Alanine Dipeptide In Aqueous Solution Research Articles

Temperature Dependence of Peptide Conformational Equilibria from Simulations at a Single Temperature.

Understanding the structure of proteins is key to unraveling their function in biological processes. Thus, significant attention has been paid to the calculation of conformational free energies. In this paper, we demonstrate a simple extension of fluctuation theory that permits the calculation of the temperature derivative of the conformational free energy, and hence the internal energy and entropy, from single-temperature simulations. The method further enables the decomposition into the contribution of different interactions present in the system to the internal energy surface. We illustrate the method for the canonical test system of alanine dipeptide in aqueous solution, for which we examine the free energy as a function of two dihedral angles. This system, like many, is most effectively treated using accelerated sampling methods and we show how the present approach is compatible with an important class of these, those that introduce a bias potential, by implementing it within metadynamics.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: Accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

A Minimal Implementation of the AMBER-PAICS Interface for Ab Initio FMO-QM/MM-MD Simulation

Abstract For the purpose of providing a realistic description of the reaction mechanisms in large molecular systems, we propose a quantum mechanical/molecular mechanical (QM/MM) method combined with the ab initio fragment molecular orbital (FMO) method, i.e., the ab initio FMO-QM/MM method. By connecting a molecular dynamics (MD) program AMBER with an FMO program PAICS, we have implemented an AMBER-PAICS interface (AP-IF). Using the AP-IF, we demonstrate three example applications: (a) a hydrogen fluoride and water molecular clusters, (b) an alanine dipeptide in aqueous solution, and (c) a prion protein–GN8 complex. From these results, it is confirmed that the FMO-QM/MM method offers a good compromise between chemical accuracy and computational cost and enables us to obtain in ab initio quality the inter- and intramolecular interaction energies between molecules or residues in large molecular systems such as solution and biomolecule, by using the dynamics-based interfragment interaction energy (IFIE) analysis.

Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials

Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.

Generalised canonical–isokinetic ensemble: speeding up multiscale molecular dynamics and coupling with 3D molecular theory of solvation

We have proposed a new canonical–isokinetic ensemble for efficient sampling of conformational space in molecular dynamics (MD) simulations which leads to the optimised isokinetic Nosé–Hoover (OIN) chain algorithm for atomic and molecular systems. We applied OIN to multiple time step (MTS) MD simulations of the rigid and flexible models of water to demonstrate its advantage over the standard canonical, isokinetic and canonical–isokinetic ensembles. With the stabilising effect of OIN thermostatting in MTS-MD, gigantic outer time steps up to picoseconds can be employed to accurately calculate equilibrium and conformational properties. Furthermore, we developed the atomic version of OIN for MTS-MD of a biomolecule in a solvent potential of mean force obtained at sequential MD steps by using the molecular theory of solvation, aka three-dimensional reference interaction site model with the Kovalenko–Hirata closure (3D-RISM-KH). The solvation forces are obtained analytically by converging the 3D-RISM-KH integral equations once per several OIN outer time steps, and are calculated in between by using solvation force-coordinate extrapolation (SFCE) in the subspace of previous successive solutions to 3D-RISM-KH. For illustration, we applied the multiscale OIN/SFCE/3D-RISM-KH algorithm to a fully flexible model of alanine dipeptide in aqueous solution. Although the computational rate of solvent sampling in OIN/SFCE/3D-RISM-KH is already 20 times faster than standard MD with explicit solvent, further substantial acceleration of sampling stems from making solute evolution steps in a statistically averaged potential of mean force obtained from 3D-RISM-KH. The latter efficiently samples the phase space for essential events with rare statistics such as exchange and localisation of solvent and ligand molecules in confined spaces, pockets and at binding sites of the solute macromolecule, as distinct from MD with explicit solvent which requires enormous computational time and number of steps in such cases.

Replica-exchange method in van der Waals radius space: Overcoming steric restrictions for biomolecules

We present a new type of the Hamiltonian replica-exchange method, where the van der Waals radius parameter and not the temperature is exchanged. By decreasing the van der Waals radii, which control spatial sizes of atoms, this Hamiltonian replica-exchange method overcomes the steric restrictions and energy barriers. Furthermore, the simulation based on this method escapes from the local-minimum free-energy states and realizes effective sampling in the conformational space. We applied this method to an alanine dipeptide in aqueous solution and showed the effectiveness of the method by comparing the results with those obtained from the conventional canonical and replica-exchange methods.

Two-Dimensional Infrared Spectroscopy of the Alanine Dipeptide in Aqueous Solution

The linear-infrared and two-dimensional infrared (2D IR) spectra in the amide-I' region of the alanine dipeptide and its (13)C isotopomers in aqueous solution (D(2)O) are reported. The two amide-I' IR transitions have been assigned unambiguously by using (13)C isotopic substitution of the carbonyl group; the amide unit at the acetyl end shows a lower transition frequency in the unlabeled species. The ratio of their transition dipole strengths remains almost unchanged upon (13)C substitution, indicating the absence of intensity transfer between two vibrators. The 2D IR cross peaks directly associated with intramode coupling in this case show a small off-diagonal anharmonicity (0.2 +/- 0.2 cm(-1)), leading to a small coupling constant (1.5 +/- 0.5 cm(-1)). The coupling and the 2D IR spectra in two different polarizations (zzzz and zxxz) are as expected for a polyproline-II (PP(II))-like conformation for dialanine, with the backbone dihedral angles (phi, psi) determined to be in the range of (-70 degrees +/- 25 degrees, +120 degrees +/- 25 degrees). Ab initio DFT calculations and normal mode decoupling analysis in the Ramachandran subspace in the neighborhood of PP(II) conformation confirm the presence of a region where the coupling is vanishingly small and support these experimental findings. The relationship between the coupling and off-diagonal anharmonicity is consolidated by examining the distribution of the latter from an ensemble averaged Hamiltonian incorporating uncorrelated diagonal frequency distributions and a small coupling (<2 cm(-1)); it is found that the most probable value for the off-diagonal anharmonicity falls into the range of experimental observations. Further, incorporating DFT results, the simulated linear-IR and 2D IR can reproduce the essential features of the measurements, including the transition frequency positions and apparent peak intensities. All the experimental results and simulations are consistent with a PP(II)-like conformation for the alanine dipeptide in aqueous solution, in which two amide-I' modes are highly localized and whose frequency distributions are uncorrelated.

An application of coupled reference interaction site model/molecular dynamics to the conformational analysis of the alanine dipeptide

We present an application of our recently proposed coupled reference interaction site model (RISM) molecular dynamics (MD) solvation free energy methodology [Freedman and Truong, Chem. Phys. Lett. 381, 362 (2003); J. Chem. Phys. 121, 2187 (2004)] to study the conformational stability of alanine dipeptide in aqueous solution. In this methodology, radial distribution functions obtained from a single MD simulation are substituted into a RISM expression for solvation free energy. Consequently, iterative solution of the RISM equation is not needed. The relative solvation free energies of seven different conformations of the alanine dipeptide in aqueous solution are calculated. Results from the coupled RISM/MD methodology are in good agreement with those from earlier simulations using the accurate free energy perturbation approach, showing that the alphaR conformation is most stabilized by solution. This study establishes a framework for applying this coupled RISM/MD method to larger biological systems.

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.

Temperature and pressure effects on conformational equilibria of alanine dipeptide in aqueous solution.

We investigated the temperature and pressure effects on conformational equilibria of N-acetyl-L-alanine-N'-methylamide (AAlaMA) in aqueous solution by Raman spectroscopy. Scattering intensities in the skeletal stretching mode of AAlaMA in aqueous solution were decomposed into some component bands by the spectra analysis. Our results indicate that each component band for AAlaMA adopts not only the P(II) and alpha(R) conformations but also the C(7eq) conformation. From temperature and pressure dependencies of the band intensities, we determined the enthalpy differences and the volume differences between the conformers. The C(7eq) conformer is enthalpically most stable due to the intramolecular hydrogen bond. The partial molar volume of the C(7eq) conformer is the smallest through the solvent-exclusion effect rather than the solute-solvent electrostatic interaction effect.

Solvation structure, thermodynamics, and conformational dependence of alanine dipeptide in aqueous solution analyzed with reference interaction site model theory

With the CHARMM22 (Chemistry at Harvard Macromolecular Mechanics) all-atom nonbonded potential parameters for alanine dipeptide solute and the transferable intermolecular potential model water for the solvent, the reference interaction site model (RISM) integral equations with the hypernetted chain closure are solved to obtain all the atomic solvent–solute radial distribution functions. The solvation structures of alanine dipeptide in its seven conformations: C7eq, C7ax, C5, αR, β, αL and PII, in aqueous solution are analyzed at the atomic level in terms of the atomic solute–solvent radial distribution functions. At a temperature of T=298.15 K and bulk water density ρ=0.9970 g cm−3, the corresponding solvation free energies are calculated by using Singer and Chandler’s analytic solvation free energy formulation [Mol. Phys. 55, 621 (1985)]. Solvation energies, enthalpies, and entropies are also calculated in the RISM theory framework. The conformational dependence of solvation for alanine dipeptide in aqueous solution is analyzed. The solvation thermodynamcs for alanine dipeptide in aqueous solution are mainly controlled by the strong hydrophobic groups: CH3 and CH, which make alanine dipeptide show strong hydrophobicity. But the differences in the solvation thermodynamics for different alanine dipeptide conformers are controlled by the carbonyl groups and amide groups, which make alanine dipeptide show some hydrophilicity and exist in various conformations in aqueous solution. Solvation of alanine dipeptide in aqueous solution is determined by the competition among the molecular packing effects, intramolecular hydrogen bonds, and intermolecular hydrogen bonds. Due to the intramolecular hydrogen bonds in the two folded C7 conformations, the two most favorable conformations in gas phase become the least solvated in aqueous solution. Due to the intermolecular hydrogen bonds, C5, PII, αL, αR, and β become more solvated in aqueous solution.

A critical analysis of continuum electrostatics: The screened Coulomb potential–implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins September 11, 2001: This article is dedicated to all those who lost their lives in the inferno of hatred that destroyed the WTC and struck the Pentagon, and the passengers and crew of United

An analysis of the screened Coulomb potential–implicit solvent model (SCP–ISM) is presented showing that general equations for both the electrostatic and solvation free energy can be derived in a continuum approach, using statistical averaging of the polarization field created by the solvent around the molecule. The derivation clearly shows how the concept of boundary, usually found in macroscopic approaches, is eliminated when the continuum model is obtained from a microscopic treatment using appropriate averaging techniques. The model is used to study the alanine dipeptide in aqueous solution, as well as the discrimination of native protein structures from misfolded conformations. For the alanine dipeptide the free energy surface in the ϕ–ψ space is calculated and compared with recently reported results of a detailed molecular dynamics simulation using an explicit representation of the solvent, and with other available data. The study showed that the results obtained using the SCP–ISM are comparable to those of the explicit water calculation and compares favorably to the FDPB approach. Both transition states and energy minima show a high correlation (r > 0.98) with the results obtained in the explicit water analysis. The study of the misfolded structures of proteins comprised the analysis of three standard decoy sets, namely, the EMBL, Park and Levitt, and Baker's CASP3 sets. In all cases the SCP–ISM discriminated well the native structures of the proteins, and the best-predicted structures were always near-native (cRMSD ∼2 Å). Proteins 2002;47:45–61. © 2002 Wiley-Liss, Inc.

Simulation of peptide folding with explicit water--a mean solvation method.

A new approach to efficiently calculate solvent effect in computer simulation of macromolecular systems has been developed. Explicit solvent molecules are included in the simulation to provide a mean solvation force for the solute conformational search. Simulations of an alanine dipeptide in aqueous solution showed that the new approach is significantly more efficient than conventional molecular dynamics method in conformational search, mainly because the mean solvation force reduced the solvent damping effect. This approach allows the solute and solvent to be simulated separately with different methods. For the macromolecule, the rigid fragment constraint dynamics method we developed previously allows large time-steps. For the solvent, a combination of a modified force-bias Monte Carlo method and a preferential sampling can efficiently sample the conformational space. A folding simulation of a 16-residue peptide in water showed high efficiency of the new approach.

A molecular dynamics study of the conformation of the alanine dipeptide in aqueous solution using a quantum mechanical potential

Molecular dynamics simulations of the aqueous solution of alanine dipeptide have been carried out for seven configurations characteristic of important regions of the Ramachandran plot. A hybrid quantum mechanical-molecular mechanical potential was used that describes the solute using the AM1 Hamiltonian and the solvent using the TIP3P model. The importance of differential solute polarization and the preferential stabilization of the extended structures αL, αR and β have been identified. The results are compared with experiment and with the predictions of the ab initio polarizable continuum model of solvation.

A molecular dynamics study of the conformation of the alanine dipeptide in aqueous solution using a quantum mechanical potential

Molecular dynamics simulations of the aqueous solution of alanine dipeptide have been carried out for seven configurations characteristic of important regions of the Ramachandran plot. A hybrid quantum mechanical-molecular mechanical potential was used that describes the solute using the AM1 Hamiltonian and the solvent using the TIP3P model. The importance of differential solute polarization and the preferential stabilization of the extended structures αL, αR and β have been identified. The results are compared with experiment and with the predictions of the ab initio polarizable continuum model of solvation.

Solvation of alanine dipeptide: a quantum mechanical treatment

The self-consistent reaction field model is used with an ab initio wavefunction to predict the structure and energetics of conformers of the alanine dipeptide in aqueous solution; the predictions are in good agreement with the limited experimental data available and with molecular dynamics simulations.

The potential of mean force surface for the alanine dipeptide in aqueous solution: a theoretical approach

Results of an application of integral equation theory to the determination of the intramolecular potential of mean force for the alanine dipeptide. N-methyl alanine acetamide, in aqueous solution are presented. The calculations are based on Ornstein—Zernike-like equations for polar systems with an intramolecular superposition approximation. The solvated free energy surface for the dipeptide as a function of the dihedral angles φ and ψ (Ramachandran plot) is determined and compared with the vaccum surface calculations. Conformations that are essentially forbidden in vaccum are found to be significant in aqueous solution. The solvent contributions to the free energy surface are decomposed into enthalpic and entropic terms. Possible applications and extensions of the method are outlined.