Potential of mean force calculations on an L-type calcium channel model

To understand the mechanisms of Na(+)/Li(+) permeation at submicromolar Ca(2+) concentrations, Na(+)/Li(+) blocking at higher Ca(2+) concentrations (10(-6)-10(-4) M) and Ca(2+) permeation at millimolar Ca(2+) concentrations, we used our recently described L-type calcium channel model. For this purpose, we obtained potential of mean force (pmf) curves for the position change of one Na(+) and one Ca(2+) ion inside the channel and for the position change of a second Ca(2+) ion when the EEEE locus is coordinated to Ca(2+). The pmf curves suggest that (i) at submicromolar Ca(2+) concentrations, because of the low velocity of Ca(2+) entry in the channel, monovalent ion flux occurs; (ii) at Ca(2+) concentrations between 10(-6) and 10(-4) M, thermodynamic equilibrium between the channel and Ca(2+) is achieved; as the coordination of Ca(2+) with the locus is more favorable than the coordination of Na(+), the monovalent ion flux is blocked; and (iii) to put a second Ca(2+) ion inside the channel at an appropriate rate, the Ca(2+) concentration should reach millimolar levels. Nevertheless, the entry of a second Ca(2+) is thermodynamically unfavorable, indicating that the competition of two Ca(2+) ions for the locus leads to Ca(2+) permeation.     

Potential of mean force for protein-protein interaction studies.

Calculating protein-protein interaction energies is crucial for understanding protein-protein associations. On the basis of the methodology of mean-field potential, we have developed an empirical approach to estimate binding free energy for protein-protein interactions. This knowledge-based approach has been used to derive distance-dependent free energies of protein complexes from a nonredundant training set in the Protein Data Bank (PDB), with a careful treatment of homology. We calculate atom pair potentials for 16 pair interactions, which can reflect the importance of hydrophobic interactions and specific hydrogen-bonding interactions. The derived potentials for hydrogen-bonding interactions show a valley of favorable interactions at a distance of approximately 3 A, corresponding to that of an established hydrogen bond. For the test set of 28 protein complexes, the calculated energies have a correlation coefficient of 0.75 compared with experimental binding free energies. The performance of the method in ranking the binding energies of different protein-protein complexes shows that the energy estimation can be applied to value binding free energies for protein-protein associations.     

Potential of mean force treatment of salt-mediated protein crystallization

In the initial stages of crystallization of proteins, monomers aggregate rapidly and form nuclei and large fractal clusters, as previously shown by dynamic light scattering experiments (Georgalis, Y., J. Schüler, J. Frank, D. M. Soumpasis, and W. Saenger. 1995. Protein crystallization screening through scattering techniques. Adv. Colloid Interface Sci. 58:57-86). In this communication we initiate an effort to understand the effective interactions controlling charged protein aggregation and crystallization using the potential of mean force (PMF) theory. We compute the PMFs of the system lysozyme-water-NaCl within the framework of the hypernetted chain approximation for a wide range of protein and salt concentrations. We show that the computed effective interactions can rationalize the experimentally observed aggregation behavior of lysozyme under crystallization conditions.     

Potential of mean force for separation of the repeating units in cellulose and hemicellulose

As a first step toward understanding the energetics of removal of cello-oligomers from the cellulose surface, we have performed umbrella sampling calculations to determine the free energy required for separation of repeating units of cellulose and hemicellulose from each other. Molecular dynamics (MD) simulations were performed for both the stacked and non-stacked arrangements of the cellobiose pair system and the xylobiose pair system. These stacked and non-stacked arrangements were taken as representative systems for the crystalline and amorphous domains in cellulose and hemicellulose. In addition, similar calculations were also carried out to determine the energetics involved in the separation of the cellobiose–xylobiose molecule pair in the non-stacked arrangement. The potential of mean force profiles exhibit a single minimum in all cases and are qualitatively similar. Our results show that the location of the minimum as well as the depth of the well can be correlated with the size of the disaccharide molecules.     

Accurate determination of the binding free energy for KcsA-charybdotoxin complex from the potential of mean force calculations with restraints

Free energy calculations for protein-ligand dissociation have been tested and validated for small ligands (50 atoms or less), but there has been a paucity of studies for larger, peptide-size ligands due to computational limitations. Previously we have studied the energetics of dissociation in a potassium channel-charybdotoxin complex by using umbrella sampling molecular-dynamics simulations, and established the need for carefully chosen coordinates and restraints to maintain the physiological ligand conformation. Here we address the ligand integrity problem further by constructing additional potential of mean forces for dissociation of charybdotoxin using restraints. We show that the large discrepancies in binding free energy arising from simulation artifacts can be avoided by using appropriate restraints on the ligand, which enables determination of the binding free energy within the chemical accuracy. We make several suggestions for optimal choices of harmonic potential parameters and restraints to be used in binding studies of large ligands.     

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.     

Sensitivity of temporomandibular joint force calculations to errors in muscle force measurements

A two-dimensional, five-muscle model was used to determine the degree of precision required for accurate calculation of temporomandibular joint force magnitude and direction. The sensitivity of the calculations to each variable were assessed by incrementing each variable through its presumed biological range and were expressed as rate of change in the joint force per unit change in each variable. Sensitivity of the calculations to variables depends upon both bite force direction and bite position. The bite force direction with maximum precision for joint force magnitude produced minimal precision for joint force direction. The accuracy needed for each muscle force varied greatly. The effect of error for each muscle parameter depended upon the magnitude, direction, and moment arm length of the muscle force relative to those of the resultant muscle force. If each of the five muscle forces was known to the nearest 1% of total muscle force magnitude, 1 degree of muscle force direction, and 1 mm of moment arm length, temporomandibular joint force magnitude could be calculated to the nearest 4 kg and joint force direction to the nearest 7 degrees. It is not known whether this precision for the muscle forces is possible.     

A computational study of barium blockades in the KcsA potassium channel based on multi-ion potential of mean force calculations and free energy perturbation

Electrophysiological studies have established that the permeation of Ba²⁺ ions through the KcsA K⁺-channel is impeded by the presence of K⁺ ions in the external solution, while no effect is observed for external Na⁺ ions. This Ba²⁺ “lock-in” effect suggests that at least one of the external binding sites of the KcsA channel is thermodynamically selective for K⁺. We used molecular dynamics simulations to interpret these lock-in experiments in the context of the crystallographic structure of KcsA. Assuming that the Ba²⁺ is bound in site S₂ in the dominant blocked state, we examine the conditions that could impede its translocation and cause the observed “lock-in” effect. Although the binding of a K⁺ ion to site S₁ when site S₂ is occupied by Ba²⁺ is prohibitively high in energy (>10 kcal/mol), binding to site S₀ appears to be more plausible (ΔG > 4 kcal/mol). The 2D potential of mean force (PMF) for the simultaneous translocation of Ba²⁺ from site S₂ to site S₁ and of a K⁺ ion on the extracellular side shows a barrier that is consistent with the concept of external lock-in. The barrier opposing the movement of Ba²⁺ is very high when a cation is in site S₀, and considerably smaller when the site is unoccupied. Furthermore, free energy perturbation calculations show that site S₀ is selective for K⁺ by 1.8 kcal/mol when S₂ is occupied by Ba²⁺. However, the same site S₀ is nonselective when site S₂ is occupied by K⁺, which shows that the presence of Ba²⁺ affects the selectivity of the pore. A theoretical framework within classical rate theory is presented to incorporate the concentration dependence of the external ions on the lock-in effect.     

The process of displacing the single-stranded DNA-binding protein from single-stranded DNA by RecO and RecR proteins

The regions of single-stranded (ss) DNA that result from DNA damage are immediately coated by the ssDNA-binding protein (SSB). RecF pathway proteins facilitate the displacement of SSB from ssDNA, allowing the RecA protein to form protein filaments on the ssDNA region, which facilitates the process of recombinational DNA repair. In this study, we examined the mechanism of SSB displacement from ssDNA using purified Thermus thermophilus RecF pathway proteins. To date, RecO and RecR are thought to act as the RecOR complex. However, our results indicate that RecO and RecR have distinct functions. We found that RecR binds both RecF and RecO, and that RecO binds RecR, SSB and ssDNA. The electron microscopic studies indicated that SSB is displaced from ssDNA by RecO. In addition, pull-down assays indicated that the displaced SSB still remains indirectly attached to ssDNA through its interaction with RecO in the RecO-ssDNA complex. In the presence of both SSB and RecO, the ssDNA-dependent ATPase activity of RecA was inhibited, but was restored by the addition of RecR. Interestingly, the interaction of RecR with RecO affected the ssDNA-binding properties of RecO. These results suggest a model of SSB displacement from the ssDNA by RecF pathway proteins.     

Novel knowledge-based mean force potential at the profile level

Background  

The development and testing of functions for the modeling of protein energetics is an important part of current research aimed at understanding protein structure and function. Knowledge-based mean force potentials are derived from statistical analyses of interacting groups in experimentally determined protein structures. Current knowledge-based mean force potentials are developed at the atom or amino acid level. The evolutionary information contained in the profiles is not investigated. Based on these observations, a class of novel knowledge-based mean force potentials at the profile level has been presented, which uses the evolutionary information of profiles for developing more powerful statistical potentials.     

Potential of mean force of the hepatitis C virus core protein–monoclonal 19D9D6 antibody interaction

Antigen–antibody interactions are critical for understanding antigen–antibody associations in immunology. To shed further light on this question, we studied a dissociation of the 19D9D6-HCV core protein antibody complex structure. However, forced separations in single molecule experiments are difficult, and therefore molecular simulation techniques were applied in our study. The stretching, that is, the distance between the center of mass of the HCV core protein and the 19D9D6 antibody, has been studied using the potential of mean force calculations based on molecular dynamics and the explicit water model. Our simulations indicate that the 7 residues Gly70, Gly72, Gly134, Gly158, Glu219, Gln221 and Tyr314, the interaction region (antibody), and the 14 interprotein molecular hydrogen bonds might play important roles in the antigen–antibody interaction, and this finding may be useful for protein engineering of this antigen–antibody structure. In addition, the 3 residues Gly134, Gly158 and Tyr314 might be more important in the development of bioactive antibody analogs.     

New tubular single-stranded helix of poly-L-amino acids suggested by molecular mechanics calculations: I. Homopolypeptides in isolated environments.

A search was made in terms of molecular mechanics calculation for tubular, or pore-forming, single-stranded helices of poly-L-amino acids. Such a helix was found in the vicinity of (phi, psi, omega) = 81 degrees, 98 degrees, 170 degrees) in the conformational space. It was the 6.2(20) helix of right-handedness. The 6.2(20) helix, here named the "mu helix," had a cylindrical pore along its helical axis. The diameter of the pore was 6.6 A on the basis of the atom centers of carbonyl carbons and amino nitrogens. The left-handed mu helix was less stable than the right-handed counterpart. The conformation energy of the mu helix, expressed relative to that of the alpha helix of the same polypeptide, depended to a great extent on amino acid composition. It varied over a range of a few kilocalories per mol per residue above and below the conformation energy of the alpha helix of the same polypeptide. This marked diversity in the relative conformation energy of the mu helix can be ascribed primarily to the difference in the relative position of alpha-carbons between the mu and the alpha helices. The conformational entropy made only a small contribution, if any, to the relative stability of the mu helix. There was a hydrogen-bonded network of side chains in the mu helices of poly-L-glutamine and poly-L-asparagine.     

Atomic force microscopy of long and short double-stranded, single-stranded and triple-stranded nucleic acids.

Atomic force microscopy (AFM, also called scanning force microscopy) is proving to be a useful technique for imaging DNA. Thus it is important to push the limits of AFM imaging in order to explore both what types of DNA can be reliably imaged and identified and also what substrates and methods of sample preparation are suitable. The following advances in AFM of DNA are presented here. (i) DNA molecules as short as 25 bases can be seen by AFM. The short single-stranded DNAs imaged here (25 and 50 bases long) appeared globular in the AFM, perhaps because they are all capable of intramolecular base pairing and because the DNAs were in a Mg(ll) buffer, which facilitates intramolecular cross-bridging. (ii) AFM images in air of short double-stranded DNA molecules, 100-200 bp, gave lengths consistent with A-DNA. (iii) AFM images of poly (A) show both short bent lumpy molecules with an apparent persistence length of 40 nm and long straight molecules with an apparent persistence length of 600 nm. For comparison, the apparent persistence length for double-stranded DNA from phX-174 under the same conditions was 80 nm. (iv) Structures believed to be triple- stranded DNA were seen in samples of poly(dA.poly(dT) and poly (dG).poly(dC). These structures were twice as high as double-stranded DNA and the same width. (v) Entire molecules of lambda DNA, approx. 16 micron long, were imaged clearly in overlapping scans. (vi) Plasmid DNA was imaged on oxidized silicon, although less clearly than on mica.     

Structure calculations for single-stranded DNA complexed with the single-stranded DNA binding protein GP32 of bacteriophage T4: a remarkable DNA structure

In this study it is established by calculation which regular conformations single-stranded DNA and RNA can adopt in the complex with the single-stranded DNA binding protein GP32 of bacteriophage T4. In order to do so, information from previous experiments about base orientations and the length and diameter of the complexes is used together with knowledge about bond lengths and valence angles between chemical bonds. It turns out that there is only a limited set of similar conformations which are in agreement with experimental data. The arrangement of neighboring bases is such that there is ample space for aromatic residues of the protein to partly intercalate between the bases, which is in agreement with a previously proposed model for the binding domain of the protein [Prigodich, R. V., Shamoo, Y., Williams, K. R., Chase, J. W., Konigsberg, W. H., & Coleman, J. E. (1986) Biochemistry 25, 3666-3671]. Both C2'endo and C3'endo sugar conformations lead to calculated DNA conformations that are consistent with experimental data. The orientation of the O2' atoms of the sugars in RNA can explain why the binding affinity of GP32 for polyribonucleotides is lower than for polydeoxyribonucleotides.     

Simplified force field calculations of the low-frequency motions of the alpha-helix

Using valence force field constants and a highly simplified model of the α-helix consisting of only two masses per repeat unit we have been able to very nearly reproduce the low frequency phonon dispersion curves which we had obtained earlier with the use of a seven mass model and a Urey-Bradley force field. Since the frequencies obtained from this latter model agree well with the observed Raman frequencies it appears that the low frequency chain motions of polypeptide chains may be calculated from a very simple model involving the amino acid residues as essentially a single mass. Such techniques appear to offer the possibility of making normal mode calculations for the chain dynamics of polypeptide chains of low symmetry such as proteins.     

Adsorption isotherms for dilute solutions via the mean force method

The adsorption of solutes from a dilute liquid solution is of great technical importance but calculations of the local density of the solute and of the adsorption isotherm by standard molecular simulation yield large scattering with increasing dilution. As alternative the mean force (MF) method was suggested where the MF on a constrained solute molecule is integrated over a path from the bulk fluid to the wall. It has already been shown that the MF method gives reliable results for the relative local density, even at high dilution. Here, an extension of this method is introduced, where the absolute value of the bulk density is determined by particle balance. Thus, it is possible to calculate adsorption isotherms from the Henry regime to any finite concentration. Molecular dynamics simulations for the local density and the adsorption isotherm were performed for a model solution consisting of tetrahedral Lennard–Jones (LJ) solvent and linear LJ solute molecules in contact with a plane wall. It is found that the MF-results show less scattering than the results from standard simulations. Moreover, results for the orientation and the selectivity are given.     

Nucleotides. VI. Syntheses and spectral properties of some deazaadenylyl-deazaadenosines (dinucleoside monophosphates with unusual CD-spectrum) and closely related dinucleoside monophosphates.

Nine dinucleoside phosphates containing 1-deaza-(1A) and 3-deazaadenosine (3A) were prepared. Hypochromicity and CD spectra of these dimers were determined. It was found that varying degrees of base-stacking are operative with these oligonucleotides and their CD spectra fall into three classes. The first class CD spectra which are more or less similar in profile to those of adenylyl-(3'-5')-adenosine includes the CD spectra of 1A2'p5'A, 1A3'p5A, 3A2'p5'A and 3A3'p5'A. The second class includes the CD spectra of A2'p5'1A and A3'p5'1A whose characteristic is that the positive Cotton band appears in the range of 280-310 nm. The third type CD spectra has the characteristics that the negative Cotton band appears in the longer wavelength region and th CD spectra are similar in profile to those of L-adenylyl-(3'-5')-L-adenosine which has the "left-handed helical" conformation. The CD spectra of A2'p5'3A, A3'p5'3A and 3A3'p5'A belong to this class. Another salient observation emerging from the CD-determination is that 3A3'p5'3A has the spectrum quite different from that of poly 3-deazaadenylic acid.