Multidimensional umbrella sampling and replica‐exchange molecular dynamics simulations for structure prediction of transmembrane helix dimers

Structural information of a transmembrane (TM) helix dimer is useful in understanding molecular mechanisms of important biological phenomena such as signal transduction across the cell membrane. Here, we describe an umbrella sampling (US) scheme for predicting the structure of a TM helix dimer in implicit membrane using the interhelical crossing angle and the TM–TM relative rotation angles as the reaction coordinates. This scheme conducts an efficient conformational search on TM–TM contact interfaces, and its robustness is tested by predicting the structures of glycophorin A (GpA) and receptor tyrosine kinase EphA1 (EphA1) TM dimers. The nuclear magnetic resonance (NMR) structures of both proteins correspond to the global free‐energy minimum states in their free‐energy landscapes. In addition, using the landscape of GpA as a reference, we also examine the protocols of temperature replica‐exchange molecular dynamics (REMD) simulations for structure prediction of TM helix dimers in implicit membrane. A wide temperature range in REMD simulations, for example, 250–1000 K, is required to efficiently obtain a free‐energy landscape consistent with the US simulations. The interhelical crossing angle and the TM–TM relative rotation angles can be used as reaction coordinates in multidimensional US and be good measures for conformational sampling of REMD simulations. © 2013 Wiley Periodicals, Inc.     

Large‐scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high‐performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta‐cyclodextrin‐heptanoate host‐guest system in the context of one‐ and two‐dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle. © 2015 Wiley Periodicals, Inc.     

Synthesis of High‐Mannose Oligosaccharide Analogues through Click Chemistry: True Functional Mimics of Their Natural Counterparts Against Lectins?

Terminal “high‐mannose oligosaccharides” are involved in a broad range of biological and pathological processes, from sperm‐egg fusion to influenza and human immunodeficiency virus infections. In spite of many efforts, their synthesis continues to be very challenging and actually represents a major bottleneck in the field. Whereas multivalent presentation of mannopyranosyl motifs onto a variety of scaffolds has proven to be a successful way to interfere in recognition processes involving high‐mannose oligosaccharides, such constructs fail at reproducing the subtle differences in affinity towards the variety of protein receptors (lectins) and antibodies susceptible to binding to the natural ligands. Here we report a family of functional high‐mannose oligosaccharide mimics that reproduce not only the terminal mannopyranosyl display, but also the core structure and the branching pattern, by replacing some inner mannopyranosyl units with triazole rings. Such molecular design can be implemented by exploiting “click” ligation strategies, resulting in a substantial reduction of synthetic cost. The binding affinities of the new “click” high‐mannose oligosaccharide mimics towards two mannose specific lectins, namely the plant lectin concanavalin A (ConA) and the human macrophage mannose receptor (rhMMR), have been studied by enzyme‐linked lectin assays and found to follow identical trends to those observed for the natural oligosaccharide counterparts. Calorimetric determinations against ConA, and X‐ray structural data support the conclusion that these compounds are not just another family of multivalent mannosides, but real “structural mimics” of the high‐mannose oligosaccharides.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Convergence of replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) method is one of the generalized-ensemble algorithms which performs random walk in energy space and helps a system to escape from local energy traps. In this work, we studied the accuracy and efficiency of REMD by examining its ability to reproduce the results of multiple extended conventional molecular dynamics (MD) simulations and to enhance conformational sampling. Two sets of REMD simulations with different initial configurations, one from the fully extended and the other from fully helical conformations, were conducted on a fast-folding 21-amino-acid peptide with a continuum solvent model. Remarkably, the two REMD simulation sets started to converge even within 1.0 ns, despite their dramatically different starting conformations. In contrast, the conventional MD within the same time and with identical starting conformations did not show obvious signs of convergence. Excellent convergence between the REMD sets for T>300 K was observed after 14.0 ns REMD simulations as measured by the average helicity and free-energy profiles. We also conducted a set of 45 MD simulations at nine different temperatures with each trajectory simulated to 100.0 and 200.0 ns. An excellent agreement between the REMD and the extended MD simulation results was observed for T>300 K, showing that REMD can accurately reproduce long-time MD results with high efficiency. The autocorrelation times of the calculated helicity demonstrate that REMD can significantly enhance the sampling efficiency by 14.3+/-6.4, 35.1+/-0.2, and 71.5+/-20.4 times at, respectively, approximately 360, approximately 300, and approximately 275 K in comparison to the regular MD. Convergence was less satisfactory at low temperatures (T<300 K) and a slow oscillatory behavior suggests that longer simulation time was needed to reach equilibrium. Other technical issues, including choice of exchange frequency, were also examined.     

Approaches toward High‐Mannose‐Type Glycan Libraries

Asparagine‐linked (N‐linked) sugar chains are widely found in the rough endoplasmic reticulum (ER), which has attracted renewed attention because of its participation in the glycoprotein quality control process. In the ER, newly formed glycoproteins are properly folded to higher‐order structures by the action of a variety of lectin chaperones and processing enzymes and are transported into the Golgi, while terminally misfolded glycoproteins are carried into the cytosol for degradation. A group of proteins related to this system are known to recognize subtle differences in the high‐mannose‐type oligosaccharide structures of glycoproteins; however, their molecular foundations are still unclear. In order to gain a more precise understanding, our group has established a strategy for the systematic synthesis of high‐mannose‐type glycans. More recently, we have developed “top‐down” chemoenzymatic approaches that allow expeditious access to theoretically all types of high‐mannose glycans. This strategy comprehensively delivered 37 high‐mannose‐type glycans, including G1M9–M3 glycans, and opened up the possibility of the elucidation of structure–function relationships with a series of high‐mannose‐type glycans.     

Coupling of replica exchange simulations to a non-Boltzmann structure reservoir

Computing converged ensemble properties remains challenging for large biomolecules. Replica exchange molecular dynamics (REMD) can significantly increase the efficiency of conformational sampling by using high temperatures to escape kinetic traps. Several groups, including ours, introduced the idea of coupling replica exchange to a pre-converged, Boltzmann-populated reservoir, usually at a temperature higher than that of the highest temperature replica. This procedure reduces computational cost because the long simulation times needed for extensive sampling are only carried out for a single temperature. However, a weakness of the approach is that the Boltzmann-weighted reservoir can still be difficult to generate. We now present the idea of employing a non-Boltzmann reservoir, whose structures can be generated through more efficient conformational sampling methods. We demonstrate that the approach is rigorous and derive a correct statistical mechanical exchange criterion between the reservoir and the replicas that drives Boltzmann-weighted probabilities for the replicas. We test this approach on the trpzip2 peptide and demonstrate that the resulting thermal stability profile is essentially indistinguishable from that obtained using very long (>100 ns) standard REMD simulations. The convergence of this reservoir-aided REMD is significantly faster than for regular REMD. Furthermore, we demonstrate that modification of the exchange criterion is essential; REMD simulations using a standard exchange function with the non-Boltzmann reservoir produced incorrect results.     

Conformational analysis of the disaccharide methyl α‐d‐mannopyranosyl‐(1→3)‐2‐O‐acetyl‐β‐d‐mannopyranoside monohydrate

The crystal structure of methyl α‐d ‐mannopyranosyl‐(1→3)‐2‐O‐acetyl‐β‐d ‐mannopyranoside monohydrate, C₁₅H₂₆O₁₂·H₂O, ( II ), has been determined and the structural parameters for its constituent α‐d ‐mannopyranosyl residue compared with those for methyl α‐d ‐mannopyranoside. Mono‐O‐acetylation appears to promote the crystallization of ( II ), inferred from the difficulty in crystallizing methyl α‐d ‐mannopyranosyl‐(1→3)‐β‐d ‐mannopyranoside despite repeated attempts. The conformational properties of the O‐acetyl side chain in ( II ) are similar to those observed in recent studies of peracetylated mannose‐containing oligosaccharides, having a preferred geometry in which the C2—H2 bond eclipses the C=O bond of the acetyl group. The C2—O2 bond in ( II ) elongates by ～0.02 Å upon O‐acetylation. The phi (?) and psi (ψ) torsion angles that dictate the conformation of the internal O‐glycosidic linkage in ( II ) are similar to those determined recently in aqueous solution by NMR spectroscopy for unacetylated ( II ) using the statistical program MA′AT, with a greater disparity found for ψ (Δ = ～16°) than for ? (Δ = ～6°).     

DIRECT‐ID: An automated method to identify and quantify conformational variations—application to β2‐adrenergic GPCR

The conformational dynamics of a macromolecule can be modulated by a number of factors, including changes in environment, ligand binding, and interactions with other macromolecules, among others. We present a method that quantifies the differences in macromolecular conformational dynamics and automatically extracts the structural features responsible for these changes. Given a set of molecular dynamics (MD) simulations of a macromolecule, the norms of the differences in covariance matrices are calculated for each pair of trajectories. A matrix of these norms thus quantifies the differences in conformational dynamics across the set of simulations. For each pair of trajectories, covariance difference matrices are parsed to extract structural elements that undergo changes in conformational properties. As a demonstration of its applicability to biomacromolecular systems, the method, referred to as DIRECT‐ID, was used to identify relevant ligand‐modulated structural variations in the β₂‐adrenergic (β₂AR) G‐protein coupled receptor. Micro‐second MD simulations of the β₂AR in an explicit lipid bilayer were run in the apo state and complexed with the ligands: BI‐167107 (agonist), epinephrine (agonist), salbutamol (long‐acting partial agonist), or carazolol (inverse agonist). Each ligand modulated the conformational dynamics of β₂AR differently and DIRECT‐ID analysis of the inverse‐agonist vs. agonist‐modulated β₂AR identified residues known through previous studies to selectively propagate deactivation/activation information, along with some previously unidentified ligand‐specific microswitches across the GPCR. This study demonstrates the utility of DIRECT‐ID to rapidly extract functionally relevant conformational dynamics information from extended MD simulations of large and complex macromolecular systems. © 2015 Wiley Periodicals, Inc.     

Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics

Histone tails are highly flexible N- or C-terminal protrusions of histone proteins which facilitate the compaction of DNA into dense superstructures known as chromatin. On a molecular scale histone tails are polyelectrolytes with high degree of conformational disorder which allows them to function as biomolecular "switches", regulating various genetic processes. Unfortunately, their intrinsically disordered nature creates obstacles for comprehensive experimental investigation of both the structural and dynamical aspects of histone tails, because of which their conformational behaviors are still not well understood. In this work we have carried out ～3 microsecond long all atom replica exchange molecular dynamics (REMD) simulations for each of four histone tails, H4, H3, H2B, and H2A, and probed their intrinsic conformational preferences. Our subsequent free energy landscape analysis demonstrated that most tails are not fully disordered, but show distinct conformational organization, containing specific flickering secondary structural elements. In particular, H4 forms β-hairpins, H3 and H2B adopt α-helical elements, while H2A is fully disordered. We rationalized observed patterns of conformational dynamics of various histone tails using ideas from physics of polyelectrolytes and disordered systems. We also discovered an intriguing re-entrant contraction-expansion of the tails upon heating, which is caused by subtle interplay between ionic screening and chain entropy.     

Efficiency of tabu‐search‐based conformational search algorithms

Efficient conformational search or sampling approaches play an integral role in molecular modeling, leading to a strong demand for even faster and more reliable conformer search algorithms. This article compares the efficiency of a molecular dynamics method, a simulated annealing method, and the basin hopping (BH) approach (which are widely used in this field) with a previously suggested tabu‐search‐based approach called gradient only tabu search (GOTS). The study emphasizes the success of the GOTS procedure and, more importantly, shows that an approach which combines BH and GOTS outperforms the single methods in efficiency and speed. We also show that ring structures built by a hydrogen bond are useful as starting points for conformational search investigations of peptides and organic ligands with biological activities, especially in structures that contain multiple rings. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Dependency of ligand free energy landscapes on charge parameters and solvent models

We performed replica-exchange molecular dynamics (REMD) simulations of six ligands to examine the dependency of their free energy landscapes on charge parameters and solvent models. Six different charge parameter sets for each ligand were first generated by RESP and AM1-BCC methods using three different conformations independently. RESP charges showed some conformational dependency. On the other hand, AM1-BCC charges did not show conformational dependency and well reproduced the overall trend of RESP charges. The free energy landscapes obtained from the REMD simulations of ligands in vacuum, Generalized-Born (GB), and TIP3P solutions were then analyzed. We found that even small charge differences can produce qualitatively different landscapes in vacuum condition, but the differences tend to be much smaller under GB and TIP3P conditions. The simulations in the GB model well reproduced the landscapes in the TIP3P model using only a fraction of the computational cost. The protein-bound ligand conformations were rarely the global minimum states, but similar conformations were found to exist in aqueous solution without proteins in regions close to the global minimum, local minimum or intermediate states.     

Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Self‐association promoted conformational transition of (3R,4S,8R,9R)‐9‐[(3,5‐bis(trifluoromethyl)phenyl))‐thiourea](9‐deoxy)‐epi‐cinchonine

The conformational diversity of the (3R,4S,8R,9R)‐9‐[(3,5‐bis(trifluoromethyl)phenyl))‐thiourea](9‐deoxy)‐epi‐cinchonine organocatalyst is discussed. Low‐temperature NMR experiments confirmed a self‐association process, which promotes the quinoline rotation between two intramolecularly hydrogen‐bonded monomeric conformers of the catalyst. The balanced population of the coexisting monomeric and dimeric species allowed us to conduct a structural study of a rather complex conformational dynamics of the pure catalyst. The study is extended by a comparison with other members of the bifunctional amine‐thiourea organocatalyst family. Changes in the molecular structure of the catalysts influence the interplay between intra‐ and intermolecular hydrogen bonding, and yield different extent of catalyst self‐association. By assessing the conformation of the individual states, we established the thermodynamic model of a self‐association promoted conformational transition. Copyright © 2009 John Wiley & Sons, Ltd.     

Repeated‐annealing sampling combined with multicanonical algorithm for conformational sampling of bio‐molecules

A novel conformational sampling method (repeated‐annealing sampling method) is proposed to execute an efficient conformational sampling at a reasonable computational cost. In the method, a molecular dynamics simulation is done with repeating an elemental process. An elemental process consists of four subprocesses: high‐temperature run, annealing, room‐temperature run, and fast heating. The sampling is done automatically according to a temperature‐control schedule. The room‐temperature run is treated with the multicanonical algorithm, and the other subprocesses are done with the conventional molecular dynamics algorithm. The method, differing from the generalized ensemble methods recently developed, is not warrantable to give the canonical ensemble because of the nonphysical process in the annealing. However, we observed that the slower the annealing and the longer the high‐temperature run, the closer the sampled conformations to those of the canonical ensemble. A test was performed with tri‐N‐acetyl‐D ‐glucosamine in vacuo, and the results were compared with those from the conventional multicanonical simulation. Not only the reweighted canonical distribution function but also the energy landscape were in good agreement with those from the conventional multicanonical simulation. The potential of mean force also showed a fairly good agreement with that from the conventional multicanonical simulation in the room‐temperature region. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1098–1106, 2001     

Construction of a High‐Mannose‐Type Glycan Library by a Renewed Top‐Down Chemo‐Enzymatic Approach

A comprehensive method for the construction of a high‐mannose‐type glycan library by systematic chemo‐enzymatic trimming of a single Man9‐based precursor was developed. It consists of the chemical synthesis of a non‐natural tridecasaccharide precursor, the orthogonal demasking of the non‐reducing ends, and trimming by glycosidases, which enabled a comprehensive synthesis of high‐mannose‐type glycans in their mono‐ or non‐glucosylated forms. It employed glucose, isopropylidene, and N‐acetylglucosamine groups for blocking the A‐, B‐, and C‐arms, respectively. After systematic trimming of the precursor, thirty‐seven high‐mannose‐type glycans were obtained. The power of the methodology was demonstrated by the enzymatic activity of human recombinant N‐acetylglucosaminyltransferase‐I toward M7–M3 glycans, clarifying the substrate specificity in the context of high‐mannose‐type glycans.     

Replica exchange molecular dynamics simulations of amyloid peptide aggregation

The replica exchange molecular dynamics (REMD) approach is applied to four oligomeric peptide systems. At physiologically relevant temperature values REMD samples conformation space and aggregation transitions more efficiently than constant temperature molecular dynamics (CTMD). During the aggregation process the energetic and structural properties are essentially the same in REMD and CTMD. A condensation stage toward disordered aggregates precedes the beta-sheet formation. Two order parameters, borrowed from anisotropic fluid analysis, are used to monitor the aggregation process. The order parameters do not depend on the peptide sequence and length and therefore allow to compare the amyloidogenic propensity of different peptides     

Observing Single‐Molecule Dynamics at Millimolar Concentrations

Single‐molecule fluorescence microscopy is a powerful tool for revealing chemical dynamics and molecular association mechanisms, but has been limited to low concentrations of fluorescent species and is only suitable for studying high affinity reactions. Here, we combine nanophotonic zero‐mode waveguides (ZMWs) with fluorescence resonance energy transfer (FRET) to resolve single‐molecule association dynamics at up to millimolar concentrations of fluorescent species. This approach extends the resolution of molecular dynamics to >100‐fold higher concentrations, enabling observations at concentrations relevant to biological and chemical processes, and thus making single‐molecule techniques applicable to a tremendous range of previously inaccessible molecular targets. We deploy this approach to show that the binding of cGMP to pacemaking ion channels is weakened by a slower internal conformational change.     

Characterization of conformational equilibria through Hamiltonian and temperature replica-exchange simulations: assessing entropic and environmental effects

Molecular dynamics simulations based on the replica-exchange framework (REMD) are emerging as a useful tool to characterize the conformational variability that is intrinsic to most chemical and biological systems. In this work, it is shown that a simple extension of the replica-exchange method, known as Hamiltonian REMD, greatly facilitates the characterization of conformational equilibria across large energetic barriers, or in the presence of substantial entropic effects, overcoming some of the difficulties of REMD based on temperature alone. In particular, a comparative assessment of the HREMD and TREMD approaches was made, through computation of the gas-phase free-energy difference between the so-called D(2d) and S(4) states of tetrabutylammonium (TBA), an ionic compound of frequently used in biophysical studies of ion channels. Taking advantage of the greater efficiency of the HREMD scheme, the conformational equilibrium of TBA was characterized in a variety of conditions. Simulation of the gas-phase equilibrium in the 100-300 K range allowed us to compute the entropy difference between these states as well as to describe its temperature dependence. Through HREMD simulations of TBA in a water droplet, the effect of solvation on the conformational equilibrium was determined. Finally, the equilibrium of TBA in the context of a simplified model of the binding cavity of the KcsA potassium channel was simulated, and density maps for D(2d) and S(4) states analogous to those derived from X-ray crystallography were constructed. Overall, this work illustrates the potential of the HREMD approach in the context of computational drug design, ligand-receptor structural prediction and more generally, molecular recognition, where one of the most challenging issues remains to account for conformational flexibility as well for the solvation and entropic effects thereon.     

Identifying Protein Conformational Dynamics Using Spin‐label ESR

Spin‐label electron spin resonance (ESR) has emerged as a powerful tool to characterize protein dynamics. One recent advance is the development of ESR for resolving dynamical components that occur or coexist during a biological process. It has been applied to study the complex structural and dynamical aspects of membranes and proteins, such as conformational changes in protein during translocation from cytosol to membrane, conformational exchange between equilibria in response to protein‐protein and protein‐ligand interactions in either soluble or membrane environments, protein oligomerization, and temperature‐ or hydration‐dependent protein dynamics. As these topics are challenging but urgent for understanding the function of a protein on the molecular level, the newly developed ESR methods to capture individual dynamical components, even in low‐populated states, have become a great complement to other existing biophysical tools.