Mechanical unfolding of a beta-hairpin using molecular dynamics

An account on the factors determining the extra stability of the β-hairpin from B1 domain of protein G

The folding-unfolding of a 16 residue polypeptide, a β-hairpin in B1 domain of protein G is investigated here to account for the factors assisting the extra stability of the polypeptide in the presence of an explicit solvent and even when a denaturant like urea is present in the medium. It is observed here that the backbone H-bond network well defines the folded state and is even capable of forming the folded state, but it is not the only criteria for making a stable β-hairpin fold. Factors such as the side chain H-bonds and the alignment of the certain hydrophobic group side chains play a prominent role in preserving the β-hairpin structure and thus providing an extra stability to the hairpin architecture. It is also affirmed that the mentioned hydrophobic groups side chain interactions are very crucial in holding the β-hairpin together and without which the hairpin collapses completely. We also confirm that the denaturant urea acts on the GB1-hairpin backbone H-bonds and in the presence of strong hydrophobic interactions with a consistent side chain H-bonding network, the denaturation being comparatively a slower process with respect to the protein devoid of the side chain interactions.Communicated by Ramaswamy H. Sarma.

Benchmarking Adaptive Steered Molecular Dynamics (ASMD) on CHARMM Force Fields

The potentials of mean force (PMFs) along the end‐to‐end distance of two different helical peptides have been obtained and benchmarked using the adaptive steered molecular dynamics (ASMD) method. The results depend strongly on the choice of force field driving the underlying all‐atom molecular dynamics, and are reported with respect to the three most popular CHARMM force field versions: c22, c27 and c36. Two small peptides, ALA10 and 1PEF, serve as the particular case studies. The comparisons between the versions of the CHARMM force fields provides both a qualitative and quantitative look at their performance in forced unfolding simulations in which peptides undergo large changes in structural conformations. We find that ASMD with the underlying c36 force field provides the most robust results for the selected benchmark peptides.

Micro-ecology restoration of colonic inflammation by in-Situ oral delivery of antibody-laden hydrogel microcapsules

In-situ oral delivery of therapeutic antibodies, like monoclonal antibody, for chronic inflammation treatment is the most convenient approach compared with other administration routes. Moreover, the abundant links between the gut microbiota and colonic inflammation indicate that the synergistic or antagonistic effect of gut microbiota to colonic inflammation. However, the antibody activity would be significantly affected while transferring through the gastrointestinal tract due to hostile conditions. Moreover, these antibodies have short serum half-lives, thus, require to be frequently administered with high doses to be effective, leading to low patient tolerance. Here, we develop a strategy utilizing thin shell hydrogel microcapsule fabricated by microfluidic technique as the oral delivering carrier. By encapsulating antibodies in these microcapsules, antibodies survive in the hostile gastrointestinal environment and rapidly release into the small intestine through oral administration route, achieving the same therapeutic effect as the intravenous injection evaluated by a colonic inflammation disease model. Moreover, the abundance of some intestinal microorganisms as the indication of the improvement of inflammation has remarkably altered after in-situ antibody-laden microcapsules delivery, implying the restoration of micro-ecology of the intestine. These findings prove our microcapsules are exploited as an efficient oral delivery agent for antibodies with programmable function in clinical application.

1.

This thin shell hydrogel microcapsules using a water-in-water-in-oil as the template by microfluidic technique for orally delivery of antibodies is generated to protect from hostile stomach microenvironment and rapid released in the small intestine without losing their activity.

2.

The shell contains a double crosslinked network attributed to its ionic crosslinking and covalent crosslinking functionalities.

3.

The antibody-laden microcapsules demonstrate great therapeutic efficacy in DSS-induced colonic inflammation disease models, which is approximated to that of the intravenous injection treatment.

4.

Orally taken antibody-laden microcapsules restore the intestinal micro-ecological dysbiosis.

Force exerted by a nanoscale capillary water bridge between two planar substrates

Molecular dynamics simulation of a nanoscale capillary water bridge between two planar substrates is used to determine the resulting force between the substrates without arbitrariness regarding geometry and location of the free surface of the bridge. The substrates are moderately hydrophilic. The force changes continuously as the separation between the substrates changes except for small gaps where it becomes discontinuous because the bridge is unable to adopt stable configurations at any distance apart. Further exploration of the bridge and the force as the substrates approach each other reveals an underlying oscillatory force with an increasing repulsive component at separation distances equivalent to few water molecules. According to the average number of hydrogen bonds per water molecule (HBN), at very small gap sizes, water molecules which are very close to the surfaces are unable to maximize HBN thus contributing to the repulsive force. Our simulation results of force versus gap size agree with calculations based on other methods, some very different, and also reproduce the typical magnitude of the experimental force. Finally, a macroscopic force balance correctly describes the force-distance curve except for bridges constituted of water layers only.

Determining the Energetics of Small β-Sheet Peptides using Adaptive Steered Molecular Dynamics

Mechanically driven unfolding is a useful computational tool for extracting the energetics and stretching pathway of peptides. In this work, two representative β-hairpin peptides, chignolin (PDB: 1UAO ) and trpzip1 (PDB: 1LE0 ), were investigated using an adaptive variant of the original steered molecular dynamics method called adaptive steered molecular dynamics (ASMD). The ASMD method makes it possible to perform energetic calculations on increasingly complex biological systems. Although the two peptides are similar in length and have similar secondary structures, their unfolding energetics are quite different. The hydrogen bonding profile and specific residue pair interaction energies provide insight into the differing stabilities of these peptides and reveal which of the pairs provides the most significant stabilization.

Force-induced unzipping transitions in an athermal crowded environment

Using theoretical arguments and extensive Monte Carlo (MC) simulations of a coarse-grained three-dimensional off-lattice model of a β-hairpin, we demonstrate that the equilibrium critical force, Fc, needed to unfold the biopolymer increases nonlinearly with increasing volume fraction occupied by the spherical macromolecular crowding agent. Both scaling arguments and MC simulations show that the critical force increases as Fc ≈ φc(α). The exponent α is linked to the Flory exponent relating the size of the unfolded state of the biopolymer and the number of amino acids. The predicted power law dependence is confirmed in simulations of the dependence of the isothermal extensibility and the fraction of native contacts on φc. We also show using MC simulations that Fc is linearly dependent on the average osmotic pressure (P) exerted by the crowding agents on the β-hairpin. The highly significant linear correlation coefficient of 0.99657 between Fc and P makes it straightforward to predict the dependence of the critical force on the density of crowders. Our predictions are amenable to experimental verification using laser optical tweezers.

The Uptake Mechanism of the Cell-Penetrating pVEC Peptide

Peptide based drug design efforts have gained renewed interest with the discovery of cargo-carrying or cell-penetrating peptides. Understanding the translocation mechanism of these peptides and identifying the residues or elements that contribute to uptake can provide valuable clues toward the design of novel peptides. To this end, we have performed steered molecular dynamics (SMD) simulations on the pVEC peptide from murine vascular endothelial-cadherin protein and its two variants. Translocation was found to occur in three stages, adsorption via the cationic residues, inclusion of the whole peptide inside the membrane accompanied by formation of a water defect, and exit of both peptide and water molecules from the bilayer. Our simulation results suggest that the precise order in which the hydrophobic, cationic, and the polar regions are located in the amphipathic pVEC peptide contributes to its uptake mechanism. These results present new opportunities for the design of novel cell-penetrating and antimicrobial peptides.

ASTRO-FOLD 2.0: an Enhanced Framework for Protein Structure Prediction

The three-dimensional (3-D) structure prediction of proteins, given their amino acid sequence, is addressed using the first principles-based approach ASTRO-FOLD 2.0. The key features presented are: (1) Secondary structure prediction using a novel optimization-based consensus approach, (2) β-sheet topology prediction using mixed-integer linear optimization (MILP), (3) Residue-to-residue contact prediction using a high-resolution distance-dependent force field and MILP formulation, (4) Tight dihedral angle and distance bound generation for loop residues using dihedral angle clustering and non-linear optimization (NLP), (5) 3-D structure prediction using deterministic global optimization, stochastic conformational space annealing, and the full-atomistic ECEPP/3 potential, (6) Near-native structure selection using a traveling salesman problem-based clustering approach, ICON, and (7) Improved bound generation using chemical shifts of subsets of heavy atoms, generated by SPARTA and CS23D. Computational results of ASTRO-FOLD 2.0 on 47 blind targets of the recently concluded CASP9 experiment are presented.

The effect of different force applications on the protein-protein complex Barnase-Barstar

Steered molecular dynamics simulations are a tool to examine the energy landscape of protein-protein complexes by applying external forces. Here, we analyze the influence of the velocity and geometry of the probing forces on a protein complex using this tool. With steered molecular dynamics, we probe the stability of the protein-protein complex Barnase-Barstar. The individual proteins are mechanically labile. The Barnase-Barstar binding site is more stable than the folds of the individual proteins. By using different force protocols, we observe a variety of responses of the system to the applied tension.

Polymers in crowded environment under stretching force: Globule-coil transitions

We study flexible polymer macromolecules in a crowded (porous) environment, modeling them as self-attracting self-avoiding walks on site-diluted percolative lattices in space dimensions d=2,3 . The influence of stretching force on the polymer folding and the properties of globule-coil transitions are analyzed. Applying the pruned-enriched Rosenbluth chain-growth method, we estimate the transition temperature TTheta between collapsed and extended polymer configurations and construct the phase diagrams of the globule-coil coexistence when varying temperature and stretching force. The transition to a completely stretched state, caused by applying force, is discussed as well.

Comparative study of generalized born models: Born radii and peptide folding

In this study, we have implemented four analytical generalized Born (GB) models and investigated their performance in conjunction with the GROMOS96 force field. The four models include that of Still and co-workers, the HCT model of Cramer, Truhlar, and co-workers, a modified form of the AGB model of Levy and co-workers, and the GBMV2 model of Brooks and co-workers. The models were coded independently and implemented in the GROMOS software package and in TINKER. They were compared in terms of their ability to reproduce the results of Poisson-Boltzmann (PB) calculations and in their performance in the ab initio peptide folding of two peptides, one that forms a beta-hairpin in solution and one that forms an alpha-helix. In agreement with previous work, the GBMV2 model is most successful in reproducing PB results while the other models tend to underestimate the effective Born radii of buried atoms. In contrast, stochastic dynamics simulations on the folding of the two peptides, the C-terminus beta-hairpin of the B1 domain of protein G and the alanine-based alpha-helical peptide 3K(I), suggest that the simpler GB models are more effective in sampling conformational space. Indeed, the Still model used in conjunction with the GROMOS96 force field is able to fold the hairpin peptide to a native-like structure without the benefit of enhanced sampling techniques. This is due in part to the properties of the united-atom GROMOS96 force field which appears to be more flexible, and hence to sample more efficiently, than force fields such as OPLSAA. Our results suggest a general strategy which involves using different combinations of force fields and solvent models in different applications, for example, using GROMOS96 and a simple GB model in sampling and OPLSAA and a more accurate GB model in refinement. The fact that various methods have been implemented in a unified way should facilitate the testing and subsequent use of different methods to evaluate conformational free energies in different applications. Our results also bear on some general issues involved in peptide folding and structure prediction which are addressed in the Discussion.

β-Hairpins with native-like and non-native hydrogen bonding patterns could form during the refolding of staphylococcal nuclease

Refolding of staphylococcal nuclease has been studied recently by hydrogen-deuterium exchange and NMR spectroscopy. These studies infer that beta-hairpin formed by strand 2 and strand 3 connected by reverse turn forms early during the refolding of nuclease. Typically, hydrogen-deuterium exchange NMR techniques are usually carried out on a time scale of milliseconds whereas beta-hairpins are known to fold on a much shorter time scale. It follows that in the experiments, the hydrogen-deuterium exchange protection patterns could be arising from a significant population of fully formed hairpins. In order to demonstrate it is the fully formed hairpins which gives rise to the hydrogen-deuterium exchange protection patterns, we have considered molecular dynamics simulation of the peptide (21)DTVKLMYKGQPMTFR(35) from staphylococcal nuclease corresponding to the beta-hairpin region, using GROMOS96 force field under NVT conditions. Starting from unfolded conformational states, the peptide folds into hairpin conformations with native-like and non-native hydrogen bonding patterns. Subsequent to folding, equilibrium conditions prevail. The computed protection factors and atom depth values, at equilibrium, of the various amide protons agree qualitatively with experimental observations. A collection of molecules following the trajectories observed in the simulations can account for experimental observations. These simulations provide a molecular picture of the formed hairpins and their conformational features during the refolding experiments on nuclease, monitored by hydrogen-deuterium exchange.

HX-ESI-MS and Optical Studies of the Unfolding of Thioredoxin Indicate Stabilization of a Partially Unfolded, Aggregation-Competent Intermediate at Low pH

Hydrogen exchange monitored by mass spectrometry (HX-MS), in conjunction with multiple optical probes, has been used to characterize the unfolding of thioredoxin. Equilibrium and kinetic studies have been carried out at pH 7 and 3. The HX-MS measurements are shown to be capable of distinguishing between native (N) and unfolded (U) protein molecules when both are present together, and their application in kinetic experiments allows the unfolding reaction to be delineated from the proline isomerization reaction to which it is coupled. At pH 7, equilibrium unfolding studies monitored by three optical probes, intrinsic fluorescence at 368 nm, ellipticity at 222 nm, and ellipticity at 270 nm, as well as by HX-MS, indicate that no intermediate is populated at pH 7, the unfolding reaction is slower than the proline isomerization reaction that follows it, and the three optical probes yield identical kinetics for unfolding, which occurs in a single kinetic phase. The fractional change in any of the three optical signals at any time of unfolding predicts the fraction of the molecules that have become U, as determined by HX-MS. Hence, unfolding at pH 7 appears to occur via a two-state N <==> U mechanism. In contrast at pH 3, HX-MS as well as optical measurements indicate that an unfolding intermediate is stabilized and hence accumulates in equilibrium with N and U, at concentrations of denaturant that define the transition zone of the equilibrium unfolding curve. The intermediate has lost the near-UV signal characteristic of N and possesses fewer amide hydrogen sites that are stable to exchange than does N. Kinetic experiments at pH 3, where unfolding is much faster than proline isomerization, show that more than one intermediate accumulates transiently during unfolding. Thus, the unfolding of thioredoxin occurs via an N <==> I <==> U mechanism, where I is a partially unfolded intermediate that is stabilized and hence populated at pH 3 but not at pH 7. It is shown that transient aggregation of this intermediate results in a deceleration of the kinetics of unfolding at high protein concentrations at pH 3 but not at pH 7.

Molecular dynamics simulations of folding processes of a β-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.

Folding and aggregation kinetics of a beta-hairpin

We have investigated the solution structure, equilibrium properties, and folding kinetics of a 17-residue beta-hairpin-forming peptide derived from the protein ubiquitin. NMR experiments show that at 4 degrees C the peptide has a highly populated beta-hairpin conformation. At protein concentrations higher than 0.35 mM, the peptide aggregates. Sedimentation equilibrium measurements show that the aggregate is a trimer, while NMR indicates that the beta-hairpin conformation is maintained in the trimer. The relaxation kinetics in nanosecond laser temperature-jump experiments reveal a concentration-independent microsecond phase, corresponding to beta-hairpin unfolding-refolding, and a concentration-dependent millisecond phase due to oligomerization. Kinetic modeling of the relaxation rates and amplitudes yields the folding and unfolding rates for the monomeric beta-hairpin, as well as assembly and disassembly rates for trimer formation consistent with the equilibrium constant determined by sedimentation equilibrium. When the net charge on the peptides and ionic strength were taken into account, the rate of trimer assembly approaches the Debye-Smoluchowski diffusion limit. At 300 K, the rate of formation of the monomeric hairpin is (17 micros)(-1), compared to rates of (0.8 micros)(-1) to (52 micros)(-1) found for other peptides. After using Kramers theory to correct for the temperature dependence of the pre-exponential factor, the activation energy for hairpin formation is near zero, indicating that the barrier to folding is purely entropic. Comparisons with previously measured rates for a series of hairpins are made to distinguish between zipper and hydrophobic collapse mechanisms. Overall, the experimental data are most consistent with the zipper mechanism in which structure formation is initiated at the turn, the mechanism predicted by the Ising-like statistical mechanical model that was developed to explain the equilibrium and kinetic data for the beta-hairpin from protein GB1. In contrast, the majority of simulation studies favor a hydrophobic collapse mechanism. However, with few exceptions, there is little or no quantitative comparison of the simulation results with experimental data.

Molecular simulation of the reversible mechanical unfolding of proteins

In this work we have combined a Wang-Landau sampling scheme [F. Wang and D. Landau, Phys. Rev. Lett. 86, 2050 (2001)] with an expanded ensemble formalism to yield a simple and powerful method for computing potentials of mean force. The new method is implemented to investigate the mechanical deformation of proteins. Comparisons are made with analytical results for simple model systems such as harmonic springs and Rouse chains. The method is then illustrated on a model 15-residue alanine molecule in an implicit solvent. Results for mechanical unfolding of this oligopeptide are compared to those of steered molecular dynamics calculations.

Mechanism of titin unfolding by force: insight from quasi-equilibrium molecular dynamics calculations

We have studied the unfolding by force of one of the immunoglobulin domains of the muscle protein titin using molecular dynamics simulations at 300 K. Previous studies, done at constant pulling rates, showed that under the effect of the force two strands connected to each other by six backbone H-bonds are pulled apart. No details about the mechanism of H-bond breaking were provided. Our simulation protocol "pull and wait" was designed to correspond to very slow pulling, more similar to the rates used in experiments than are the protocols used in previous computational studies. Under these conditions interstrand backbone H-bonds are not "ripped apart" by the application of the force. Instead, small elongations produced by the force weaken specific backbone H-bonds with respect to water-backbone H-bonds. These weakened bonds allow a single water molecule to make H-bonds to the CO and the NH of the same backbone H-bond while they are still bound to each other. The backbone H-bond then breaks (distance > 3.6 A), but its donor and acceptor atoms remain bound to the same water molecule. Further separation of the chains takes place when a second water molecule makes an H-bond with either the protein backbone donor or acceptor atom. Thus, the force does not directly break the main chain H-bonds: it destabilizes them in such a way that they are replaced by H-bonds to water. With this mechanism, the force necessary to break all the H-bonds required to separate the two strands will be strongly dependent on the pulling speed. Further simulations carried out at low forces but long waiting times (> or = 500 ps, < or = 10 ns) show that, given enough time, even a very small pulling force (< 400 pN) is sufficient to destabilize the interstrand H-bonds and allow them to be replaced by H-bonds to two water molecules. As expected, increasing the temperature to 350 K allows the interstrand H-bonds to break at lower forces than those required at 300 K.

Src kinase activation: A switched electrostatic network

Src tyrosine kinases are essential in numerous cell signaling pathways, and improper functioning of these enzymes has been implicated in many diseases. The activity of Src kinases is regulated by conformational activation, which involves several structural changes within the catalytic domain (CD): the orientation of two lobes of CD; rearrangement of the activation loop (A-loop); and movement of an alpha-helix (alphaC), which is located at the interface between the two lobes, into or away from the catalytic cleft. Conformational activation was investigated using biased molecular dynamics to explore the transition pathway between the active and the down-regulated conformation of CD for the Src-kinase family member Lyn kinase, and to gain insight into the interdependence of these changes. Lobe opening is observed to be a facile motion, whereas movement of the A-loop motion is more complex requiring secondary structure changes as well as communication with alphaC. A key result is that the conformational transition involves a switch in an electrostatic network of six polar residues between the active and the down-regulated conformations. The exchange between interactions links the three main motions of the CD. Kinetic experiments that would demonstrate the contribution of the switched electrostatic network to the enzyme mechanism are proposed. Possible implications for regulation conferred by interdomain interactions are also discussed.

Calculation of the entropy and free energy from monte carlo simulations of a peptide stretched by an external force

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy, S, and free energy, F, from a trajectory generated by any simulation technique. HSMC was applied initially to fluids (argon and water) and later to peptides and self-avoiding walks on a lattice. In this paper we make a step further and apply it to a model of decaglycine (at T = 300 K) in vacuum with constant bond lengths where external stretching forces are exerted at the end points; the changes in S and F are calculated as the forces are increased. The molecule is placed initially in a helical structure, which is changed to an extended structure after a short simulation time due to the exerted forces. This study has relevance to problems in polymers (e.g., rubber elasticity) and to the analysis of experiments where individual molecules are stretched by atomic force microscopy (AFM), for example. The results for S and F are accurate and are significantly better than those obtained by the quasi-harmonic approximation and the local states method. However, the molecule is quite stiff due to the strong bond angle potentials and the extensions are small even for relatively large forces. Correspondingly, as the force is increased the decrease in the entropy is relatively small while the potential energy is enhanced significantly. Still, differences, TDeltaS, for different forces are obtained with very good accuracy of approximately 0.2 kcal/mol.

Thermodynamic calculations in biological systems

The ability to compute intra- and inter-molecular interactions provides the opportunity to gain a deeper understanding of previously intractable problems in biochemistry and biophysics. This review presents three examples in which molecular dynamics calculations were used to gain insight into the atomic detail underlying important experimental observations. The three examples are the following: (1) Entropic contribution to rate acceleration that results from conformational constraints imposed on the reactants; (2) Mechanism of force unfolding of a small protein molecule by the application of a force that separates its N- and C-terminals; and (3) Loss of translational entropy experienced by small molecules when they bind to proteins.

Dissecting the mechanical unfolding of ubiquitin

The unfolding behavior of ubiquitin under the influence of a stretching force recently was investigated experimentally by single-molecule constant-force methods. Many observed unfolding traces had a simple two-state character, whereas others showed clear evidence of intermediate states. Here, we use Monte Carlo simulations to investigate the force-induced unfolding of ubiquitin at the atomic level. In agreement with experimental data, we find that the unfolding process can occur either in a single step or through intermediate states. In addition to this randomness, we find that many quantities, such as the frequency of occurrence of intermediates, show a clear systematic dependence on the strength of the applied force. Despite this diversity, one common feature can be identified in the simulated unfolding events, which is the order in which the secondary-structure elements break. This order is the same in two- and three-state events and at the different forces studied. The observed order remains to be verified experimentally but appears physically reasonable.

Simulation Studies of Amide I IR Absorption and Two-Dimensional IR Spectra of β Hairpins in Liquid Water

Amide I IR absorption and two-dimensional (2D) IR photon echo spectra of a model beta hairpin in aqueous solution are theoretically studied and simulated by combining semiempirical quantum chemistry calculations and molecular dynamics simulation methods. The instantaneous normal-mode analysis of the beta hairpin in solution is performed to obtain the density of states and the inverse participation ratios of the one-exciton states. The motional and exchange narrowing processes are taken into account by employing the time-correlation function theory for the linear and nonlinear response functions. Numerically simulated IR absorption and 2D spectra are then found to be determined largely by the amide I normal modes delocalized on the peptides in the two strands. The site-specific isotope-labeling effects on the IR and 2D IR spectra are discussed. The simulation results for the ideal (A17) beta hairpin are directly compared with those of the realistic 16-residue (GB1) beta hairpin from an immunoglobulin G-binding protein. It was found that the characteristic features in IR and 2D spectra of both the ideal (A17) beta hairpin and the GB1 beta hairpin are the same. The simulated IR spectrum of the GB1 beta hairpin is found to be in good agreement with experiment, which demonstrates that the present computational method is quantitatively reliable.

Probing protein mechanics: residue-level properties and their use in defining domains

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.

Energy landscape distortions and the mechanical unfolding of proteins

Molecular simulations and an energy landscape analysis are used to examine the stretching of a model protein. A mapping of the energy landscape shows that stretching the protein causes energy minima and energy barriers to flatten out and disappear, and new energy minima to be created. The implications of these landscape distortions depend on the timescale regime under which the protein is stretched. When the timescale for thermally activated processes is longer than the timescale of stretching, the disappearances of energy barriers provide the mechanism for protein unfolding. When the timescale for thermally activated processes is shorter than the timescale of stretching, the landscape distortions influence the stretching process by changing the number and types of energy minima in which the system can exist.

Unfolding single RNA molecules by mechanical force: a stochastic kinetic method

Using simple polymer elastic theory and known RNA free energies, we study the single RNA folding and unfolding on the secondary structure level under mechanical constant force by stochastic kinetic simulation. As a primary application, this method is used to simulate the experiment performed by Science 292, 733 (2001)]. The extension-force curves in equilibrium and kinetic reaction rate constants for folding and unfolding are calculated. Our results show that the agreement between simulation and experimental measurements is satisfactory.

ASTRO-FOLD: a combinatorial and global optimization framework for Ab initio prediction of three-dimensional structures of proteins from the amino acid sequence

The field of computational biology has been revolutionized by recent advances in genomics. The completion of a number of genome projects, including that of the human genome, has paved the way toward a variety of challenges and opportunities in bioinformatics and biological systems engineering. One of the first challenges has been the determination of the structures of proteins encoded by the individual genes. This problem, which represents the progression from sequence to structure (genomics to structural genomics), has been widely known as the structure-prediction-in-protein-folding problem. We present the development and application of ASTRO-FOLD, a novel and complete approach for the ab initio prediction of protein structures given only the amino acid sequences of the proteins. The approach exhibits many novel components and the merits of its application are examined for a suite of protein systems, including a number of targets from several critical-assessment-of-structure-prediction experiments.

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.

Commitment and Nucleation in the Protein G Transition State

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.

Expected and unexpected results from combined β-hairpin design elements

A model beta-hairpin dodecapeptide [EFGWVpGKWTIK] was designed by including a favorable D-ProGly Type II' beta-turn sequence and a Trp-zip interaction, while also incorporating a beta-strand unfavorable glycine residue in the N-terminal strand. This peptide is highly folded and monomeric in aqueous solution as determined by combined analysis with circular dichroism and 1H NMR spectroscopy. A peptide representing the folded conformation of the model beta-hairpin [cyclic(EFGWVpGKWTIKpG)] and a linear peptide representing the unfolded conformation [EFGWVPGKWTIK] yield unexpected relative deviations between the CD and 1H NMR spectroscopic results that are attributed to variations in the packing interactions of the aromatic side chains. Mutational analysis of the model beta-hairpin indicates that the Trp-zip interaction favors folding and stability relative to an alternate hydrophobic cluster between Trp and Tyr residues [EFGYVpGKWTIK]. The significance of select diagonal interactions in the model beta-hairpin was tested by rearranging the cross-strand hydrophobic interactions to provide a folded peptide [EWFGIpGKTYWK] displaying evidence of an unusual backbone conformation at the hydrophobic cluster. This unusual conformation does not appear to be a result of the glycine residue in the beta-strand, as replacement with a serine results in a peptide [EWFSIpGKTYWK] with a similar and seemingly characteristic CD spectrum. However, an alternate arrangement of hydrophobic residues with a Trp-zip interaction in a similar position to the parent beta-hairpin [EGFWVpGKWITK] results in a folded beta-hairpin conformation. The differences between side chain packing of these peptides precludes meaningful thermodynamic analysis and illustrates the caution necessary when interpreting beta-hairpin folding thermodynamics that are driven, at least in part, by aromatic cross strand interactions.

Pulling geometry defines the mechanical resistance of a beta-sheet protein

Proteins show diverse responses when placed under mechanical stress. The molecular origins of their differing mechanical resistance are still unclear, although the orientation of secondary structural elements relative to the applied force vector is thought to have an important function. Here, by using a method of protein immobilization that allows force to be applied to the same all-beta protein, E2lip3, in two different directions, we show that the energy landscape for mechanical unfolding is markedly anisotropic. These results, in combination with molecular dynamics (MD) simulations, reveal that the unfolding pathway depends on the pulling geometry and is associated with unfolding forces that differ by an order of magnitude. Thus, the mechanical resistance of a protein is not dictated solely by amino acid sequence, topology or unfolding rate constant, but depends critically on the direction of the applied extension.

Energy landscape and dynamics of the beta-hairpin G peptide and its isomers: Topology and sequences

We have investigated free energy landscape [MM/PBSA + normal modes entropy] of permutations in the G peptide (41-56) from the protein G B1 domain by studying six isomers corresponding to moving the hydrophobic cluster along the beta-strands (toward the turn: T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE; toward the end: E1, WTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape, toward a less stable beta-hairpin structure. Moving the hydrophobic cluster outside toward the end region causes a greater change in the energy landscape. alpha-Helical instead of a beta-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" beta-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance.

Similarity of force-induced unfolding of apomyoglobin to its chemical-induced unfolding: an atomistic molecular dynamics simulation approach

We have compared force-induced unfolding with traditional unfolding methods using apomyoglobin as a model protein. Using molecular dynamics simulation, we have investigated the structural stability as a function of the degree of mechanical perturbation. Both anisotropic perturbation by stretching two terminal atoms and isotropic perturbation by increasing the radius of gyration of the protein show the same key event of force-induced unfolding. Our primary results show that the native structure of apomyoglobin becomes destabilized against the mechanical perturbation as soon as the interhelical packing between the G and H helices is broken, suggesting that our simulation results share a common feature with the experimental observation that the interhelical contact is more important for the folding of apomyoglobin than the stability of individual helices. This finding is further confirmed by simulating both helix destabilizing and interhelical packing destabilizing mutants.

Unfolding proteins in an external field: can we always observe the intermediate states?

A protein molecule under the stress of an external denaturing force acting on a terminal end or on the entire molecule is expected to unfold, possibly through a few intermediate stages depending on the magnitude of the denaturing force. We have investigated two protein minimal models under various types of denaturing force fields using the collision molecular-dynamics simulation, in order to critically examine the relationship between the folding pathways observed in different protein denaturing experiments.

Surface expansion is independent of and occurs faster than core solvation during the unfolding of barstar

The denaturant-induced unfolding kinetics of the 89-residue protein, barstar, have been examined using fluorescence resonance energy transfer (FRET) at 25 degrees C and pH 8.0. The core tryptophan, Trp53, in barstar serves as a fluorescence donor, and a thionitrobenzoic acid moiety (TNB) attached to a cysteine residue acts as an acceptor to form an efficient FRET pair. Four different single-cysteine containing mutants of barstar with cysteine residues at positions 25, 40, 62, and 82 were studied. The unfolding kinetics of the four mutant forms of barstar were monitored by measurement of the changes in the fluorescence intensity of Trp53 in the unlabeled and TNB-labeled proteins. The rate of change of fluorescence of the single-tryptophan residue, Trp53, in the unlabeled protein, where no FRET occurs, yields the rate of solvation of the core. This rate is similar for all four unlabeled proteins. The rate of the increase in the fluorescence of Trp53 in the labeled protein, where FRET from the tryptophan to the TNB label occurs, yields the rate of decrease in FRET efficiency during unfolding. The decrease in FRET efficiency for proteins labeled at either of the two buried positions (Cys40 or Cys82) occurs at a rate similar to the rate of core solvation. The decrease in FRET efficiency for the acceptor at Cys40 is also shown to be sensitive to the isomerization of the Tyr47-Pro48 cis bond. For the proteins where the label is at a solvent-exposed position (Cys25 and Cys62), the decrease in FRET efficiency occurs in two kinetic phases; 15-25% of the FRET efficiency decreases in the faster phase, and the remaining FRET efficiency decreases in a slower phase, the rate of which is the same as the rate of core solvation. These results clearly indicate that, during unfolding, the protein surface expands faster than, and independently of, water intrusion into the core.

Prediction of beta-sheet topology and disulfide bridges in polypeptides

An ab initio method has been developed to predict beta architectures in polypeptides. The approach predicts the topology of beta-sheets and disulfide bridges through a novel superstructure-based mathematical framework originally established for chemical process synthesis problems. Two types of superstructure are introduced, both of which emanate from the principle that hydrophobic interactions drive the formation of a beta-structure. The mathematical formulation of the problem results in a set of integer linear programming (ILP) problems that can be solved to global optimality to identify the optimal beta-configuration. These (ILP) models can also predict a ranked ordered list of the best, second-best, third-best, etc., topologies of beta-sheets and disulfide bridges. The approach is shown to perform very well for several benchmark polypeptide systems, as well as polypeptides exhibiting challenging nonsequential beta-sheet topologies folds (56 to 187 amino acids).

Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing

Atomistic simulations of protein folding have the potential to be a great complement to experimental studies, but have been severely limited by the time scales accessible with current computer hardware and algorithms. By employing a worldwide distributed computing network of tens of thousands of PCs and algorithms designed to efficiently utilize this new many-processor, highly heterogeneous, loosely coupled distributed computing paradigm, we have been able to simulate hundreds of microseconds of atomistic molecular dynamics. This has allowed us to directly simulate the folding mechanism and to accurately predict the folding rate of several fast-folding proteins and polymers, including a nonbiological helix, polypeptide alpha-helices, a beta-hairpin, and a three-helix bundle protein from the villin headpiece. Our results demonstrate that one can reach the time scales needed to simulate fast folding using distributed computing, and that potential sets used to describe interatomic interactions are sufficiently accurate to reach the folded state with experimentally validated rates, at least for small proteins.

Thermal folding and mechanical unfolding pathways of protein secondary structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an alpha-helix and a beta-hairpin structure. In a tandem of two alpha-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented.

Unfolding proteins under external forces: a solvable model under the self-consistent pair contact probability approximation

We extend a model of Micheletti et al. [Phys. Rev. Lett. 87, 088102 (2001)]] used to study protein con-formations to the case in which there is an external force field. Under the self-consistent pair contact probability approximation, this residue-level resolution model can still be solved under pulling forces. We implement the algorithm using heterogeneous parameters and study the force-induced unfolding of a helical segment from the protein transformylase and of the beta-stranded domains from the protein titin. The results are qualitatively consistent with the results from more expensive, atomistic dynamics simulation. Despite the mean-field-like approach, we observed a sharp and cooperative unfolding transition.