Amino Acid Side Chain Analogues Research Articles

Mixing MARTINI: Electrostatic Coupling in Hybrid Atomistic–Coarse-Grained Biomolecular Simulations

Hybrid molecular dynamics simulations of atomistic (AA) solutes embedded in coarse-grained (CG) environment can substantially reduce the computational cost with respect to fully atomistic simulations. However, interfacing both levels of resolution is a major challenge that includes a balanced description of the relevant interactions. This is especially the case for polar solvents such as water, which screen the electrostatic interactions and thus require explicit electrostatic coupling between AA and CG subsystems. Here, we present and critically test computationally efficient hybrid AA/CG models. We combined the Gromos atomistic force field with the MARTINI coarse-grained force field. To enact electrostatic coupling, two recently developed CG water models with explicit electrostatic interactions were used: the polarizable MARTINI water model and the BMW model. The hybrid model was found to be sensitive to the strength of the AA-CG electrostatic coupling, which was adjusted through the relative dielectric permittivity εr(AA-CG). Potentials of mean force (PMFs) between pairs of amino acid side chain analogues in water and partitioning free enthalpies of uncharged amino acid side chain analogues between apolar solvent and water show significant differences between the hybrid simulations and the fully AA or CG simulations, in particular for charged and polar molecules. For apolar molecules, the results obtained with the hybrid AA/CG models are in better agreement with the fully atomistic results. The structures of atomistic ubiquitin solvated in CG water and of a single atomistic transmembrane α-helix and the transmembrane portion of an atomistic mechanosensitive channel in CG lipid bilayers were largely maintained during 50-100 ns of AA/CG simulations, partly due to an overstabilization of intramolecular interactions. This work highlights some key challenges on the way toward hybrid AA/CG models that are both computationally efficient and sufficiently accurate for biomolecular simulations.

Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness.

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

Derivation of fixed partial charges for amino acids accommodating a specific water model and implicit polarization.

We have developed the IPolQ method for fitting nonpolarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest, followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side-chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general and applicable to arbitrary solutes.

Proton affinity of polar amino acid sidechain analogues anchored to the outer wall of single walled carbon nanotubes

We investigate the proton affinity values of sidechain analogues of Ser, Asp, His and Tyr covalently attached to the the outer wall of single walled carbon nanotubes both in the gas phase and in the presence of a polar solvent. The proton affinity values, estimated by B3LYP/SVP method, show marked sensitivity to the anchoring hydrophobic surface. His and Tyr-like sidechains exhibit high propensities towards accepting a proton from a neighboring –OH group similarly tethered to the carbon nanotube wall. Compared to Tyr sidechain in the gas phase, a marked increase in proton affinity values of Tyr-like sidechains is observed in functionalized systems if, in addition to the proton donor –OH group, an additional –OH group is present covalently attached to the wall within hydrogen bonding distance of the proton acceptor sidechain.

Salting Effects on Protein Components in Aqueous NaCl and Urea Solutions: Toward Understanding of Urea-Induced Protein Denaturation

The mechanism of urea-induced protein denaturation is explored through studying the salting effect of urea on 14 amino acid side chain analogues, and N-methylacetamide (NMA) which mimics the protein backbone. The solvation free energies of the 15 molecules were calculated in pure water, aqueous urea, and NaCl solutions. Our results show that NaCl displays strong capability to salt out all 15 molecules, while urea facilitates the solvation (salting-in) of all the 15 molecules on the other hand. The salting effect is found to be largely enthalpy-driven for both NaCl and urea. Our observations can explain the higher stability of protein's secondary and tertiary structures in typical salt solutions than that in pure water. Meanwhile, urea's capability to better solvate protein backbone and side-chain components can be extrapolated to explain protein's denaturation in aqueous urea solution. Urea salts in molecules through direct binding to solute surface, and the strength is linearly dependent on the number of heavy atoms of solute molecules. The van der Waals interactions are found to be the dominant force, which challenges a hydrogen-bonding-driven mechanism proposed previously.

Statistical Convergence of Equilibrium Properties in Simulations of Molecular Solutes Embedded in Lipid Bilayers.

In recent years, atomistic molecular simulations have become a method of choice for studying the interaction of small molecules, peptides, and proteins with biological membranes. Here, we critically examine the statistical convergence of equilibrium properties in molecular simulations of two amino acid side-chain analogs, leucine and arginine, in the presence of a hydrated phospholipid bilayer. To this end, the convergence of the standard binding free energy for the reversible insertion of the solutes in the bilayer is systematically assessed by evaluating dozens of separate sets of umbrella sampling calculations for a total simulation time exceeding 400 μs. We identify rare and abrupt transitions in bilayer structure as a function of solute insertion depth. These transitions correspond to the slow reorganization of ionic interactions involving zwitterionic phospholipid headgroups when the solutes penetrate the lipid-water interface and when arginine is forced through the bilayer center. These rare events are shown to constitute hidden sampling barriers that limit the rate of convergence of equilibrium properties and result in systematic sampling errors. Our analysis demonstrates that the difficulty of attaining convergence for lipid bilayer-embedded solutes has, in general, been drastically underestimated. This information will assist future studies in improving accuracy by selecting a more appropriate reaction coordinate or by focusing computational resources on those regions of the reaction coordinate that exhibit slow convergence of equilibrium properties.

Free Energy Calculations of the Adsorption of Amino Acid Analogues at the Aqueous Titania Interface

The potential of mean constraint force approach, in partnership with atomistic molecular dynamics simulations, is used to calculate the change in free energy upon adsorption of amino acid side chain analogues at the aqueous rutile titania (110) interface. Our results indicate that both positively charged and negatively charged moieties have favorable free energy of binding to the titania surface. Stable contact, mediated via the first two solvent layers at the interface, is also indicated for the charged adsorbates. Hydrophobic adsorbates showed no appreciable binding to the titania surface. In contrast, the binding for our serine analogue (methanol) features a slight possibility to bind via hydrogen bonding to the titania surface. Our calculated results indicate very good agreement with available experimental data. In partnership with other information regarding peptide conformation and intrapeptide interactions, our findings should be helpful in building design principles for peptide sequences with pred...

Electrostatic solvation free energy of amino acid side chain analogs: Implications for the validity of electrostatic linear response in water

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLS-AA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirms that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.

Accounting for Polarization Cost When Using Fixed Charge Force Fields. II. Method and Application for Computing Effect of Polarization Cost on Free Energy of Hydration

Polarization cost is the energy needed to distort the wave function of a molecule from one appropriate to the gas phase to one appropriate for some condensed phase. Although it is not currently standard practice, polarization cost should be considered when deriving improved fixed charge force fields based on fits to certain types of experimental data and when using such force fields to compute observables that involve changes in molecular polarization. Building on earlier work, we present mathematical expressions and a method to estimate the effect of polarization cost on free energy and enthalpy implied by a charge model meant to represent a solvated state. The charge model can be any combination of point charges, higher-order multipoles, or even distributed charge densities, as long as they do not change in response to environment. The method is illustrated by computing the effect of polarization cost on free energies of hydration for the neutral amino acid side chain analogues as predicted using two popular fixed charge force fields and one based on electron densities computed using quantum chemistry techniques that employ an implicit model to represent aqueous solvent. From comparison of the computed and experimental hydration free energies, we find that two commonly used force fields are too underpolarized in their description of the solute-water interaction. On the other hand, a charge model based on the charge density from a hybrid density functional calculation that used an implicit model for aqueous solvent performs well for hydration free energies of these molecules after the correction for dipole polarization is applied. As such, an improved description of the density (e.g., B3LYP, MP2) in conjunction with an implicit solvent (e.g., PCM) or explicit solvent (e.g., QM/MM) approach may offer promise as a starting point for the development of improved fixed charge models for force fields.

Cargo surface hydrophobicity is sufficient to overcome the nuclear pore complex selectivity barrier

To fulfil their function, nuclear pore complexes (NPCs) must discriminate between inert proteins and nuclear transport receptors (NTRs), admitting only the latter. This specific permeation is thought to depend on interactions between hydrophobic patches on NTRs and phenylalanine-glycine (FG) or related repeats that line the NPC. Here, we tested this premise directly by conjugating different hydrophobic amino-acid analogues to the surface of an inert protein and examining its ability to cross NPCs unassisted by NTRs. Conjugation of as few as four hydrophobic moieties was sufficient to enable passage of the protein through NPCs. Transport of the modified protein proceeded with rates comparable to those measured for the innate protein when bound to an NTR and was relatively insensitive both to the nature and density of the amino acids used to confer hydrophobicity. The latter observation suggests a non-specific, small, and plant interaction network between cargo and FG repeats.

Free energy profiles of amino acid side chain analogs near water‐vapor interface obtained via MD simulations

Solvation of 13 neutral amino acid side chain analogs at water-vapor interface was studied by computing high precision free energy profiles of the molecules across the interface using molecular dynamics (MD) simulations. The SPC water model (Berendsen, H. J. C., Postma, J. P. M., van Gunsteren, W. F., Hermans, P. A. K. J., Dixon, R., Cornell, W., Fox, T., Chipot, C., Pohorille, A. In: Wilkinson, A., Weiner, P. and van Gunsteren, W. F. editors. Intermolecular Forces, 1981, 3, 331) and OPLS-AA (Jorgensen et al., J Am Chem Soc, 1996, 118, 11225) potential parameter sets were used. A rigorous approach for the computation of high precision free energy profiles at water-vapor interface using constraint force technique is implemented. Methodology of obtaining high precision potential of mean force (PMF) profiles free of simulation artifacts in MD simulations is outlined and discussed. The accuracy of the calculations is examined by comparing the hydration free energies of studied solutes obtained from PMF calculations and separately using Bennett acceptance ratio technique by decoupling solvent-solute interactions in the bulk. All molecules exhibit a free energy minimum at interface. No significant desolvation barrier is observed for any of the studied species. Adsorption energies for studied molecules at water-vapor interface are estimated and compared with experimental observations. We find that for modeled neutral compounds pronounced surface influence on solute solvation vanishes already at 6-7 A behind the water surface as the solvation free energy approaches the bulk value. The possibility of force field refinement using adsorption free energies is outlined.

Efficient and precise solvation free energies via alchemical adiabatic molecular dynamics

A new molecular dynamics method for calculating free energies associated with transformations of the thermodynamic state or chemical composition of a system (also known as alchemical transformations) is presented. The new method extends the adiabatic dynamics approach recently introduced by Rosso et al. [J. Chem. Phys. 116, 4389 (2002)] and is based on the use of an additional degree of freedom, lambda, that is used as a switching parameter between the potential energy functions that characterize the two states. In the new method, the coupling parameter lambda is introduced as a fictitious dynamical variable in the Hamiltonian, and a system of switching functions is employed that leads to a barrier in the lambda free energy profile between the relevant thermodynamic end points. The presence of such a barrier, therefore, enhances sampling in the end point (lambda = 0 and lambda = 1) regions which are most important for computing relevant free energy differences. In order to ensure efficient barrier crossing, a high temperature T(lambda) is assigned to lambda and a fictitious mass m(lambda) is introduced as a means of creating an adiabatic separation between lambda and the rest of the system. Under these conditions, it is shown that the lambda free energy profile can be directly computed from the adiabatic probability distribution function of lambda without any postprocessing or unbiasing of the output data. The new method is illustrated on two model problems and in the calculation of the solvation free energy of amino acid side-chain analogs in TIP3P water. Comparisons to previous work using thermodynamic integration and free energy perturbation show that the new lambda adiabatic free energy dynamics method results in very precise free energy calculations using significantly shorter trajectories.

Energy barriers of proton transfer reactions between amino acid side chain analogs and water from ab initio calculations

Proton transfer reactions were studied in all titratable pairs of amino acid side chains where, under physiologically reasonable conditions, one amino acid may function as a donor and the other one as an acceptor. Energy barriers for shifting the proton from donor to acceptor atom were calculated by electronic structure methods at the MP2/6-31++G(d,p) level, and the well-known double-well potentials were characterized. The energy difference between both minima can be expressed by a parabola using as argument the donor-acceptor distance R(DA). In this work, the fit parameters of the quadratic expression are determined for each donor-acceptor pair. Moreover, it was found previously that the energy barriers of the reactions can be expressed by an analytical expression depending on the distance between donor and acceptor and the energy difference between donor and acceptor bound states. The validity of this approach is supported by the extensive new data set. This new parameterization of proton transfer barriers between titratable amino acid side chains allows us to very efficiently estimate proton transfer probabilities in molecular modelling studies or during classical molecular dynamics simulation of biomolecular systems.

New-Generation Amber United-Atom Force Field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.

Force Field Evaluation for Biomolecular Simulation: Free Enthalpies of Solvation of Polar and Apolar Compounds in Various Solvents

Recently, the GROMOS biomolecular force field parameter set 53A6--which has been parametrized to reproduce experimentally determined free enthalpies of hydration and solvation in cyclohexane of amino acid side-chain analogs--was presented. To investigate the transferability of the new parameter set, we calculated free enthalpies of solvation of a range of polar and apolar compounds in different solvents (methanol, dimethyl sulfoxide (DMSO), acetonitrile, and acetone) from molecular dynamics simulations using the GROMOS 53A6 force field. For methanol and DMSO, parameters were used that are available in the 53A6 parameter set. For acetonitrile, a recently developed model was taken and for acetone, two models available in literature were used. We found that trends in and values for the solvation free enthalpies are in satisfactory agreement with experiment, except for the solvation in acetone for which deviations from experiment can be explained in terms of the properties of the models used.

Solvation free energies of amino acid side chain analogs for common molecular mechanics water models

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). In order to examine the accuracy of a range of common water models used for protein simulation for their solute/solvent properties, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from the OPLS-AA parameter set with the TIP3P, TIP4P, SPC, SPC/E, TIP3P-MOD, and TIP4P-Ew water models. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02-0.06 kcal/mol, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. We find that TIP3P-MOD, a model designed to give improved free energy of hydration for methane, gives uniformly the closest match to experiment; we also find that the ability to accurately model pure water properties does not necessarily predict ability to predict solute/solvent behavior. We also evaluate the free energies of a number of novel modifications of TIP3P designed as a proof of concept that it is possible to obtain much better solute/solvent free energetic behavior without substantially negatively affecting pure water properties. We decrease the average error to zero while reducing the root mean square error below that of any of the published water models, with measured liquid water properties remaining almost constant with respect to our perturbations. This demonstrates there is still both room for improvement within current fixed-charge biomolecular force fields and significant parameter flexibility to make these improvements. Recent research in computational efficiency of free energy methods allows us to perform simulations on a local cluster that previously required large scale distributed computing, performing four times as much computational work in approximately a tenth of the computer time as a similar study a year ago.

A generalized Born formalism for heterogeneous dielectric environments: Application to the implicit modeling of biological membranes

Reliable computer simulations of complex biological environments such as integral membrane proteins with explicit water and lipid molecules remain a challenging task. We propose a modification of the standard generalized Born theory of homogeneous solvent for modeling the heterogeneous dielectric environments such as lipid/water interfaces. Our model allows the representation of biological membranes in the form of multiple layered dielectric regions with dielectric constants that are different from the solute cavity. The proposed new formalism is shown to predict the electrostatic component of solvation free energy with a relative error of 0.17% compared to exact finite-difference solutions of the Poisson equation for a transmembrane helix test system. Molecular dynamics simulations of melittin and bacteriorhodopsin are carried out and performed over 10 ns and 7 ns of simulation time, respectively. The center of melittin along the membrane normal in these stable simulations is in excellent agreement with the relevant experimental data. Simulations of bacteriorhodopsin started from the experimental structure remained stable and in close agreement with experiment. We also examined the free energy profiles of water and amino acid side chain analogs upon membrane insertion. The results with our implicit membrane model agree well with the experimental transfer free energy data from cyclohexane to water as well as explicit solvent simulations of water and selected side chain analogs.

Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). We use large-scale distributed computing to access sufficient computational resources to extensively sample molecular systems and thus reduce statistical uncertainty of measured free energies. In order to examine the accuracy of a range of common models used for protein simulation, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from recent versions of the OPLS-AA, CHARMM, and AMBER parameter sets in TIP3P water using thermodynamic integration. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02–0.05 kcal/mol, which are in general an order of magnitude smaller than those found in other studies. Notably, this level of precision is comparable to that obtained in experimental hydration free energy measurements of the same molecules. Root mean square differences from experiment over the set of molecules examined using AMBER-, CHARMM-, and OPLS-AA-derived parameters were 1.35 kcal/mol, 1.31 kcal/mol, and 0.85 kcal/mol, respectively. Under the simulation conditions used, these force fields tend to uniformly underestimate solubility of all the side chain analogs. The relative free energies of hydration between amino acid side chain analogs were closer to experiment but still exhibited significant deviations. Although extensive computational resources may be needed for large numbers of molecules, sufficient computational resources to calculate precise free energy calculations for small molecules are accessible to most researchers.

Geometry of metal-ligand interactions in proteins.

The geometry of metal-ligand interactions in proteins is examined and compared with information for small-molecule complexes from the Cambridge Structural Database (CSD). The paper deals with the metals Ca, Mg, Mn, Fe, Cu, Zn and with metal-donor atom distances, coordination numbers and extent of distortion from ideal geometry (octahedral, tetrahedral etc.). It assesses the agreement between geometry found in all metalloprotein structures in the Protein Data Bank (PDB) determined at resolution < or = 1.6 A with that predicted from the CSD for ligands which are analogues of amino-acid side chains in proteins [Harding (1999), Acta Cryst. D55, 1432-1443; Harding (2000), Acta Cryst. D56, 857-867]. The agreement is reasonably good for these structures but poorer for many determined at lower resolution (examined to 2.8 A resolution). For metal-donor distances, the predictions from the CSD, with minor adjustments, provide good targets either for validation or for restraints in refinement of structures where only poorer resolution data is available. These target distances are tabulated and the use of restraints is recommended. Validation of angles or the use in refinement of restraints on angles at the metal atom is more difficult because of the inherent flexibility of these angles. A much simplified set of parameters for angle restraints with quite large standard deviations is provided. (Despite the flexibility of the angles, acceptable and preferred coordination numbers and shapes are well established and a summary table is provided.) An unusual and perhaps biochemically important feature of Zn coordination with carboxylate seen in the CSD examples is also clearly present in metalloprotein structures. With metals like Ca, carboxylate coordination is monodentate or bidentate (two M-O bonds of nearly equal length). In Zn carboxylates a continuous range between monodentate and bidentate coordination is found, with one Zn-O bond of normal length and another of any length between this and a van der Waals contact.

A General Treatment of Solvent Effects Based on Screened Coulomb Potentials

A new implicit solvent model for Monte Carlo simulations of peptides and proteins is presented. The important features of the model are: electrostatics of polar solvation described by nonlinear, distance-dependent screened Coulomb potentials that are formally connected to classical dielectric theory of polar solvation; the self-energy is derived from the integral form of the Born equation; and the introduction of the Born radius of an atom embedded in a protein modeled as a dielectric continuum. The model was parametrized in the context of the CHARMM PAR22 force field by fitting to experimental solvation free energies of amino acid side chain analogues. Introduction of an intrinsic vacuum screening constant for each amino acid was required to obtain the correct screening behavior in solution. Solvation energies of several peptides in different conformations were calculated and compared with the corresponding quantities calculated with the Poisson−Boltzmann equation. The comparative results were highly correlated in all cases, and the correlation was independent of peptide length and charge. Moreover, the self-energy terms and the electrostatic interaction energies, separately calculated from the two methods, were also highly correlated. The computing time required for the model is about 5 times the vacuum calculation for small systems (∼100 atoms), but decreases to a factor of 3 as the system size increases. The development of a new hydrogen-bonding algorithm as well as initial results of using the new model for sequence-to-structure calculations on peptides is presented in the accompanying paper. The combination results in a complete continuum solvation model.