Multistep Brownian dynamics: application to short wormlike chains

Brownian dynamics simulations of short wormlike chains are carried out using the method of Ermak and McCammon [(1978) J. Chem. Phys. 69 , 1352–1360]. Following Hagerman and Zimm [(1981) Biopolymers 20 , 1481–1502], the wormlike chain is modeled as a string of beads. In each simulation, the dynamic evolution of an ensemble of 100 randomly generated chains is calculated for a period of from 3 to 200 ns. Two different “experiments,” fluorescence depolarization and dynamic light scattering, were performed in these simulations. Since we are primarily interested in the bending motions and not the torsional motions in this work, we have placed the transition moments along the local symmetry axis of the wormlike chain in the fluorescence depolarization “experiment.” As predicted by the Barkley and Zimm theory [(1979) J. Chem. Phys. 70 , 2991–3008], a considerable amount of rapid bending motion was detected by fluorescence depolarization, though not as much as predicted by theory. We conclude that these differences are primarily due to differences between the model used in the theory and the simulations. The light-scattering experiment was found to be insensitive to internal motion in the low scattering angle limit.     

Conformations of alanine-based peptides in water probed by FTIR, Raman, vibrational circular dichroism, electronic circular dichroism, and NMR spectroscopy

We have used a combination of FTIR, VCD, ECD, Raman, and NMR spectroscopies to probe the solution conformations sampled by H-(AAKA)-OH by utilizing an excitonic coupling model and constraints imposed by the 3JCalphaHNH coupling constants of the central residues to simulate the amide I' profile of the IR, isotropic Raman, anisotropic Raman, and VCD spectra in terms of a mixture of three conformations, i.e., polyproline II, beta-strand and right-handed helical. The representative coordinates of the three conformations were obtained from published coil libraries. Alanine was found to exhibit PPII fractions of 0.60 or greater, mixed with smaller fractions of helices and beta-strand conformations. Lysine showed no clear conformational propensity in that it samples polyproline II, beta-strand, and helical conformations with comparable probability. This is at variance with results obtained earlier for ionized polylysine, which suggest a high polyproline II propensity. We reanalyzed previously investigated tetra- and trialanine by combining published vibrational spectroscopy data with 3JCalphaHNH coupling constants and obtained again blends dominated by PPII with smaller admixtures of beta-strand and right-handed helical conformations. The polyproline II propensity of alanine was found to be higher in tetraalanine than in trialanine. For all peptides investigated, our results rule out a substantial population of turn-like conformations. Our results are in excellent agreement with MD simulations on short alanine peptides by Gnanakaran and Garcia [(2003) J. Phys. Chem. B 107, 12555-12557] but at variance with multiple MD simulations particularly for the alanine dipeptide.     

On the statistical thermodynamics of membrane formation

Modifying a procedure developed by Scheutjens and Fleer (J. Phys. Chem. 83 (1979) 1619: J. Phys. Chem. 84 (1980) 178) to describe adsorption of polymers, a lattice theory is proposed to formulate the formation and properties of amphiphilic bilayer membranes. In this theory individual conformations are distinguished and lateral interactions are taken into account in a Flory-Huggins approximation. Probability distributions of head tail and solvent segments are computed and it is shown that they are not narrow, i.e., membrane properties are subject to considerable fluctuations. The average concentration of the water in the hydrophobic core is nonzero. Various extensions, consequences and applications are proposed.     

Comparison of Poisson-Boltzmann and condensation model expression for the colligative properties of cylindrical polyions

Closed-form expression have been derived for the polyelectrolyte contribution to the colligative properties of solutions containing rodlike polyions in the presence of excess added salt. The derivations are based on: the conventional Poisson-Boltzmann equation for cylindrical symmetry; the thermodynamics of the cell model developed by Marcus [J. Chem. Phys. 23 , 1057–1068 (1955)]; and an equation derived from the cylindrical Poisson-Boltzmann cell model by Anderson and Record [Biophys. Chem. 11 , 353–360 (1980)]. Subject to the inherent limitations of the Poisson-Boltzmann approximation [Fixman (1979) J. Chem. Phys. 70 , 4995–5005], the resulting expressions are nevertheless applicable outside the “limit of infinite dilution.” They conform over a range of salt concentrations to the limiting laws deduced by Manning from the hypothesis of counterion condensation [J. Chem. Phys. 51 , 924–933 (1969)]. This hypothesis is found to be compatible with the Poisson-Boltzmann cell model but is not required in the derivation of the thermodynamic coefficients presented here. It is demonstrated that the magnitude of the polyion axial charge density plays a critical role in determining the low-salt limiting forms of the colligative properties obtained from the Poisson-Boltzmann equation, in close analogy with Manning's model.     

Reassessment of the random coil conformation: vibrational CD study of proline oligopeptides and related polypeptides.

The "random coil" conformational problem is examined by comparison of vibrational CD (VCD) spectra of various polypeptide model systems with that of proline oligomers [(Pro)n] and poly(L-proline). VCD, ir and uv CD spectra of blocked L-proline oligopeptides [(Pro)n, n = 2-12] in different solvents are reported and compared to the spectra of poly(L-proline) II, poly(L-glutamic acid), and unblocked proline oligomers. Based on the chain-length dependence of the VCD and electronic CD (ECD) spectra of proline oligomers, it is established that VCD spectra are dominated by short-range interactions. The VCD of random coil model polypeptides is shown to be identical in shape but smaller in magnitude than poly(L-proline) II and of similar magnitude to that of (Pro)n (n = 3, 4). Based on the spectral evidence, it is concluded that the "random coil" conformation has a large fraction of helical regions, conformationally similar to the left-handed, 3(1) polyproline II helix, as was previously suggested by Krimm and co-workers. This conclusion is further supported by studies of effects of salt (CaCl2, LiBr, LiClO4), temperature (5-75 degrees C), and pH on the VCD spectra of L-proline oligomers, poly(L-proline) II, and poly(L-glutamic acid). These show that, after each of these perturbations, a significant local ordering remains in the oligomers and polymers studied, and that charged polypeptides such as poly(L-glutamic acid) are more flexible than are polyproline or even L-proline oligomers.     

Absorption and magnetic circular dichroism of chlorophyll a and b dimers

The dimerization of chlorophyll a to the so-called special pair, in which the two monomers are linked together by two nucleophilic molecules (alcohol or water), leads to shifts and splittings of the absorption and magnetic circular dichroism (MCD) spectral bands. The changes in the Q-band region are described starting from a model proposed previously (L.L. Shipman. J.R. Morris and J.J. Katz. J. Phys. Chem. 80 (1976) 877). and which we extended to include the MCD. The parameters alpha(x) and alpha(y), containing the exciton and environmental parameters (L.L. Shipman. J.R. Norris and J.J. Katz, J. Phys. Chem. 80 (1976) 877) and the relative orientation of the monomers in the dimer, determine the spectral features. Spectral simulation leads to the conclusion that in the special pair alpha(x) and alpha(y), are in the region of 0.6-0.8 and that the dimer has C2 symmetry. The model was also applied to the case of the pure dimer of chlorophyll b where the monomers are bound together directly. With similar values for alpha(x) and alpha(y) the spectra could be reconstructed assuming almost parallel monomers in the dimer, the equilibrium constant for the association 2M <==> M2 was determined as 0.8(+/-0.2) x 10(6) mol(-1)/I. The present choice of compounds was based merely on practical reasons. The model may be applied equally well to other similar cases.     

Studies on the size and shape of rabbit intestinal glucoamylase-maltase complex.

Rabbit intestinal glucoamylase-maltase was examined in detail with respect to its molecular weight, sedimentation, diffusion and viscosity. It is a large asymmetrical molecule, with a molecular weight of 750 000-760 000. Its appearance under the electron microscope supports the idea that it is a long string (62.0 nm) consisting of eight beads of diameter 6.0 nm each and a surface-to-surface interbead distance of approx. 2.0 nm. The shape of the enzyme derived from its hydrodynamic behaviour by using the string-of-spherical-beads model originally proposed by Kuhn [(1932) Z. Phys. Chem. Abt. A 161, 1-32] and later modified by Shulman [(1953) J. Am. Chem. Soc. 75, 5846-5852] fits moderately well with the electron-microscopic picture. The beads might represent about six subunits, and the absence of sulphur from the enzyme and the inability to dissociate the enzyme by conventional methods indicate the possibility of unusual covalent cross-linking between the subunits and between the beads.     

An efficient conformational sampling method for homology modeling

The structural refinement of protein models is a challenging problem in protein structure prediction (Moult et al., Proteins 2003;53(Suppl 6):334-339). Most attempts to refine comparative models lead to degradation rather than improvement in model quality, so most current comparative modeling procedures omit the refinement step. However, it has been shown that even in the absence of alignment errors and using optimal templates, methods based on a single template have intrinsic limitations, and that refinement is needed to improve model accuracy. It is thought that failure of current methods originates on one hand from the inaccuracy of the effective free energy functions adopted, which do not represent properly the energetic balance in the native state, and on the other hand from the difficulty to sample the high dimensional and rugged free energy landscape of protein folding, in the search for the global minimum. Here, we address this second issue. We define the evolutionary and vibrational armonics subspace (EVA), a reduced sampling subspace that consists of a combination of evolutionarily favored directions, defined by the principal components of the structural variation within a homologous family, plus topologically favored directions, derived from the low frequency normal modes of the vibrational dynamics, up to 50 dimensions. This subspace is accurate enough so that the cores of most proteins can be represented within 1 A accuracy, and reduced enough so that Replica Exchange Monte Carlo (Hukushima and Nemoto, J Phys Soc Jpn 1996;65:1604-1608; Hukushima et al., Int J Mod Phys C: Phys Comput 1996;7:337-344; Mitsutake et al., J Chem Phys 2003;118:6664-6675; Mitsutake et al., J Chem Phys 2003;118:6676-6688) (REMC) can be applied. REMC is one of the best sampling methods currently available, but its applicability is restricted to spaces of small dimensionality. We show that the combination of the EVA subspace and REMC can essentially solve the optimization problem for backbone atoms in the reduced sampling subspace, even for rather rugged free energy landscapes. Applications and limitations of this methodology are finally discussed.     

Reading the three-dimensional structure of lattice model-designed proteins from their amino acid sequence.

While all the information required for the folding of a protein is contained in its amino acid sequence, one has not yet learned how to extract this information to predict the detailed, biological active, three-dimensional structure of a protein whose sequence is known. Using insight obtained from lattice model simulations of the folding of small proteins (fewer than 100 residues), in particular of the fact that this phenomenon is essentially controlled by conserved contacts (Mirny et al., Proc Natl Acad Sci USA 1995;92:1282) among (few) strongly interacting ("hot") amino acids (Tiana et al., J Chem Phys 1998;108:757-761), which also stabilize local elementary structures formed early in the folding process and leading to the (postcritical) folding core when they assemble together (Broglia et al., Proc Natl Acad Sci USA 1998;95:12930, Broglia & Tiana, J Chem Phys 2001;114:7267), we have worked out a successful strategy for reading the three-dimensional structure of lattice model-designed proteins from the knowledge of only their amino acid sequence and of the contact energies among the amino acids.     

Vector correlations in the F + HO → HF + O reaction and its isotopic variant

The F + H(D)O → HF(DF) + O reactions have been studied using quasi-classical trajectory (QCT) calculation method, based on the three different potential energy surfaces (PESs) of Gomez-Carrasco et al. (J Chem Phys 2004, 121:4605; J Chem Phys 2005, 123:114310; Chem Phys Lett 2007, 435:188). Facilitated with the analysis of the QCT results, the pictures for product scattering and product polarizations have been presented to investigate the vector correlations in the two reactions, with effects of isotope substitution and electronic state as well as collision energy being revealed at a chemical stereodynamical level.     

Comparison of alpha-lactalbumin and lysozyme using vibrational circular dichroism. Evidence for a difference in crystal and solution structures

The conformation of the milk protein alpha-lactalbumin has been studied using vibrational circular dichroism (VCD) and compared to parallel studies on lysozyme. These proteins have been shown by Acharya et al. [(1989) J. Mol. Biol. 208, 99-127] to have very similar three-dimensional crystal structures. However, their VCD spectra in D2O solution are quite different. The VCD of lysozyme in D2O more resembles that of alpha-lactalbumin in 33% propanol/D2O, under which conditions alpha-lactalbumin has conformationally transformed to a structure with increased helical fraction. These results can be seen to be consistent with UVCD and resolution-enhanced FTIR spectra of alpha-lactalbumin and lysozyme in both D2O and H2O environments. The solvent sensitivity of the alpha-lactalbumin spectra and hence of its conformation contrasted with the lack of such sensitivity for lysozyme suggest that the alpha-lactalbumin crystal structure represents a conformation different from that which is dominant in aqueous solution.     

Enhanced sensitivity to conformation in various proteins. Vibrational circular dichroism results

Vibrational circular dichroism (VCD) spectra of several globular proteins dissolved in D2O are presented and compared to conventional UV-CD results. It can be seen that, for the alpha, beta, and alpha + beta categories of Levitt and Chothia [(1976) Nature 261, 552], VCD evidences much larger band shape variations, including sign alteration, than does UV-CD. A direct parallel is seen between the VCD of the alpha-helix found in model polypeptides and the amide I' VCD of myoglobin. Since all structural aspects of the protein contribute to the VCD on a roughly equal footing, a similar correlation of the chymotrypsin amide I' VCD with that of beta-sheet models is not as clear. In addition, the VCD of "random-coil"-type proteins is found to be clearly related to VCD results from "random-coil" polypeptides. Finally, simulations are presented to postulate the expected VCD for protein structures having conformations that lie between the limiting cases discussed here.     

Conformational study of sequential Lys and Leu based polymers and oligomers using vibrational and electronic CD spectra

Vibrational CD (VCD) and electronic CD (ECD) spectra of some sequential Lys and Leu based oligo- and polypeptides were studied as a function of added salt and (for ECD) as a function of concentration in aqueous solution. For these samples, the VCD spectra can only be measured at relatively high concentrations under which the well-known salt-induced transition to a β-sheet form can be observed for the KL based species, but only the end-state α-helical conformation is obvious for the LKKL based samples. ECD concentration dependence demonstrates that, at high concentration with no added or with added salt, LKKL based oligomers and polymers give α-helical spectra. These data provide evidence of aggregation induced secondary structure formation in an exceptionally simple peptide system. Similarly, the KL based oligomers and polymers give β-sheet like spectra at high concentration or at high salt. These systems further provide model systems under “normal” aqueous conditions that yield VCD band shapes that correlate to the major secondary structural types of polypeptides. They are in substantial agreement with those spectra obtained on homopolypeptides and on proteins, confirming the relative independence of the VCD technique from side-chain and solvent effects. © 1994 John Wiley & Sons, Inc.     

Theoretical determination of conformational paths in citrate synthase.

Two methods are developed for the theoretical determination of a conformational path between two well-documented forms, a closed form and the open form [Remington et al. (1982) J. Mol. Biol. 158, 111-152] of pig heart citrate synthase, a dimeric enzyme of 2 x 437 residues. The first method uses the minimization of the sum of the potential energies at a set of equidistant points, according to Elber and Karplus [(1987) Chem. Phys. Lett. 139, 375-380]. The initialization of the algorithm is modified to account for large-angle rotations of many groups by performing the interpolations in the space of internal polar coordinates of a set of generalized Jacobi vectors earlier introduced by Durup [(1991) J. Phys. Chem. 95, 1817-1829] and by carefully testing all choices of directions of rotation for determining the initialized midpoint between the known forms. The path includes intermediate points, created by successive splittings of each interval into two equal parts, with a partial energy minimization performed after each splitting. The minimization encounters the well-known local-minima problem, which here is handled by low-temperature molecular dynamics annealing. It is shown that the best ratio of potential energy decrease to rms deviation is achieved by running the dynamics at 50 K, as compared to 100 K and above. The main character of the path obtained is the occurrence of strong to-and-fro variations of some dihedral angles at specific stages along the path. The second method, which we name directed dynamics, uses only low-temperature molecular dynamics simulations by starting trajectories from each of the two known forms with initial velocities directed toward the other one. The procedure is iterated by restarting trajectory pairs after the points of closest approach of the preceding pair. The two half-paths thus built eventually meet after 70 iterations. This method provides a second path with strong similarities, as well as some differences, with respect to the path obtained by the first method.     

Optimized intermolecular potential for nitriles based on Anisotropic United Atoms model

An extension of the anisotropic united atoms intermolecular potential model is proposed for nitriles. The electrostatic part of the intermolecular potential is calculated using atomic charges obtained by a simple Mulliken population analysis. The repulsion-dispersion interaction parameters for methyl and methylene groups are taken from transferable AUA4 literature parameters [Ungerer et al., J. Chem. Phys., 2000, 112, 5499]. Non-bonding Lennard-Jones intermolecular potential parameters are regressed for the carbon and nitrogen atoms of the nitrile group (–C≡N) from experimental vapor-liquid equilibrium data of acetonitrile. Gibbs Ensemble Monte Carlo simulations and experimental data agreement is very good for acetonitrile, and better than previous molecular potential proposed by Hloucha et al. [J. Chem. Phys., 2000, 113, 5401]. The transferability of the resulting potential is then successfully tested, without any further readjustment, to predict vapor-liquid phase equilibrium of propionitrile and n-butyronitrile. Figure Saturated vapour pressure of nitriles calculated in this work by molecular simulation compared to experimental data: a) for acetonitrile and b) for both propionitrile and butyronitrile     

Effect of a molecular dipole on the ionic strength dependence of a biomolecular rate constant. Identification of the site of reaction.

A theory is proposed for determining the location of a reaction site on a protein of known tertiary structure with an asymmetric charge distribution by an analysis of the effect of ionic strength on the rate of reaction of the protein with a small ion, using equations of Brønsted (J. N. Brønsted, 1922, Z. Phys, Chem. 102:169-207), Debye and Hückel (P. Debye and E. Hückel, 1923, Phys. Z. 24:185-206), and Kirkwood (J. G. Kirkwood, 1934, J. Chem. Phys. 2:351-361). The theory is based on the fact that the dipole moment of the transition complex differs from that of the protein, which will be reflected in the ionic strength dependence of the reaction. The location of the small ion with respect to the dipole axis of the protein can be calculated from this difference. For protein-protein reactions, an a priori assumption has to be made about the orientation of one of the reaction partners, since many different orientations of the reactants with respect to each other result in dipole moments of the same magnitude.     

Examination of the limiting laws of polyelectrolytes and counterion condensation II

The two phase model of polyelectrolyte solutions, which has been developed recently, is examined in a further detail. The binding free energy, which was introduced in the previous paper (J. Chem. Phys. 81 (1977) 1929), is replaced by the entropy of the condensed phase. This replacement leads to a detailed picture of the condensed phase. In a mixed system of mono- and divalent counterions, a couple of possibilities are examined in interpreting the condensation volume, which corresponds to the condensation entropy.     

Diffusion-controlled protein–DNA association: Influence of segemental diffusion of the DNA

The intrachain reaction theory of Wilemki and Fixman [(1974) J. Chem. Phys. 60 , 866–877] is used to assess the influence of internal DNA motions on various protein–DNA association schemes. It is found that, for large proteins, the diffusional association rate can be totally dominated by these motions rather than by the free-trans-lational diffusion rates. Also, the time required for the diffusion together of two DNA segments is estimated. This estimate can be used to provide an upper limit for the rate of intrachain cyclization, and also for the effective intrachain transfer rate of a protein bound to a DNA chain.     

Further quasi-classical trajectory studies on the C++ H2O reaction

Further trajectory studies on the C⁺ + H₂O reaction have been performed using a potential energy surface described through a finite element method in its p version. In former trajectory studies [Y. Ishikawa, T. Ikegami and R.C. Binning Jr., Direct ab initio molecular dynamics study of C⁺+H₂O: angular distribution of products and distribution of product kinetic energies, Chem. Phys. Lett. 370 (2003), pp. 490–495; J.R. Flores, Quasichemical trajectories on a finite element density functional potential energy surface: the C⁺+H₂O reaction revisited, J. Chem. Phys. 125 (2006), 164309], tunnelling was not taken into account. The present results together with the analysis of the electronic excited states [J.R. Flores and A.B. González, The role of the excited electronic states in the C⁺+H₂O reaction, J. Chem. Phys. 128 (2008), 144310] are useful to interpret the mechanism of the title reaction, which has been the subject of crossed beam experiments [D.M. Sonnenfroh, R.A. Curtiss and J.M. Farrar, Collision complex formation in the reaction of C⁺ with H₂O, J. Chem. Phys. 83 (1985), pp. 3958–3964] and can be considered a prototypical ion–molecule reaction.     

Vibrational circular dichroism of A-, B-, and Z-form nucleic acids in the PO2-stretching region.

Vibrational circular dichroism (VCD) spectra were measured for H2O solutions of several natural and model DNAs (single and double strands, oligomers and polymers) in the B-form, poly(dG-dC)-poly(dG-dC) in the Z-form, and various duplex RNAs in an A-form over the PO2-stretching region. Only the symmetric PO2 stretch at approximately 1075 cm-1 yields a significant intensity VCD signal. Differences of the PO2-stretching VCD spectra found for these conformational types are consistent with the spectral changes seen in the base region, but no sequence dependence was seen in contrast to VCD for base modes. The B to Z transition is accompanied by an inversion of the PO2- VCD spectra, which is characteristic of the change in the helical sense of the nucleic acid backbone. A-RNAs give rise to the same sense of couplet VCD as do B-DNAs but have a somewhat different shape because of overlapping ribose modes. These PO2- VCD spectral characteristics have been successfully modeled using simple dipole coupling calculations. The invariability of the symmetric PO2- stretching mode VCD spectra to the base sequence as opposed to that found for the C = O stretching and base deformation modes is evidence that this mode will provide a stable indication of the DNA helical sense.