Solvent dependence of dimensions of unfolded protein chains.

The radii of gyration of unfolded apo-cytochrome C at pH 2.3 have been determined in three conditions: (i) 20 mM sodium phosphate buffer; (ii) 0.25 M NaCl; and (iii) 6.65 M GuHCl by small-angle X-ray scattering, and (iii) from translational diffusion coefficients measured by dynamic light scattering. The radius of gyration of the unfolded protein chain depends remarkably on the quality of the solvent, decreasing in the order 20 mM sodium phosphate greater than 6.65 M GuHCl greater than 0.25 M NaCl. The value of the radius of gyration in 0.25 M NaCl and also the value estimated for infinite ionic strength are close to the value predicted theoretically for the theta-point. This means that water in the absence of electrostatic interactions is a poor solvent for an unfolded protein while 6.65 M GuHCl is a better solvent.     

Conformational statistics of pectin substances in solution by a Metropolis Monte Carlo study

Using a Metropolis Monte Carlo algorithm, various average properties of several pectic polysaccharide models were calculated based on the conformational energies for parent disaccharides. The relaxed potential energy surfaces of disaccharides were calculated using the CHARMm force field. Solvent effects were evaluated by calculating a solvation energy for each conformational state by estimating contributions from a cavity formation, and from the electrostatic and dispersion interactions between solvent and solute molecules. The behavior of the mean characteristic ratio, the squared radius of gyration, and the persistence length versus chain length is discussed for various structural models, temperature, and solvent. It is found that the unrefined model of the alternating co-polymer polygalacto-galacturonic acid in vacuum is consistent with the experimentally measured dimension of pectin in salt excess. This model is used to generate computer images of the characteristic conformation of pectin chain.     

Physicochemical investigation of k-carrageenan in the random state

Light-scattering, viscosity, and sedimentation experiments on aqueous solutions of k-carrageenan show that this sulfated polygalactose is an expanded flexible random coil. This expansion is due to long-range interactions that are predominantly electrostatic. Extrapolation of viscosity data to infinite ionic strength provided values for the intrinsic viscosity which were subjected to the Stockmayer-Fixman analysis, giving a value for the Mark-Houwink coefficient under theta-conditions, K_θ, of 0.27. The characteristic ratio, C_∞, under these conditions is 7.8, and the conformation factor σ is 2. In a solution of 0.118 ionic strength, where a Mark-Houwink exponent a_η of 0.86 is found, the radii of gyration calculated from viscosity data are lower than those found from the angular dependence of scattered light. On the other hand, the radius of gyration found from the sedimentation rate agrees well with the light-scattering radius. The relations between molecular parameters are corrected for the poly-dispersity of the sample.     

Comparison of hard-cylinder and screened coulomb interactions in the modeling of supercoiled DNAs

A 1000 base pair (bp) model supercoiled DNA is simulated using spherical screened Coulomb interactions between subunits on one hand and equivalent hard-cylinder interactions on the other. The amplitudes, or effective charges, of the spherical screened Coulomb electrostatic potentials are chosen so that the electrostatic potential surrounding the middle of a linear array of 2001 subunits (31.8 Å diameter) closely matches the solution of the nonlinear Poisson-Boltzmann equation for a cylinder with 12 Å radius and the full linear charge density of DNA at all distances beyond the 24 Å hard-core diameter. This superposition of spherical screened Coulomb potentials is practically identical to the particular solution of the cylindrical linearized Poisson-Boltzmann equation that matches the solution of the nonlinear Poisson-Boltzmann equation at large distances. The interaction energy between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter is chosen following Stigter's protocol for matching second virial coefficients, but for the full linear charge density of DNA. The electrostatic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cylinder model is adjusted to match that of the screened Coulomb model for each ionic condition. Simulations for a superhelix density σ = -0.05 using a spherical screened Coulomb interaction plus a 24 Å hard-cylinder core (SCPHC) potential indicate that the radius of gyration of this 1000 bp DNA actually undergoes a slight increase as the NaCl concentration is raised from 0.01 to 1.0M. Thus, merely softening the potential from hard-cylinder to screened Coulomb form does not produce a large decrease in radius of gyration with increasing NaCl concentration for DNAs of this size. Radii of gyration, static structure factors, and diffusion coefficients obtained using the equivalent hard-cylinder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These conclusions differ in significant respects from those obtained in previous studies. © 1997 John Wiley & Sons, Inc. Biopoly 42: 455–470, 1997     

Analysis of the effect of electrostatic energy truncation in molecular dynamics simulations of immunoglobulin G light chain dimer

Molecular dynamics (MD) simulations of immunoglobulin G (IgG) light chain dimer using particle mesh Ewald (PME) and cutoff methods of treating electrostatic interactions were performed. The results indicate that structural parameters (RMSD, radius of gyration, solvent accessible surface) are very similar for both schemes; however, PME simulation shows increased mobility of side chains. This leads to larger fluctuations in the distance between the monomers in the dimer molecule, and, as a consequence, results in decreased number of interactions across the dimer interface. The wall clock time of the simulations was also compared. It was shown that the PME method is approximately 30% faster than the cutoff method for the system studied on a single processor.Figure Backbone order parameters for PME (red) and cutoff (green) calculations. Thick, horizontal lines show stable secondary structures     

Electrostatic screening in molecular dynamics simulations.

The screened Coulombic potential has been shown to describe satisfactorily equilibrium properties like pK shifts, the effects of charged groups on redox potentials and binding constants of metal ions. To test how well the screening of the electrostatic potential describes the dynamical trajectory of a macromolecular system, a series of comparative simulations have been carried out on a protein system which explicitly included water molecules and a system in vacuo. For the system without solvent the results of using (i) the standard potential form were compared with results of (ii) the potential where the Coulomb term was modified by the inclusion of a distance dependent dielectric, epsilon (r), to model the screening effect of bulk water, and (iii) standard potential modified by reducing the charge on ionized residue side chains. All molecular dynamics simulations have been carried out on bovine pancreatic trypsin inhibitor. Comparisons between the resulting trajectories, averaged structures, hydrogen bonding patterns and properties such as solvent accessible surface area and radius of gyration are described. The results show that the dynamical behaviour of the protein calculated with a screened electrostatic term compares more favourably with the time-dependent structural changes of the full system with explicitly included water than the standard vacuum simulation.     

Molecular dynamics study of complexes of poly(glutamate) and dodecyltrimethylammonium

The supramolecular organization of self-assembled stoichiometric complexes formed by dodecyltrimethylammonium cations and ionized poly(gamma-glutamic) acid has been investigated in chloroform solution. Atomistic molecular dynamics simulations have been performed considering three different starting conformations for the polyelectrolyte chain, two sets of electrostatic parameters, and two methods for evaluating the electrostatic interactions. Results indicate that the polypeptide chain tends to adopt an alpha-like helix conformation similar to that obtained in aqueous solution for the un-ionized poly(gamma-glutamic) acid. On the other hand, both surfactant...amide and surfactant...carboxylate interactions were identified in the complex, this multiple pattern being previously observed in other surfactant...polypeptide complexes. Although the influence of the force-field in the results has been found to be negligible, the method used to evaluate the electrostatic interactions affects significantly the dynamics of the system. The more important differences between the results obtained using the spherical cutoff and Particle Mesh Ewald methods are discussed.     

Temperature and solvent dependence of the dynamical landscape of tau protein conformations

We report the variation with temperature of the ensemble distribution of conformations spanned by the tau protein in its dynamical states measured by small-angle X-ray scattering (SAXS) using synchrotron radiation. The SAXS data show a clear temperature variation of the distribution of occupied protein conformations from 293 to 318 K. More conformations with a smaller radius of gyration are occupied at higher temperature. The protein–solvent interactions are shown by computer simulation to be essential for controlling the dynamics of protein conformations, providing evidence for the key role of water solvent in the protein dynamics, as proposed by Giorgio Careri.     

Denaturant-induced Expansion and Compaction of a Multi-domain Protein: IgG

It is generally believed that unfolded or denatured proteins show random-coil statistics and hence their radius of gyration simply scales with solvent quality (or concentration of denaturant). Indeed, nearly all proteins studied thus far have been shown to undergo a gradual and continuous expansion with increasing concentration of denaturant. Here, we use fluorescence correlation spectroscopy (FCS) to show that while protein A, a multi-domain and predominantly helical protein, expands gradually and continuously with increasing concentration of guanidine hydrochloride (GdnHCl), the F(ab′)₂ fragment of goat anti-rabbit antibody IgG, a multi-subunit all β-sheet protein does not show such continuous expansion behavior. Instead, it first expands and then contracts with increasing concentration of GdnHCl. Even more striking is the fact that the hydrodynamic radius of the most expanded F(ab′)₂ ensemble, observed at 3-4 M GdnHCl, is ∼ 3.6 times that of the native protein. Further FCS measurements involving urea and NaCl show that the unusually expanded F(ab′)₂ conformations might be due to electrostatic repulsions. Taken together, these results suggest that specific interactions need to be considered while assessing the conformational and statistical properties of unfolded proteins, particularly under conditions of low solvent quality.     

Time-resolved small-angle X-ray scattering investigation of the folding dynamics of heme oxygenase: implication of the scaling relationship for the submillisecond intermediates of protein folding

Polypeptide collapse is generally observed as the initial folding dynamics of proteins with more than 100 residues, and is suggested to be caused by the coil-globule transition explained by Flory's theory of polymers. To support the suggestion by establishing a scaling behavior between radius of gyration (Rg) and chain length for the initial folding intermediates, the folding dynamics of heme oxygenase (HO) was characterized by time-resolved, small-angle X-ray scattering. HO is a highly helical protein without disulfide bridges, and is the largest protein (263 residues) characterized by the method. The folding process of HO was found to contain a transient oligomerization; however, the conformation within 10 ms was demonstrated to be monomeric and to possess Rg of 26.1(+/-1.1) A. Together with the corresponding data for proteins with different chain lengths, the seven Rg values demonstrated the scaling relationship to chain length with a scaling exponent of 0.35+/-0.11, which is close to the theoretical value of 1/3 predicted for globules in solutions where monomer-monomer interactions are favored over monomer-solvent interactions (poor solvent). The finding indicated that the initial folding dynamics of proteins bears the signature of the coil-globule transition, and offers a clue to explain the folding mechanisms of proteins with different chain lengths.     

Molecular dynamics simulation provides a possible structure for substance P-like peptides in aqueous solution.

A hypothetical conformation of the undecapeptide Substance P in aqueous solution is generated by molecular dynamics simulation for 284 ps. The conformation takes explicit solvent interactions into account as well as entropic effects to the extent that phase space is sampled in simulation. The initial conformation is taken from energy minimization studies and modified. In spite of fluctuations through 180 degrees in some backbone dihedral angles, the peptide settles with all backbone dihedrals within +/- 60 degrees from the initial values. In 130 ps, the radius of gyration decreases from 6.2 A to 5.5 A, whereas only fluctuation (+/- .2 A) is observed during the last 150 ps. The root-mean-square deviation at optimal superposition for a pair of conformations from the last 150 ps is 0.6 A, based on backbone atoms. The final structure is close-knit, nearly globular, and stabilized by several long-lived hydrogen bonds. The simulation conformation agrees with the scarce experimental data including a large number of structure-activity relationships. Thus, the simulation conformation is a likely candidate for one of the several conformations, the existence of which has been deduced from nuclear magnetic resonance data. Simulation results and experimental modification studies suggest that Phe 8 and Leu 10 are involved in the primary binding of SP to its receptors.     

Dodecylsulfate-induced dissociation of human alpha 2-macroglobulin. An investigation using small-angle neutron scattering and the equilibrium dialysis technique

The dodecylsulfate-induced dissociation of the tetrameric alpha 2-macroglobulin molecule from human plasma has been investigated by the small-angle neutron scattering (SANS) method. The great advantage with the SANS method is that, by using deuterated dodecylsulfate, and contrast variation by changing the D2O/H2O ratio of the solvent, we can selectively study just the protein part, or the dodecylsulfate part, of the protein-dodecylsulfate complex. More than a thousandfold excess of dodecylsulfate (on a molar basis) is needed in order to dissociate alpha 2-macroglobulin to particles with, on average, half the original molecular mass. By combining the SANS data with results obtained by the equilibrium dialysis technique it follows that, under these circumstances, approximately one thousand dodecylsulfate molecules are associated per alpha 2-macroglobulin molecule. From the significant increase in the radius of gyration, which accompanies the dissociation process, we can conclude that the dissociation is associated with a drastic change in conformation of the protein molecule. From measurements where the dodecylsulfate part of the complex dominates the SANS signal we also get an indication that the dodecylsulfate is randomly distributed along the polypeptide chain, rather than being arranged in large clusters at certain regions of the protein molecule. By fitting the parameters of a binding model to the experimental data we obtain the result that most of the more than one thousand bound dodecylsulfate molecules, necessary for dissociation, are involved in the change in conformation, and the dissociation process is, in fact, driven by the binding of a very few extra dodecylsulfate molecules to the dissociation products. These data indicate that the dodecylsulfate-induced dissociation of alpha 2-macroglobulin is probably more complicated than just breaking, for instance, a hydrophobic interaction.     

Comparison of Generalised Born/Surface Area with Periodic Boundary Simulations to Study Protein Unfolding

Simulations comparing the rapid unfolding behaviour of the model protein barnase under explicit and implicit solvent systems have been undertaken in order to validate a faster implicit solvent method for studying proteins which are kinetically stable in silico. A comparison is made between all-atom explicitly solvated simulations of barnase undertaken using Particle Mesh Ewald electrostatic interactions with all-atom implicit solvent simulations undertaken using the generalised born/surface area (GBSA) method with a long non-bonded cut-off. The two explicit solvent unfolding trajectories appear to explore slightly different pathways showing the importance of having statistically valid ensembles which are not accessible from a single trajectory. The 500?K GBSA trajectory is unsuitable for exploring intermediate structures on the unfolding pathway of barnase, as the protein almost immediately jumps to a predominately random coil conformation. However, dropping the temperature to 400?K gives rise to trajectories where the protein is unable to climb out of the energy well containing the first intermediate state, in a reasonable timescale. A similar pattern to the explicit solvent unfolding trajectories is seen in 450?K GBSA runs, with the intermediate states differing between trajectories. The development of computer simulation methods suitable for application to more kinetically stable proteins will offer insight into the atomic detail of the conformational changes associated with protein unfolding diseases.     

Small-angle x-ray scattering of κ-carrageenan based systems: Sols,gels, and blends with carob galactomannan

Small-angle x-ray scattering using a synchroton x-ray monochromatic radiation was carried out to investigate the structure of different polysaccharides in aqueous medium: carob galactomannan, κ-carrageenan in the sol and in the gel states, and κ-carrageenan-carob galactomannan mixed systems. Experiments performed on a 0.2% carob galactomannan solutions confirmed that this polysaccharide behaved as a neutral polymer in a good solvent. For K-carrageenan in the / state, either in the sodium form or in the cesium form, a maximum in the scattering curve was evidenced. Position and height of this maximum changed with K-carrageenan concentration in close agreement with what is expected for wormlike polyelectrolyte in semidilute solution. In the case of k-carrageenan in the gel state, in the cesium form, scattering curves also exhibited a maximum at an intermediate Q value. The position of this correlation peak did not change with concentration while its intensity increased. This effect was ascribed to a packing of rodlike structures by analogy with a suspension of colloidal elongated particles. This local structure could be viewed as bundles of parallel double helices. Addition of carobgalactomannan in κ-carrageenan gels induced dramatic structural changes. As the galactomannan concentration increased, the correlation peak tended to vanish. In contrast, no change in the cross-sectional radius of gyration was noticed. This phenomenon suggested a screening effect of the galactomannan, resulting in a loss of the correlation between the κ-carrageenan double helices. © 1995 John Wiley & Sons, Inc.     

Interaction between DNA and charged colloids could be hydrophobically driven

The interaction of DNA with amino-functionalized polystyrene particles has been studied by using a dynamic light scattering (DLS) technique. In 10 mM NaBr solution the particles have a hydrodynamic radius of 76 nm and the DNA macromolecule investigated (double stranded) has a hydrodynamic radius of 107 nm. At very low DNA concentrations, DNA adopts a flat conformation on the particle surface. If the DNA concentration is increased above 0.1 microg/mL, the thickness of the DNA layer increases, suggesting the presence of large loops and tails. Although the particles contain primary amino groups, they have a negative net charge under the conditions used in this work. Thus, the driving force for DNA adsorption is not of electrostatic origin but rather due to a hydrophobic effect. Addition of cationic surfactant to the DNA-precoated amino-functionalized particles induces changes in the adsorbed layer conformation, in agreement with the coadsorption of cationic surfactant.     

Hinging of rabbit myosin rod

The question of hinging in myosin rod from rabbit skeletal muscle has been reexamined. Elastic light scattering and optical rotation have been used to measure the radius of gyration and fraction helix, respectively, as a function of temperature for myosin rod, light meromyosin (LMM), and long subfragment 2 (long S-2). The radius of gyration vs temperature profile of myosin rod is shifted with respect to the optical rotation melting curve by about -5 degrees C. Similar studies on both LMM and long S-2 show virtually superimposable profiles. To correlate changes in the secondary structure with the overall conformation, plots of radius of gyration vs fraction helix are presented for each myosin subfragment. Myosin rod exhibits a marked decrease in the radius of gyration from 43 nm to approximately 35 nm, while the fraction helix remains at nearly 100%. LMM and long S-2 did not show this behavior. Rather, a decrease in the radius of gyration of these fragments occurred with comparable changes in fraction helix. These results are interpreted in terms of hinging of the myosin rod within the LMM/S-2 junction.     

Interparticle interactions and structural changes of nucleosome core particles in low-salt solution

The structural behavior of the nucleosome core particles in the range of solvent Na+ concentration from 10.45 to 0.45 mM has been studied by small-angle neutron and synchroton radiation X-ray scattering, sedimentation, atomic absorption spectroscopy, density measurements, and circular dichroism. With decreasing salt concentration, the appearance of a scattering peak that is assignable to interparticle interactions, an intraparticle structural transition, a decrease in the sedimentation velocity of the particle, and a release of bound Na+ ions from the particle are all observed concurrently when the ratio of solvent Na+ ions per particle is below approximately 1000. These observations are interpreted to indicate that a release of bound Na+ ions from the particle brings about structural rearrangements and weakens the electrostatic shielding of the particle, and this introduces long-range repulsive ordering of the particle in low-salt solution. Analyses of the scattering data indicate that the rearrangement within the core particle in low-salt solution is slight, changing the particle's shape slightly from cylindrical to a more spherical form by moving the center of the mass of the DNA somewhat inward with accompanying small decreases in the radii of gyration of both the DNA and the histones.     

The conformation of polyriboadenylic acid at low temperature and neutral pH. A single-stranded rodlike structure.

The conformation of single-stranded polyrA in aqueous solution has been measured at temperatures down to ?12°C. The radius of gyration of low-molecular-weight polyrA varies very little with temperature in this range. By studying the dependence of radius of gyration on temperature for several polyrA fractions, we show that the dependence of the radius upon chain length is consistent with formation of a single-stranded rodlike structure at low temperature. The structure has an approximate length of 3.2 Å/nucleotide.