Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.     

Molecular structures of fluid phase phosphatidylglycerol bilayers as determined by small angle neutron and X-ray scattering

We have determined the molecular structures of commonly used phosphatidylglycerols (PGs) in the commonly accepted biologically relevant fluid phase. This was done by simultaneously analyzing small angle neutron and X-ray scattering data, with the constraint of measured lipid volumes. We report the temperature dependence of bilayer parameters obtained using the one-dimensional scattering density profile model - which was derived from molecular dynamics simulations - including the area per lipid, the overall bilayer thickness, as well as other intrabilayer parameters (e.g., hydrocarbon thickness). Lipid areas are found to be larger than their phosphatidylcholine (PC) counterparts, a result likely due to repulsive electrostatic interactions taking place between the charged PG headgroups even in the presence of sodium counterions. In general, PG and PC bilayers show a similar response to changes in temperature and chain length, but differ in their response to chain unsaturation. For example, compared to PC bilayers, the inclusion of a first double bond in PG lipids results in a smaller incremental change to the area per lipid and bilayer thickness. However, the extrapolated lipid area of saturated PG lipids to infinite chain length is found to be similar to that of PCs, an indication of the glycerol-carbonyl backbone's pivotal role in influencing the lipid-water interface.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Distance-scaled,finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction

The distance-dependent structure-derived potentials developed so far all employed a reference state that can be characterized as a residue (atom)-averaged state. Here, we establish a new reference state called the distance-scaled, finite ideal-gas reference (DFIRE) state. The reference state is used to construct a residue-specific all-atom potential of mean force from a database of 1011 nonhomologous (less than 30% homology) protein structures with resolution less than 2 A. The new all-atom potential recognizes more native proteins from 32 multiple decoy sets, and raises an average Z-score by 1.4 units more than two previously developed, residue-specific, all-atom knowledge-based potentials. When only backbone and C(beta) atoms are used in scoring, the performance of the DFIRE-based potential, although is worse than that of the all-atom version, is comparable to those of the previously developed potentials on the all-atom level. In addition, the DFIRE-based all-atom potential provides the most accurate prediction of the stabilities of 895 mutants among three knowledge-based all-atom potentials. Comparison with several physical-based potentials is made.     

Lipid bilayer pressure profiles and mechanosensitive channel gating

The function of membrane proteins often depends on the proteins' interaction with their lipid environment, spectacularly so in the case of mechanosensitive channels, which are gated through tension mediated by the surrounding lipids. Lipid bilayer tension is distributed quite inhomogeneously, but neither the scale at which relevant variation takes place nor the effect of varying lipid composition or tension has yet been investigated in atomic detail. We calculated lateral pressure profile distributions in lipid bilayers of various composition from all-atom molecular dynamics simulations totaling 110.5 ns in length. Reproducible pressure profile features at the 1 A length scale were determined. Lipids with phosphatidylcholine headgroups were found to shift the lateral pressure out of the hydrophobic core and into the headgroup region by an amount that is independent of area per lipid. POPE bilayers simulated at areas smaller than optimal exerted dramatically higher lateral pressure in a narrow region at the start of the aliphatic chain. Stretching of POPC bilayers increased tension predominantly in the same region. A simple geometric analysis for the gating of the mechanosensitive channel MscL suggests that pressure profiles affect its gating through the second moment of the profile in a tension-independent manner.     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

Molecular conformation of bovine A1 basic protein, a coiling macromolecule in aqueous solution.

Aqueous solutions of bovine A1 protein, the major component of the basic protein fraction of myelin, were studied by small angle X-ray diffraction. The experimentally determined molecular weight, 17,800, is within 3% of that corresponding to the amino acid sequence, 18, 395, and the radius of gyration was found to be 46.3 A. No equivalent scattering particle of uniform electron density could be found which was compatible with all parameters evaluated from the diffraction measurements. The possibility of a coiled shape was therefore investigated using a worm-like chain model. This yielded a contour length of 439 A and a persistence length of 15.7 A. The radius of gyration of this model chain, 47.1 A, is in quite reasonable accord with the experimental value. The latter, after correction for excluded volume effects and finite chain length, yields for the characteristic ratio, ro2/nplp-2, 5.4. This may be compared with the value, 6.1, obtained after applying a correction for finite chain length to the viscosity data given by Tanford et al. for 12 proteins in 6 M guanidine hydrochloride and 0.1 M beta-mercaptoethanol. These two experimental values fall in the expected order, since the 15% glycine content of the A1 protein is considerably higher than the average for other proteins, which is about 8%. The corresponding values predicted from conformational calculations by Miller et al. for random copolymers of the L-alanine-glycine type are 5.9 (18% glycine) and 7.0 (8% glycine). We conclude that the A1 protein exists predominately, if not exclusively, as a random coil in aqueous solution.     

Complexes of RecA protein in solution. A study by small angle neutron scattering

RecA complexes on DNA and self-polymers were analysed by small-angle neutron scattering in solution. By Guinier analysis at small angles and by model analysis of a subsidiary peak at wider angles, we find that the filaments fall into two groups: the DNA complex in the presence of ATP gamma S, an open helix with pitch 95 A, a cross-sectional radius of gyration of 33 A and a mass per length of about six RecA units per turn, which corresponds to the state of active enzyme; and the compact form (bound to single-stranded DNA in the absence of ATP, or binding ATP gamma S in the absence of DNA, or just the protein on its own), a helical structure with pitch 70 A, cross-sectional radius of gyration 40 A and mass per length about five RecA units per turn, which corresponds to the conditions of inactive enzyme. The results are discussed in the perspective of unifying previous conflicting structural results obtained by electron microscopy.     

Evidence that the kinesin light chain domain contains tetratricopeptide repeat units

Homology models were built for various length sequences of the kinesin-1 light chain (KLC) domain of Drosophila melanogaster and subjected to 200 ns of all-atom molecular dynamics. We also cloned, expressed and characterized these regions spectroscopically. Results confirm that KLC contains tetratricopeptide repeat units; a regular array of repeating 34-residue helix-loop-helix monomers. Experimental and computational evidence is provided confirming the stability and overall helicity of individual TPR repeats as well as individual TPR units incorporated into a multi-TPR structure.     

Short-range order and collective dynamics of DMPC bilayers: a comparison between molecular dynamics simulations, X-ray, and neutron scattering experiments

We present an extensive comparison of short-range order and short wavelength dynamics of a hydrated phospholipid bilayer derived by molecular dynamics simulations, elastic x-ray, and inelastic neutron scattering experiments. The quantities that are compared between simulation and experiment include static and dynamic structure factors, reciprocal space mappings, and electron density profiles. We show that the simultaneous use of molecular dynamics and diffraction data can help to extract real space properties like the area per lipid and the lipid chain ordering from experimental data. In addition, we assert that the interchain distance can be computed to high accuracy from the interchain correlation peak of the structure factor. Moreover, it is found that the position of the interchain correlation peak is not affected by the area per lipid, while its correlation length decreases linearly with the area per lipid. This finding allows us to relate a property of the structure factor quantitatively to the area per lipid. Finally, the short wavelength dynamics obtained from the simulations and from inelastic neutron scattering are analyzed and compared. The conventional interpretation in terms of the three-effective-eigenmode model is found to be only partly suitable to describe the complex fluid dynamics of lipid chains.     

FOUR-STRANDED DNA AS DETERMINED BY ELECTRON MICROSCOPY

Pneumococcus DNA, of weight-average molecular weight 1.6 million by light scattering, had a weight-average length of 4300 A by electron microscopy. Thus, the average mass per unit length was 370 molecular-weight units per A, or approximately two times that expected (208) for a Watson-Crick double helix. This corresponds to an average of 3.6 strands per molecule, which is close to that obtained by other methods. Morphologically, all the particles in the micrographs were relatively stiff, and had a cross-sectional height of 20 to 30 A. Some divided into two stiff branches of the same height, apparently double helical. Where the branches combined into one (minimally four-stranded) structure they apparently lay side by side in close association.     

Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature

The structural parameters of fluid phase bilayers composed of phosphatidylcholines with fully saturated, mixed, and branched fatty acid chains, at several temperatures, have been determined by simultaneously analyzing small-angle neutron and X-ray scattering data. Bilayer parameters, such as area per lipid and overall bilayer thickness have been obtained in conjunction with intrabilayer structural parameters (e.g. hydrocarbon region thickness). The results have allowed us to assess the effect of temperature and hydrocarbon chain composition on bilayer structure. For example, we found that for all lipids there is, not surprisingly, an increase in fatty acid chain trans-gauche isomerization with increasing temperature. Moreover, this increase in trans-gauche isomerization scales with fatty acid chain length in mixed chain lipids. However, in the case of lipids with saturated fatty acid chains, trans-gauche isomerization is increasingly tempered by attractive chain-chain van der Waals interactions with increasing chain length. Finally, our results confirm a strong dependence of lipid chain dynamics as a function of double bond position along fatty acid chains.     

Hydrodynamic modes of arbitrarily shaped flexible macromolecules: Influence on dynamic light scattering

The diffusional motions of flexible macromolecules are analyzed with an increasingly realistic Rouse–Zimm model, i.e., by modeling the molecule as an arbitrary set of spheres connected by nearly harmonic springs. New features include (1) nearly arbitrary arrangements of spheres, (2) arbitrary arrangements of translational and torsional springs, (3) significant anharmonic corrections to the elastic potential surface, and (4) inclusion of torsional damping and various hydrodynamic cross-coupling effects (including two types of translational-rotational coupling) with no additional fitted parameters. The hydrodynamic interactions [R. F. Goldstein (1985) Journal of Chemical Physics, Vol. 83, pp. 2390–2397] contain no adjustable parameters other than temperature, viscosity, and the radii and positions of the spheres. These hydrodynamic interactions allow accurate calculations of rigid body diffusion as well as flexible motions. Given the positions, radii, and spring constant matrix, one can calculate a full set of three-dimensional diffusional modes. Because one uses an off-diagonal hydrodynamic resistance matrix instead of a diagonal mass matrix, the diffusional modes are different in structure from vacuum normal modes, and give rise to different rms motions in the laboratory frame. These hydrodynamic modes include the effects of vibrational-translational cross-coupling (i.e., motion along a vibrational coordinate may give rise to a translational force, and vice versa). The diffusional modes are used to simulate dynamic light scattering (DLS). I examine various molecules with different shapes, flexibilities, and with different scattering vectors. Radial and angular motions influence DLS decays differently. These effects are dependent upon the molecular shape (straight, bent, or curved) and type of flexibility (stretching or bending). Furthermore, small cubic corrections to the potential surface can be significant for DLS of certain geometries such as straight rods and semicircles. © 1993 John Wiley & Sons, Inc.     

How PEGylation enhances the stability and potency of insulin: a molecular dynamics simulation

While the effectiveness of PEGylation in enhancing the stability and potency of protein pharmaceuticals has been validated for years, the underlying mechanism remains poorly understood, particularly at the molecular level. A molecular dynamics simulation was developed using an annealing procedure that allowed an all-atom level examination of the interaction between PEG polymers of different chain lengths and a conjugated protein represented by insulin. It was shown that PEG became entangled around the protein surface through hydrophobic interaction and concurrently formed hydrogen bonds with the surrounding water molecules. In addition to enhancing its structural stability, as indicated by the root-mean-square difference (rmsd) and secondary structure analyses, conjugation increased the size of the protein drug while decreasing the solvent accessible surface area of the protein. All these thus led to prolonged circulation life despite kidney filtration, proteolysis, and immunogenic side effects, as experimentally demonstrated elsewhere. Moreover, the simulation results indicated that an optimal chain length exists that would maximize drug potency underpinned by the parameters mentioned above. The simulation provided molecular insight into the interaction between PEG and the conjugated protein at the all-atom level and offered a tool that would allow for the design of PEGylated protein pharmaceuticals for given applications.     

Solution conformations of pectin polysaccharides: Determination of chain characteristics by small angle neutron scattering,viscometry, and molecular modeling

The solution behavior of pectin polysaccharides has been investigated by small angle neutron scattering (SANS), viscosimetric, and molecular modeling studies. The samples used in the experimental study were obtained from apple and citrus and had degrees of methylation ranging from 28 to 73%, with a rhamnose content lying between 0.6 and 2.2%. Persistence lengths, derived from intrinsic viscosity measurements, ranged from 59 to 126 Å, whereas those derived by SANS were between 45 and 75 Å. These values correspond to 10–17 monomer units. The modeling simulations were performed for both homogalacturonan itself and homogalacturonan carrying various degrees of rhamnose inserts (rhamnogalacturonan). This required the evaluation of the accessible conformational space for the eight disaccharides that represent the constituent repeating segments of the homogalacturonan and rhamnogalacturonan polysaccharides. For each dimer, complete conformational analysis was accomplished using the flexible residue method of the MM3 molecular mechanics procedure and the results used to access the configurational statistics of representative pectic polysaccharide chains. For homogalacturonan, an extended chain conformation having a persistence length of 135 Å (corresponding to 30 monomers) was predicted. The inclusion of varying amounts of rhamnose units (5–25%) in the model in strict alternating sequence with galacturonate residues (equivalent to the rhamnogalacturonan “hairy region” chains) only slightly reduced the calculated persistence length. The extended overall chain conformation remained relatively unchanged as a consequence of the self-cancellation of the kinking effects of successive paired rhamnose units. © 1996 John Wiley & Sons, Inc.     

Conformational equilibria of valine studied by dynamics simulation.

The conformational probability distribution of a valine residue in the valine dipeptide and of the valine side chain in an alpha-helix, as well as the change in helix stability for replacing alanine with valine, has been calculated by molecular dynamics simulations of explicitly hydrated systems: dipeptide, tetrapeptide and 10-, 14- and 18-residue oligoalanine helices. All computed free-energy differences are means from at least eight separate slow-growth simulations, four in each direction and are reported with their root-mean-square deviations. Different values for the change in free energy of folding (delta delta G degrees) have been calculated with the use of forcefields having an all-atom and a central-atom representation of methyl groups, etc. The value obtained with the all-atom forcefield agrees well with new experimental values (3 kJ/mol = 0.7 kcal/mol). Furthermore, the most stable valine side-chain rotamer in the helix is different for these two representations. The most stable rotamer for the all atom conformation is the same one that predominates for valines in alpha-helices in proteins of known conformation. The lower conformational freedom of the valine side chain in the helix contributes 1 kJ/mol to the difference in stability computed with the all-atom potential; unfavorable interactions of the side chain with helix, even in the most stable conformation, further increase delta delta G degrees.