Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations

Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering, and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechanical unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie and the polypeptide chain to completely extend. These distinct unfolding pathways proceed via either a two- or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus providing a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation was observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechanical unfolding pathway of AFV3-109 and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.     

Pulling direction as a reaction coordinate for the mechanical unfolding of single molecules

The folding and unfolding kinetics of single molecules, such as proteins or nucleic acids, can be explored by mechanical pulling experiments. Determining intrinsic kinetic information, at zero stretching force, usually requires an extrapolation by fitting a theoretical model. Here, we apply a recent theoretical approach describing molecular rupture in the presence of force to unfolding kinetic data obtained from coarse-grained simulations of ubiquitin. Unfolding rates calculated from simulations over a broad range of stretching forces, for different pulling directions, reveal a remarkable "turnover" from a force-independent process at low force to a force-dependent process at high force, akin to the "roll-over" in unfolding rates sometimes seen in studies using chemical denaturant. While such a turnover in rates is unexpected in one dimension, we demonstrate that it can occur for dynamics in just two dimensions. We relate the turnover to the quality of the pulling direction as a reaction coordinate for the intrinsic folding mechanism. A novel pulling direction, designed to be the most relevant to the intrinsic folding pathway, results in the smallest turnover. Our results are in accord with protein engineering experiments and simulations which indicate that the unfolding mechanism at high force can differ from the intrinsic mechanism. The apparent similarity between extrapolated and intrinsic rates in experiments, unexpected for different unfolding barriers, can be explained if the turnover occurs at low forces.     

Geometrical features of the protein folding mechanism are a robust property of the energy landscape: a detailed investigation of several reduced models

The concept of a funneled energy landscape and the principle of minimal frustration are the theoretical foundation justifying the applicability of structure-based models. In simulations, a protein is commonly reduced to a C(alpha)-bead representation. These simulations are sufficient to predict the geometrical features of the folding mechanism observed experimentally utilizing a concise formulation of the Hamiltonian with low computational costs. Toward a better understanding of the interplay between energetic and geometrical features in folding, the side chain is now explicitly included in the simulations. The simplest choice is the addition of C(beta)-beads at the center-of-mass position of the side chains. While one varies the energetic parameters of the model, the geometric aspects of the folding mechanism remain robust for a broad range of parameters. Energetic properties like folding barriers and protein stability are sensitive to the details of simulations. This robustness to geometry and sensitivity to energetic properties provide flexibility in choosing different parameters to represent changes in sequences, environments, stability or folding rate effects. Therefore, minimal frustration and the funnel concept guarantee that the geometrical features are robust properties of the folding landscape, while mutations and/or changes in the environment easily influence energy-dependent properties like folding rates or stability.     

Computer simulations of the refolding of sperm whale apomyoglobin from high-temperature denaturated state

The refolding mechanism of apomyoglobin (apoMb) subsequent to high-temperature unfolding has been examined using computer simulations with atomic level detail. The folding of this protein has been extensively studied experimentally, providing a large database of folding parameters which can be probed using simulations. In the present study, 4-folding trajectories of apoMb were computed starting from coiled structures. A crystal structure of sperm whale myoglobin taken from the Protein Data Bank was used to construct the final native conformation by removal of the heme group followed by energy optimization. The initial unfolded conformations were obtained from high-temperature molecular dynamics simulations. Room-temperature refolding trajectories at neutral pH were obtained using the stochastic difference equation in length algorithm. The folding trajectories were compared with experimental results and two previous molecular dynamics studies at low pH. In contrast to the previous simulations, an extended intermediate with large helical content was not observed. In the present study, a structural collapse occurs without formation of helices or native contacts. Once the protein structure is more compact (radius of gyration<18 A) secondary and tertiary structures appear. These results suggest that apoMb follows a different folding pathway after high-temperature denaturation.     

Simulation of chaperonin effect on protein folding: a shift from nucleation-condensation to framework mechanism

The iterative annealing mechanism (IAM) of chaperonin-assisted protein folding is explored in a framework of a well-established coarse-grained protein modeling tool, which enables the study of protein dynamics in a time-scale well beyond classical all-atom molecular mechanics. The chaperonin mechanism of action is simulated for two paradigm systems of protein folding, B domain of protein A (BdpA) and B1 domain of protein G (GB1), and compared to chaperonin-free simulations presented here for BdpA and recently published for GB1. The prediction of the BdpA transition state ensemble (TSE) is in perfect agreement with experimental findings. It is shown that periodic distortion of the polypeptide chains by hydrophobic chaperonin interactions can promote rapid folding and leads to a decrease in folding temperature. It is also demonstrated how chaperonin action prevents kinetically trapped conformations and modulates the observed folding mechanisms from nucleation-condensation to a more framework-like.     

Folding of small proteins using a single continuous potential

Extensive Monte Carlo folding simulations for four proteins of various structural classes are carried out, using a single continuous potential (united-residue force field). In all cases, collapse occurs at a very early stage, and proteins fold into their nativelike conformations at appropriate temperatures. We also observe that glassy transitions occur at low temperatures. The simulation results demonstrate that the folding mechanism is controlled not only by thermodynamic factors but also by kinetic factors: The way a protein folds into its native structure is also determined by the convergence point of early folding trajectories, which cannot be obtained by the free energy surface.     

Extensive structural change of the envelope protein of dengue virus induced by a tuned ionic strength: conformational and energetic analyses

The Dengue has become a global public health threat, with over 100 million infections annually; to date there is no specific vaccine or any antiviral drug. The structures of the envelope (E) proteins of the four known serotype of the dengue virus (DENV) are already known, but there are insufficient molecular details of their structural behavior in solution in the distinct environmental conditions in which the DENVs are submitted, from the digestive tract of the mosquito up to its replication inside the host cell. Such detailed knowledge becomes important because of the multifunctional character of the E protein: it mediates the early events in cell entry, via receptor endocytosis and, as a class II protein, participates determinately in the process of membrane fusion. The proposed infection mechanism asserts that once in the endosome, at low pH, the E homodimers dissociate and insert into the endosomal lipid membrane, after an extensive conformational change, mainly on the relative arrangement of its three domains. In this work we employ all-atom explicit solvent Molecular Dynamics simulations to specify the thermodynamic conditions in that the E proteins are induced to experience extensive structural changes, such as during the process of reducing pH. We study the structural behavior of the E protein monomer at acid pH solution of distinct ionic strength. Extensive simulations are carried out with all the histidine residues in its full protonated form at four distinct ionic strengths. The results are analyzed in detail from structural and energetic perspectives, and the virtual protein movements are described by means of the principal component analyses. As the main result, we found that at acid pH and physiological ionic strength, the E protein suffers a major structural change; for lower or higher ionic strengths, the crystal structure is essentially maintained along of all extensive simulations. On the other hand, at basic pH, when all histidine residues are in the unprotonated form, the protein structure is very stable for ionic strengths ranging from 0 to 225 mM. Therefore, our findings support the hypothesis that the histidines constitute the hot points that induce configurational changes of E protein in acid pH, and give extra motivation to the development of new ideas for antivirus compound design.     

Solvent viscosity dependence of the protein folding dynamics

Solvent viscosity has been frequently adopted as an adjustable parameter in various computational studies (e.g., protein folding simulations) with implicit solvent models. A common approach is to use low viscosities to expedite simulations. While using viscosities lower than that of aqueous is unphysical, such treatment is based on observations that the viscosity affects the kinetics (rates) in a well-defined manner as described by Kramers' theory. Here, we investigate the effect of viscosity on the detailed dynamics (mechanism) of protein folding. On the basis of a simple mathematical model, we first show that viscosity may indeed affect the dynamics in a complex way. By applying the model to the folding of a small protein, we demonstrate that the detailed dynamics is affected rather pronouncedly especially at unphysically low viscosities, cautioning against using such viscosities. In this regard, our model may also serve as a diagnostic tool for validating low-viscosity simulations. It is also suggested that the viscosity dependence can be further exploited to gain information about the protein folding mechanism.     

A role for confined water in chaperonin function

Chaperonins engulf other proteins and accelerate their folding by an unknown mechanism. Here, we combine all-atom molecular dynamics simulations with data from experimental assays of the activity of the bacterial chaperonin GroEL to demonstrate that a chaperonin's ability to facilitate folding is correlated with the affinity of its interior surface for water. Our results suggest a novel view of the behavior of confined water for models of in vivo protein folding scenarios.     

Molecular dynamics characterization of the structures and induction mechanisms of a reverse phenotype of the tetracycline receptor

Molecular-dynamics simulations have been used to investigate the mechanism of induction of a mutant (revTetR) of the tetracycline repressor protein (TetR) that shows the reverse phenotype (i.e., it is induced in the absence of tetracyclines and not in their presence). Low-frequency, normal-mode analyses demonstrate that the reverse phenotype is reproduced by the simulations on the basis of criteria established for wild-type TetR. The reverse phenotype is caused by the fact that the DNA-binding heads in revTetR are closer than the ideal distance needed for DNA-binding when no inducer is present. This distance increases on binding an inducer. Whereas this distance increase makes the interhead distance too large in wild-type TetR, it increases to the ideal value in revTetR. Thus, the mechanism of induction is the same for the two proteins, but the consequences are reversed because of the smaller interhead distance in revTetR when no inducer is present.     

Molecular simulation to characterize the adsorption behavior of a fibrinogen gamma-chain fragment

Implants invoke inflammatory responses from the body even if they are chemically inert and nontoxic. It has been shown that a crucial precedent event in the inflammatory process is the spontaneous adsorption of fibrinogen (Fg) on implant surfaces, which is typically followed by the presence of phagocytic cells. Interactions between the phagocyte integrin Mac-1 and two short sequences within the fibrinogen gamma chain, gamma190-202 and gamma377-395, may partially explain phagocyte accumulation at implant surfaces. These two sequences are believed to form an integrin binding site that is inaccessible when Fg is in its soluble-state structure but then becomes available for Mac-1 binding following adsorption, presumably due to adsorption-induced conformational changes. The objective of this research was to theoretically investigate this possibility by using molecular dynamics simulations of the gamma-chain fragment of Fg over self-assembled monolayer (SAM) surfaces presenting different types of surface chemistry. The GROMACS software package was used to carry out the molecular simulations in an explicit solvation environment over a 5 ns period of time. The adsorption of the gamma-chain of fibrinogen was simulated on five types of SAM surfaces. The simulations showed that this protein fragment exhibits distinctly different adsorption behavior on the different surface chemistries. Although the trajectory files showed that significant conformational changes did not occur in this protein fragment over the time frame of the simulations, it was predicted that the protein does undergo substantial rotational and translational motions over the surface prior to stabilizing in various preferred orientations. This suggests that the kinetics of surface-induced conformational changes in a protein's structure might be much slower than the kinetics of orientational changes, thus enabling the principles of adsorption thermodynamics to be used to guide adsorbing proteins into defined orientations on surfaces before large conformational changes can occur. This finding may be very important for biomaterial surface design as it suggests that surface chemistry can potentially be used to directly control the orientation of adsorbing proteins in a manner that either presents or hides specific bioactive sites contained within a protein's structure, thereby providing a mechanism to control cellular responses to the adsorbed protein layer.     

Growth mechanism of a gas clathrate hydrate from a dilute aqueous gas solution: a molecular dynamics simulation of a three-phase system

A molecular dynamics simulation of a three-phase system including a gas clathrate, liquid water, and a gas was carried out at 298 K and high pressure in order to investigate the growth mechanism of the clathrate from a dilute aqueous gas solution. The simulation indicated that the clathrate grew on interfaces between the clathrate and the liquid water, after transfer of the gas molecules from the gas phase to the interfaces. The results suggest a two-step process for growth: first, gas molecules are arranged at cage sites, and second, H(2)O molecules are ordered near the gas molecules. The results also suggest that only the H(2)O molecules, which are surrounded or sandwiched by the gas molecules, form the stable polygons that constitute the cages of the clathrate. In addition, the growth of the clathrate from a concentrated aqueous gas solution was also simulated, and the results suggested a growth mechanism in which many H(2)O and gas molecules correctively form the structure of the clathrate. The clathrate grown from the concentrated solution contained some empty cages, whereas the formation of empty cages was not observed during the growth from the dilute solution. The results obtained by both simulations are compared with the results of an experimental study, and the growth mechanism of the clathrate in a real system is discussed.     

Steric trigger as a mechanism for CB1 cannabinoid receptor activation

To determine the moiety that behaves as the steric trigger to activate the CB(1) cannabinoid receptor, conformational properties of the nonclassical cannabinoid CP55244, one of the most potent CB(1) receptor agonists, were characterized by conformational analysis, rotational barrier calculations, and molecular dynamics (MD) simulations. It was shown from the present MD simulations that the torsion angles phi1 and phi4 of the C3 side chain showed the most dramatic change when compared with the ground-state receptor-bound conformation, indicating that rotation around these torsion angles is responsible for releasing the ligand strain energy. Multiple stages would be involved in the ligand conformational change. As a molecular mechanism for the ligand-induced CB(1) receptor conformational change, we propose that the C3 side chain serves as the steric trigger, while the ACD-ring moiety of CP55244 serves as the plug. Steric clash with helices within the binding pocket would induce microconformational adaptation within the protein. This mechanism would suggest that rotational flexibility in a ligand may be as important a determinant of agonist activity as the pharmacophoric elements that can be identified.     

Insights into the phosphoryl-transfer mechanism of cAMP-dependent protein kinase from quantum chemical calculations and molecular dynamics simulations

To investigate the molecular details of the phosphoryl-transfer mechanism catalyzed by cAMP-dependent protein kinase, we performed quantum mechanical (QM) calculations on a cluster model of the active site and molecular dynamics (MD) simulations of a ternary complex of the protein with Mg(2)ATP and a 20-residue peptide substrate. Overall, our theoretical results confirm the participation of the conserved aspartic acid, Asp(166), as an acid/base catalyst in the reaction mechanism catalyzed by protein kinases. The MD simulation shows that the contact between the nucleophilic serine side chain and the carboxylate group of Asp(166) is short and dynamically stable, whereas the QM study indicates that an Asp(166)-assisted pathway is structurally and energetically feasible and is in agreement with previous experimental results.     

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.     

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 A? in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.     

Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.     

Fractal aggregates in protein crystal nucleation

Monte Carlo simulations of homogeneous nucleation for a protein model with an exceedingly short-ranged attractive potential yielded a nonconventional crystal nucleation mechanism, which proceeds by the formation of fractal, low-dimensional aggregates followed by a concurrent collapse and increase of the crystallinity of these aggregates to become compact ordered nuclei. This result corroborates a recently proposed two-step mechanism for protein crystal nucleation from solution.     

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.