for short peptides, which does not allow a simple treatment of the interaction of amino acids with their surroundings. For homogeneous peptides longer than five residues, the results from both methods are in quite good agreement and solvation energies are to a good extent additive.

The heat transfer analysis of nanoparticle heat source in alanine tissue by molecular dynamics

The purpose of this study is to simulate the heat transfer problem when the 3-D Alanine tissue is heated by the gold nanoparticle in the field of molecular dynamics. In this paper, the Alanine molecule is adopted and its parameters are available in the GROMACS protein data bank. A computing algorithm is developed to evaluate the heat transfer phenomena in the nano-scale biological system based on the molecular dynamics and the protein data bank. The value of the thermal conductivity of Alanine is calculated from the autocorrelation function of the Green-Kubo formalism and this result has a roughly approximation with the bulk thermal conductivity reported by experimental data . Two kinds of problems are investigated in the paper. One is the Alanine tissue heated by the constant heat source and the other is by the time-varying heat source. The numerical results show that a temperature jump exists around the source and the temperature profiles drop to the environmental temperature within a very short distance. It concludes that only a small region around the nano-scale heat source is affected by the heated process. Therefore, the results of the nanoparticle-heated method could be applied to the clinical therapy of tumor, and the normal cells are destroyed only within a smaller region than those of chemotherapy or surgery.

Free energy surfaces of miniproteins with a ββα motif: Replica exchange molecular dynamics simulation with an implicit solvation model

Designed miniproteins with a betabetaalpha motif, such as BBA5, 1FSD, and 1PSV can serve as a benchmark set to test the validity of all-atom force fields with computer simulation, because they contain all the basic structural elements in protein folding. Unfortunately, it was found that the standard all-atom force fields with the generalized Born (GB) implicit solvation model tend to produce distorted free energy surfaces for the betabetaalpha proteins, not only because energetically those proteins need to be described by more balanced weights of the alpha- and beta-strands, but also because the GB implicit solvation model suffers from overestimated salt bridge effects. In an attempt to resolve these problems, we have modified one of the standard all-atom force fields in conjunction with the GB model, such that each native state of the betabetaalpha proteins is in its free energy minimum state with reasonable energy barriers separating local minima. With this modified energy model, the free energy contour map in each protein was constructed from the replica exchange molecular dynamics REMD simulation. The resulting free energy surfaces are significantly improved in comparison with previous simulation results and consistent with general views on small protein folding behaviors with realistic topology and energetics of all three proteins.

Solvophobic and Steric Effects of Side Groups on Polymer Folding: Molecular Modeling Studies of Amine-Functionalized m-Poly(phenyleneethynylene) Foldamers in Aqueous Solution

The folding behavior of five different amine-functionalized m-poly(phenyleneethynylene) (m-PPE) oligomers containing 24 phenyl rings (12 residues, where a residue includes 2 phenyl rings) in water was examined by using a combination of molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulation techniques. The REMD method employed the highly parallelized GROMACS MD software and a modified OPLS-AA force field to simulate 44 replicas of each solvated system in parallel, with temperatures ranging from 300 to 577 K. Our results showed that the REMD method was more effective in predicting the helical conformation of the m-PPE in water, from an extended structure, than canonical MD methods in the same simulation time. Furthermore, we observed from canonical MD simulations of the explicitly solvated helical m-PPEs at 300 K that the radius of gyration, average helix inner diameter, and average helix pitch of the helical structure all pass through a minima when the side group is R = OC(2)H(5) as R is changed from R = H through OC(4)H(9).

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.

Equilibrium structure and folding of a helix-forming peptide: circular dichroism measurements and replica-exchange molecular dynamics simulations

We have performed experimental measurements and computer simulations of the equilibrium structure and folding of a 21-residue alpha-helical heteropeptide. Far ultraviolet circular dichroism spectroscopy is used to identify the presence of helical structure and to measure the thermal unfolding curve. The observed melting temperature is 296 K, with a folding enthalpy of -11.6 kcal/mol and entropy of -39.6 cal/(mol K). Our simulations involve 45 ns of replica-exchange molecular dynamics of the peptide, using eight replicas at temperatures between 280 and 450 K, and the program CHARMM with a continuum solvent model. In a 30-ns simulation started from a helical structure, conformational equilibrium at all temperatures was reached after 15 ns. This simulation was used to calculate the peptide melting curve, predicting a folding transition with a melting temperature in the 330-350 K range, enthalpy change of -10 kcal/mol, and entropy change of -30 cal/(mol K). The simulation results were also used to analyze the peptide structural fluctuations and the free-energy surface of helix unfolding. In a separate 15-ns replica-exchange molecular dynamics simulation started from the extended structure, the helical conformation was first attained after approximately 2.8 ns, and equilibrium was reached after 10 ns of simulation. These results showed a sequential folding process with a systematic increase in the number of hydrogen bonds until the helical state is reached, and confirmed that the alpha-helical state is the global free-energy minimum for the peptide at low temperatures.

Free energy surfaces of β-hairpin and α-helical peptides generated by replica exchange molecular dynamics with the AGBNP implicit solvent model

We have studied the potential of mean force of two peptides, one known to adopt a beta-hairpin and the other an alpha-helical conformation in solution. These peptides are, respectively, residues 41-56 of the C-terminus (GEWTYDDATKTFTVTE) of the B1 domain of protein G and the 13 residue C-peptide (KETAAAKFERQHM) of ribonuclease A. Extensive canonical ensemble sampling has been performed using a parallel replica exchange method. The effective potential employed in this work consists of the OPLS all-atom force field (OPLS-AA) and an analytical generalized Born (AGB) implicit solvent model including a novel nonpolar solvation free energy estimator (NP). An additional dielectric screening parameter has been incorporated into the AGBNP model. In the case of the beta-hairpin, the nonpolar solvation free energy estimator provides the necessary effective interactions for the collapse of the hydrophobic core (W43, Y45, F52, and V54), which the more commonly used surface-area-dependent nonpolar model does not provide. For both the beta-hairpin and the alpha-helix, increased dielectric screening reduces the stability of incorrectly formed salt bridges, which tend to disrupt the formation of the hairpin and helix, respectively. The fraction of beta-hairpin and alpha-helix content we obtained using the AGBNP model agrees well with experimental results. The thermodynamic stability of the beta-hairpin from protein G and the alpha-helical C-peptide from ribonuclease A as modeled with the OPLS-AA/AGBNP effective potential reflects the balance between the nonpolar effective potential terms, which drive compaction, and the polar and hydrogen bonding terms, which promote secondary structure formation.