Alanine Dipeptide In Water Research Articles

Parameter Optimization Method in Multidimensional Umbrella Sampling.

Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.

Emle-engine: A Flexible Electrostatic Machine Learning Embedding Package for Multiscale Molecular Dynamics Simulations.

We present in this work the emle-engine package (https://github.com/chemle/emle-engine)─the implementation of a new machine learning embedding scheme for hybrid machine learning potential/molecular-mechanics (ML/MM) dynamics simulations. The package is based on an embedding scheme that uses a physics-based model of the electronic density and induction with a handful of tunable parameters derived from in vacuo properties of the subsystem to be embedded. This scheme is completely independent of the in vacuo potential and requires only the positions of the atoms of the machine learning subsystem and the positions and partial charges of the molecular mechanics environment. These characteristics allow emle-engine to be employed in existing QM/MM software. We demonstrate that the implemented electrostatic machine learning embedding scheme (named EMLE) is stable in enhanced sampling molecular dynamics simulations. Through the calculation of free energy surfaces of alanine dipeptide in water with two different ML options for the in vacuo potential and three embedding models, we test the performance of EMLE. When compared to the reference DFT/MM surface, the EMLE embedding is clearly superior to the MM one based on fixed partial charges. The configurational dependence of the electronic density and the inclusion of the induction energy introduced by the EMLE model leads to a systematic reduction in the average error of the free energy surface when compared to MM embedding. By enabling the usage of EMLE embedding in practical ML/MM simulations, emle-engine will make it possible to accurately model systems and processes that feature significant variations in the charge distribution of the ML subsystem and/or the interacting environment.

Realization of the structural fluctuation of biomolecules in solution: Generalized Langevin mode analysis.

A new theoretical method, referred to as Generalized Langevin Mode Analysis (GLMA), is proposed to analyze the mode of structural fluctuations of a biomolecule in solution. The method combines the two theories in the statistical mechanics, or the Generalized Langevin theory and the RISM/3D-RISM theory, to calculate the second derivative, or the Hessian matrix, of the free energy surface of a biomolecule in aqueous solution, which consists of the intramolecular interaction among atoms in the biomolecule and the solvation free energy. The method is applied to calculate the wave-number spectrum of an alanine dipeptide in water for which the optical heterodyne-detected Raman-induced spectroscopy (RIKES) spectrum is available to compare with. The theoretical analysis reproduced the main features of the experimental spectrum with respect to the peak positions of the four bands around ~90 cm-1 , ~240 cm-1 , ~370 cm-1 , and 400 cm-1 , observed in the experimental spectrum, in spite that the physics involved in the two spectrum was not exactly the same: the experimental spectrum includes the contributions from the dipeptide and the water molecules interacting with the solute, while the theoretical one is just concerned with the solute molecule, influenced by solvation. Two major discrepancies between the theoretical and experimental spectra, one in the band intensity around ~100 cm-1 , and the other in the peak positions around ~370 cm-1 , are discussed in terms of the fluctuation mode of water molecules interacting with the dipeptide, which is not taken explicitly into account in the theoretical analysis.

Conformational Free-Energy Landscapes of Alanine Dipeptide in Hydrated Ionic Liquids from Enhanced Sampling Methods.

Understanding the interaction of the ionic liquid (IL) with protein is vital to find the origin of the conformational changes of proteins in these alternative solvents. Here, we performed biased molecular dynamics simulations of alanine dipeptide (ADP), a widely used model for protein backbone structure, in water and two hydrated ionic liquids (ILs): 80% (w/w) 1-ethyl-3-methylimidazolium acetate ([EMIm][Ac]) and 80% (w/w) choline dihydrogen phosphate ([Cho][DHP]). We employed three different biasing methods, metadynamics (metaD), well-tempered metadynamics (WT-metaD), and adaptive biasing force (ABF), to construct the free-energy landscapes of the ADP conformations using the backbone dihedral angles (ϕ and ψ) as the collective variables. The calculations were also performed in water; the free-energy landscapes of ADP in water obtained from three methods are similar and agree well with the previously reported results. In hydrated [EMIm][Ac], α-planar conformation emerges as a minimum, which is comparable to that of α and β conformations corresponding to α-helix and β-sheet-like conformations of proteins. Investigation of corresponding conformations suggests that the imidazolium ring of [EMIm] cation is stacked with the amide bonds of ADP. Acetate anion makes hydrogen bonds with the amide hydrogens of the ADP. The amide-π stacking interaction is the driving force for α-planar conformation to become one of the minimum energy conformations in this IL, which destabilizes the protein conformation. However, α and β conformations are more stable in hydrated [Cho][DHP] compared to α-planar and β-planar conformations; therefore, this IL stabilizes the protein conformation. These findings are in good correlation with the previous study of proteins in these ILs. Our study helps to understand the interaction of proteins with the ionic entities and their stability in ILs.

Comparing generalized ensemble methods for sampling of systems with many degrees of freedom.

We compare two standard replica exchange methods using temperature and dielectric constant as the scaling variables for independent replicas against two new corresponding enhanced sampling methods based on non-equilibrium statistical cooling (temperature) or descreening (dielectric). We test the four methods on a rough 1D potential as well as for alanine dipeptide in water, for which their relatively small phase space allows for the ability to define quantitative convergence metrics. We show that both dielectric methods are inferior to the temperature enhanced sampling methods, and in turn show that temperature cool walking (TCW) systematically outperforms the standard temperature replica exchange (TREx) method. We extend our comparisons of the TCW and TREx methods to the 5 residue met-enkephalin peptide, in which we evaluate the Kullback-Leibler divergence metric to show that the rate of convergence between two independent trajectories is faster for TCW compared to TREx. Finally we apply the temperature methods to the 42 residue amyloid-β peptide in which we find non-negligible differences in the disordered ensemble using TCW compared to the standard TREx. All four methods have been made available as software through the OpenMM Omnia software consortium (http://www.omnia.md/).

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

The amide III vibrational circular dichroism band as a probe to detect conformational preferences of alanine dipeptide in water

The conformational preferences of blocked alanine dipeptide (ADP), Ac-Ala-NHMe, in aqueous solution were studied using vibrational circular dichroism (VCD) together with density functional theory (DFT) calculations. DFT calculations of three most representative conformations of ADP surrounded by six explicit water molecules immersed in a dielectric continuum have proven high sensitivity of amide III VCD band shape that is characteristic for each conformation of the peptide backbone. The polyproline II (PII ) and αR conformation of ADP are associated with a positive VCD band while β conformation has a negative VCD band in amide III region. Knowing this spectral characteristic of each conformation allows us to assign the experimental amide III VCD spectrum of ADP. Moreover, the amide III region of the VCD spectrum was used to determine the relative populations of conformations of ADP in water. Based on the interpretation of the amide III region of VCD spectrum we have shown that dominant conformation of ADP in water is PII which is stabilized by hydrogen bonded water molecules between CO and NH groups on the peptide backbone.

Hamiltonian replica exchange in GROMACS: a flexible implementation

A simple and general implementation of Hamiltonian replica exchange for the popular molecular dynamics software GROMACS is presented. In this implementation, arbitrarily different Hamiltonians can be used for the different replicas without incurring in any significant performance penalty. The implementation was validated on a simple toy model – alanine dipeptide in water – and applied to study the rearrangement of an RNA tetraloop, where it was used to compare recently proposed force-field corrections.

High performance computing for drug development on K computer

Massively parallel computations (MP-CAFEE) ware developed to calculate absolute binding free energies of small molecules bound to a protein by all-atom molecular dynamics. It uses the nonequilibrium work measurement and Bennett acceptance ratio methods to calculate the free energy difference between the bound and unbound states. The FUJI force field was developed in order to assign force field parameters to arbitrary organic molecules in a unified manner including proteins and nucleic acids. Its dihedral parameters agree with the torsion energy profiles calculated by high-level ab initio molecular orbital theory for the model systems of protein backbone. Comparing with various force fields it agrees well with recent observations by vibrational spectroscopy on Ramachandran angle's population of alanine dipeptide in water. MP-CAFEE with FUJI force field has an efficient parallel algorithm and enough accuracy for computer aided drug design.

Instantaneous normal mode analysis of the vibrational relaxation of the amide I mode of alanine dipeptide in water

Nonequilibrium Molecular Dynamics (MD) simulations coupled to instantaneous normal modes (INMs) analysis are used to study the vibrational relaxation of the acetyl and amino-end amide I modes of the alanine dipeptide (AlaD) molecule dissolved in water (D2O). The INMs are assigned in terms of the equilibrium normal modes using the Effective Atomic Min-Cost algorithm as adapted to make use of the outputs of standard MD packages, a method which is well suited for the description of flexible molecules. The relaxation energy curves of both amide I modes show multiexponential decays, in good agreement with the experimental findings. It is found that ~85%-90% of the energy relaxes through intramolecular vibrational redistribution. The main relaxation pathways are also identified. The rate at which energy is transferred into the solvent is similar for the acetyl-end and amino-end amide I modes. The conformational changes occurring during relaxation are investigated, showing that the populations of the alpha and beta region conformers are altered by energy transfer in such a way that it takes 15 ps for the equilibrium conformational populations to be recovered after the initial excitation of the AlaD molecule.

A Bayesian method for construction of Markov models to describe dynamics on various time-scales

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This paper presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (τ,P,T), where τ is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N(P)×N(P) transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N(P) is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. (1) The method uses Bayesian analysis to determine the partition as well as the transition probabilities. (2) The method allows the construction of a Markov model for any chosen mesoscopic time-scale τ. (3) It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a "consistent mesoscopic Markov model" (CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time-scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P,T) for any chosen τ. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time-scale τ was generated by the CMMM specified by (P,T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time-scales.

TNAMD: Implementation of TIGER2 in NAMD

Replica-exchange molecular dynamics (REMD) must be used to enhance sampling when there are significant (relative to kT) barriers between different parts of the phase space. TIGER2 is a next-generation REMD method that offers more efficient sampling compared to the original REMD method by reducing the number of replicas required to span a given temperature range. In this paper, we present an implementation of the TIGER2 algorithm in the NAMD software package. This implementation exploits the capacity of NAMD to interpret Tcl scripts. The Tcl script implementing TIGER2 is provided and explained in detail, and demonstrated for alanine dipeptide in water. Program summary Program title: TNAMD Catalogue identifier: AEHH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 837 No. of bytes in distributed program, including test data, etc.: 610 107 Distribution format: tar.gz Programming language: Tcl 8.5 Computer: Clusters, workstations. Tested on Intel Clovertown, Atom. Operating system: Linux, Windows (with Linux shell) Has the code been vectorised or parallelised?: Yes. Parallelised with MPI Classification: 3 External routines: NAMD 2.6 ( http://www.ks.uiuc.edu/Research/namd/) Nature of problem: Replica-exchange molecular dynamics. Solution method: Replicas are assigned to unique processes, and pass through a series of cycles of heating, equilibration, quenching and sampling; after which temperatures are swapped between replicas. Running time: The test run can take up to twenty minutes.

Are Current Semiempirical Methods Better Than Force Fields? A Study from the Thermodynamics Perspective

The semiempirical Hamiltonians MNDO, AM1, PM3, RM1, PDDG/MNDO, PDDG/PM3, and SCC-DFTB, when used as part of a hybrid QM/MM scheme for the simulation of biological molecules, were compared on their abilities to reproduce experimental ensemble averages at or near room temperatures for the model system alanine dipeptide in water. Free energy surfaces in the (phi, psi) dihedral angle space, (3)J(H(N),H(alpha)) NMR dipolar coupling constants, basin populations, and peptide-water radial distribution functions (RDF) were calculated from replica exchange simulations and compared to both experiment and fully classical force field calculations using the Amber ff99SB force field. In contrast with the computational chemist's intuitive idea that the more expensive a method the better its accuracy, the ff99SB force field results were more accurate than most of the semiempirical methods, with the exception of RM1. None of the methods, however, was able to accurately reproduce the experimental data. Analysis of the results indicate that the specific QM/MM interactions have little influence on the sampling of free energy surfaces, and the differences are well explained simply by the intrinsic properties of the various QM methods.

Equilibrium exchange enhances the convergence rate of umbrella sampling

Umbrella sampling, a technique for sampling energetically unfavorable states by computer simulation, is subject to systematic sampling errors arising from quasi-nonergodicity. In order to address this problem, we compare free energy profiles generated along the backbone dihedral angles φ and ψ of alanine dipeptide in water using umbrella sampling successively with and without the provision of equilibrium exchange between umbrellas. The results show that the addition of equilibrium exchange to umbrella sampling alleviates these errors by restoring the utilization of transition paths that leave and reenter the specified sampling region.

Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: Comparisons with IR and vibrational circular dichroism spectra

We have implemented the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken population analysis. For the classical MD simulations, the solute is treated with the polarizable or nonpolarizable AMBER and polarizable CHARMM force fields and water is treated with the TIP3P, TIP4P, or TIP5P model. It is found that the relative populations of right-handed alpha-helix and extended beta and P(II) conformations in the simulation trajectory strongly depend on the simulation method. For the QM/MM MD simulations, the PM3/MM shows that the P(II) conformation is dominant, whereas the AM1/MM predicts that the dominant conformation is alpha(R). Polarizable CHARMM force field gives almost exclusively P(II) conformation and other force fields predict that both alpha-helical and extended (beta and P(II)) conformations are populated with varying extents. Solvation environment around the dipeptide is investigated by examining the radial distribution functions and numbers and lifetimes of hydrogen bonds. Comparing the simulated IR and vibrational circular dichroism spectra with experimental results, we concluded that the dipeptide adopts the P(II) conformation and PM3/MM, AMBER03 with TIP4P water, and AMBER polarizable force fields are acceptable for structure determination of the dipeptide considered in this paper.

An improved replica-exchange sampling method: Temperature intervals with global energy reassignment

In a molecular dynamics (MD) simulation, representative sampling over the entire phase space is desired to obtain an accurate canonical distribution at a given temperature. For large molecules, such as proteins, this is problematic because systems tend to become trapped in local energy minima. The extensively used replica-exchange molecular dynamics (REMD) simulation technique overcomes this kinetic-trapping problem by allowing Boltzmann-weighted configuration exchange processes to occur between numerous thermally adjacent and compositionally identical simulations that are thermostated at sequentially higher temperatures. While the REMD method provides much better sampling than conventional MD, there are two substantial difficulties that are inherent in its application: (1) the large number of replicas that must be used to span a designated temperature range and (2) the subsequent long time required for configurations sampled at high temperatures to exchange down for potential inclusion within the low-temperature ensemble of interest. In this work, a new method based on temperature intervals with global energy reassignment (TIGER) is presented that overcomes both of these problems. A TIGER simulation is conducted as a series of short heating-sampling-quenching cycles. At the end of each cycle, the potential energies of all replicas are simultaneously compared at the same temperature using a Metropolis sampling method and then globally reassigned to the designated temperature levels. TIGER is compared with regular MD and REMD methods for the alanine dipeptide in water. The results indicate that TIGER increases sampling efficiency while substantially reducing the number of central processing units required for a comparable conventional REMD simulation.

Self-healing Umbrella Sampling: A Non-equilibrium Approach for Quantitative Free Energy Calculations

We propose a new approach for the umbrella sampling method in molecular dynamics simulations of complex systems. An accelerated sampling of the slow degrees of freedom is achieved by generating a single self-adaptive trajectory that tends to span uniformly the reaction coordinate using a time dependent bias potential derived from the preceding history of the system. To show the convergent behavior and the efficiency of the method, we present the free energy surface of alanine dipeptide in water as a function of the backbone dihedral angles.

Long-Time Conformational Transitions of Alanine Dipeptide in Aqueous Solution: Continuous and Discrete-State Kinetic Models

We present an analysis of the thermodynamics, conformational dynamics, and kinetics of the solvated alanine dipeptide molecule. Solvation was treated in the framework of the OPLS/analytic generalized born with nonpolar interactions effective potential model. The effective free energy map was generated in a series of multiwindow umbrella sampling all-atom simulations using the weighted histogram analysis method. A Brownian dynamics approach was used to examine the room-temperature dynamics of the dipeptide. To emulate the realistic dynamics of conformational interconversions of the alanine dipeptide in water, the parameters that govern the time evolution of the reduced model were chosen to mimic the intermediate-time dynamics of a model which treats both the solute and the solvent explicitly. The characteristic time (mean first passage time) for the “fast” C7eq → αR transition was found to be around 249 ps in good agreement with the results of previously reported studies. From an ensemble of microsecond Brownian dynamics trajectories we were able to numerically estimate with high statistical precision the mean transition time for the “slow” transition αR → C7ax, which was found to be approximately 11 ns. Conformational kinetics of the dipeptide was further analyzed by introducing a discrete-state kinetic model consisting of four states (αR, β/C5/C7eq, αL, and C7ax) and 12 rate constants, which reproduces the long-time behavior of the Brownian dynamics simulations. The simulations described here complement and help to motivate single-molecule spectroscopic studies of alanine dipeptide and other peptides in aqueous solution. The close correspondence established between the continuous dynamics and a discrete-state kinetic model provides a possible route for studying the long-time kinetic behavior of larger polypeptides using detailed all-atom effective potentials.

Role of solvent in determining conformational preferences of alanine dipeptide in water.

Evidence from a variety of spectroscopic probes indicates that (phi, psi) values corresponding to the left-handed polyproline II helix (P(II)) are preferred for short alanine-based peptides in water. On the basis of results from theoretical studies, it is believed that the observed preference is dictated by favorable peptide-solvent interactions, which are realized through formation of optimal hydrogen-bonding water bridges between peptide donor and acceptor groups. In the present study, we address this issue explicitly by analyzing the hydration structure and thermodynamics of 16 low-energy conformers of the alanine dipeptide (N-acetylalanine-N'-methylamide) in liquid water. Monte Carlo simulations in the canonical ensemble were performed under ambient conditions with all-atom OPLS parameters for the alanine dipeptide and the TIP5P model for water. We find that the number of hydrogen-bonded water molecules connecting the peptide group donor and acceptor atoms has no effect on the solvation thermodynamics. Instead, the latter are determined by the work done to fully hydrate the peptide. This work is minimal for conformations that are characterized by a minimal overlap of the primary hydration shells around the peptide donor and acceptor atoms. As a result, peptide-solvent interactions favor "compact" conformations that do not include P(II)-like geometries. Our main conclusion is that the experimentally observed preference for P(II) does not arise due to favorable direct interactions between the peptide and water molecules. Instead, the latter act to unmask underlying conformational preferences that are a consequence of minimizing intrapeptide steric conflicts.

Grid−Flux Method for Learning the Solvent Contribution to the Mechanisms of Reactions

We present a trajectory-based method with which to learn information about the qualitative role that solvent molecules play in dynamic simulations of reactions that occur in solution. A spatial grid is superimposed on the system being simulated, and average fluxes of solvent molecules between cells on the grid are calculated along reactive trajectories. The average solvent fluxes form a much smaller set of variables and provide a much simpler description of the reaction under study than the full list of atomic positions and momenta. The feasibility and utility of the method are demonstrated by producing reduced descriptions of the mechanisms of the dissociation reaction of NaCl in water and of the rearrangement of the alanine dipeptide in water. Comparisons between our method and other possible data reduction techniques are discussed.