Random Coil Model Research Articles

Random-coil model for glomerular sieving of dextran

Random-coil model for glomerular sieving of dextran

Helix propensity of Ala and Val: A free energy perturbation study

Difference in helix propensity between Ala and Val was examined by a molecular dynamics/free energy perturbation method. Simulations were based on a simple two state model of helix-coil transition. Val 10 in an Ala based 17mer peptide (Y 1K 2A 3A 4A 5A 6K 7A 8A 9V 10A 11K 12A 13A 14A 15A 16K 17) used as the α-helical model, or in an extended trimer (A 9V 10A 11) used as the random coil model, was perturbed to Ala by a slow growth method. The computed ΔΔ G (−1.27 ± 0.92 kcal/mol) reproduced semiquantitatively the experimental ΔΔ G (−0.7 kcal/mol; Padmanabhan et al., Nature 344 (1990) 268). Inclusion of intraperturbed contributions was essential. Free energy component analysis showed that intra-perturbed interaction within Val 10 contributed positive value to Δδ G and that interaction between Lys 7 and Val 10 contributed negative value. The latter dominated the former, which resulted in the larger helix propensity of Ala.

Random coils of polyisoprene in solution—a small angle x-ray scattering study

We report a systematic investigation of the structure of polyisoprene in solution by means of small angle X-ray scattering (SAXS). The SAXS results show that in solution there is little long range interaction between the polyisoprene chains with the scattering function being well fitted by the random coil model.

Monoalkylitaconates–vinylpyrrolidone copolymers. 2. Reactivity ratios and viscometric behaviour in dilute solutions

AbstractCopolymerization of mono‐n‐decyl and mono‐n‐decyl and mono‐n‐dodecyl itaconate with vinylpyrrolidone (MOI‐VP, MDI‐VP and MDoI‐VP) was carried out using AIBN as initiator. The monomer reactivity ratios were determined by the Fineman‐Ross and Kelen‐Tüdös methods. Values of r1 and r2 were found to be less than unity for MOI‐VP, MDI‐VP and MDoI‐VP, corresponding to random copolymers with some tendency to alternance. Copolymers of various compositions were studied in solution, and Mark‐Houwink‐Kuhn‐Sakurada relationships were established in ethanol for MOI‐VP and MDI‐VP copolymers, and in 1‐propanol for MDoI‐VP. The rigidity factors s̀ and the characteristic ratio C∞ were obtained from Kθ values determined by using the Stockmayer‐Fixman relation. In all the copolymers the introduction of vinylpyrrolidone units produces flexibility of the polymer chain relative to the poly(monoitaconate) homopolymers, and the solution properties of these copolymers can be described by assuming a random coil model instead of a rigid rod or wormlike model as in poly(monoitaconates).

Hydrogen exchange in native and denatured states of hen egg-white lysozyme.

The hydrogen exchange kinetics of 68 individual amide protons in the native state of hen lysozyme have been measured at pH 7.5 and 30 degrees C by 2D NMR methods. These constitute the most protected subset of amides, with exchange half lives some 10(5)-10(7) times longer than anticipated from studies of small model peptides. The observed distribution of rates under these conditions can be rationalized to a large extent in terms of the hydrogen bonding of individual amides and their burial from bulk solvent. Exchange rates have also been measured in a reversibly denatured state of lysozyme; this was made possible under very mild conditions, pH 2.0 35 degrees C, by lowering the stability of the native state through selective cleavage of the Cys-6-Cys-127 disulfide cross-link (CM6-127 lysozyme). In this state the exchange rates for the majority of amides approach, within a factor of 5, the values anticipated from small model peptides. For a few amides, however, there is evidence for significant retardation (up to nearly 20-fold) relative to the predicted rates. The pattern of protection observed under these conditions does not reflect the behavior of the protein under strongly native conditions, suggesting that regions of native-like structure do not persist significantly in the denatured state of CM6-127 lysozyme. The pattern of exchange rates from the native protein at high temperature, pH 3.8 69 degrees C, resembles that of the acid-denatured state, suggesting that under these conditions the exchange kinetics are dominated by transient global unfolding. The rates of folding and unfolding under these conditions were determined independently by magnetization transfer NMR methods, enabling the intrinsic exchange rates from the denatured state to be deduced on the basis of this model, under conditions where the predominant equilibrium species is the native state. Again, in the case of most amides these rates showed only limited deviation from those predicted by a simple random coil model. This reinforces the view that these denatured states of lysozyme have little persistent residual order and contrasts with the behavior found for compact partially folded states of proteins, including an intermediate detected transiently during the refolding of hen lysozyme.

Auto-antibodies to human sperm basic nuclear proteins in infertile and vasectomized men: Characterization of antigens and epitopes recognized by antibodies

The sera of vasectomized men and of patients with immune infertility were used to study the antigens and epitopes of sperm nuclear proteins that bind antibodies in these sera. No reaction with sperm histones was observed except for one serum. P1, P2 protamines and pro-P2 protamines were recognized by auto-antibodies. Studies with peptides derived from P1 and P2 protamines and with mammalian protamines related to HP1 showed that antibodies are mainly specific for a folded protamine molecule, more especially antibodies from vasectomized men. These results disagree with the random coil model proposed for protamines by several previous works. A cross-reactivity between P1 and P2 protamines was observed only for the whole molecules and not for peptides derived from them. This observation suggests that the two classes of protamines, different in sequence, may have a similar folding and thereby may be functionally equivalent.

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.

Two-dimensional chain structures observed in carbon-ion-implanted nickel thin films

Two-dimensional polycrystalline chain structures were observed in carbon-ion-implanted nickel thin films. The significant excluded-volume effect to a randomly folded highly polydispersive configuration, as compared with the random coil model in three dimensions. Individual chains had a fractal dimension ranging from 1.24 to 1.45, depending on whether they exhibited linear or branching behaviour as related to the local growth environment. A microscopic feature of the chain structure was a sausage-like aggregation of polycrystals, which was attributed to the dense distribution of polycrystals and to the requirement of reduced surface energy.

Molecular arrangements and conformations of the alkyl chains in spherical micelles and droplets

We have modeled two systems of spherical micelles and of n-alkane droplets, each consisting of 52 molecules comprised by 13 units each in a spherical region of approximately 1.6 nm radius, by the Monte Carlo simulation method. The simulated model micelle exhibits the distribution of chain segments in good agreement with the results of neutron scattering and NMR experiments on micelles having similar compositions. Both the micelle and the droplet models show that the segments in the interior of the chains tend to stay away from the interfaces, resulting in enhanced chain-end densities at the surface region. Moreover, chain segments in contact with the interface tend to orient along the interface,thus exhibiting negative order parameters with respect to the radius vector. Despite this local anisotropic orientation, however, the average conformation of the alkyl groups is only slightly different from that of the unperturbed random-coil model.

Theoretical study of the thermoelastic properties of elastin model chains

The origin of the elastic behaviour of the bioelastomer elastin has been a matter of some controversy in recent years, as has been the degree of stable secondary structure present in the native state. Available data on the primary sequence of the protein chains constituting the elastin network has indicated a significant incidence of three repeat peptides of length four, five and six, with all containing a Pro-Gly pair within them. The present investigation involved the calculation of the temperature coefficient of the mean-square end-to-end distance 〈 r 2〉 0 of random-coil model chains composed exclusively of one of the three repeat peptides. This configuration-dependent property is directly related to the experimentally obtained energetic component of the elastic force. The values of dln〈r 2〉 0 dT for each model chain were evaluated through the use of semi-empirical energy calculations on terminally-blocked residues present in the aforementioned repeat peptides, and subsequent use of established matrix techniques for calculating 〈 r 2〉 0 for polypeptides within a scheme involving independently rotating virtual bonds. Three levels of hydrogen bonding inclusion were investigated to help establish the importance of this contribution. The small positive value of the energetic component of the elastic force for elastin in the literature was found to be adequately reproduced in these calculations on the random-coil model chains.

The influence of polymer size and shape on self-diffusion of polysaccharides and solvents

Self-diffusion data obtained using pulsed-field-gradient nuclear magnetic resonance spectroscopy are presented for the poly- d-glucose molecules, dextran, amylopectin and glycogen in water and dimethyl sulphoxide. A model is developed for the influence of macroparticle shape on the concentration-dependence of polymer self-diffusion. The concentration-dependence of solvent and polymer self-diffusion indicates that amylopectin is planar with an axial ratio in excess of 6. In contrast, the dextran and glycogen data are consistent with random coil and spherical particle models, respectively. Both amylopectin and glycogen exhibit significantly different dimensions in the two solvent used.

Models of amorphous solids

The three classical models of amorphous solids are: the continuous random network model for covalent glasses (Zachariasen), the random close packing model for metallic glasses (Bernal), and the random coil model for polymeric glasses (Flory). Basic aspects of these models, their relationships, and their dimensionality dependences, are reviewed. The possible relevance of higher-dimensional packings is discussed, and Raman studies are presented of a glass exhibiting conversion from rcp to crn structure.

Human β‐endorphin

1H spectra at 270 MHz of the beta h-endorphin glycyl residues in aqueous solution are reported. The chemical shifts, coupling constants and temperature coefficients are compared with those of the glycyl residues in Met-enkephalin and in a random coil model peptide. The local conformation of Tyr-Gly-Gly-Phe-segment observed in Met-enkephalin is maintained in beta h-endorphin.

Statistical thermodynamics of alkyl chain conformations in lipid bilayers

An examination is made of the conformations and packing of the chains in bulk n-alkane in low temperature crystals, the intermediate α-crystal state and in the liquid state. Flory's ‘random-coil model’ of liquid alkane is examined. The phase behaviour of the fully hydrated dipalmitoyl lecithin (DPPC) bilayer is analysed and comparisons are made with n-alkanes. The state of the DPPC chains above the gel/liquid-crystal phase transition is discussed in detail and it is argued that the chains exist as slightly perturbed random-coils. An examination is made of the changes in chain packing which occur when the lipid chains are unsaturated, and when cholesterol or protein are introduced into the membrane. The possibility of rigid-body re-orientation of the lipid chains around the normal to the bilayer is examined. It is argued that such motion is not sufficiently collective to invalidate the perturbed random-coil model. With the introduction of a substantial mole fraction of cholesterol, however, rigid-body tilting becomes the dominant form of disorder in the hydrophobic region of the bilayer.

Chain conformation of polystyrene in bulk by small-angle X-ray scattering

Small-angle x-ray scattering from solid solutions of different molecular weight fractions of partially brominated polystyrene in polystyrene has been studied. The results of this study indicate that polymer chains in bulk have a radius of gyration proportional to the square root of molecular weight, which is consistent with the random coil model. However, these radii are approximately 20% larger than the unperturbed radii deduced by light scattering in dilute solutions.

Small-angle neutron scattering studies of isotropic polypropylene

Small-angle neutron scattering studies have been made of molten and crystalline polypropylene using samples containing small amounts of deuterated polypropylene in a protonated polypropylene matrix. The specimens were characterized by small- and wide-angle X-ray scattering to determine the d-spacing and the degree of crystallinity χ and by gel permeation chromatography to determine molecular weight, M w , and molecular weight distribution. The degree of crystallinity was varied from 0.5 to 0.7, the d-spacing from 120 to 250 Å and the molecular weight from 34 000 to 1 540 000. Clustering was not observed. The radius of gyration 〈s 2〉 w 1 2 of the tagged molecules was approximately proportional to M w 1 2 and almost independent of d and χ. In the melt similar values were obtained which are, within experimental uncertainties, the same as in a θ-solution. For 〈 s 2〉 w k 2⪢ 1 the scattering law approaches a k −2 dependence. The results are discussed with reference to the chain-folded model but a fit cannot be obtained over all molecular weights. A simple random coil model fits the neutron scattering data partly but this does not explain the origin of the d-spacing.

Intramolecular crosslinking

AbstractWhen a high molecular weight polymer, in a solution of concentration above the critical concentration for entanglement, is lightly crosslinked to effect only a few bonds per macromolecule, its solution viscosity is significantly affected. The random coil model predicts a monotonous increase in viscosity as a function of crosslink density, leading to a fast gelation. The macromolecular domain model predicts that, under the same conditions, the viscosity will pass through a minimum before progressing to gelation. As the molecular weight of the polymer decreases, the differences between the models become indistinguishable. In this inquiry it is shown that at least the four polymers polyacrylamide, polyvinylalcohol, polyethyleneimine and high molecular weight epoxy (phenoxy), adhere to the prediction of the macromolecular domain model.

Frequency dependence of intrinsic stress and birefringence tensor of bead/spring model of polymer solutions

The recently obtained complete solution of the simultaneous diagonalization of matrices H A and H in the hydrodynamic diffusion equation has basically changed the diagonal values vp of the symmetric matrix H of hydrodynamic interaction between all the beads of the elastic random coil model of the isolated macromolecule in solution. Since these values enter explicitly the expressions for the intrinsic stress and refractive index tensor in an alternating flow field if based on the concept of internal viscosity of the model one had to recalculate all values obtained formerly by using the then generally accepted erroneous set of vp data. The new vp equal unity independent of p while the old values were larger than 1 for small p and smaller for large p. Hence their too large contributions in the former range are partially compensated by their too small contributions in the latter region. As a consequence in the whole range investigated, between 3 and 300 chain links, the differences in rheological and rheooptical effects are relatively small, up to a factor of 2, although at higher link number the differences tend to grow with the logarithm of this number.

Macromolecular properties of heparin in dilute solution: 2. Dimensional parameters as a function of pH, ionic strength and desulphation

A bovine heparin fraction was examined by sedimentation analysis and intrinsic viscosity measurements as a function of ionic strength in the range of 0·1 to 1·0 M, and at pH 2·5 and 6·0. The following experimental parameters were obtained: M, S 0 20,W, D 0 20,W, V ̄ , and [η]. Other physical parameters were calculated based on a random coil model (supported by the theory of Mandelkern and Flory) e.g., ( r ̄ 2) 1 2 , ( s ̄ 2) 1 2 . Similar studies were made on a heparin sample as a function of desulphation as resulting from graded mild hydrolysis. Since desulphation is accompanied by decreasing anticoagulant activity of heparin, the latter was correlated with various calculated and measured physical parameters. Significantly ( r ̄ 2) 1 2 decreases with decreased desulphation and therefore decreased biological activity.

Excluded Volume Effect of Chain Polymers

The excluded volume effect of chain polymers is calculated by using the flexible random coil model. The intramolecular energy of polymer is assumed to be given by the product of the binary cluster integral of polymer segments and their contact probability which is determined from a segments-distribution function appropriately assumed. This intramolecular energy becomes a function linearly decreasing with the end to end distance of the polymer. The result of excluded volume effect obtained from this potential function coincides almost with that by the third order perturbation theory. The expansion coefficient α of the end to end distance can be given by the approximate equation α x -α x -2 =(2π/3) 1/2 z , x =4.3∼5.0, where z is the interaction parameter of segments. The intramolecular energy function assumed is compared with the expression obtained by Fujita et al. , and the segments-distribution function is recalculated, which is found to be nearly the same as that first assumed.