Molecular dynamics simulations of forced conformational transitions in 1,6-linked polysaccharides

Effects of pullulan on the biomechanical and anti-collapse properties of dicalcium phosphate dihydrate bone cement

In this work, a modified dicalcium phosphate dihydrate (DCPD) bone cement with unique biodegradable ability in a calcium phosphate cement system was prepared by the hydration reaction of monocalcium phosphate monohydrate and calcium oxide and integration with pullulan (Pul), a non-toxic, biocompatible, viscous, and water-soluble polysaccharide that has been successfully used to improve defects in DCPD bone cement, especially its rapid solidification, fragile mechanical properties, and easy collapse. The effect of different contents of Pul on the structure and properties of DCPD were also studied in detail. The modified cement was characterised by X-ray diffraction, Fourier-transform infrared spectroscopy, scanning electron microscopy, ultraviolet-visible absorption, X-ray photoelectron spectroscopy analysis, and rheological property measurements. The results indicated that Pul promoted the hydration formation of DCPD, and interface bonding occurred between Pul and DCPD. With increasing content of Pul, the setting time of the DCPD bone cement increased from 2.6 min to 42.3 min, the compressive strength increased from 0 MPa to 20.4 MPa, and the anti-collapse ability also improved owing to the strong interface bonding, implying that the DCPD bone cement improved by Pul has better potential for application in the field of non-loading bone regenerative medicine compared to unmodified DCPD bone cement.

Predicting the Structures of Glycans, Glycoproteins, and Their Complexes

Complex carbohydrates are ubiquitous in nature, and together with proteins and nucleic acids they comprise the building blocks of life. But unlike proteins and nucleic acids, carbohydrates form nonlinear polymers, and they are not characterized by robust secondary or tertiary structures but rather by distributions of well-defined conformational states. Their molecular flexibility means that oligosaccharides are often refractory to crystallization, and nuclear magnetic resonance (NMR) spectroscopy augmented by molecular dynamics (MD) simulation is the leading method for their characterization in solution. The biological importance of carbohydrate-protein interactions, in organismal development as well as in disease, places urgency on the creation of innovative experimental and theoretical methods that can predict the specificity of such interactions and quantify their strengths. Additionally, the emerging realization that protein glycosylation impacts protein function and immunogenicity places the ability to define the mechanisms by which glycosylation impacts these features at the forefront of carbohydrate modeling. This review will discuss the relevant theoretical approaches to studying the three-dimensional structures of this fascinating class of molecules and interactions, with reference to the relevant experimental data and techniques that are key for validation of the theoretical predictions.

The Role of Single-Molecule Force Spectroscopy in Unraveling Typical and Autoimmune Heparin-induced Thrombocytopenia

For the last two decades, heparins have been widely used as anticoagulants. Besides numerous advantages, up to 5% patients with heparin administration suffer from a major adverse drug effect known as heparin-induced thrombocytopenia (HIT). This typical HIT can result in deep vein thrombosis, pulmonary embolism, occlusion of a limb artery, acute myocardial infarct, stroke, and a systemic reaction or skin necrosis. The basis of HIT may lead to clinical insights. Recent studies using single-molecule force spectroscopy (SMFS)-based atomic force microscopy revealed detailed binding mechanisms of the interactions between platelet factor 4 (PF4) and heparins of different lengths in typical HIT. Especially, SMFS results allowed identifying a new mechanism of the autoimmune HIT caused by a subset of human-derived antibodies in patients without heparin exposure. The findings proved that not only heparin but also a subset of antibodies induce thrombocytopenia. In this review, the role of SMFS in unraveling a major adverse drug effect and insights into molecular mechanisms inducing thrombocytopenia by both heparins and antibodies will be discussed.

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

We performed dynamic force spectroscopy of single dextran and titin I27 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that for such low-frequency dithering experiments, recorded phase information can be unambiguously interpreted within the framework of a transparent theoretical model that starts from a well-known partial differential equation to describe the dithering of an atomic force microscope cantilever and a single molecule attached to its end system, uses an appropriate set of initial and boundary conditions, and does not exploit any implicit suggestions. We conclude that the observed phase (dissipation) signal is due completely to the dissipation related to the dithering of the cantilever itself (i.e., to the change of boundary conditions in the course of stretching). For both cases, only the upper bound of the dissipation of a single molecule has been established as not exceeding 3⋅10(-7)kg/s. We compare our results with previously reported measurements of the viscoelastic properties of single molecules, and we emphasize that extreme caution must be taken in distinguishing between the dissipation related to the stretched molecule and the dissipation that originates from the viscous damping of the dithered cantilever. We also present the results of an amplitude channel data analysis, which reveal that the typical values of the spring constant of a I27 molecule at the moment of module unfolding are equal to 4±1.5mN/m, and the typical values of the spring constant of dextran at the moment of chair-boat transition are equal to 30-50mN/m.

Single-molecule force spectroscopy applied to heparin-induced thrombocytopenia

Heparin-induced thrombocytopenia (HIT), occurring up to approximately 1% to 5% of patients receiving the antithrombotic drug heparins, has a complex pathogenesis involving multiple partners ranging from small molecules to cells/platelets. Recently, insights into the mechanism of HIT have been achieved by using single-molecule force spectroscopy (SMFS), a methodology that allows direct measurements of interactions among HIT partners. Here, the potential of SMFS in unraveling the mechanism of the initial steps in the pathogenesis of HIT at single-molecule resolution is highlighted. The new findings ranging from the molecular binding strengths and kinetics to the determination of the boundary between risk and non-risk heparin drugs or platelet-surface and platelet-platelet interactions will be reviewed. These novel results together have contributed to elucidate the mechanisms underlying HIT and demonstrate how SMFS can be applied to develop safer drugs with a reduced risk profile.

Revision of the GROMOS 56A6(CARBO) force field: Improving the description of ring-conformational equilibria in hexopyranose-based carbohydrates chains

This article describes a revised version 56A6(CARBO_R) of the GROMOS 56A6(CARBO) force field for hexopyranose-based carbohydrates. The simulated properties of unfunctionalized hexopyranoses are unaltered with respect to 56A6CARBO . In the context of both O1 -alkylated hexopyranoses and oligosaccharides, the revision stabilizes the regular (4) C1 chair for α-anomers, with the opposite effect for β-anomers. As a result, spurious ring inversions observed in α(1→4)-linked chains when using the original 56A6(CARBO) force field are alleviated. The (4) C1 chair is now the most stable conformation for all d-hexopyranose residues, irrespective of the linkage type and anomery, and of the position of the residue along the chain. The methylation of a d-hexopyranose leads to a systematic shift in the ring-inversion free energy ((4) C1 to (1) C4 ) by 7-8 kJ mol(-1), positive for the α-anomers and negative for the β-anomers, which is qualitatively compatible with the expected enhancement of the anomeric effect upon methylation at O1. The ring-inversion free energies for residues within chains are typically smaller in magnitude compared to those of the monomers, and correlate rather poorly with the latter. This suggests that the crowding of ring substituents upon chain formation alters the ring flexibility in a nonsystematic fashion. In general, the description of carbohydrate chains afforded by 56A6(CARBO_R) suggests a significant extent of ring flexibility, i.e., small but often non-negligible equilibrium populations of inverted chairs, and challenges the "textbook" picture of conformationally locked carbohydrate rings.

Nanomechanics of β-rich proteins related to neuronal disorders studied by AFM, all-atom and coarse-grained MD methods

Computer simulations of protein unfolding substantially help to interpret force-extension curves measured in single-molecule atomic force microscope (AFM) experiments. Standard all-atom (AA) molecular dynamics simulations (MD) give a good qualitative mechanical unfolding picture but predict values too large for the maximum AFM forces with the common pulling speeds adopted here. Fine tuned coarse-grain MD computations (CG MD) offer quantitative agreement with experimental forces. In this paper we address an important methodological aspect of MD modeling, namely the impact of numerical noise generated by random assignments of bead velocities on maximum forces (F_max) calculated within the CG MD approach. Distributions of CG forces from 2000 MD runs for several model proteins rich in β structures and having folds with increasing complexity are presented. It is shown that F_max have nearly Gaussian distributions and that values of F_max for each of those β-structures may vary from 93.2 ± 28.9 pN (neurexin) to 198.3 ± 25.2 pN (fibronectin). The CG unfolding spectra are compared with AA steered MD data and with results of our AFM experiments for modules present in contactin, fibronectin and neurexin. The stability of these proteins is critical for the proper functioning of neuronal synaptic clefts. Our results confirm that CG modeling of a single molecule unfolding is a good auxiliary tool in nanomechanics but large sets of data have to be collected before reliable comparisons of protein mechanical stabilities are made.

Figure

The dynamics of the conformational changes in the hexopyranose ring: a transition path sampling approach

The transition paths corresponding to the conformational rearrangements in the ring of hexapyranose (α-d- and β-d-glucose) molecules were described by applying the transition path sampling method.

A reoptimized GROMOS force field for hexopyranose-based carbohydrates accounting for the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers

This article presents a reoptimization of the GROMOS 53A6 force field for hexopyranose-based carbohydrates (nearly equivalent to 45A4 for pure carbohydrate systems) into a new version 56A(CARBO) (nearly equivalent to 53A6 for non-carbohydrate systems). This reoptimization was found necessary to repair a number of shortcomings of the 53A6 (45A4) parameter set and to extend the scope of the force field to properties that had not been included previously into the parameterization procedure. The new 56A(CARBO) force field is characterized by: (i) the formulation of systematic build-up rules for the automatic generation of force-field topologies over a large class of compounds including (but not restricted to) unfunctionalized polyhexopyranoses with arbritrary connectivities; (ii) the systematic use of enhanced sampling methods for inclusion of experimental thermodynamic data concerning slow or unphysical processes into the parameterization procedure; and (iii) an extensive validation against available experimental data in solution and, to a limited extent, theoretical (quantum-mechanical) data in the gas phase. At present, the 56A(CARBO) force field is restricted to compounds of the elements C, O, and H presenting single bonds only, no oxygen functions other than alcohol, ether, hemiacetal, or acetal, and no cyclic segments other than six-membered rings (separated by at least one intermediate atom). After calibration, this force field is shown to reproduce well the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers. As a result, the 56A(CARBO) force field should be suitable for: (i) the characterization of the dynamics of pyranose ring conformational transitions (in simulations on the microsecond timescale); (ii) the investigation of systems where alternative ring conformations become significantly populated; (iii) the investigation of anomerization or epimerization in terms of free-energy differences; and (iv) the design of simulation approaches accelerating the anomerization process along an unphysical pathway.

Chains are more flexible under tension

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely-jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations the choice is not clear and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model which describes the force-deformation curve in terms of the chain bending constant K and bond length b. This model demonstrates that the worm-like and freely-jointed chain models correspond to two different regimes of polymer deformation and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K>1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ Kk(B)T/b and as a freely-jointed chain for f ≥ Kk(B)T/b (k(B) is the Boltzmann constant and T is the absolute temperature). The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules.

Equilibrium sampling for biomolecules under mechanical tension

In the studies of force-induced conformational transitions of biomolecules, the large timescale difference from experiments presents the challenge of obtaining convergent sampling for molecular dynamics simulations. To circumvent this fundamental problem, an approach combining the replica-exchange method and umbrella sampling (REM-US) was developed to simulate mechanical stretching of biomolecules under equilibrium conditions. Equilibrium properties of conformational transitions can be obtained directly from simulations without further assumptions. To test the performance, we carried out REM-US simulations of atomic force microscope (AFM) stretching and relaxing measurements on the polysaccharide pustulan, a (1-->6)-beta-D-glucan, which undergoes well-characterized rotameric transitions in the backbone bonds. With significantly enhanced sampling convergence and efficiency, the REM-US approach closely reproduced the equilibrium force-extension curves measured in AFM experiments. Consistent with the reversibility in the AFM measurements, the new approach generated identical force-extension curves in both stretching and relaxing simulations-an outcome not reported in previous studies, proving that equilibrium conditions were achieved in the simulations. REM-US may provide a robust approach to modeling of mechanical stretching on polysaccharides and even nucleic acids.

Theory of Biopolymer Stretching at High Forces

We provide a unified theory for the high force entropic elasticity of biopolymers solely in terms of the persistence length, ξ_p , and the monomer spacing, a. When the force f>ℱ _h ~ k_BTξ_p /a² the biopolymers behave as freely jointed chains (FJCs) while in the range ℱ _l ~ k_BT/ξ_p <f<ℱ _h the worm-like chain (WLC) is a better model. We show that ξ_p can be estimated from the force extension curve (FEC) at the extension x ≈ ¹/₂ (normalized by the contour length of the biopolymer). After validating the theory using simulations, we provide a quantitative analysis of the FECs for a diverse set of biopolymers (dsDNA, ssRNA, ssDNA, polysaccharides, and unstructured PEVK domain of titin) for x ≥ ¹/₂. The success of a specific polymer model (FJC or WLC) to describe the FEC of a given biopolymer is naturally explained by the theory. Only by probing the response of biopolymers over a wide range of forces can the f-dependent elasticity be fully described.

Fructan and its relationship to abiotic stress tolerance in plants

Numerous studies have been published that attempted to correlate fructan concentrations with freezing and drought tolerance. Studies investigating the effect of fructan on liposomes indicated that a direct interaction between membranes and fructan was possible. This new area of research began to move fructan and its association with stress beyond mere correlation by confirming that fructan has the capacity to stabilize membranes during drying by inserting at least part of the polysaccharide into the lipid headgroup region of the membrane. This helps prevent leakage when water is removed from the system either during freezing or drought. When plants were transformed with the ability to synthesize fructan, a concomitant increase in drought and/or freezing tolerance was confirmed. These experiments indicate that besides an indirect effect of supplying tissues with hexose sugars, fructan has a direct protective effect that can be demonstrated by both model systems and genetic transformation.

Plant fructans in stress environments: emerging concepts and future prospects

Plants are sessile and sensitive organisms known to possess various regulatory mechanisms for defending themselves under stress environments. Fructans are fructose-based polymers synthesized from sucrose by fructosyltransferases (FTs). They have been increasingly recognized as protective agents against abiotic stresses. Using model membranes, numerous in vitro studies have demonstrated that fructans can stabilize membranes by direct H-bonding to the phosphate and choline groups of membrane lipids, resulting in a reduced water outflow from the dry membranes. Inulin-type fructans are flexible random-coiled structures that can adopt many conformations, allowing them to insert deeply within the membranes. The devitrification temperature (T(g)) can be adjusted by their varying molecular weights. In addition, above T(g) their low crystallization rates ensure prolonged membrane protection. Supporting, in vivo studies with transgenic plants expressing FTs showed fructan accumulation and an associated improvement in freezing and/or chilling tolerance. The water-soluble nature of fructans may allow their rapid adaptation as cryoprotectants in order to give optimal membrane protection. One of the emerging concepts for delivering vacuolar fructans to the extracellular space for protecting the plasma membrane is vesicle-mediated, tonoplast-derived exocytosis. It should, however, be noted that natural stress tolerance is a very complex process that cannot be explained by the action of a single molecule or mechanism.

Measuring polysaccharide mechanics by atomic force microscopy

INTRODUCTIONPolysaccharides are frequently subjected to mechanical forces in vivo. Because these forces affect a wide range of biological activities, it is important to develop methods that directly investigate the mechanical properties of these molecules. Recent progress in techniques that allow the mechanical manipulation of biopolymers at a single-molecule level has revealed the complex nature of the elasticity of polysaccharides. The atomic force microscope (AFM) is an excellent force spectrometer for probing the mechanical properties (e.g., length and tension) of individual polysaccharides. The following protocol describes the use of AFM for stretch-release measurements of polysaccharide chains.

Interrogation of Single Synthetic Polymer Chains and Polysaccharides by AFM-Based Force Spectroscopy

This contribution reviews selected mechanical experiments on individual flexible macromolecules using single-molecule force spectroscopy (SMFS) based on atomic force microscopy. Focus is placed on the analysis of elasticity and conformational changes in single polymer chains upon variation of the external environment, as well as on conformational changes induced by the mechanical stress applied to individual macromolecular chains. Various experimental strategies regarding single-molecule manipulation and SMFS testing are discussed, as is theoretical analysis through single-chain elasticity models derived from statistical mechanics. Moreover, a complete record, reported to date, of the parameters obtained when applying the models to fit experimental results on synthetic polymers and polysaccharides is presented.

Conformational transitions in single polymer molecules modeled with a complete energy landscape: continuous two-state model

An extension of the two-state Freely Jointed Chain model is presented in which the discrete energies of the two conformers are replaced by continuous functions of the conformer length. The statistical mechanics is initially developed in the Gibbs ensemble and leads to a conformational multi-state model. This is used to fit the equilibrium force-extension curve for Dextran. The continuous model also allows the use of Transfer Matrix methods to calculate all statistical properties in the Helmholtz ensemble, including thermal fluctuations. The latter are obtained with near perfect agreement to experiment.

Entropy and barrier-controlled fluctuations determine conformational viscoelasticity of single biomolecules

Biological macromolecules have complex and nontrivial energy landscapes, endowing them with a unique conformational adaptability and diversity in function. Hence, understanding the processes of elasticity and dissipation at the nanoscale is important to molecular biology and emerging fields such as nanotechnology. Here we analyze single molecule fluctuations in an atomic force microscope, using a generic model of biopolymer viscoelasticity that includes local "internal" conformational dissipation. Comparing two biopolymers, dextran and cellulose (polysaccharides with and without local bistable transitions), demonstrates that signatures of simple conformational change are minima in both the elastic and internal friction constants around a characteristic force. A novel analysis of dynamics on a bistable energy landscape provides a simple explanation: an elasticity driven by the entropy, and friction by a barrier-controlled hopping time of populations between states, which is surprisingly distinct to the well-known relaxation time. This nonequilibrium microscopic analysis thus provides a means of quantifying new dynamical features of the energy landscape of the glucopyranose ring, revealing an unexpected underlying roughness and information on the shape of the barrier of the chair-boat transition in dextran. The results presented herein provide a basis toward probing the viscoelasticity of macromolecular conformational transitions on more complex energy landscapes, such as during protein folding.

Molecular dynamics simulation of dextran extension by constant force in single molecule AFM

The extension of 1-6 polysaccharides has been studied in a series of recent single molecule AFM experiments. For dextran, a key finding was the existence of a plateau in the force-extension curve at forces between 700 and 1000 pN. We studied the extension of the dextran 10-mer under constant force using atomistic simulation with various force fields. All the force fields reproduce the experimental plateau on the force-extension curve. With AMBER94 and AMBER-GLYCAM04 force fields the plateau can be explained by a transition of the glucopyranose rings in the dextran monomers from the chair ((4)C(1)) to the inverted chair ((1)C(4)) conformation while other processes occur at smaller (rotation around C5-C6 bond) or higher (chairs to boat transitions) forces. The CHARMM force field provides a different picture which associates the occurrence of the plateau to chair-boat transitions of the glucopyranose rings.

Simulating force-induced conformational transitions in polysaccharides with the SMD replica exchange method

Conventional steered molecular dynamics (SMD) simulations do not readily reproduce equilibrium conditions of atomic force microscopy (AFM) stretch and release measurements of polysaccharides undergoing force-induced conformational transitions because of the gap between the timescales of computer simulations ( approximately 1 mus) and AFM measurements ( approximately 1 s). To circumvent this limitation, we propose using the replica exchange method (REM) to enhance sampling during SMD simulations. By applying REM SMD to a small polysaccharide system and comparing the results with those from AFM stretching experiments, we demonstrate that REM SMD reproduces the experimental results not only qualitatively but quantitatively, approaching near equilibrium conditions of AFM measurements. As tested in this work, hysteresis and computational time of REM SMD simulations of short polysaccharide chains are significantly reduced as compared to regular SMD simulations, making REM SMD an attractive tool for studying forced-induced conformational transitions of small biopolymer systems.

Monosaccharide composition, chain length and linkage type influence the interactions of oligosaccharides with dry phosphatidylcholine membranes

Sugars play an important role in the desiccation tolerance of most anhydrobiotic organisms and disaccharides have been extensively investigated for their ability to stabilize model membranes in the dry state. Much less is known about the ability of oligosaccharides to protect dry membranes. However, it has been shown that different structural families of oligosaccharides have different efficacies to interact with and protect membranes during drying. Here, we have compared three families of linear oligosaccharides (fructans, malto-oligosaccharides, manno-oligosaccharides) for their chain-length dependent lyoprotective effect on egg phosphatidylcholine liposomes. We found increased protection with chain length for the fructans, a moderate decrease in protection with chain length for malto-oligosaccharides, and a strong decrease for manno-oligosaccharides. Using Fourier-transform infrared spectroscopy and differential scanning calorimetry, we show that the degree of lyoprotection of the different sugars is closely related to their influence on the gel to liquid-crystalline phase behavior of the dry membranes and to the extent of H-bonding to different groups (C=O, P=O, choline) in the lipids. Possible structural characteristics of the different oligosaccharides that may determine the extent to which they are able to interact with and protect membranes are discussed.

Sub-angstrom conformational changes of a single molecule captured by AFM variance analysis

A system's equilibrium variance can be analyzed to probe its underlying dynamics at higher resolution. Here, using single-molecule atomic-force microscope techniques, we show how the variance in the length of a single dextran molecule can be used to establish thermodynamic equilibrium and to detect conformational changes not directly observable with other methods. Dextran is comprised of a chain of pyranose rings that each undergoes an Angstrom-scale transition from a chair to boat conformation under a stretching force. Our analysis of the variance of the molecule's fluctuations verifies equilibrium throughout the force-extension curve, consistent with the expected thermodynamic ensemble. This validates further analysis of the variance in the transition region, which reveals an intermediate conformation between the chair and the boat on the sub-Angstrom scale. Our test of thermal equilibrium as well as our variance analysis can be readily extended to a wide variety of molecules, including proteins.

Inferring the diameter of a biopolymer from its stretching response

We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve depends on the polymer structural parameters: its thickness and granularity (spacing of the monomers). The expression is used to analyze experimental data for the stretching of various different types of biopolymers: polypeptides, polysaccharides, and nucleic acids. Besides recovering elastic parameters (such as the persistence length) that are consistent with those obtained from standard entropic models, the approach allows us to extract viable estimates for the polymers diameter and granularity. This shows that the basic structural polymer features have such a profound impact on the elastic behavior that they can be recovered with the sole input of stretching measurements.