Long timescale simulations

Using High-Throughput Molecular Dynamics Simulation to Enhance the Computational Design of Kemp Elimination Enzymes

Computational enzyme design has been successfully applied to identify new alternatives to natural enzymes for the biosynthesis of important compounds. However, the moderate catalytic activities of de novo designed enzymes indicate that the modeling accuracy of current computational enzyme design methods should be improved. Here, high-throughput molecular dynamics simulations were used to enhance computational enzyme design, thus allowing the identification of variants with higher activities in silico. Different time schemes of high-throughput molecular dynamics simulations were tested to identify the catalytic features of evolved Kemp eliminases. The 20 × 1 ns molecular dynamics simulation scheme was sufficiently accurate and computationally viable to screen the computationally designed massive variants of Kemp elimination enzymes. The developed hybrid computational strategy was used to redesign the most active Kemp eliminase, HG3.17, and five variants were generated and experimentally confirmed to afford higher catalytic efficiencies than that of HG3.17, with one double variant (D52Q/A53S) exhibiting a 55% increase. The hybrid computational enzyme design strategy is general and computationally economical, with which we anticipate the efficient creation of practical enzymes for industrial biocatalysis.

High Energy Channeling and Malleable Transition States: Molecular Dynamics Simulations and Free Energy Landscapes for the Thermal Unfolding of Protein U1A and 13 Mutants

The spliceosome protein U1A is a prototype case of the RNA recognition motif (RRM) ubiquitous in biological systems. The in vitro kinetics of the chemical denaturation of U1A indicate that the unfolding of U1A is a two-state process but takes place via high energy channeling and a malleable transition state, an interesting variation of typical two-state behavior. Molecular dynamics (MD) simulations have been applied extensively to the study of two-state unfolding and folding of proteins and provide an opportunity to obtain a theoretical account of the experimental results and a molecular model for the transition state ensemble. We describe herein all-atom MD studies including explicit solvent of up to 100 ns on the thermal unfolding (UF) of U1A and 13 mutants. Multiple MD UF trajectories are carried out to ensure accuracy and reproducibility. A vector representation of the MD unfolding process in RMSD space is obtained and used to calculate a free energy landscape for U1A unfolding. A corresponding MD simulation and free energy landscape for the protein CI2, well known to follow a simple two state folding/unfolding model, is provided as a control. The results indicate that the unfolding pathway on the MD calculated free energy landscape of U1A shows a markedly extended transition state compared with that of CI2. The MD results support the interpretation of the observed chevron plots for U1A in terms of a high energy, channel-like transition state. Analysis of the MDUF structures shows that the transition state ensemble involves microstates with most of the RRM secondary structure intact but expanded by ~14% with respect to the radius of gyration. Comparison with results on a prototype system indicates that the transition state involves an ensemble of molten globule structures and extends over the region of ~1-35 ns in the trajectories. Additional MDUF simulations were carried out for 13 U1A mutants, and the calculated φ-values show close accord with observed results and serve to validate our methodology.

gmx_MMPBSA: A New Tool to Perform End-State Free Energy Calculations with GROMACS

Molecular mechanics/Poisson-Boltzmann (Generalized-Born) surface area is one of the most popular methods to estimate binding free energies. This method has been proven to balance accuracy and computational efficiency, especially when dealing with large systems. As a result of its popularity, several programs have been developed for performing MM/PB(GB)SA calculations within the GROMACS community. These programs, however, present several limitations. Here we present gmx_MMPBSA, a new tool to perform end-state free energy calculations from GROMACS molecular dynamics trajectories. gmx_MMPBSA provides the user with several options, including binding free energy calculations with different solvation models (PB, GB, or 3D-RISM), stability calculations, computational alanine scanning, entropy corrections, and binding free energy decomposition. Noteworthy, several promising methodologies to calculate relative binding free energies such as alanine scanning with variable dielectric constant and interaction entropy have also been implemented in gmx_MMPBSA. Two additional tools-gmx_MMPBSA_test and gmx_MMPBSA_ana-have been integrated within gmx_MMPBSA to improve its usability. Multiple illustrating examples can be accessed through gmx_MMPBSA_test, while gmx_MMPBSA_ana provides fast, easy, and efficient access to different graphics plotted from gmx_MMPBSA output files. The latest version (v1.4.3, 26/05/2021) is available free of charge (documentation, test files, and tutorials included) at https://github.com/Valdes-Tresanco-MS/gmx_MMPBSA.

Computationally efficient and accurate enantioselectivity modeling by clusters of molecular dynamics simulations

Computational approaches could decrease the need for the laborious high-throughput experimental screening that is often required to improve enzymes by mutagenesis. Here, we report that using multiple short molecular dynamics (MD) simulations makes it possible to accurately model enantioselectivity for large numbers of enzyme-substrate combinations at low computational costs. We chose four different haloalkane dehalogenases as model systems because of the availability of a large set of experimental data on the enantioselective conversion of 45 different substrates. To model the enantioselectivity, we quantified the frequency of occurrence of catalytically productive conformations (near attack conformations) for pairs of enantiomers during MD simulations. We found that the angle of nucleophilic attack that leads to carbon-halogen bond cleavage was a critical variable that limited the occurrence of productive conformations; enantiomers for which this angle reached values close to 180° were preferentially converted. A cluster of 20-40 very short (10 ps) MD simulations allowed adequate conformational sampling and resulted in much better agreement to experimental enantioselectivities than single long MD simulations (22 ns), while the computational costs were 50-100 fold lower. With single long MD simulations, the dynamics of enzyme-substrate complexes remained confined to a conformational subspace that rarely changed significantly, whereas with multiple short MD simulations a larger diversity of conformations of enzyme-substrate complexes was observed.

Finding semirigid domains in biomolecules by clustering pair-distance variations

Dynamic variations in the distances between pairs of atoms are used for clustering subdomains of biomolecules. We draw on a well-known target function for clustering and first show mathematically that the assignment of atoms to clusters has to be crisp, not fuzzy, as hitherto assumed. This reduces the computational load of clustering drastically, and we demonstrate results for several biomolecules relevant in immunoinformatics. Results are evaluated regarding the number of clusters, cluster size, cluster stability, and the evolution of clusters over time. Crisp clustering lends itself as an efficient tool to locate semirigid domains in the simulation of biomolecules. Such domains seem crucial for an optimum performance of subsequent statistical analyses, aiming at detecting minute motional patterns related to antigen recognition and signal transduction.

Molecular dynamics modeling of the sub-THz vibrational absorption of thioredoxin from E. coli

Sub-terahertz (THz) vibrational modes of the protein thioredoxin in a water environment were simulated using molecular dynamics (MD) in order to find the conditions needed for simulation convergence, improve the correlation between experimental and simulated absorption frequencies, and ultimately enhance the predictive capabilities of computational modeling. Thioredoxin from E. coli was used as a model molecule for protocol development and to optimize the simulation parameters. The empirically parameterized software packages Amber 8 and 10 were used in this work. Using atomic trajectories from the constant energy and volume MD simulations, thioredoxin's sub-THz vibrational spectra and absorption coefficients were calculated in a quasi-harmonic approximation. An optimal production run length ~100 ps was found, in agreement with experimental data on thioredoxin relaxation dynamics. At the same time, a new procedure was developed for averaging correlation matrices of atomic coordinates in MD simulations. In particular, the open source package ptraj was edited to improve a matrix-analyzing function. Averaging only six matrices gave much more consistent results, with absorption peak intensities exceeding those from the individual spectra and a rather good correlation between simulated vibrational frequencies and experimental data.

Substrate binding process and mechanistic functioning of type 1 11β-hydroxysteroid dehydrogenase from enhanced sampling methods

In humans, type 1 11β-hydroxysteroid dehydrogenase (11β-HSD-1) plays a key role in the regulation of the glucocorticoids balance by converting the inactive hormone cortisone into cortisol. Numerous functional aspects of 11β-HSD-1 have been understood thanks to the availability at the Worldwide Protein Data Bank of a number of X-ray structures of the enzyme either alone or in complex with inhibitors, and to several experimental data. However at present, a complete description of the dynamic behaviour of 11β-HSD-1 upon substrate binding is missing. To this aim we firstly docked cortisone into the catalytic site of 11β-HSD-1 (both wild type and Y177A mutant), and then we used steered molecular dynamics and metadynamics to simulate its undocking. This methodology helped shedding light at molecular level on the complex relationship between the enzyme and its natural substrate. In particular, the work highlights a) the reason behind the functional dimerisation of 11β-HSD-1, b) the key role of Y177 in the cortisone binding event, c) the fine tuning of the active site degree of solvation, and d) the role of the S228-P237 loop in ligand recognition.

Multiple molecular dynamics simulations of TEM beta-lactamase: dynamics and water binding of the omega-loop

The Omega-loop of TEM beta-lactamase is involved in substrate recognition and catalysis. Its dynamical properties and interaction with water molecules were investigated by performing multiple molecular dynamics simulations of up to 50 ns. Protein flexibility was assessed by calculating the root mean-square fluctuations and the generalized order parameter, S(2). The residues in secondary structure elements are highly ordered, whereas loop regions are more flexible, which is in agreement with previous experimental observations. Interestingly, the Omega-loop (residues 161-179) is rigid with order parameters similar to secondary structure elements, with the exception of the tip of the loop (residues 173-177) that has a considerably higher flexibility and performs an opening and closing motion on the 50-ns timescale. The rigidity of the main part of the Omega-loop is mediated by stabilizing and highly conserved water bridges inside a cavity lined by the Omega-loop and residues 65-69 of the protein core. In contrast, the flexible tip of the Omega-loop lacks these interactions. Hydration of the cavity and exchange of the water molecules with the bulk solvent occurs via two pathways: the flexible tip that serves as a door to the cavity, and a temporary water channel involving the side chain of Arg(164).

Computational identification of slow conformational fluctuations in proteins

Conformational flexibility of proteins has been linked to their designated functions. Slow conformational fluctuations occurring at the microsecond to millisecond time scale, in particular, have recently attracted considerable interest in connection to the mechanism of enzyme catalysis. Computational methods are providing valuable insights into the connection between protein structure, flexibility, and function. In this report, we present studies on identification and characterization of microsecond flexibility of ubiquitin, based on quasi-harmonic analysis (QHA) and normal-mode analysis (NMA). The results indicate that the slowest 10 QHA modes, computed from the 0.5 mus molecular dynamics ensemble, contribute over 78% of all motions. The identified slow movements show over 75% similarity with the conformational fluctuations observed in nuclear magnetic resonance ensemble and also agree with displacements in the set of X-ray structures. The slowest modes show high flexibility in the beta1-beta2, alpha1-beta3, and beta3-beta4 loop regions, with functional implications in the mechanism of binding other proteins. NMA of ubiquitin structures was not able to reproduce the long time scale fluctuations, as they were found to strongly depend on the reference structures. Further, conformational fluctuations coupled to the cis/trans isomerization reaction catalyzed by the enzyme cyclophilin A (CypA), occurring at the microsecond to millisecond time scale, have also been identified and characterized on the basis of QHA of conformations sampled along the reaction pathway. The results indicate that QHA covers the same conformational landscape as the experimentally observed CypA flexibility. Overall, the identified slow conformational fluctuations in ubiquitin and CypA indicate that the intrinsic flexibility of these proteins is closely linked to their designated functions.

Coarse-grained ions without charges: reproducing the solvation structure of NaCl in water using short-ranged potentials

A coarse-grained model of NaCl in water is presented where the ions are modeled without charge to avoid computationally challenging electrostatics. A monatomic model of water [V. Molinero and E. B. Moore, J. Phys. Chem. B 113, 4008 (2009)] is used as the basis for this coarse-grain approach. The ability of Na(+) to disrupt the native tetrahedral arrangement of water molecules, and of Cl(-) to integrate within this organization, is preserved in this mW-ion model through parametrization focused on water's solvation of these ions. This model successfully reproduces the structural effect of ions on water, referenced to observations from experiments and atomistic molecular dynamics simulations, while using extremely short-ranged potentials. Without Coulomb interactions the model replicates details of the ion-water structure such as distinguishing contact and solvent-separated ion pairs and the free energy barriers between them. The approach of mimicking ionic effects with short-ranged interactions results in performance gains of two orders of magnitude compared to Ewald methods. Explored over a broad range of salt concentration, the model reproduces the solvation structure and trends of diffusion relative to atomistic simulations and experimental results. The functional form of the mW-ion model can be parametrized to represent other electrolytes. With increased computational efficiency and reliable structural fidelity, this model promises to be an asset for accessing significantly longer simulation time scales with an explicit solvent in a coarse-grained system involving, for example, polyelectrolytes such as proteins, nucleic acids, and fuel-cell membranes.

Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II

In the past decade, new theoretical approaches have been developed to determine, predict and understand the struc-ture of chemical compounds. The central element of these methods has been the investigation of the energy landscape of chemical systems. Applications range from extended crystalline and amorphous compounds over clusters and molecular crystals to proteins. In this review, we are going to give an introduction to energy landscapes and methods for their investigation, together with a number of examples. These include structure prediction of extended and mo-lecular crystals, structure prediction and folding of proteins, structure analysis of zeolites, and structure determination of crystals from powder diffraction data.

Application of Multiplexed Replica Exchange Molecular Dynamics to the UNRES Force Field: Tests with alpha and alpha+beta Proteins

The replica exchange (RE) method is increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. Recently, we implemented the united-residue UNRES force field for mesoscopic MD. Initial results from UNRES MD simulations show that we are able to simulate folding events that take place in a microsecond or even a millisecond time scale. To speed up the search further, we applied the multiplexing replica exchange molecular dynamics (MREMD) method. The multiplexed variant (MREMD) of the RE method, developed by Rhee and Pande, differs from the original RE method in that several trajectories are run at a given temperature. Each set of trajectories run at a different temperature constitutes a layer. Exchanges are attempted not only within a single layer but also between layers. The code has been parallelized and scales up to 4000 processors. We present a comparison of canonical MD, REMD, and MREMD simulations of protein folding with the UNRES force-field. We demonstrate that the multiplexed procedure increases the power of replica exchange MD considerably and convergence of the thermodynamic quantities is achieved much faster.

Dynamic properties of pH-dependent structural organization of the amyloidogenic beta-protein (1-40)

The structural organization of the amyloidogenic beta-protein containing 40 amino acid residues (Abeta40) was studied by the high temperature molecular dynamics simulations in the acidic (pH approximately 3) and basic (pH approximately 8) pH regions. The obtained data suggest that the central Ala21-Gly29 segment of Abeta40 can adopt folded and partially unfolded structures. At the basic pH, this segment forms folded structures stabilized by electrostatic interactions and hydrogen bonds. At the acidic pH, it forms partially unfolded structures. Two other segments flanking to the central segment exhibit the propensity to adopt unstable interconverting alpha-helical, 3(10)-helical and turn-like structures. One of these segments is comprised of the Ala30-Val36 residues at both of the considered pHs. The second segment is comprised of the Glu11-Phe20 at the basic pH and of the Glu11-Val24 residues at the acidic pHs. The revealed pH-dependent structuration of the Abeta40 allowed us to suggest a possible scenario for initial Abeta aggregation. According to this scenario, the occurrence of the partially unfolded states of the Ala21-Gly29 segment plays main role in the Abeta oligomerization process.

Identifying stabilizing key residues in proteins using interresidue interaction energy matrix

We are proposing an interresidue interaction energy map (IEM)--a new tool for protein structure analysis and protein bioinformatics. This approach employs the sum of pair-wise interaction energies of a particular residue as a measure of its structural importance. We will show that the IEM can serve as a means for identifying key residues responsible for the stability of a protein. Our method can be compared with the interresidue contact map but has the advantage of weighting the contacts by the stabilization energy content which they bring to the protein structure. For the theoretical adjustment of the proposed method, we chose the Trp-cage mini protein as a model system to compare a spectrum of computational methods ranging from the ab initio MP2 level through the DFT method to empirical force-field methods. The IEM method correctly identifies Tryptophane 6 as the key residue in the Trp-cage. The other residues with the highest stabilizing contributions correspond to the structurally important positions in the protein. We have further tested our method on the Trp2Cage miniprotein--a P12W mutant of the Trp-cage and on two proteins from the rubredoxin family that differ in their thermostability. Our method correctly identified the thermodynamically more stable variants in both cases and therefore can also be used as a tool for the relative measurement of protein stability. Finally, we will point out the important role played by dispersion energy, which contributes significantly to the total stabilization energy and whose role in aromatic pairs is clearly dominant. Surprisingly, the dispersion energy plays an even more important role in the interaction of prolines with aromatic systems.

Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

To provide evidence for the interpretation of temperature-dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz-Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One-dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's beta-sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable beta-strands I and II and those of the less stable strands III-V. Although the original ME model successfully captures folding features of zipper-like one-dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the beta-strands III-V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T-jump experiment at high temperature. The calculation also reports a high stability for the alpha-helix of ubiquitin.

Stabilization of the Catalytic Thiolate in a Mammalian Glutaredoxin: Structure, Dynamics and Electrostatics of Reduced Pig Glutaredoxin and its Mutants

The variety of functions performed by proteins of the thioredoxin superfamily, including glutaredoxins, involves the wide range of redox potential associated with the -Cys-X-X-Cys- motif found in their active sites. The determinants of these differences in redox potential are still obscure. A better understanding requires a detailed characterization of the reduced state of these enzymes, especially because the lowered pK(a) of the reduced N-terminal active-site cysteine is a key feature of these enzymes' chemistry, including their redox potential. Analysis of the factors controlling this pK(a) is complicated by the apparent structural heterogeneity of the reduced active sites across glutaredoxins. In this family, pig glutaredoxin (pGrx) was one of the first to be functionally characterized, including some intriguing mutagenesis data, but a structure of its reduced state has been lacking. We used long molecular dynamics simulations and electrostatic calculations to analyze the structure, dynamics and electrostatics of reduced pGrx and some of its mutants. Comparison with experimental data is drawn whenever possible. It is shown that a dynamic model is essential to capture the structural properties of the cationic side-chains around the -Cys22-Pro23-Phe24-Cys25- sequence in the pGrx active site. Examples include Arg26, which can swing to stack on this sequence, and Lys19 which can contact the thiolate. However, contrary to a commonly held hypothesis, these cationic side-chains provide little stabilization for the thiolate, implying that they affect the enzymatic activity via other mechanisms. The pK(a) value of nucleophilic cysteine 22 (pK(a)(22)) is dominated by local hydrogen-bonds, formed only in a well-defined active-site conformation, supported by a comparison between the calculated and experimental values of pK(a)(22). The edge of the aromatic ring of Phe24 is polar enough to contribute to stabilize the thiolate, consistent with the conserved aromatic side-chain at this position in the glutaredoxin motif. The locality and directionality of the hydrogen bonds in the active site suffice to explain the vast difference between the pK(a) values of its two cysteine residues. A control of the cysteine pK(a) values by local hydrogen bonds implies that the peripheral ionized side-chains can evolve independently of the maintenance of these pK(a) values, maybe guided instead by substrate recognition. Comparison with other glutaredoxins indicates that the calculated pK(a) values of the N-terminal cysteine are better conserved than those of the C-terminal cysteine. Overall, a methodological strategy to systematically compare all reduced enzymes of this family emerges.

On the characterization of protein native state ensembles

Describing and understanding the biological function of a protein requires a detailed structural and thermodynamic description of the protein's native state ensemble. Obtaining such a description often involves characterizing equilibrium fluctuations that occur beyond the nanosecond timescale. Capturing such fluctuations remains nontrivial even for very long molecular dynamics and Monte Carlo simulations. We propose a novel multiscale computational method to exhaustively characterize, in atomistic detail, the protein conformations constituting the native state with no inherent timescale limitations. Applications of this method to proteins of various folds and sizes show that thermodynamic observables measured as averages over the native state ensembles obtained by the method agree remarkably well with nuclear magnetic resonance data that span multiple timescales. By characterizing equilibrium fluctuations at atomistic detail over a broad range of timescales, from picoseconds to milliseconds, our method offers to complement current simulation techniques and wet-lab experiments and can impact our understanding and description of the relationship between protein flexibility and function.

Dynamics of lysozyme structure network: probing the process of unfolding

Recently we showed that the three-dimensional structure of proteins can be investigated from a network perspective, where the amino acid residues represent the nodes in the network and the noncovalent interactions between them are considered for the edge formation. In this study, the dynamical behavior of such networks is examined by considering the example of T4 lysozyme. The equilibrium dynamics and the process of unfolding are followed by simulating the protein at 300 K and at higher temperatures (400 K and 500 K), respectively. The snapshots of the protein structure from the simulations are represented as protein structure networks in which the strength of the noncovalent interactions is considered an important criterion in the construction of edges. The profiles of the network parameters, such as the degree distribution and the size of the largest cluster (giant component), were examined as a function of interaction strength at different temperatures. Similar profiles are seen at all the temperatures. However, the critical strength of interaction (Icritical) and the size of the largest cluster at all interaction strengths shift to lower values at 500 K. Further, the folding/unfolding transition is correlated with contacts evaluated at Icritical and with the composition of the top large clusters obtained at interaction strengths greater than Icritical. Finally, the results are compared with experiments, and predictions are made about the residues, which are important for stability and folding. To summarize, the network analysis presented in this work provides insights into the details of the changes occurring in the protein tertiary structure at the level of amino acid side-chain interactions, in both the equilibrium and the unfolding simulations. The method can also be employed as a valuable tool in the analysis of molecular dynamics simulation data, since it captures the details at a global level, which may elude conventional pairwise interaction analysis.

Evolution of conformational changes in the dynamics of small biological molecules: a hybrid MD/RRK approach

The dynamics of long timescale evolution of conformational changes in small biological molecules is described by a hybrid molecular dynamics/RRK algorithm. The approach employs classical trajectories for transitions between adjacent structures separated by a low barrier, and the classical statistical RRK approximation when the barrier involved is high. In determining the long-time dynamics from an initial structure to a final structure of interest, an algorithm is introduced for determining the most efficient pathways (sequence of the intermediate conformers). This method uses the Dijkstra algorithm for finding optimal paths on networks. Three applications of the method using an AMBER force field are presented: a detailed study of conformational transitions in a blocked valine dipeptide; a multiple reaction path study of the blocked valine tripeptide; and the evolution in time from the beta hairpin to alpha helix structure of a blocked alanine hexapeptide. Advantages and limitations of the method are discussed in light of the results.

Thermal Denaturing of Mutant Lysozyme with Both the OPLSAA and the CHARMM Force Fields

Biomolecular simulations enabled by massively parallel supercomputers such as BlueGene/L promise to bridge the gap between the currently accessible simulation time scale and the experimental time scale for many important protein folding processes. In this study, molecular dynamics simulations were carried out for both the wild-type and the mutant hen lysozyme (TRP62GLY) to study the single mutation effect on lysozyme stability and misfolding. Our thermal denaturing simulations at 400-500 K with both the OPLSAA and the CHARMM force fields show that the mutant structure is indeed much less stable than the wild-type, which is consistent with the recent urea denaturing experiment (Dobson et al. Science 2002, 295, 1719-1722; Nature 2003, 424, 783-788). Detailed results also reveal that the single mutation TRP62GLY first induces the loss of native contacts in the beta-domain region of the lysozyme protein at high temperatures, and then the unfolding process spreads into the alpha-domain region through Helix C. Even though the OPLSAA force field in general shows a more stable protein structure than does the CHARMM force field at high temperatures, the two force fields examined here display qualitatively similar results for the misfolding process, indicating that the thermal denaturing of the single mutation is robust and reproducible with various modern force fields.

Relating Protein Motion to Catalysis

This review examines the linkage between protein conformational motions and enzyme catalysis. The fundamental issues related to this linkage are probed in the context of two enzymes that catalyze hydride transfer, namely dihydrofolate reductase and liver alcohol dehydrogenase. The extensive experimental and theoretical studies addressing the role of protein conformational changes in these enzyme reactions are summarized. Evidence is presented for a network of coupled motions throughout the protein fold that facilitate the chemical reaction. This network is comprised of fast thermal motions that are in equilibrium as the reaction progresses along the reaction coordinate and that lead to slower equilibrium conformational changes conducive to the chemical reaction.

Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: deciphering the effect of intermolecular interactions on computational structure prediction of the p27Kip1 protein bound to the cyclin A-cyclin-dependent kinase 2 complex

The relationship between folding mechanism coupled to binding and structure prediction of the tertiary complexes is studied for the p27(Kip) (1) protein which has an intrinsically disordered unbound form and undergoes a functional folding transition during complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Hierarchy of p27(Kip1) structural loss determined in our earlier studies from temperature-induced Monte Carlo simulations and subsequent characterization of the transition state ensemble (TSE) for the folding reaction have shown that simultaneous ordering of the p27(Kip1) native intermolecular interface for the beta-hairpin and beta-strand secondary structure elements is critical for nucleating a rapid kinetic transition to the native tertiary complex. In the present study, we investigate the effect of forming specific intermolecular interactions on structure prediction of the p27(Kip1) tertiary complex. By constraining different secondary structure elements of p27(Kip1) in their native bound conformations and conducting multiple simulated annealing simulations, we analyze differences in the success rate of predicting the native structure of p27(Kip1) in the tertiary complex. In accordance with the nucleation-condensation mechanism, we have found that further stabilization of the native intermolecular interface for the beta-hairpin and beta-strand elements of p27(Kip1), that become ordered in the TSE, but are hardly populated in the unbound state, results in a consistent acquisition of the native bound structure. Conversely, the excessive stablization of the local secondary structure elements, which are rarely detected in the TSE, has a detrimental effect on convergence to the native bound structure.

Kinetics and thermodynamics of type VIII beta-turn formation: a CD, NMR, and microsecond explicit molecular dynamics study of the GDNP tetrapeptide

We report an experimental and theoretical study on type VIII beta-turn using a designed peptide of sequence GDNP. CD and NMR studies reveal that this peptide exists in equilibrium between type VIII beta-turn and extended conformations. Extensive MD simulations give a description of the free energy landscape of the peptide in which we retrieve the same two main conformations suggested by the experiments. The free energy difference between the two conformational states is very small and the transition between them occurs within a few kT at 300 K on a nanosecond timescale. The equilibrium is mainly driven by entropic contribution, which favors extended conformations over beta-turns. This confirms other theoretical studies showing that beta-turns are marginally stable in water solution because of the larger entropy of the extended state unless some stabilizing interactions exist. Our observations may be extended to any type of beta-turn and have important consequences for protein folding. A comparison of our MD and CD results also suggests a possible type VIII beta-turn CD signature indicated by one main band at 200 nm, close to that of random coil, and a fairly large shoulder at 220 nm. Last, our results clearly show that the XXXP motif can only fold into a type VIII beta-turn, which is consistent with its fairly strong propensity for this type of turn. This important finding may help for peptide design and is in line with recent studies on bioactive elastin peptides.

Multiple folding mechanisms of protein ubiquitin

Based on the C(alpha) Go-type model, the folding kinetics and mechanisms of protein ubiquitin with mixed alpha/beta topology are studied by molecular dynamics simulations. The relaxation kinetics shows that there are three phases, namely the major phase, the intermediate phase and the slowest minor phase. The existence of these three phases are relevant to the phenomenon found in experiments. According to our simulations, the folding at high temperatures around the folding transition temperature T(f) is of a two-state process, and the folding nucleus is consisted of contacts between the front end of alpha-helix and the turn(4). The folding at low temperature (approximately T = 0.8) is also studied, where an A-state like structure is found lying on the major folding pathway. The appearance of this structure is related to the stability of the first part (residue 1-51) of protein ubiquitin. As the temperature decreases, the formation of secondary structures, tertiary structures and collapse of the protein are found to be decoupled gradually and the folding mechanism changes from the nucleation-condensation to the diffusion-collision. This feature indicates a unifying common folding mechanism for proteins. The intermediate phase is also studied and is found to represent a folding process via a long-lived intermediate state which is stabilized by strong interactions between the beta(1) and the beta(5) strand. These strong interactions are important for the function of protein ubiquitin as a molecular chaperone. Thus the intermediate phase is assumed as a byproduct of the requirement of protein function. In addition, the validity of the current Go-model is also investigated, and a lower limited temperature for protein ubiquitin T(limit) = 0.8 is proposed. At temperatures higher than this value, the kinetic traps due to glass dynamics cannot be significantly populated and the intermediate states can be reliably identified although there is slight chevron rollover in the folding rates. At temperature lower than T(limit), however, the traps due to glass dynamics become dominant and may be mistaken for real intermediate states. This limitation of valid temperature range prevents us to reveal the burst phase intermediate in the major folding phase since it might only be stabilized at temperatures lower than T(limit), according to experiments. Our works show that caution must be taken when studying low-temperature intermediate states by using the C(alpha) Go-models.

Calculation of absolute protein-ligand binding affinity using path and endpoint approaches

A comparative analysis is provided of rigorous and approximate methods for calculating absolute binding affinities of two protein-ligand complexes: the FKBP protein bound with small molecules 4-hydroxy-2-butanone and FK506. Our rigorous approach is an umbrella sampling technique where a potential of mean force is determined by pulling the ligand out of the protein active site over several simulation windows. The results of this approach agree well with experimentally observed binding affinities. Also assessed is a commonly used approximate endpoint approach, which separately estimates enthalpy, solvation free energy, and entropy. We show that this endpoint approach has numerous variations, all of which are prone to critical shortcomings. For example, conventional harmonic and quasiharmonic entropy estimation procedures produce disparate results for the relatively simple protein-ligand systems studied in this work.

Unfolding dynamics of the protein ubiquitin: insight from simulation

The temperature-induced unfolding pathway of ubiquitin has been investigated by molecular dynamics simulation at four different temperatures. It has been observed that the sequences of the unfolding events are same at all the temperatures. However, the time scale of the dynamics at different temperatures are different. The transition states at various temperatures also possess similar secondary structural elements. The intermediate conformations visited by the protein at different temperatures can help determination of the transition states. The well known " state" of ubiquitin, hitherto found to be stable only in methanol water mixture, have been observed to be a common transient intermediate conformation in the unfolding path of the protein in water. Our observation about the similarities of the unfolding process at different temperatures strongly recommend for a defined pathway for the unfolding process.

Describing partially unfolded states of proteins from sparse NMR data

Proteins involved in signal transduction can usually be present in two states: an inactive and an active (signaling) state. In the case of photoreceptors such as PYP, it has been shown that the signaling state has a large degree of structural and dynamic disorder. Conventional structural NMR approaches present difficulties in describing such partially unfolded states. Owing to the disordered dynamical and transient nature of such states classical NOE-based information, when present, is sparse. Chemical shift changes upon partial unfolding can, however, be easily monitored from HSQC spectra. We show here that such states can be modeled by defining native-like inter-residue contacts for those residues that do not shift significantly upon partial unfolding. The feasibility of this approach is demonstrated using lysozyme as a test case and applied to model the partially unfolded signaling state (pB) of a truncated form of the photoactive yellow protein for which a "classical" NOE-based structure is available for validation. This approach should be generally applicable to systems in which part of the structure remains in a well-defined native-like conformation.

Effects of disulfide bonds on folding behavior and mechanism of the beta-sheet protein tendamistat

Tendamistat, a small disulfide-bonded beta-sheet protein, and its three single/double-disulfide mutants are investigated by using a modified Gō-like model, aiming to understand the folding mechanism of disulfide-bonded protein as well as the effects of removal of disulfide bond on the folding process. Our simulations show that tendamistat and its two single-disulfide mutants are all two-state folders, consistent with the experimental observations. It is found that the disulfide bonds as well as three hydrogen bonds between the N-terminal loop-0 and strand-6 are of significant importance for the folding of tendamistat. Without these interactions, their two-state behaviors become unstable and the predictions of the model are inconsistent with experiments. In addition, the effect of disulfide bonds on the folding process are studied by comparing the wild-type tendamistat and its two mutants; it is found that the removal of either of the C11-C27 or C45-C73 disulfide bond leads to a large decrease in the thermodynamical stability and loss of structure in the unfolded state, and the effect of the former is stronger than that of the later. These simulation results are in good agreement with experiments and, thus, validate our model. Based on the same model, the detailed folding pathways of the wild-type tendamistat and two mutants are studied, and the effect of disulfide bonds on the folding kinetics are discussed. The obtained results provide a detailed folding picture of these proteins and complement experimental findings. Finally, the folding nuclei predicted to be existent in this protein tendamistat as well as its mutants are firstly identified in this work. The positions of the nucleus are consistent with those argued in experimental studies. Therefore, a nucleation/growth folding mechanism that can explain the two-state folding manner is clearly characterized. Moreover, the effect by the removal of each disulfide bond on the folding thermodynamics and dynamics can also be well interpreted from their influence on the folding nucleus. The implementation of this work indicates that the modified Gō-like model really describes the folding behavior of protein tendamistat and could be used to study the folding of other disulfide-bonded proteins.

Symmetric connectivity of secondary structure elements enhances the diversity of folding pathways

The influence of native connectivity of secondary structure elements (SSE) on folding is studied using coarse-grained models of proteins with mixed alpha and beta structure and the analysis of the structural database of wild-type proteins. We found that the distribution of SSE along a sequence determines the diversity of folding pathways. If alpha and beta SSE are localized in different parts of a sequence, the diversity of folding pathways is restricted. An even (symmetric) distribution of alpha and beta SSE with respect to sequence midpoint favors multiple folding routes. Simulations are supplemented by the database analysis of the distribution of SSE in wild-type protein sequences. On an average, two-thirds of wild-type proteins with mixed alpha and beta structure have symmetric distribution of alpha and beta SSE. The propensity for symmetric distribution of SSE is especially evident for large proteins with the number of SSE > or = 10. We suggest that symmetric SSE distribution in protein sequences may arise due to nearly random allocation of alpha and beta structure along wild-type sequences. The tendency of long sequences to misfold is perhaps compensated by the enhanced pathway diversity. In addition, folding pathways are shown to progress via hierarchic assembly of SSE in accordance with their proximity along a sequence. We demonstrate that under mild denaturation conditions folding and unfolding pathways are similar. However, the reversibility of folding/unfolding pathways is shown to depend on the distribution of SSE. If alpha and beta SSE are localized in different parts of a sequence, folding and unfolding pathways are likely to coincide.

Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: hierarchy of structural loss from all-atom Monte Carlo simulations of p27Kip1 unfolding-unbinding and structural determinants of the binding mechanism

Conformational transitions coupled to binding are studied for the p27(Kip1) protein which undergoes a functional disorder-to-order folding transition during tertiary complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Temperature-induced Monte Carlo simulations of p27(Kip1) unfolding-unbinding carried out from the crystal structure of the tertiary complex have revealed a systematic trend in the hierarchy of structural loss for p27(Kip1) and a considerable difference in mobility of p27(Kip1) secondary structure elements. The most persistent interactions of p27(Kip1) at the intermolecular interface during unfolding-unbinding simulations are formed by beta-hairpin and beta-strand that on average maintain their structural integrity considerably longer than other p27(Kip1) elements. We have found that the ensemble of unfolded p27(Kip1) conformations is characterized by transitions between mostly unbound, collapsed conformations and entropically favorable p27(Kip1) conformations, which are weakly bound to the cyclin A side of the binary complex. The results of this study are consistent with the experimental evidence pointing to this region of the intermolecular interface as a potential initiation docking site during binding reaction and may reconcile conflicting experimental hypotheses on the recognition of substrate recruitment motifs.

Determination of enzyme mechanisms by molecular dynamics: studies on quinoproteins, methanol dehydrogenase, and soluble glucose dehydrogenase

Molecular dynamics (MD) simulations have been carried out to study the enzymatic mechanisms of quinoproteins, methanol dehydrogenase (MDH), and soluble glucose dehydrogenase (sGDH). The mechanisms of reduction of the orthoquinone cofactor (PQQ) of MDH and sGDH involve concerted base-catalyzed proton abstraction from the hydroxyl moiety of methanol or from the 1-hydroxyl of glucose, and hydride equivalent transfer from the substrate to the quinone carbonyl carbon C5 of PQQ. The products of methanol and glucose oxidation are formaldehyde and glucolactone, respectively. The immediate product of PQQ reduction, PQQH- [-HC5(O-)-C4(=O)-] and PQQH [-HC5(OH)-C4(=O)-] converts to the hydroquinone PQQH2 [-C5(OH)=C4(OH)-]. The main focus is on MD structures of MDH * PQQ * methanol, MDH * PQQH-, MDH * PQQH, sGDH * PQQ * glucose, sGDH * PQQH- (glucolactone, and sGDH * PQQH. The reaction PQQ-->PQQH- occurs with Glu 171-CO2- and His 144-Im as the base species in MDH and sGDH, respectively. The general-base-catalyzed hydroxyl proton abstraction from substrate concerted with hydride transfer to the C5 of PQQ is assisted by hydrogen-bonding to the C5=O by Wat1 and Arg 324 in MDH and by Wat89 and Arg 228 in sGDH. Asp 297-COOH would act as a proton donor for the reaction PQQH(-)-->PQQH, if formed by transfer of the proton from Glu 171-COOH to Asp 297-CO2- in MDH. For PQQH-->PQQH2, migration of H5 to the C4 oxygen may be assisted by a weak base like water (either by crystal water Wat97 or bulk solvent, hydrogen-bonded to Glu 171-CO2- in MDH and by Wat89 in sGDH).

The glutaredoxin -C-P-Y-C- motif: influence of peripheral residues

The variety of cellular functions performed by proteins of the thioredoxin superfamily is made possible by the wide range of redox potential associated with their active site -Cys-X-X-Cys- motif. The determinants of these differences in redox potential are of considerable interest but are not well understood. E. coli Glutaredoxin 1 (Grx1) and 3 (Grx3) are important model systems with different redox properties, despite sharing the same -Cys-Pro-Tyr-Cys- motif, very similar overall structures, and 33% sequence identity. Very long molecular dynamics simulations (0.25 micros total) and electrostatic calculations provide a revised view of the reduced Grx1 active site, which now can be reconciled with biochemical and functional data. Comparison of this new model to Grx3 uncovers differences in the structure, dynamics, and electrostatics of these active sites. The influence of peripheral residues on the properties of the -Cys-X-X-Cys- motif is illustrated specifically with the effect of a Lys to Arg substitution.

Enhanced sampling by multiple molecular dynamics trajectories: carbonmonoxy myoglobin 10 μs A0 → A1–3 transition from ten 400 picosecond simulations

The utility of multiple trajectories to extend the time scale of molecular dynamics simulations is reported for the spectroscopic A-states of carbonmonoxy myoglobin (MbCO). Experimentally, the A0-->A(1-3) transition has been observed to be 10 micros at 300 K, which is beyond the time scale of standard molecular dynamics simulations. To simulate this transition, 10 short (400 ps) and two longer time (1.2 ns) molecular dynamics trajectories, starting from five different crystallographic and solution phase structures with random initial velocities centered in a 37 A radius sphere of water, have been used to sample the native-fold of MbCO. Analysis of the ensemble of structures gathered over the cumulative 5.6 ns reveals two biomolecular motions involving the side chains of His64 and Arg45 to explain the spectroscopic states of MbCO. The 10 micros A0-->A(1-3) transition involves the motion of His64, where distance between His64 and CO is found to vary up to 8.8 +/- 1.0 A during the transition of His64 from the ligand (A(1-3)) to bulk solvent (A0). The His64 motion occurs within a single trajectory only once, however the multiple trajectories populate the spectroscopic A-states fully. Consequently, multiple independent molecular dynamics simulations have been found to extend biomolecular motion from 5 ns of total simulation to experimental phenomena on the microsecond time scale.

Orchestration of cooperative events in DNA synthesis and repair mechanism unraveled by transition path sampling of DNA polymerase beta's closing

Our application of transition path sampling to a complex biomolecular system in explicit solvent, the closing transition of DNA polymerase beta, unravels atomic and energetic details of the conformational change that precedes the chemical reaction of nucleotide incorporation. The computed reaction profile offers detailed mechanistic insights into, as well as kinetic information on, the complex process essential for DNA synthesis and repair. The five identified transition states extend available experimental and modeling data by revealing highly cooperative dynamics and critical roles of key residues (Arg-258, Phe-272, Asp-192, and Tyr-271) in the enzyme's function. The collective cascade of these sequential conformational changes brings the DNA/DNA polymerase beta system to a state nearly competent for the chemical reaction and suggests how subtle residue motions and conformational rate-limiting steps affect reaction efficiency and fidelity; this complex system of checks and balances directs the system to the chemical reaction and likely helps the enzyme discriminate the correct from the incorrect incoming nucleotide. Together with the chemical reaction, these conformational features may be central to the dual nature of polymerases, requiring specificity (for correct nucleotide selection) as well as versatility (to accommodate different templates at every step) to maintain overall fidelity. Besides leading to these biological findings, our developed protocols open the door to other applications of transition path sampling to long-time, large-scale biomolecular reactions.

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.

Kinetics of the coil-to-helix transition on a rough energy landscape

The kinetics of folding of a fully atomic seven-residue polyalanine peptide in an implicit solvent are studied using molecular dynamics simulations. The use of an implicit solvent is found to dramatically increase the frustration of the energy landscape relative to simulations performed in an explicit solvent [Phys. Rev. Lett. 85, 2637 (2000)]. While the native state in both implicit and explicit solvent simulations is an alpha-helix, the kinetics of the coil-to-helix transition differ significantly. In contrast to the explicit solvent simulations, the native state in the implicit solvent simulations is not kinetically accessible at temperatures where it is thermodynamically stable and could not be brought into equilibrium with other conformational states. At temperatures where statistical equilibrium was achieved, the conformational diffusion folding mechanism, found earlier to be adequate for this peptide in an explicit solvent [Phys. Rev. Lett. 85, 2637 (2000)], is met with only limited success. Issues relating to the evaluation of the quality of implicit solvent models on the basis of thermodynamic criteria only are reexamined.