A Monte Carlo study of the amylosic chain conformation

Atomic-Resolution Experimental Structural Biology and Molecular Dynamics Simulations of Hyaluronan and Its Complexes

This review summarizes the atomic-resolution structural biology of hyaluronan and its complexes available in the Protein Data Bank, as well as published studies of atomic-resolution explicit-solvent molecular dynamics simulations on these and other hyaluronan and hyaluronan-containing systems. Advances in accurate molecular mechanics force fields, simulation methods and software, and computer hardware have supported a recent flourish in such simulations, such that the simulation publications now outnumber the structural biology publications by an order of magnitude. In addition to supplementing the experimental structural biology with computed dynamic and thermodynamic information, the molecular dynamics studies provide a wealth of atomic-resolution information on hyaluronan-containing systems for which there is no atomic-resolution structural biology either available or possible. Examples of these summarized in this review include hyaluronan pairing with other hyaluronan molecules and glycosaminoglycans, with ions, with proteins and peptides, with lipids, and with drugs and drug-like molecules. Despite limitations imposed by present-day computing resources on system size and simulation timescale, atomic-resolution explicit-solvent molecular dynamics simulations have been able to contribute significant insight into hyaluronan's flexibility and capacity for intra- and intermolecular non-covalent interactions.

Conformation of Pullulan in Aqueous Solution Studied by Small-Angle X-Ray Scattering

Small-angle X-ray scattering functions were measured for six pullulan samples with molecular weights ranging from 2.3 × 10⁴ to 7.4 × 10⁵ in 0.05 M aqueous NaCl at 25 °C and fitted by the perturbed wormlike chain model, comprising touched-bead sub-bodies, to obtain wormlike chain parameters. The parameter values determined were consistent with those determined from previously reported dilute solution properties of aqueous pullulan. Because radii of gyration of not only pullulan polymers, but also pullulan oligomers were consistently explained by the touched-bead wormlike chain model perturbed by the excluded volume effect, the pullulan chain takes a local conformation considerably different from the amylose chain, although both polysaccharides are flexible polymers with an approximately same characteristic ratio.

Conformational analysis of oligosaccharides and polysaccharides using molecular dynamics simulations

Complex carbohydrates usually have a large number of rotatable bonds and consequently a large number of theoretically possible conformations can be generated (combinatorial explosion). The application of systematic search methods for conformational analysis of carbohydrates is therefore limited to disaccharides and trisaccharides in a routine analysis. An alternative approach is to use Monte-Carlo methods or (high-temperature) molecular dynamics (MD) simulations to explore the conformational space of complex carbohydrates. This chapter describes how to use MD simulation data to perform a conformational analysis (conformational maps, hydrogen bonds) of oligosaccharides and how to build realistic 3D structures of large polysaccharides using Conformational Analysis Tools (CAT).

Marine polysaccharides in microencapsulation and application to aquaculture: "from sea to sea"

This review's main objective is to discuss some physico-chemical features of polysaccharides as intrinsic determinants for the supramolecular structures that can efficiently provide encapsulation of drugs and other biological entities. Thus, the general characteristics of some basic polysaccharides are outlined in terms of their conformational, dynamic and thermodynamic properties. The analysis of some polysaccharide gelling properties is also provided, including the peculiarity of the charged polysaccharides. Then, the way the basic physical chemistry of polymer self-assembly is made in practice through the laboratory methods is highlighted. A description of the several literature procedures used to influence molecular interactions into the macroscopic goal of the encapsulation is given with an attempt at classification. Finally, a practical case study of specific interest, the use of marine polysaccharide matrices for encapsulation of vaccines in aquaculture, is reported.

Structural Stability of V-Amylose Helices in Water-DMSO Mixtures Analyzed by Molecular Dynamics

Computational techniques have been employed to fundamentally understand the behavior of helically structured amylose in water/DMSO mixtures. Using a computationally generated amylose helix of 55 glucose residues, we have investigated the time-dependent behavior of intra- and intermolecular hydrogen bonds, particularly between O2 and O3 of adjacent glucose molecules and between O6 and neighboring O2 and O3 groups. The helix character was defined by the total number of residually existing hydrogen bonds. Our results parallel the experimental finding that increasing the percentage of DMSO results in increasing helical stability. It can be shown that O6-O2/O3 hydrogen bonds are preferentially lost when the helix starts to unfold to a finally resulting random coil structure. While water is small enough to interact with every hydroxyl group at the helix surface and finally penetrate the helix coil, DMSO can initially only form single hydrogen bonds to part of the OH groups of the amylose molecule, thereby allowing a longer conservation of intramolecular hydrogen bonds that are necessary to maintain the helix. However, given a long enough time for interaction, the helical structure of amylose is lost in water as well as in DMSO, yielding a random orientation of the glucose strand.

Higher order structure of (1,3)-beta-D-glucans and its influence on their biological activities and complexation abilities

(1,3)-beta-D-Glucans form a group of biologically active biopolymers that exist in different structural organizations depending on the environmental conditions. The biological effect of (1,3)-beta-D-glucans is a core issue stimulating large research efforts of the molecular properties and their consequences for action as biological response modifiers. The fascination for these molecules increased further following the finding of their ability to form complexes of defined geometry with a number of structures, ranging from linear architectures as polymers or carbon nanotubes, to globular structures as gold particles or dye molecules. The fascinating information concerning the relationship between sample treatment history and molecular organization has not yet reached out to all the contributors within the field, resulting in unnecessary apparent inconsistencies in the literature. In addition to environmental conditions, the sample history is known to influence on the precise structural organization of these molecules. The present knowledge related to the structure of native as well as denatured, renatured and annealed (1,3)-beta-D-glucans is reviewed. The influence of their structural organization on the biological activity and complexation abilities is discussed, and some factors hindering progress in the understanding of their biological effects or complexation abilities are pointed out.

Experimental approaches to hyaluronan structure

A review of the literature describing experimental studies on hyaluronan (HA) is presented. Methods sensitive to the hydrodynamic properties of HA, analyzed in neutral aqueous solution containing NaCl at physiological concentration, can be shown to fit the expected behavior of a high molecular weight linear semi-flexible polymer. The significant nonideality of HA solutions can be predicted by a simple treatment for hydrodynamic interactions between polymer chains. Nuclear magnetic resonance and circular dichroism studies of HA are also in agreement with a model incorporating dynamically formed and broken hydrogen bonds, contributing to the semi-flexibility of the polymer chain, and segmental motions on the nanosecond time scale. HA shows the capability for self-association in the formation of a viscoelastic putty state at pH 2.5 in the presence of salt, and a gel state at pH 2.5 in mixed organic/aqueous solution containing salt. Ordered and associated structures have also been observed for HA on the surfaces, especially in the presence of surface-structured water. These phenomena can be understood in terms of counterion-mediated polyelectrolyte interactions. The possibility that hyaluronan exists in vivo in environments that induce ordered structures and assemblies is discussed.

Conformational features of cepacian: the exopolysaccharide produced by clinical strains of Burkholderia cepacia

Conformational energy calculations and molecular dynamics investigations, both in water and in dimethyl sulfoxide, were carried out on the exopolysaccharide cepacian produced by the majority of the clinical strains of Burkholderia cepacia, an opportunistic pathogen causing serious lung infection in patients affected by cystic fibrosis, The investigation was aimed at defining the structural and conformational features, which might be relevant for clarification of the structure-function relationships of the polymer. The molecular dynamics calculations were carried out by Ramachandran-type energy plots of the disaccharides that constitute the polymer repeating unit. The dynamics of an oligomer composed of three repeating units were investigated in water and in Me2SO, a non-aggregating solvent. Analysis of the time persistence of hydrogen bonds showed the presence of a large number of favourable interactions in water, which were less evident in Me2SO. The calculations on the cepacian chain indicated that polymer conformational features in water were affected by the lateral chains, but were also largely dictated by the presence of solvent. Moreover, the large number of intra-chain hydrogen bonds in water disappeared in Me2SO solution, increasing the average dimension of the polymer chains.

Effect of the carbohydrate side-chain on the conformation of a glycoconjugate polystyrene in aqueous solution

An oligomaltose-carrying polystyrene "glycoconjugate polystyrene" was synthesized by the homopolymerization of 4-vinylbenzylamine oligomaltonic amides, derived from maltose, maltotriose, maltopentaose, and maltoheptaose. The resultant amphiphilic glycoconjugate polystyrenes were dissolved in 0.1 M aqueous urea, and their structures characterized by small-angle X-ray scattering and molecular modeling. "Glycoconjugate polystyrene" was found to behave as a "molecular bottle brush", composed of a large pseudo-helical polystyrene backbone and carbohydrate brushes. A large pseudo-helical polystyrene backbone is formed by a random sequence of TT, TG, and/or TTGG. The results indicate that the cross-section of a backbone chain with smaller oligosaccharide side-chains is obliged to expand more than that with longer side-chains. Even with rigid hydrophilic pendant oligosaccharide chains, the larger pseudo-helix of the main chain could orient the side-chains so as to envelop the hydrophobic backbone in aqueous solution. Thus the conformation of the main chain is determined not only by the chemical nature of an oligosaccharide chain but also by its length.

Hyaluronan chain conformation and dynamics

An overview of the present state of research in the field of hyaluronan chain conformational aspects is presented. The relationship between structure and dynamics are illustrated for a series of hyaluronan oligomers. Conformational characteristics of hyaluronan chains are discussed, together with the dynamic chain patterns, evaluated by using a theoretical approach to diffusive polymer dynamics. The dependence of correlation times and NMR relaxation parameters from the chain dimension are investigated. Topological features and dimensional properties are related to the structural determinants by using classical computational methods of molecular mechanics and Monte Carlo simulation.

Monte Carlo study of cycloamylose: chain conformation, radius of gyration, and diffusion coefficient

Cyclic (1 --> 4)-alpha-D-glucan chains with or without excluded volume have been collected from a huge number (about 10(7)) of linear amylosic chains generated by the Monte Carlo method with a conformational energy map for maltose, and their mean-square radii of gyration <S(2)> and translational diffusion coefficients D (based on the Kirkwood formula) have been computed as functions of x (the number of glucose residues in a range from 7 to 300) and the excluded-volume strength represented by the effective hard-core radius. Both <S(2)>/x and D in the unperturbed state weakly oscillate for x < 30 and the helical nature of amylose appears more pronouncedly in cyclic chains than in linear chains. As x increases, these properties approach the values expected for Gaussian rings. Though excluded-volume effects on them are always larger in cycloamylose than in the corresponding linear amylose, the ratios of <S(2)> and the hydrodynamic radius of the former to the respective properties of the latter in good solvents can be slightly lower than or comparable to the (asymptotic) Gaussian-chain values when x is not sufficiently large. An interpolation expression is constructed for the relation between the gyration-radius expansion factors for linear and cyclic chains from the present Monte Carlo data and the early proposed asymptotic relation with the aid of the first-order perturbation theories.

Imaging of carrageenan macrocycles and amylose using noncontact atomic force microscopy

Samples of kappa-carrageenan, iota-carrageenan, and synthetic amylose have been examined by atomic force microscopy (AFM). All samples were spray deposited from aqueous solutions onto freshly cleaved mica, air dried, and imaged in air using noncontact atomic force microscopy (NCAFM). Images of single stranded amylose and carrageenan are presented. At relatively low polymer concentrations in the presence of NaCl iota-carrageenan formed circles that appear to be predominantly head-to-tail associated unimeric duplex (double stranded) structures. At higher iota-carrageenan concentrations the polymer forms circles and aggregates that appear to involve dimeric duplex structure. Direct comparison of synthetic amylose molecular weights determined from NCAFM images with results from solution measurements showed that NCAFM provides an excellent way to measure amylose molecular weight and molecular weight distribution. It is shown that synthetic amylose is single stranded in aqueous solution and that the chain length distribution is broader than the Poisson distribution anticipated from polymerization theory.

Modeling polysaccharides: present status and challenges

The most recent tools that have been developed for modeling the three-dimensional features of polysaccharides and carbohydrate polymers are presented. The presentation starts with a description of the conformations of the monosaccharides, and of the flexible rings such as in the case of five-membered rings, and a thorough description of the conformational space that is available for a disaccharide unit, either in vacuo or in an aqueous phase. The extension to the modeling of the parent polysaccharides is addressed, based on the assumption that owing to the size and relative rigidity of the intervening monosaccharides units, the rotations at a particular linkage can be, under some conditions, considered as independent of nearest neighbor interactions. Appropriate modeling techniques are described that can provide insights into the dimensions of the chain in a solution which is best described as a random coil accompanied by the occurrence of local "helical" regions. With the help of such descriptors such as helical parameters, the ordered state of polysaccharide strands can be readily characterized. The generation of double or triple helices can be then attempted in order to explore the occurrence of such multi-stranded arrangements that may be energetically stable. The final step in the determination of the structure of polysaccharides in the ordered state, is the investigation of the interactions of different helices. This may lead to either the best arrangement(s) between two polymeric chains, or to the prediction of the dimensions, and the symmetry of a three-dimensional lattice. Some of the tools which have been developed should allow automatic scarches for meaningful correlations between structures and functions, through exploratory data analysis. Structure-function or structure-property correlation could be then used to model changes arising from structural alterations. This would open the field of polysaccharide engineering.

A molecular builder for carbohydrates: application to polysaccharides and complex carbohydrates

A new procedure (POLYS) for producing three-dimensional structures of polysaccharides and complex carbohydrates is described. This employs a builder concept combining a database of monosaccharide structures with a database containing information on populations of independent neighboring glycosidic linkages in disaccharide fragments. The computer program is written in C, and it can cope with both the complexity and the diversity of carbohydrates and the unique topological features arising from multiple branching. A simple ASCII syntax was developed for describing the primary structures in accordance with IUPAC nomenclature. The translation of the primary structure is made through the combined use of a lexical analyzer and a command interpreter. In this way the program can be considered as a compiler of primary structures of carbohydrates. However, it also generates secondary and tertiary structures in the form of Cartesian coordinates in formats used by most molecular mechanics programs and packages. In our laboratory POLYS was exhaustively tested on standard homopolysaccharide systems such as cellulose and mannan and found to work very well. We now report the ease of use and the efficiency of the molecular builder in applications to more complex carbohydrate systems. These include the structural exploration of a pentaantennary oligosaccharide having 135 residues, the complex family of pectic polysaccharides including the organization and distribution of side chains (arabinan, arabinogalactan, and galactan) on the rhamnogalacturonan backbone.

Conformation of cyclic and linear (1 --> 2)-beta-D-glucans in aqueous solution

The conformations of cyclic (1 --> 2)-beta-D-glucan chains having degree of polymerization (dp) 17 to 24 were characterized by means of small-angle X-ray scattering and Monte Carlo simulation. The results indicate that cyclic (1 --> 2)-beta-D-glucan chains adopt the shape of a doughnut-like ring with a thickness of about 10 A for all the samples. The diameter of the annulus for the cyclic glucan having dp 21 is estimated to be only about 4-5 A. Two linear (1 --> 2)-beta-D-glucans possessing dp 19 and 21 prepared by acid hydrolysis of a cyclic glucan and subsequent fractionation showed different scattering profiles from those obtained for cyclic glucans having the corresponding dp. Although the Monte Carlo simulation does not completely reproduce the scattering profiles observed by small-angle X-ray scattering, linear (1 --> 2)-beta-D-glucans seem to possess a characteristic cylindrical shape with cross-sectional diameters of 11.8 and 13.2 A for linear glucans of dp 19 and 21, respectively.

The dependence of glucan conformational dynamics on linkage position and stereochemistry

The 13C NMR T1 relaxation times for the (1-->4)-linked maltooligomers (Mi) and the (1-->6)-linked isomaltooligomers (IMi) with i = 2, 4, 6, and 8 were measured in aqueous solution at 22 and 65 degrees C at a concentration (3%) low enough to have removed concentration-dependent effects on the measured T1 values. Separate T1 values were measured for each carbon in the residue at the reducing end of the oligosaccharide, in the residue at the non-reducing end, and in the interior, i.e., non-terminal, residue(s). Analogous data for the corresponding high polymers show that at 22 degrees C the relaxation times for the carbons of the interior residues of the oligomers have converged to their high chain length asymptotes at about i = 10. This observation suggests that at room temperature polymeric motions in the frequency domain effective for 13C NMR relaxation at a magnetic field strength of 11.7 T have a "wavelength" of the order of 10 residues. The relaxation times characterizing the two ends of the chain are different, with longer T1 values for the carbons of the reducing end than for those of the non-reducing end. Carbons of alpha-anomeric residues at the reducing end have shorter relaxation times than those of the corresponding beta-anomeric reducing sugars. Carbons of the interior residues have T1 values shorter than the carbons of either type of terminal residue. For oligomers of a given dp there is no T1 difference between oligomers of the Mi and IMi series at room temperature. This observation is seemingly at odds with the great differences in the inherent conformational freedom of the (1-->4)- and (1-->6)-linkages. At elevated temperatures the orientational relaxation behavior of the two series of oligomers measured by 13C T1 values show interesting differences, and in the case of the Mi series, structure develops in the chain length dependence of the T1 values.

Computer modelling of sulfated carbohydrates: applications to carrageenans

In this study, X-ray crystallographic data of sulfated monosaccharides have been used to derive appropriate parameters for sulfate groups in the Tripos force field, previously parameterized for carbohydrates. A database of nine sulfated monosaccharides occurring as building blocks of sulfated polysaccharides such as carrageenans and sulfated glycosaminoglycans has been built. These tools have then been used to evaluate the conformational energies of the repeating units of the kappa-, iota- and lambda-carrageenan polymers, taking into account the rotation around the sulfate groups. In a third step, helical conformations of carrageenans have been explored and the results compared with the experimental data obtained by X-ray fibre diffraction. Stable, single, right-handed helices, with geometric and helical parameters in close correspondence with the best models derived from X-ray diffraction data, have been generated. Finally, the configurational statistics of random-coil carrageenan chains have been investigated and compared with experimental data currently available on these polymers. A highly flexible character is predicted for kappa- and iota-carrageenans, with lambda-carrageenan showing slightly more extension.

Conformational features of galacturonans. II. Configurational statistics of pectic polymers

The unperturbed dimensions of poly-alpha-D-galacturonic acid (PGA) as a function of the degree of polymerization (n) and degree of ionization (%GalA-) have been determined by molecular mechanics and Monte Carlo methods. Chain extensions appear to depend substantially on contributions arising from local redistributions of charge on charged and uncharged galacturonic acid residues. Inclusion of methyl-esterified galacturonic acid units results in increased chain extensions. Incorporation of alpha-(1-->2)-L-rhamnose units causes abrupt changes in chain propagation and a reduction in calculated chain extension.

Macrocyclization of polysaccharides visualized by electron microscopy

Topological features of the polysaccharides schizophyllan, l-carrageenan and gellan gum were studied using electron microscopy. Electron micrographs of schizophyllan not subjected to any thermal or solvent composition history destabilizing the triple helix, show stiff, linear chains consistent with the structure being triple helical and with contour length proportional to the molecular weight in solution. A blend of linear, cyclic and hairpin topologies and higher molecular weight clusters were observed after renaturation, i.e. return to conditions favouring the triple helical structure, from solvent conditions dissociating the triple helix. Electron micrographs of l-carrageenan in salt-free solution reveal linear extended structures. Addition of 0.15 M LiI to the solution before preparation for electron microscopy, i.e. salt conditions that favour ordering but not gelation, yields a large fraction of cyclic structures with circumference of different lengths. Likewise, adding KCl to aqueous gellan gum changes their appearance from dispersed polymers to suprastrands with several associated chains. Macrocyclic species can also be observed in gellan gum after the addition of a gel-promoting salt. The tendency to form macrocyclic structures in competition with intermolecular aggregates is determined by the three factors: (1) chain stiffness relative to overall length; (2) parallel or antiparallel alignment of interacting chain segments; and (3) polymer concentration. The present study indicates that electron microscopy provides information about the topology adopted by polysaccharides.

Conformational features of carrabiose polymers: I. Configurational statistics of kappa-carrageenan

Potential energy functions evaluating both repulsive-attractive van der Waals non-bonding interactions and electrostatic interactions have been used to evaluate the conformational energies of the repeating units of the kappa-carrageenan polymers. Structural parameters have been obtained by minimization MNDO procedures (MOPAC). Energy maps have been calculated for the (1-3) alpha-D-galactose-4-sulphate (GS) and the (1-4)-3,6-anhydro-alpha-D-galactose (A) residues, taking into account the conformational freedom of the sulphate group. The configurational statistics of the random coiled kappa-carrageenan chain have been explored, disclosing a highly flexible character, which can mainly be ascribed to the random occurrence of two different conformers of the GS-A dimeric unit.

A Monte Carlo method for conformational analysis of saccharides

A Metropolis Monte Carlo (MMC) algorithm was applied to explore conformational spaces spanned by the exocyclic dihedral angles of four disaccharides alpha-D-Man(1-->3)-alpha-D-Man(1-->O)Me (1), alpha-D-Man(1-->2)-alpha-D-Man(1-->O)Me (2), methyl beta-cellobioside (3), and methyl beta-maltoside (4). The simulation method uses the HSEA force field and randomly samples the conformational space with an automatic preference for low-energy states. In comparison to a systematic grid search, MMC offers a much more convenient and efficient protocol for the computation of ensemble average values of experimentally accessible NMR parameters such as NOE effects or 3J coupling constants. Energy barriers of a few kcal/mol were found to be surmounted easily when running the simulations with the temperature parameter set at room temperature, whereas passing significantly higher barriers required elevated temperature parameters. Ensemble average NOE values were calculated using the MMC technique and a conventional systematic grid search showing that the MMC method adequately samples the conformational spaces of 1-4. Theoretical NOEs derived for global or local minimum conformations are different from ensemble average values, and it is shown that averaged NOEs agree significantly better with experimental data. Ensemble average NOEs for 1 derived from MMC/HSEA, and previously reported MM2CARB and AMBER calculations all showed good agreement with experimental data, with MMC/HSEA giving the closest fit.

Comparison of the conformational dynamics of the (1----4)- and (1----6)-linked alpha-D-glucans using 13C-NMR relaxation

The conformational dynamics of alpha-(1----4)- and alpha-(1----6)-glucan homooligomers in the nanosecond time domain have been compared by measuring the 13C-nmr longitudinal relaxation times T1 for carbons of the terminal and interior sugar residues. Measurements are reported on monomeric glucose and on oligomers containing up to ten glucose residues at room temperature in aqueous solution at concentrations of 3 and 20 g/dL. The carbons of terminal residues display longer relaxation times than do those of interior residues, presumably as a consequence of a greater degree of conformational mobility of the chain ends. The T1s of the reducing terminal residues of all oligomers are significantly longer than those of the corresponding nonreducing termini, a phenomenon that we associate tentatively with the anomeric equilibrium at the reducing end. Carbons of the reducing terminal residues in the beta-anomeric form relax more slowly than their alpha-anomeric counterparts. At 20 g/dL the mean T1s for carbons of the terminal and interior residues attain asymptotic behavior with increasing chain length at a chain length of about six residues, and carbons of the alpha-(1----4)-linked maltooligomers relax significantly more slowly than those of the corresponding alpha-(1----6)-linked isomaltooligomers. The T1s of both glucan series increase with decreasing concentration. This concentration dependence disappears below 3 g/dL, where the T1s of the two series of homoligomers are no longer distinguishable. This suggests that in dilute aqueous solution at room temperature viscous damping effects predominate over contributions to the T1-sensitive conformational dynamics from structural differences in the glycosidic linkage region. At 3 g/dL the approach to long chain-length asymptotic behavior is more protracted than at 20 g/dL, and the T1s of carbons of interior oligomeric residues appear to match the corresponding high-polymer behavior at a chain length of eight and greater.