Conformational free energies of methyl-α-L-iduronic and methyl-β-D-glucuronic acids in water

Clustering one million molecular structures on GPU within seconds

Structure clustering is a general but time-consuming work in the study of life science. Up to now, most published tools do not support the clustering analysis on graphics processing unit (GPU) with root mean square deviation metric. In this work, we specially write codes to do the work. It supports multiple threads on multiple GPUs. To show the performance, we apply the program to a 33-residue fragment in protein Pin1 WW domain mutant. The dataset contains 1,400,000 snapshots, which are extracted from an enhanced sampling simulation and distribute widely in the conformational space. Various testing results present that our program is quite efficient. Particularly, with two NVIDIA RTX4090 GPUs and single precision data type, the clustering calculation on 1 million snapshots is completed in a few seconds (including the uploading time of data from memory to GPU and neglecting the reading time from hard disk). This is hundreds of times faster than central processing unit. Our program could be a powerful tool for fast extraction of representative states of a molecule among its thousands to millions of candidate structures.

Comparative Bindings of Glycosaminoglycans with CXCL8 Monomer and Dimer: Insights from Conformational Dynamics and Kinetics of Hydrogen Bonds

GAGs bind to both the monomeric and dimeric forms of CXCL8, helping to form a concentration gradient of the chemokine that facilitates the recruitment of neutrophils to an injury site and supports other biological functions. In this study, atomistic molecular dynamics simulations were conducted to investigate the binding behavior of two hexameric GAGs sulfated at two different positions, chondroitin sulfate (CS) and heparan sulfate (HS), with the monomer (SIL8) and dimer (DIL8) forms of the CXCL8 protein. The results support that the conformational diversity of CS and HS appeared to be more when binding with monomer SIL8 than dimer DIL8. CS gained more configurational entropy from glycosidic linkage flexibility when bound to SIL8 than DIL8, with a higher energy barrier, whereas HS exhibited a lower energy barrier for configurational entropy when bound to SIL8 and DIL8. The monomer SIL8 exhibited more favorable and preferential binding with GAGs compared to DIL8. Formation of hydrogen bonds with the basic amino acids of SIL8 and GAG was more rigid and required higher activation energy to break than the other identified hydrogen bondings. Water molecules involved in hydrogen bonding with GAGs, excluding those with basic amino acids of DIL8, showed longer lifetimes and slower relaxation compared to SIL8. This suggests that water-mediated interactions also favor binding of DIL8 with GAGs. Despite having more basic amino acids, DIL8 did not display stronger binding than SIL8, indicating the significant role of basic residues in stabilizing the GAG-protein interactions in the monomers. The reason could be that the greater number of nonbasic amino acids in dimeric CXCL8 stabilizes the complex by forming water-mediated hydrogen bonds, reducing the conformational preferences for binding with GAGs. In contrast, the monomeric form of CXCL8 exhibits a higher conformational preference for protein-GAG interactions.

Sulfation Effects of Chondroitin Sulfate to Bind a Chemokine in Aqueous Medium: Conformational Heterogeneity and Dynamics from Molecular Simulation

The sulfation patterns and degree of sulfation of chondroitin sulfate (CS), an important class of glycosaminoglycans (GAG), and their interactions with chemokines are accountable for various diseases. To realize the underlying mechanism of such complex biological phenomena at a molecular level and their application in rational drug design, a study on conformations and dynamics of CSs is necessary. To explore this, in this study, we performed a series of atomistic molecular dynamics (MD) simulations with different sulfated variants of octadecasaccharide CS, like CS-C, CS-E, and CS-T, in their free forms and when bound to the protein chemokine CXCL8 dimer in an aqueous medium. The calculated binding free energy of CSs with the CXCL8 dimer is favorable, and the degree of sulfation favors the complexation process further with prominent hydrophobic and hydrogen-bonded interactions. We find that the recognition is associated with the configurational entropy loss of the CS molecules as calculated from the Gaussian mixture approach, which supports that the degree of sulfation regulates the process. Cluster analysis through the k-means algorithm and end-to-end distance measurement revealed that although the free CS molecules adopted linear conformations, the nonlinear conformations during binding with protein were noted. Adaptation of nonlinear forms in the bound forms is noteworthy for the less-sulfated CS-C and CS-E. Apart from favorable 4C1 conformations, the occasional appearance of skew-boat forms from the free-energy map of ring pucker for the GlcUA unit was observed, which remains unaffected by the sulfation. We find that during recognition, the average relaxation time of intra-CS and inter-CS-CXCL8 hydrogen bonds (HBs) is about a magnitude lesser than that of CS-water HBs, most prominent on the involvement of higher sulfated CS-T analogues. The translational motion of surrounded water molecules in CSs exhibited sublinear diffusion, and the degree of sublinearity increases around the heavily sulfated molecules due to the hindrance created by them as well as the presence of the chemokine and exhibited markedly slow heterogeneous diffusion.

Effect of Sulfation on the Conformational Dynamics of Dermatan Sulfate Glycosaminoglycan: A Gaussian Accelerated Molecular Dynamics Study

Glycosaminoglycans (GAGs) are anionic biopolymers present on cell surfaces as a part of proteoglycans. The biological activities of GAGs depend on the sulfation pattern. In our study, we have considered three octadecasaccharide dermatan sulfate (DS) chains with increasing order of sulfation (dp6s, dp7s, and dp12s) to illuminate the role of sulfation on the GAG units and its chain conformation through 10 μs-long Gaussian accelerated molecular dynamics simulations. DS is composed of repeating disaccharide units of iduronic acid (IdoA) and N-acetylgalactosamine (N-GalNAc). Here, N-GalNAc is linked to IdoA via β(1-4), while IdoA is linked to N-GalNAc through α(1-3). With the increase in sulfation, the DS structure becomes more rigid and linear, as is evident from the distribution of root-mean-square deviations (RMSDs) and end-to-end distances. The tetrasaccharide linker region of the main chain shows a rigid conformation in terms of the glycosidic linkage. We have observed that upon sulfation (i.e., dp12s), the ring flip between two chair forms vanished for IdoA. The dynamic cross-correlation analysis reveals that the anticorrelation motions in dp12s are reduced significantly compared to dp6s or dp7s. An increase in sulfation generates relatively more stable hydrogen-bond networks, including water bridging with the neighboring monosaccharides. Despite the favorable linear structures of the GAG chains, our study also predicts few significant bendings related to the different puckering states, which may play a notable role in the function of the DS. The relation between the global conformation with the micro-level parameters such as puckering and water-mediated hydrogen bonds shapes the overall conformational space of GAGs. Overall, atomistic details of the DS chain provided in this study will help understand their functional and mechanical roles, besides developing new biomaterials.

Characterization of Heparin's Conformational Ensemble by Molecular Dynamics Simulations and Nuclear Magnetic Resonance Spectroscopy

Heparin is a highly charged, polysulfated polysaccharide and serves as an anticoagulant. Heparin binds to multiple proteins throughout the body, suggesting a large range of potential therapeutic applications. Although its function has been characterized in multiple physiological contexts, heparin's solution conformational dynamics and structure-function relationships are not fully understood. Molecular dynamics (MD) simulations facilitate the analysis of a molecule's underlying conformational ensemble, which then provides important information necessary for understanding structure-function relationships. However, for MD simulations to afford meaningful results, they must both provide adequate sampling and accurately represent the energy properties of a molecule. The aim of this study is to compare heparin's conformational ensemble using two well-developed force fields for carbohydrates, known as GLYCAM06 and CHARMM36, using replica exchange molecular dynamics (REMD) simulations, and to validate these results with NMR experiments. The anticoagulant sequence, an ultra-low-molecular-weight heparin, known as Arixtra (fondaparinux, sodium), was simulated with both parameter sets. The results suggest that GLYCAM06 matches experimental nuclear magnetic resonance three-bond J-coupling values measured for Arixtra better than CHARMM36. In addition, NOESY and ROESY experiments suggest that Arixtra is very flexible in the sub-millisecond time scale and does not adopt a unique structure at 25 C. Moreover, GLYCAM06 affords a much more dynamic conformational ensemble for Arixtra than CHARMM36.

Pyranose Ring Puckering Thermodynamics for Glycan Monosaccharides Associated with Vertebrate Proteins

The conformational properties of carbohydrates can contribute to protein structure directly through covalent conjugation in the cases of glycoproteins and proteoglycans and indirectly in the case of transmembrane proteins embedded in glycolipid-containing bilayers. However, there continue to be significant challenges associated with experimental structural biology of such carbohydrate-containing systems. All-atom explicit-solvent molecular dynamics simulations provide a direct atomic resolution view of biomolecular dynamics and thermodynamics, but the accuracy of the results depends on the quality of the force field parametrization used in the simulations. A key determinant of the conformational properties of carbohydrates is ring puckering. Here, we applied extended system adaptive biasing force (eABF) all-atom explicit-solvent molecular dynamics simulations to characterize the ring puckering thermodynamics of the ten common pyranose monosaccharides found in vertebrate biology (as represented by the CHARMM carbohydrate force field). The results, along with those for idose, demonstrate that the CHARMM force field reliably models ring puckering across this diverse set of molecules, including accurately capturing the subtle balance between 4C1 and 1C4 chair conformations in the cases of iduronate and of idose. This suggests the broad applicability of the force field for accurate modeling of carbohydrate-containing vertebrate biomolecules such as glycoproteins, proteoglycans, and glycolipids.

Investigating the folding mechanism of the N-terminal domain of ribosomal protein L9

Protein folding is a popular topic in the life science. However, due to the limited sampling ability of experiments and simulations, the general folding mechanism is not yet clear to us. In this work, we study the folding of the N-terminal domain of ribosomal protein L9 (NTL9) in detail by a mixing replica exchange molecular dynamics method. The simulation results are close to previous experimental observations. According to the Markov state model, the folding of the protein follows a nucleation-condensation path. Moreover, after the comparison to its 39-residue β-α-β motif, we find that the helix at the C-terminal has a great influence on the folding process of the intact protein, including the nucleation of the key residues in the transition state ensemble and the packing of the hydrophobic residues in the native state.

Simulation Study of the Plasticity of k-Turn Motif in Different Environments

The k-turn is a widespread and important motif in RNA. According to the internal hydrogen bond network, it has two stable states, called N1 and N3. The relative stability between the states changes with the environment. It is able to accept different conformations in different environments. This is called the "plasticity" of a molecule. In this work, we study the plasticity of k-turn by the mixing REMD method in explicit solvent. The results are concluded as follows. First, N1 and N3 are almost equally stable when k-turn is in the solvent alone. The molecule is quite flexible as a hinge. However, after binding to different proteins, such as the proteins L7Ae and L24e, k-turn falls into one global minimum. The preferred state could be either N1 or N3. On the contrary, the other nonpreferred state becomes unstable with a weaker binding affinity to the protein. It reveals that RNA-binding protein is able to modulate the representative state of k-turn at equilibrium. This is in agreement with the findings in experiments. Moreover, free energy calculations show that the free energy barrier between the N1 and N3 states of k-turn increases in the complexes. The state-to-state transition is greatly impeded. We also give a deep discussion on the mechanism of the high plasticity of k-turn in different environments.

The conformation of the idopyranose ring revisited: How subtle O-substituent induced changes can be deduced from vicinal 1H-NMR coupling constants

The idopyranose ring plays a pivotal role in the conformational, dynamical, and intermolecular binding aspects of glycosaminoglycans like heparin and dermatan sulfate and it was early on assigned a role in the Sugar Code governing biological recognition processes. There is consensus that next to the two canonical ¹C₄ and ⁴C₁ chair conformations, the conformational space accessible to the idopyranose ring entails a ²S_O skew-boat conformation, but the equilibrium between these three ring puckers has evaded satisfactory quantification. In this study a meta-analysis of X-ray solid-state data and vicinal NMR coupling constants is presented, based on the Truncated Fourier Puckering (TFP) formalism and the generalized Karplus (CAGPLUS) equation. This approach yields a model-free, granular and consistent reckoning of 159 idopyranose solution puckering equilibria studied by NMR and allows us to reproduce the involved 636 NMR vicinal couplings with an overall residual RMS(J_obs-J_calc) of 0.184 Hz. Our analyses show that for all ring systems examined, the idopyranosyl chair conformations take up the same ring pucker irrespective of the ring substituent pattern or a vast variety in experimental conditions. Instead, it is the (skew-)boat conformation that adapts to the substitution pattern of the idopyranose ring or a specific sulfation pattern of neighboring saccharides. All idopyranose rings are involved in conformational equilibria that subsume the aforementioned conformers which turn out to differ only a few kJ/mole in conformational energy. Thus, the plasticity and flexibility of idopyranose remains intact under practically all circumstances and, as the glycosidic linkages in heparin are considered to be relatively stiff, the iduronic moiety functions as the linchpin of heparin flexibility thereby being rather a "space(r)" than a "letter" in the alleged Sugar Code alphabet.

Computational study on the polymerization reaction of d-aminopeptidase for the synthesis of d-peptides

Almost all natural proteins are composed exclusively of l-amino acids, and this chirality influences their properties, functions, and selectivity. Proteases can recognize proteins composed of l-amino acids but display lower selectivity for their stereoisomers, d-amino acids. Taking this as an advantage, d-amino acids can be used to develop polypeptides or biobased materials with higher biostability. Chemoenzymatic peptide synthesis is a technique that uses proteases as biocatalysts to synthesize polypeptides, and d-stereospecific proteases can be used to synthesize polypeptides incorporating d-amino acids. However, engineered proteases with modified catalytic activities are required to allow the incorporation of d-amino acids with increased efficiency. To understand the stereospecificity presented by proteases and their involvement in polymerization reactions, we studied d-aminopeptidase. This enzyme displays the ability to efficiently synthesize poly d-alanine-based peptides under mild conditions. To elucidate the mechanisms involved in the unique specificity of d-aminopeptidase, we performed quantum mechanics/molecular mechanics simulations of its polymerization reaction and determined the energy barriers presented by the chiral substrates. The enzyme faces higher activation barriers for the acylation and aminolysis reactions with the l-stereoisomer than with the d-substrate (10.7 and 17.7 kcal mol-1 higher, respectively). The simulation results suggest that changes in the interaction of the substrate with Asn155 influence the stereospecificity of the polymerization reaction.

Ring Puckering Landscapes of Glycosaminoglycan-Related Monosaccharides from Molecular Dynamics Simulations

The conformational flexibility of the glycosaminoglycans (GAGs) is known to be key in their binding and biological function, for example in regulating coagulation and cell growth. In this work, we employ enhanced sampling molecular dynamics simulations to probe the ring conformations of GAG-related monosaccharides, including a range of acetylated and sulfated GAG residues. We first perform unbiased MD simulations of glucose anomers and the epimers glucuronate and iduronate. These calculations indicate that in some cases, an excess of 15 μs is required for adequate sampling of ring pucker due to the high energy barriers between states. However, by applying our recently developed msesMD simulation method (multidimensional swarm-enhanced sampling molecular dynamics), we were able to quantitatively and rapidly reproduce these ring pucker landscapes. From msesMD simulations, the puckering free energy profiles were then compared for 15 further monosaccharides related to GAGs; this includes to our knowledge the first simulation study of sulfation effects on β-GalNAc ring puckering. For the force field employed, we find that in general the calculated pucker free energy profiles for sulfated sugars were similar to the corresponding unsulfated profiles. This accords with recent experimental studies suggesting that variation in ring pucker of sulfated GAG residues is primarily dictated by interactions with surrounding residues rather than by intrinsic conformational preference. As an exception to this, however, we predict that 4-O-sulfation of β-GalNAc leads to reduced ring rigidity, with a significant lowering in energy of the ¹C₄ ring conformation; this observation may have implications for understanding the structural basis of the biological function of β-GalNAc-containing glycosaminoglycans such as dermatan sulfate.

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

Constructing a free energy landscape for a large molecule is difficult. One has to use either a high temperature or a strong driving force to enhance the sampling on the free energy barriers. In this work, we propose a mixed method that combines these two kinds of acceleration strategies into one simulation. First, it applies an adaptive biasing potential to some replicas of the molecule. These replicas are particularly accelerated in a collective variable space. Second, it places some unbiased and exchangeable replicas at various temperature levels. These replicas generate unbiased sampling data in the canonical ensemble. To improve the sampling efficiency, biased replicas transfer their state variables to the unbiased replicas after equilibrium by Monte Carlo trial moves. In comparison to previous integrated methods, it is more convenient for users. It does not need an initial reference biasing potential to guide the sampling of the molecule. And it is also unnecessary to insert many replicas for the requirement of passing the free energy barriers. The free energy calculation is accomplished in a single stage. It samples the data as fast as a biased simulation and it processes the data as simple as an unbiased simulation. The method provides a minimalist approach to the construction of the free energy landscape. © 2019 Wiley Periodicals, Inc.

Insights into the Stereospecificity in Papain-Mediated Chemoenzymatic Polymerization from Quantum Mechanics/Molecular Mechanics Simulations

Chemoenzymatic peptide synthesis is an efficient and clean method to generate polypeptides for new applications in the fields of biomedical and functional materials. However, this enzyme-mediated synthesis is dependent on the reaction rate of the protease biocatalyst, which is essentially determined by the natural substrate specificity of the enzyme. Papain, one of the most studied cysteine proteases, is extensively used for the chemoenzymatic synthesis of new polypeptides. Similar to most proteases, papain displays high stereospecificity toward l-amino acids, with limited reactivity for the d-stereoisomer counterparts. However, the incorporation of d-amino acids into peptides is a promising approach to increase their biostability by conferring intrinsic resistance to proteolysis. Herein, we determined the stereospecific-limiting step of the papain-mediated polymerization reaction with the chiral substrates l/d-alanine ethyl ester (Ala-OEt). Afterward, we used Quantum Mechanics/Molecular Mechanics (QM/MM) simulations to study the catalytic mechanism at atomic level of detail and investigate the origin of its stereospecificity. The experimental and computational results show that papain is able to attack both l- and d-stereoisomers of Ala-OEt, forming an enzyme-substrate intermediate, and that the two reactions display a similar activation barrier. Moreover, we found that the reduced catalytic activity of papain in the polymerization of d-amino acids arises from the aminolysis step of the reaction, in which l-Ala-OEt displays a significantly lower free-energy barrier (12 kcal/mol) than d-Ala-OEt (30 kcal/mol). Further simulations suggest that the main factor affecting the polymerization of d-amino acids is the configuration of the d-acyl-intermediate enzyme, and in particular the orientation of its methyl group, which hinders the nucleophilic attack by other monomers and thus the formation of polypeptides.

Perspective on computational simulations of glycosaminoglycans

Glycosaminoglycans (GAGs) represent a formidable frontier for chemists, biochemists, biologists, medicinal chemists and drug delivery specialists because of massive structural complexity. GAGs are arguably the most complex, natural linear biopolymers with theoretical diversity orders of magnitude higher than proteins and nucleic acids. Yet, this diversity remains generally untapped. Computational approaches offer major routes to understand GAG structure and dynamics so as to enable novel applications of these biopolymers. In fact, computational algorithms, softwares, online tools and techniques have reached a level of sophistication that help understand atomistic details of conformational variation and protein recognition of individual GAG sequences. This review describes current approaches and challenges in computational study of GAGs. It presents a history of major findings since the earliest mention of GAGs (the 1960s), the development of parameters and force fields specific for GAGs, and the application of these tools in understanding GAG structure-function relationship. This review also presents a section on how to perform simulation of GAGs, which is directed toward researchers interested in entering this promising field with potential to impact therapy.

Extension of the GROMOS 56a6CARBO/CARBO_R Force Field for Charged, Protonated, and Esterified Uronates

An extension of the GROMOS 56a6_{CARBO/CARBO_R} force field for hexopyranose-based carbohydrates is presented. The additional parameters describe the conformational properties of uronate residues. The three distinct chemical states of the carboxyl group are considered: deprotonated (negatively charged), protonated (neutral), and esterified (neutral). The parametrization procedure was based on quantum-chemical calculations, and the resulting parameters were tested in the context of (i) flexibility of the pyranose rings under different pH conditions, (ii) conformation of the glycosidic linkage of the (1 → 4)-type for uronates with different chemical states of carboxyl moieties, (iii) conformation of the exocyclic (i.e., carboxylate and lactol) moieties, and (iv) structure of the Ca²⁺-linked chain-chain complexes of uronates. The presently proposed parameters in combination with the 56a6_{CARBO/CARBO_R} set can be used to describe the naturally occurring polyuronates, composed either of homogeneous (e.g., glucuronans) or heterogeneous (e.g., pectins, alginates) segments. The results of simulations relying on the new set of parameters indicate that the conformation of glycosidic linkage is nearly unaffected by the chemical state of the carboxyl group, in contrary to the ring conformational equilibria. The calculations for the poly(α-d-galacturonate)-Ca²⁺ and poly(α-l-guluronate)-Ca²⁺ complexes show that both parallel and anitiparallel arrangements of uronate chains are possible but differ in several structural aspects.

Multiscale modeling of glycosaminoglycan structure and dynamics: current methods and challenges

Glycosaminoglycans are long unbranched and complex polysaccharides that are an essential component of mammalian extracellular matrices. Characterization of their molecular structure, dynamics and interactions are essential to understand important biological phenomena in health and disease, and will lead to novel therapeutics and medical devices. However, this has proven to be a challenge experimentally and theoretical techniques are needed to develop new hypotheses, and interpret experiments. This review aims to examine the current theoretical (rather than experimental) methods used by researchers to investigate glycosaminoglycan structure, dynamics and interactions, from the monosaccharide to the macromolecular scale. It will consider techniques such as quantum mechanics, molecular mechanics, molecular dynamics, coarse graining and docking.

Constructing a multidimensional free energy surface like a spider weaving a web

Complete free energy surface in the collective variable space provides important information of the reaction mechanisms of the molecules. But, sufficient sampling in the collective variable space is not easy. The space expands quickly with the number of the collective variables. To solve the problem, many methods utilize artificial biasing potentials to flatten out the original free energy surface of the molecule in the simulation. Their performances are sensitive to the definitions of the biasing potentials. Fast-growing biasing potential accelerates the sampling speed but decreases the accuracy of the free energy result. Slow-growing biasing potential gives an optimized result but needs more simulation time. In this article, we propose an alternative method. It adds the biasing potential to a representative point of the molecule in the collective variable space to improve the conformational sampling. And the free energy surface is calculated from the free energy gradient in the constrained simulation, not given by the negative of the biasing potential as previous methods. So the presented method does not require the biasing potential to remove all the barriers and basins on the free energy surface exactly. Practical applications show that the method in this work is able to produce the accurate free energy surfaces for different molecules in a short time period. The free energy errors are small in the cases of various biasing potentials. © 2017 Wiley Periodicals, Inc.

Structure and Dynamics of DNA and RNA Double Helices of CAG and GAC Trinucleotide Repeats

CAG trinucleotide repeats are known to cause 10 late-onset progressive neurodegenerative disorders as the repeats expand beyond a threshold, whereas GAC repeats are associated with skeletal dysplasias and expand from the normal five to a maximum of seven repeats. The TR secondary structure is believed to play a role in CAG expansions. We have carried out free energy and molecular dynamics studies to determine the preferred conformations of the A-A noncanonical pairs in (CAG)_n and (GAC)_n trinucleotide repeats (n = 1, 4) and the consequent changes in the overall structure of the RNA and DNA duplexes. We find that the global free energy minimum corresponds to A-A pairs stacked inside the core of the helix with anti-anti conformations in RNA and (high-anti)-(high-anti) conformations in DNA. The next minimum corresponds to anti-syn conformations, whereas syn-syn conformations are higher in energy. Transition rates of the A-A conformations are higher for RNA than DNA. Mechanisms for these various transitions are identified. Additional structural and dynamical aspects of the helical conformations are explored, with a focus on contrasting CAG and GAC duplexes. The neutralizing ion distribution around the noncanonical pairs is described.

Fast exploration of an optimal path on the multidimensional free energy surface

In a reaction, determination of an optimal path with a high reaction rate (or a low free energy barrier) is important for the study of the reaction mechanism. This is a complicated problem that involves lots of degrees of freedom. For simple models, one can build an initial path in the collective variable space by the interpolation method first and then update the whole path constantly in the optimization. However, such interpolation method could be risky in the high dimensional space for large molecules. On the path, steric clashes between neighboring atoms could cause extremely high energy barriers and thus fail the optimization. Moreover, performing simulations for all the snapshots on the path is also time-consuming. In this paper, we build and optimize the path by a growing method on the free energy surface. The method grows a path from the reactant and extends its length in the collective variable space step by step. The growing direction is determined by both the free energy gradient at the end of the path and the direction vector pointing at the product. With fewer snapshots on the path, this strategy can let the path avoid the high energy states in the growing process and save the precious simulation time at each iteration step. Applications show that the presented method is efficient enough to produce optimal paths on either the two-dimensional or the twelve-dimensional free energy surfaces of different small molecules.

Calculation of the Local Free Energy Landscape in the Restricted Region by the Modified Tomographic Method

The free energy landscape is the most important information in the study of the reaction mechanisms of the molecules. However, it is difficult to calculate. In a large collective variable space, a molecule must take a long time to obtain the sufficient sampling during the simulation. To save the calculation quantity, decreasing the sampling region and constructing the local free energy landscape is required in practice. However, the restricted region in the collective variable space may have an irregular shape. Simply restricting one or more collective variables of the molecule cannot satisfy the requirement. In this paper, we propose a modified tomographic method to perform the simulation. First, it divides the restricted region by some hyperplanes and connects the centers of hyperplanes together by a curve. Second, it forces the molecule to sample on the curve and the hyperplanes in the simulation and calculates the free energy data on them. Finally, all the free energy data are combined together to form the local free energy landscape. Without consideration of the area outside the restricted region, this free energy calculation can be more efficient. By this method, one can further optimize the path quickly in the collective variable space.

Improving the replica-exchange molecular-dynamics method for efficient sampling in the temperature space

Replica-exchange molecular dynamics (REMD) is a popular sampling method in the molecular simulation. By frequently exchanging the replicas at different temperatures, the molecule can jump out of the minima and sample efficiently in the conformational space. Although REMD has been shown to be practical in a lot of applications, it does have a critical limitation. All the replicas at all the temperatures must be simulated for a period between the replica-exchange steps. This may be problematic for the reaction with high free energy barriers. In that case, too many replicas are required in the simulation. To reduce the calculation quantity and improve its performance, in this paper we propose a modified REMD method. During the simulation, each replica at each temperature can stay in either the active or inactive state and only switch between the states at the exchange step. In the active state, the replica moves freely in the canonical ensemble by the normal molecular dynamics, and in the inactive state, the replica is frozen temporarily until the next exchange step. The number of the replicas in the active states (active replicas) depends on the number of CPUs in the computer. Using the additional inactive replicas, one can perform an REMD simulation in a wider temperature space. The practical applications show that the modified REMD method is reliable. With the same number of active replicas, this REMD method can produce a more reasonable free energy surface around the free energy minima than the standard REMD method.

Calculation of Raman optical activity spectra for vibrational analysis

This review provides the necessary knowledge to accurately model ROA spectra of solvated systems and interpret their vibrational characteristics.

Glycosaminoglycan monosaccharide blocks analysis by quantum mechanics, molecular dynamics, and nuclear magnetic resonance

Glycosaminoglycans (GAGs) play an important role in many biological processes in the extracellular matrix. In a theoretical approach, structures of monosaccharide building blocks of natural GAGs and their sulfated derivatives were optimized by a B3LYP6311ppdd//B3LYP/6-31+G(d) method. The dependence of the observed conformational properties on the applied methodology is described. NMR chemical shifts and proton-proton spin-spin coupling constants were calculated using the GIAO approach and analyzed in terms of the method's accuracy and sensitivity towards the influence of sulfation, O1-methylation, conformations of sugar ring, and ω dihedral angle. The net sulfation of the monosaccharides was found to be correlated with the ¹H chemical shifts in the methyl group of the N-acetylated saccharides both theoretically and experimentally. The ω dihedral angle conformation populations of free monosaccharides and monosaccharide blocks within polymeric GAG molecules were calculated by a molecular dynamics approach using the GLYCAM06 force field and compared with the available NMR and quantum mechanical data. Qualitative trends for the impact of sulfation and ring conformation on the chemical shifts and proton-proton spin-spin coupling constants were obtained and discussed in terms of the potential and limitations of the computational methodology used to be complementary to NMR experiments and to assist in experimental data assignment.

Toward an accurate conformational modeling of iduronic acid

Iduronic acid (IdoA), unlike most other monosaccharides, can adopt different ring conformations, depending on the context of the molecular structure. Accurate modeling of this building block is essential for understanding the role of glycosaminoglycans and other glycoconjugates. Here, we use metadynamics to predict equilibria of (1)C(4), (4)C(1) and (2)S(O) conformations of α-L-IdoA-OMe and α-L-IdoA2S-OMe. Different schemes of scaling of atoms separated by three bonds (1-4 interaction) were tested. It was found that scaling (reduction) of 1-4 electrostatic interactions significantly changes conformational preferences toward the (4)C(1) conformation. More interestingly, scaling of 1-4 van der Waals interaction favors skew-boat conformations. This shows that a minor modification of noncovalent 1-4 interactions parameters can provide a good agreement between populations of conformers of iduronic acid in water from simulations and experiments.

Recipes for free energy calculations in biomolecular systems

During the last decade, several methods for sampling phase space and calculating various free energies in biomolecular systems have been devised or refined for molecular dynamics (MD) simulations. Thus, state-of-the-art methodology and the ever increasing computer power allow calculations that were forbidden a decade ago. These calculations, however, are not trivial as they require knowledge of the methods, insight into the system under study, and, quite often, an artful combination of different methodologies in order to avoid the various traps inherent in an unknown free energy landscape. In this chapter, we illustrate some of these concepts with two relatively simple systems, a sugar ring and proline oligopeptides, whose free energy landscapes still offer considerable challenges. In order to explore the configurational space of these systems, and to surmount the various free energy barriers, we combine three complementary methods: a nonequilibrium umbrella sampling method (adaptively biased MD, or ABMD), replica-exchange molecular dynamics (REMD), and steered molecular dynamics (SMD). In particular, ABMD is used to compute the free energy surface of a set of collective variables; REMD is used to improve the performance of ABMD, to carry out sampling in space complementary to the collective variables, and to sample equilibrium configurations directly; and SMD is used to study different transition mechanisms.

Reaction path ensemble of the B-Z-DNA transition: a comprehensive atomistic study

Since its discovery in 1979, left-handed Z-DNA has evolved from an in vitro curiosity to a challenging DNA structure with crucial roles in gene expression, regulation and recombination. A fundamental question that has puzzled researchers for decades is how the transition from B-DNA, the prevalent right-handed form of DNA, to Z-DNA is accomplished. Due to the complexity of the B–Z-DNA transition, experimental and computational studies have resulted in several different, apparently contradictory models. Here, we use molecular dynamics simulations coupled with state-of-the-art enhanced sampling techniques operating through non-conventional reaction coordinates, to investigate the B–Z-DNA transition at the atomic level. Our results show a complex free energy landscape, where several phenomena such as over-stretching, unpeeling, base pair extrusion and base pair flipping are observed resulting in interconversions between different DNA conformations such as B-DNA, Z-DNA and S-DNA. In particular, different minimum free energy paths allow for the coexistence of different mechanisms (such as zipper and stretch–collapse mechanisms) that previously had been proposed as independent, disconnected models. We find that the B–Z-DNA transition—in absence of other molecular partners—can encompass more than one mechanism of comparable free energy, and is therefore better described in terms of a reaction path ensemble.

Synthesis and scalable conversion of L-iduronamides to heparin-related di- and tetrasaccharides

A diastereomerically pure cyanohydrin, preparable on kilogram scale, is efficiently converted in one step into a novel L-iduronamide. A new regioselective acylation of this iduronamide and a new mild amide hydrolysis method mediated by amyl nitrite enables short, scalable syntheses of an L-iduronate diacetate C-4 acceptor, and also L-iduronate C-4 acceptor thioglycosides. Efficient conversions of these to a range of heparin-related gluco-ido disaccharide building blocks (various C-4 protection options) including efficient multigram access to key heparin-building block ido-thioglycoside donors are described. A 1-OAc disaccharide is converted into a heparin-related tetrasaccharide, via divergence to both acceptor and donor disaccharides. X-ray and NMR data of the 1,2-diacetyl iduronate methyl ester and the analogous iduronamide show that while both adopt (1)C(4) conformations in solution, the iduronate ester adopts the (4)C(1) conformation in solid state. An X-ray structure is also reported for the novel, (4)C(1)-conformationally locked bicyclic 1,6-anhydro iduronate lactone along with an X-ray structures of a novel distorted (4)C(1) iduronate 4,6-lactone. Deuterium labeling also provides mechanistic insight into the formation of lactone products during the novel amyl nitrite-mediated hydrolysis of iduronamide into the parent iduronic acid functionality.

Conformational flexibility of N-glycans in solution studied by REMD simulations

Protein-glycan recognition regulates a wide range of biological and pathogenic processes. Conformational diversity of glycans in solution is apparently incompatible with specific binding to their receptor proteins. One possibility is that among the different conformational states of a glycan, only one conformer is utilized for specific binding to a protein. However, the labile nature of glycans makes characterizing their conformational states a challenging issue. All-atom molecular dynamics (MD) simulations provide the atomic details of glycan structures in solution, but fairly extensive sampling is required for simulating the transitions between rotameric states. This difficulty limits application of conventional MD simulations to small fragments like di- and tri-saccharides. Replica-exchange molecular dynamics (REMD) simulation, with extensive sampling of structures in solution, provides a valuable way to identify a family of glycan conformers. This article reviews recent REMD simulations of glycans carried out by us or other research groups and provides new insights into the conformational equilibria of N-glycans and their alteration by chemical modification. We also emphasize the importance of statistical averaging over the multiple conformers of glycans for comparing simulation results with experimental observables. The results support the concept of "conformer selection" in protein-glycan recognition.

Carbohydrate force fields

Carbohydrates present a special set of challenges to the generation of force fields. First, the tertiary structures of monosaccharides are complex merely by virtue of their exceptionally high number of chiral centers. In addition, their electronic characteristics lead to molecular geometries and electrostatic landscapes that can be challenging to predict and model. The monosaccharide units can also interconnect in many ways, resulting in a large number of possible oligosaccharides and polysaccharides, both linear and branched. These larger structures contain a number of rotatable bonds, meaning they potentially sample an enormous conformational space. This article briefly reviews the history of carbohydrate force fields, examining and comparing their challenges, forms, philosophies, and development strategies. Then it presents a survey of recent uses of these force fields, noting trends, strengths, deficiencies, and possible directions for future expansion.

Are long-range structural correlations behind the aggregration phenomena of polyglutamine diseases?

We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntington's disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including - and -strands, and - and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena.

Nine neurodegenerative diseases are caused by polyglutamine (polyQ) expansions greater than a given threshold in proteins with little or no homology except for the polyQ regions. The diseases all share a common feature: the formation of polyQ aggregates and eventual neuronal death. Using molecular dynamics simulations, we have explored the conformations of polyQ peptides. Results indicate that for peptides (i.e., just above the pathological length for Hungtington's disease), the equilibrium conformations were found to consist primarily of disordered, compact structures with a non-negligible -helical and turn content. We also observed a small population of extended structures suitable for forming aggregates. For peptides below the pathological length, the population of these structures was found to be considerably lower. For longer peptides, we found evidence for long-range correlations among the dihedral angles. This correlation turns out to be short-range for the smaller polyQ peptides, and is suppressed (along with the extended structural motifs) when a C-terminal polyproline tail is added to the peptides. We believe that the existence of these long-range correlations in above-threshold polyQ peptides, along with the presence of rare motifs, could be responsible for the experimentally observed aggregation phenomena associated with polyQ diseases.

CHARMM additive all-atom force field for carbohydrate derivatives and its utility in polysaccharide and carbohydrate-protein modeling

Monosaccharide derivatives such as xylose, fucose, N-acetylglucosamine (GlcNAc), N-acetylgalactosamine (GlaNAc), glucuronic acid, iduronic acid, and N-acetylneuraminic acid (Neu5Ac) are important components of eukaryotic glycans. The present work details development of force-field parameters for these monosaccharides and their covalent connections to proteins via O-linkages to serine or threonine sidechains and via N-linkages to asparagine sidechains. The force field development protocol was designed to explicitly yield parameters that are compatible with the existing CHARMM additive force field for proteins, nucleic acids, lipids, carbohydrates, and small molecules. Therefore, when combined with previously developed parameters for pyranose and furanose monosaccharides, for glycosidic linkages between monosaccharides, and for proteins, the present set of parameters enables the molecular simulation of a wide variety of biologically-important molecules such as complex carbohydrates and glycoproteins. Parametrization included fitting to quantum mechanical (QM) geometries and conformational energies of model compounds, as well as to QM pair interaction energies and distances of model compounds with water. Parameters were validated in the context of crystals of relevant monosaccharides, as well NMR and/or x-ray crystallographic data on larger systems including oligomeric hyaluronan, sialyl Lewis X, O- and N-linked glycopeptides, and a lectin:sucrose complex. As the validated parameters are an extension of the CHARMM all-atom additive biomolecular force field, they further broaden the types of heterogeneous systems accessible with a consistently-developed force-field model.

PPII propensity of multiple-guest amino acids in a proline-rich environment

There has been considerable debate about the intrinsic PPII propensity of amino acid residues in denatured polypeptides. Experimentally, this scale is based on the behavior of guest amino acid residues placed in the middle of proline-based hosts. We have used classical molecular dynamics simulations combined with replica-exchange methods to carry out a comprehensive analysis of the conformational equilibria of proline-based host oligopeptides with multiple guest amino acids including alanine, glutamine, valine, and asparagine. The tracked structural characteristics include the secondary structural motifs based on the Ramachandran angles and the cis/trans isomerization of the prolyl bonds. In agreement with our recent study of single amino acid guests, we did not observe an intrinsic PPII propensity in any of the guest amino acids in a multiple-guest setting. Instead, the experimental results can be explained in terms of (i) the steric restrictions imposed on the C-terminal guest amino acid that is immediately followed by a proline residue and (ii) an increase in the trans content of the prolyl bonds due to the presence of guest residues. In terms of the latter, we found that the more guests added to the system, the larger the increase in the trans content of the prolyl bonds, which results in an effective increase in the PPII content of the peptide.

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.