Algorithmic generation of freely jointed hard sphere chains and properties of their inertial tensors

A statistical algorithm, capable of generating a large number of freely jointed hard sphere chains, is presented. This is the first of a series of algorithms being developed to model unfolded proteins by different modes of hard sphere chains. The aim of these studies is to systematically investigate the effects of different factors, such as atomic radii, bond angles, torsion angles, chain length, etc., on the conformation of unfolded proteins and other random polymers. As continuous models, various types of hard sphere chains enable one to isolate the aforementioned factors one at a time for investigation and thus are advantageous over discrete lattice models. In particular, the freely jointed hard sphere chain model allows one to evaluate the excluded volume effect. As a first step in this endeavor, the average determinant D(N, r) and the average trace T(N, r) of the inertial tensor A of the random chains were calculated at various sphere radii r and chain lengths N. It is found that both the average determinant D(N, r) and the average trace T(N, r) scale linearly with chain length N after logarithmic transformation. However, the critical exponent of D(N, r) increases with r faster than that of T(N, r) as a result of the non-commutativity between the det operator and the average operator < >. The significance of the algorithm and the results obtained on understanding random polypeptide chains are discussed.     

A comparison of model linear chain molecules with constrained and flexible bond lengths under planar Couette and extensional flows

We compare directly under flow two commonly used coarse grained models of linear polymers, namely the flexible finitely extensible nonlinear elastic (FENE) chain, and the freely jointed tangent sphere chain, otherwise known as the freely jointed chain. The comparison is based on viscometric, structural and dynamical properties. We use non-equilibrium molecular dynamics to simulate steady-state systems under planar Couette flow and planar extensional flow. Computed properties include shear and elongational viscosities, normal stresses, radius of gyration and end-to-end distances, order parameters, alignment angles and spin angular velocities. In all computed properties we observe very little difference between the two molecular models. Therefore, the choice of either model is suitable, though there is a computational advantage in the use of the FENE model.     

Loop energy in DNA

The loop function ?(N), representing the statistical weight of N complementary residues in a closed ring, has been determined by analysis of high-resolution melting curves of a series of recombinant homopoly(A · T)_N inserts in pBR322 DNA, where 150 > N > 50 base pairs (bp). Loops are found more stable and therefore presumably less elastic than expected for an ideal, freely jointed chain. A value of 97 ± 2 bp is obtained for the empirical orientation-stiffness parameter D in the expression for nonideal chains, ?(N) = (N + D)^?1.7. The 10% increase in apparent stiffness over that of an ideal chain closely coincides with the extent of residual stacking in the loop. It is thus concluded that the more favorable loop energy, such as expected of smaller loops, is due to the incipient helical orientation of some residues, predisposing the loop to reclosure. A quantitative loop function is essential for the prediction and assignment of domains in DNA.     

Repeat unit polysaccharides of bacteria: a model for polymerization resembling that of ribosomes and fatty acid synthetase, with a novel mechanism for determining chain length

We report the identification and sequence from Escherichia coli and Salmonella enterica strains of the cld gene, encoding the chain-length determinant (CLD) which confers a modal distribution of chain length on the O-antigen component of lipopolysaccharide (LPS). The distribution of chain lengths in the absence of this gene fits a model in which as the chain is extended there is a constant probability of 0.165 of transfer of growing chain to LPS core, with termination of chain extension. The data for E. coli 0111 fit a model in which the CLD reduces this probability for short chains and increases it to 0.4 for longer chains, leading to a reduced number of short chain molecules but an increase in numbers of longer molecules and transfer of essentially all molecules by chain length 21. We put forward a model for O-antigen polymerase which resembles the ribosome and fatty acid synthetase in having two sites, with the growing chain being transferred from a D site onto the new unit at the R site to extend the chain and then back to the D site to repeat the process. It is proposed that the CLD protein and polymerase form a complex which has two states:‘E’facilitating extension and T facilitating transfer to core. The complex is postulated to enter the E state as O-antigen polymerization starts, and to shift to the T state after a predetermined time, the CLD acting as a molecular clock. The CLD is not O-antigen or species-specific but the modal value does depend on the source of the cld gene.     

Electrophoretic charge density and persistence length of DNA as measured by fluorescence microscopy

Individual ethidium-stained DNA molecules, embedded in an agarose gel made with electrophoresis buffer (0.05 molar salt), are observed using a fluorescence microscope. In the first experiment, open circular 66 kilobase pair (kbp) plasmids, immobilized by agarose fibers threaded through their centers, display entropic "rubber" elasticity. The charged molecules extend in an electric field of several volts per centimeter and contract to a compact random coil when the field is removed. The extension of the plasmids as a function of field strength is consistent with the freely jointed chain model when the effective electrophoretic charge density is set at 15 e-per persistence length. In a second experiment, stained linear 48.5 kbp DNA molecules are observed as random coils immobilized in agarose. A measure of their size, here named the "maximal-X-extent," is taken for 100 molecules and found to average 1.47 mu. A Monte Carlo computer simulation of random coils (freely jointed chain model) gives the same maximal-X-extent value when the persistence length is set at 0.08 mu.     

Influence of local and residual structures on the scaling behavior and dimensions of unfolded proteins

Although recent spectroscopic studies of chemically denatured proteins hint at significant nonrandom residual structure, the results of extensive small angle X-ray scattering studies suggest random coil behavior, calling for a coherent understanding of these seemingly contradicting observations. Here, we report the results of a Monte Carlo study of the effects of two types of local structures, alpha helix and Polyproline II (PPII) helix, on the dimensions of random coil polyalanine chains viewed as a model of highly denatured proteins. We find that although Flory's power law scaling, long regarded as a signature of random coil behavior, holds for chains containing up to 90% alpha or PPII helix, the absolute magnitude of the chain dimensions is sensitive to helix content. As residual alpha helix content increases, the chain contracts until it reaches a minimum radius at approximately 70% helix, after which the chain dimensions expand rapidly. With an alpha helix content of approximately 20%, corresponding to the Ramachandran probability of being in the helical basin, experimentally observed radii of gyration are recovered. Experimental radii are similarly recovered at an alpha helix content of approximately 87%, providing an explanation for the previously puzzling experimental finding that the dimensions of the highly helical methanol-induced unfolded state are experimentally indistinguishable from those of the helix-poor urea-unfolded state. In contrast, the radius of gyration increases monotonically with increasing PPII content, and is always more expanded than the dimensions observed experimentally. These results suggest that PPII is unlikely the sole, dominant preferred conformation for unfolded proteins.     

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, whereas exterior single-stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasiequilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasiequilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. (2001).     

NMR experiments for resonance assignments of 13C, 15N doubly-labeled flexible polypeptides: Application to the human prion protein hPrP(23–230)

A combination of three heteronuclear three-dimensional NMR experiments tailored for sequential resonance assignments in uniformly ¹⁵N, ¹³C-labeled flexible polypeptide chains is described. The 3D (H)N(CO-TOCSY)NH, 3D (H)CA(CO-TOCSY)NH and 3D (H)CBCA(CO-TOCSY)NH schemes make use of the favorable ¹⁵N chemical shift dispersion in unfolded polypeptides, exploit the slow transverse ¹⁵N relaxation rates of unfolded polypeptides in high resolution constant-time [¹H, ¹⁵N]-correlation experiments, and use carbonyl carbon homonuclear isotropic mixing to transfer magnetization sequentially along the amino acid sequence. Practical applications are demonstrated with the 100-residue flexible tail of the recombinant human prion protein, making use of spectral resolution up to 0.6 Hz in the ¹⁵N dimension, simultaneous correlation with the two adjacent amino acid residues to overcome problems associated with spectral overlap, and the potential of the presently described experiments to establish nearest-neighbor correlations across proline residues in the amino acid sequence.     

Kinetics of Contact Formation and End-to-End Distance Distributions of Swollen Disordered Peptides

Unstructured polypeptide chains are subject to various degrees of swelling or compaction depending on the combination of solvent condition and amino acid sequence. Highly denatured proteins generally behave like random-coils with excluded volume repulsion, whereas in aqueous buffer more compact conformations have been observed for the low-populated unfolded state of globular proteins as well as for naturally disordered sequences. To quantitatively account for the different mechanisms inducing the swelling of polypeptides, we have examined three 14-residues peptides in aqueous buffer and in denaturant solutions, including the well characterized AGQ repeat as a reference and two variants, in which we have successively introduced charged side chains and removed the glycines. Quenching of the triplet state of tryptophan by close contact with cysteine has been used in conjunction with Förster resonance energy transfer to study the equilibrium and kinetic properties of the peptide chains. The experiments enable accessing end-to-end root mean-square distance, probability of end-to-end contact formation and intrachain diffusion coefficient. The data can be coherently interpreted on the basis of a simple chain model with backbone angles obtained from a library of coil segments of proteins and hard sphere repulsion at each C_α position. In buffered water, we find that introducing charges in a glycine-rich sequence induces a mild chain swelling and a significant speed-up of the intrachain dynamics, whereas the removal of the glycines results in almost a two-fold increase of the chain volume and a drastic slowing down. In denaturants we observe a pronounced swelling of all the chains, with significant differences between the effect of urea and guanidinium chloride.     

Dilute solution properties of proteoglycan fractions from bovine nasal cartilage

Fresh proteogycans (adult bovine nasal cartilage) isolated from the densest portion of a dissociative density gradient had a weight-average molecular weight of ca. 10⁶ in 4M guanidine hydrochloride (GdnHCI) by light scattering. Fractions of such material obtained by elution with 4M GdnHCI from 2% agarose gel, both normal and cross-linkd, has proteoglycan subunit molecular weights ranging from 0.8 to 2.6 × 10⁶ and root-mean-square radii ranging from 35 to 52 nm in the same solvent. The protein molecular weight per proteoglycan subunit was about 1.2 × 10⁵ and that of keratan sulfate about 1.8 × 10⁵, both independent of total molecular weight. A random-flight “graft copolymer” model having uniform side chains of chondroitin sulfate (40 disaccharides) and keratan sulfate (15 disaccharides) and a random-coil polypeptide back bone was used to estimate the unperturbed radius, whihc was about 19 nm for a mol wt of 1.5 × 10⁶. Experimental light-scattering data for fractions were fitted very well by theoretical curves for the particale scattering factor for both linear and appropriate branched polymers. Examination of coil expansion on the basis of perturbation calculations for branched polymer models suggested that expansion did not account for the experimentally observed radii in terms of unperturbed radii calculated from the model. A possible explanation is that substantial local stiffening of the polypeptide chain due to substitution of side-chain clusters increases the unperturbed radii. The intrinsic viscosity [η] is 4M GdnHCI ranged from 120 to 180 ml/g, and could be interpreted in terms of th eequivalent sphere model; the Flory number has approximately its normal value for flexible linear polymers. The treatment of the sedimentation coefficient by this is less successful, since the Man delkern-Flory parameter β apparently increases with increasing molecular weight; average value are similar to those for flexible polymers, but the variation in β makes this method useful only for rough estimation of molecular weight of proteoglycans. Molecular weights of purified proteoglycans are the same in 0.2M NaCI as in 4M GdnHCI, while crude preparations gave higher molecular weights in 0.2M NaCI, probably because of association due to incomplete removel of “linking” proteins.     

A Novel Fungal Endo-β-N-acetylglucosaminidase that Specifically Acts on Plant Glycoproteins

An endo-β-N-acetylglucosaminidase specific for plant glycoprotein oligosaccharides was purified from the culture fluid of a fungus. The Mr of the purified enzyme was 89,000. This enzyme was stable at pH 5.5-7.0, up to 30°C, and showed the highest activity at pH 6.0. Among sugar chains tested, xylose-containing sugar chains (M3X, M3FX, and M2FX) were the most favored substrates. Oligomannose type (M3, M5, and M9) and hybrid type (GNM3) sugar chains were hydrolyzed much more slowly than xylose-containing sugar chains, and a complex type sugar chain (GN2M3) was not hydrolyzed at all by the enzyme. Moreover, the enzyme released sugar chains from native horseradish peroxidase and stem bromelain, which were not hydrolyzed by other endo-β-N-acetylglucosaminidases (Endo H, D, and F). The enzyme could transfer the xylose-containing sugar chain from bromelain to DNS-Asn-GlcNAc-Fuc.     

Comprehensive determination of <Superscript>3</Superscript>J<Subscript>HNHα</Subscript> for unfolded proteins using <Superscript>13</Superscript>C′-resolved spin-echo difference spectroscopy

An experiment is presented to determine ³J_HNHα coupling constants, with significant advantages for applications to unfolded proteins. The determination of coupling constants for the peptide chain using 1D ¹H, or 2D and 3D ¹H-¹⁵N correlation spectroscopy is often hampered by extensive resonance overlap when dealing with flexible, disordered proteins. In the experiment detailed here, the overlap problem is largely circumvented by recording ¹H-¹³C′ correlation spectra, which demonstrate superior resolution for unfolded proteins. J-coupling constants are extracted from the peak intensities in a pair of 2D spin-echo difference experiments, affording rapid acquisition of the coupling data. In an application to the cytoplasmic domain of human neuroligin-3 (hNlg3cyt) data were obtained for 78 residues, compared to 54 coupling constants obtained from a 3D HNHA experiment. The coupling constants suggest that hNlg3cyt is intrinsically disordered, with little propensity for structure.     

Monte Carlo generation of polypeptide random coil conformations; the persistence vector and the chain vector distribution

Polypeptide random coil conformations of various chain lenghts (N = 5, 10, 20, 40, 80 peptide units) are generated by a Monte Carlo procedure. The characteristic ratio obtained for the sets of generated conformations is identical with the exact value calculated with the average transformation matrix procedure, indicating the equivalence of the two treatments. On the basic of the generated sets of conformations the length and direction of the persistence vector (the averaged chain vector expressed in the reference frame of the first two skeletal bonds) are investigated for various chain lengths. The radial distribution function for the chain vector shows the length of the chain vector for small polypeptides (N = 5, 10) not to deviate far from its most probable value. Also for larger chains up to chains of 80 peptide units very significant deviations from a gaussian distribution are observed.The distribution of the length of the vector connecting the remote end of the chain with the end of the persistence vector exhibited behavior much doser to the gaussian approximation, an improvement especially significant for the short chains.     

A Monte Carlo study of the excluded-volume effect on the amylosic chain conformation

A Monte Carlo procedure was used to determine the effect of excluded volume on the conformational dimensions of amylosic chains. The excluded volume was introduced into the model by assuming that hard spheres, which cannot overlap each other, exist at the center of mass of each glucose unit in the chain sequence. Monte Carlo chains, which were generated to be distributed consistent with the potential energy of nonbonded nearest-neighbor interactions, underwent self-intersections, and the attrition rate in the generation of self-avoiding chains was found to obey an exponential decay law with increasing chain length x. Thus, in order to generate effectively a large number of self-avoiding chains with long sequences, we used the Wall–Erpenbeck s-p method of chain enrichment [F. T. Wall and J. J. Erpenbeck (1959) J. Chem. Phys. 30 , 634–637]. By examination of the radial distribution of the end-to-end distance and the chain-length dependence of the quantity 〈r²〉/xl² (〈r²〉 is the mean square end-to-end distance and l is the virtual bond length), it was found that unperturbed amylosic chains change in overall conformation from a non-Gaussian chain having a helical character to Gaussian as x is increased, whereas perturbed chains do not show Gaussian behavior even at x = 500. For the perturbed chains, 〈r²〉 can be expressed by the equation 〈r²〉 = ax^b in the range of 100 ≤ x ≤ 500, where a and b > 1 are constants. From comparisons of the persistence vectors and perspective drawings of representative unperturbed and perturbed chains, we felt the local conformation of the amylosic chains, i.e., the local helical character, is also affected by the long-range excluded-volume interaction.     

Glass transition temperature of hard chairside reline materials after post‐polymerisation treatments

doi:10.1111/j.1741‐2358.2009.00312.x
Glass transition temperature of hard chairside reline materials after post‐polymerisation treatments Objective: This study evaluated the effect of post‐polymerisation treatments on the glass transition temperature (T_g) of five hard chairside reline materials (Duraliner II‐D, Kooliner‐K, New Truliner‐N, Ufi Gel hard‐U and Tokuso Rebase Fast‐T). Materials and methods: Specimens (10 × 10 × 1 mm) were made following the manufacturers’ instructions and divided into three groups (n = 5). Control group specimens were left untreated. Specimens from the microwave group were irradiated with pre‐determined power/time combinations, and specimens from the water‐bath group were immersed in hot water at 55°C for 10 min. Glass transition (°C) was performed by differential scanning calorimetry. Data were analysed using anova, followed by post hoc Tukey’s test (α = 0.05). Results: Both post‐polymerisation treatments promoted a significant (p < 0.05) increase in the T_g of reline material K. Materials K, D and N showed the lowest T_g (p < 0.05). No significant difference between T and U specimens was observed. Conclusion: Post‐polymerisation treatments improved the glass transition of material Kooliner, with the effect being more pronounced for microwave irradiation.     

Polymorphisms within the HLA-DRw6 haplotype

We have analyzed the HLA class II gene products from HLA-DRw6 homozygous cells. Epstein-Barr virus-transformed B-cell lines were internally labeled with [³⁵S]-methionine. An NP-40 lysate of the cells was subjected to immunoprecipitation, first with a DRw52-like-specific monoclonal antibody and subsequently with a DR-specific framework antibody. The DR region-encoded gene products were analyzed by one-dimensional gel isoelectric focusing and two-dimensional gel electrophoresis. It is shown that DRw6 homozygous cell lines contain at least two nonallelic DR chains, one carrying a DRw52 determinant and one DRw52-negative population. Both chains appear to be polymorphic between the cellularly defined subtypes of DRw6. The determinant responsible for the differential mixed lymphocyte culture reactivity of Dw18 and Dw19 cells resides on the DRw52-positive population, whereas the Dw6-Dw9 differences are attributed to determinants on both populations of DR light chains. The Dw16-derived DRw52⁺ chain much resembles the Dw18 DRw52⁺ light chain whereas there is a clear-cut difference between these two subtypes in the DRw52^– population. We conclude that, for DRw6 homozygous cells, the cellularly recognized D determinants are probably located on DR-encoded molecules, both DRw52⁺ and DRw52^–, and that charge shift of these chains is at least partly responsible for differential recognition of these cells in mixed lymphocyte cultures.Abbreviations used in this paper: MLC mixed lymphocyte culture - 1D-IEF one-dimensional isoelectric focusing - 2D two-dimensional - moab monoclonal antibody     

Excluded volume of hard cylinders of variable aspect ratio

In this article, we report expressions for the excluded volume, v _ex and second virial coefficient, B ₂, of hard cylinders as a function of their aspect ratio (𝒜 = L/D), where L and D are the length and diameter of the cylinder, respectively. These expressions are valid for aspect ratio values within the interval 0.001 < 𝒜 < 100, that covers from thin plates to long rods and reproduce Monte Carlo (MC) simulation values. We compare these results with Onsager's predictions and with reported values of hard bodies of similar geometry, as cut spheres (CS), hard spherocylinders (HSC) and linear tangent hard sphere chains (LTHSC). Simulation values for v _ex were obtained with an overlap algorithm that is also presented in detail. The obtained results can be applied in theoretical and computer simulation studies of discotic liquid crystals.