Solvent molecules bridge the mechanical unfolding transition state of a protein

Structural Water Stabilizes Protein Motifs in Liquid Protein Phase: The Folding Mechanism of Short β-Sheets Coupled to Phase Transition

Macromolecular associates, such as membraneless organelles or lipid-protein assemblies, provide a hydrophobic environment, i.e., a liquid protein phase (LP), where folding preferences can be drastically altered. LP as well as the associated phase change from water (W) is an intriguing phenomenon related to numerous biological processes and also possesses potential in nanotechnological applications. However, the energetic effects of a hydrophobic yet water-containing environment on protein folding are poorly understood. Here, we focus on small β-sheets, the key motifs of proteins, undergoing structural changes in liquid–liquid phase separation (LLPS) and also model the mechanism of energy-coupled unfolding, e.g., in proteases, during W → LP transition. Due to the importance of the accurate description for hydrogen bonding patterns, the employed models were studied by using quantum mechanical calculations. The results demonstrate that unfolding is energetically less favored in LP by ~0.3–0.5 kcal·mol⁻¹ per residue in which the difference further increased by the presence of explicit structural water molecules, where the folded state was preferred by ~1.2–2.3 kcal·mol⁻¹ per residue relative to that in W. Energetics at the LP/W interfaces was also addressed by theoretical isodesmic reactions. While the models predict folded state preference in LP, the unfolding from LP to W renders the process highly favorable since the unfolded end state has >1 kcal·mol⁻¹ per residue excess stabilization.

The Stabilizing Excipients in Dry State Therapeutic Phage Formulations

Phage therapy has gained prominence due to the increasing pathogenicity of "super bugs" and the rise of their multidrug resistance to conventional antibiotics. Dry state formulation of therapeutic phage is attractive to improve their "druggability" by increasing their shelf life, improving their ease of handling, and ultimately retaining their long-term potency. The use and selection of excipients are critical to stabilize phage in solid formulations and protect their viability from stresses encountered during the solidification process and long-term storage prior to use. Here, this review focuses on the current classes of excipients used to manufacture dry state phage formulations and their ability to stabilize and protect phage throughout the process, as discussed in the literature. We provide perspective of outstanding challenges involved in the formulation of dry state phage. We suggest strategies to improve excipient identification and selection, optimize the potential excipient combinations to improve phage viability during formulation, and evaluate new methodologies that can provide greater insight into phage-excipient interactions to improve design criteria to improve formulation of dry state phage therapeutics. Addressing these challenges opens up new opportunities to re-design and re-imagine phage formulations for improved efficacy as a pharmaceutical product.

Nonexponential kinetics of ion pair dissociation in electrofreezing water

Temporally- or spatially-heterogeneous environments can participate in many kinetic processes, from chemical reactions and self-assembly to the forced dissociation of biomolecules. Here, we simulate the molecular dynamics of a model ion pair forced to dissociate in an explicit, aqueous solution. Triggering dissociation with an external electric field causes the surrounding water to electrofreeze and the ion pair population to decay nonexponentially. To further probe the role of the aqueous environment in the kinetics, we also simulate dissociation events under a purely mechanical force on the ion pair. In this case, regardless of whether the surrounding water is a liquid or already electrofrozen, the ion pair population decays exponentially with a well-defined rate constant that is specific to the medium and applied force. These simulation data, and the rate parameters we extract, suggest the disordered kinetics in an electrofreezing medium are a result of the comparable time scales of two concurrent processes, electrofreezing and dissociation.

DNA hairpin stabilization on a hydrophobic surface

DNA hybridization in the vicinity of surfaces is a fundamental process for self-assembled nanoarrays, nanocrystal superlattices, and biosensors. It is widely recognized that solid surfaces alter molecular forces governing hybridization relative to a bulk solution, and these effects can either favor or disfavor the hybridized state depending on the specific sequence and surface. Results presented here provide new insights into the dynamics of DNA hairpin-coil conformational transitions in the vicinity of hydrophilic oligo(ethylene glycol) (OEG) and hydrophobic trimethylsilane (TMS) surfaces. Single-molecule methods are used to observe the forward and reverse hybridization hairpin-coil transition of adsorbed species while simultaneously measuring molecular surface diffusion in order to gain insight into surface interactions with individual DNA bases. At least 35 000 individual molecular trajectories are observed on each type of surface. It is found that unfolding slows and the folding rate increases on TMS relative to OEG, despite stronger attractions between TMS and unpaired nucleobases. These rate differences lead to near-complete hairpin formation on hydrophobic TMS and significant unfolding on hydrophilic OEG, resulting in the surprising conclusion that hydrophobic surface coatings are preferable for nanotechnology applications that rely on DNA hybridization near surfaces.

Pulling-spring modulation as a method for improving the potential-of-mean-force reconstruction in single-molecule manipulation experiments

The free-energy calculation is usually limited to close to equilibrium perturbation regimes because faster perturbations introduce a bias into the estimate. The Jarzynski equality offers a solution to this problem by directly connecting the free-energy difference and the external work, regardless how far from equilibrium that work may be. However, a limited sampling coupled to the fast perturbation introduces a slowly converging bias into the Jarzynski free-energy estimate also. In this paper we present two perturbation protocols devised with the intention to overcome the convergence issues of the Jarzynski-based potential of mean force estimation in the single-molecule, constant velocity manipulation experiments. The protocols are designed to improve the convergence issues by increasing the variation of the external work through the modulation of the spring used to pull a molecule. Of the two methods, the one which continuously changes the amplitude of the spring stiffness offers an excellent reconstruction and requires less than one tenth of the samples required by the normal, constant spring pulling to produce the same quality of the reconstruction.

Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes

We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.

Thermodynamic analysis of water molecules at the surface of proteins and applications to binding site prediction and characterization

Water plays an essential role in determining the structure and function of all biological systems. Recent methodological advances allow for an accurate and efficient estimation of the thermodynamic properties of water molecules at the surface of proteins. In this work, we characterize these thermodynamic properties and relate them to various structural and functional characteristics of the protein. We find that high-energy hydration sites often exist near protein motifs typically characterized as hydrophilic, such as backbone amide groups. We also find that waters around alpha helices and beta sheets tend to be less stable than waters around loops. Furthermore, we find no significant correlation between the hydration site-free energy and the solvent accessible surface area of the site. In addition, we find that the distribution of high-energy hydration sites on the protein surface can be used to identify the location of binding sites and that binding sites of druggable targets tend to have a greater density of thermodynamically unstable hydration sites. Using this information, we characterize the FKBP12 protein and show good agreement between fragment screening hit rates from NMR spectroscopy and hydration site energetics. Finally, we show that water molecules observed in crystal structures are less stable on average than bulk water as a consequence of the high degree of spatial localization, thereby resulting in a significant loss in entropy. These findings should help to better understand the characteristics of waters at the surface of proteins and are expected to lead to insights that can guide structure-based drug design efforts.

Transient-state fluctuationlike relation for the driving force on a biomolecule

In experiments and simulations the force acting on a single biomolecular system has been observed as a fluctuating quantity if the system is driven under constant velocity. We ask the question that is analogous to transient state entropy production and work fluctuation relations whether the force fluctuations observed in the single biomolecular system satisfy a transient state fluctuationlike relation, and the answer is in the affirmative. Using a constant velocity pulling steered molecular dynamics simulation study for protein unfolding, we confirm that the force fluctuations of this single biomolecular system satisfy a transient-state fluctuationlike relation 1/γ(T,v) ln[P(v)(+f)/P(v)(-f)] = f. P(v)(±f) is the probability of positive and negative values of forces f = f · for a given unfolding velocity of magnitude v and the pulling direction n, nis the unit vector of n, and γ(T,v) is a factor that depends on initial equilibrium temperature T and the unfolding velocity. For different unfolding velocities we find that the system in the nonequilibrium pulling region displays substantial negative fluctuation in its unfolding force when velocity decreases. A negative value of force may indicate the emergence of refolding behavior during protein unfolding. We also find that γ(T,v) ~ T(-δ)v(α) and the system relaxation time τ(T,v) ~ T(δ)v(-(1+α), where α and δ are scaling exponents.

Protein-excipient interactions: mechanisms and biophysical characterization applied to protein formulation development

The purpose of this review is to demonstrate the critical importance of understanding protein-excipient interactions as a key step in the rational design of formulations to stabilize and deliver protein-based therapeutic drugs and vaccines. Biophysical methods used to examine various molecular interactions between solutes and protein molecules are discussed with an emphasis on applications to pharmaceutical excipients in terms of their effects on protein stability. Key mechanisms of protein-excipient interactions such as electrostatic and cation-pi interactions, preferential hydration, dispersive forces, and hydrogen bonding are presented in the context of different physical states of the formulation such as frozen liquids, solutions, gels, freeze-dried solids and interfacial phenomenon. An overview of the different classes of pharmaceutical excipients used to formulate and stabilize protein therapeutic drugs is also presented along with the rationale for use in different dosage forms including practical pharmaceutical considerations. The utility of high throughput analytical methodologies to examine protein-excipient interactions is presented in terms of expanding formulation design space and accelerating experimental timelines.

Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein

Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ(‡). Here we used single molecule force-clamp spectroscopy to directly determine the value of υ(‡) for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG(‡) = 71 ± 5 kJ/mol and an exponential prefactor υ(‡) ∼4 × 10(9) s(-1). Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10(12) s(-1)), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10(7) M(-1) s(-1)). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.

Probing osmolyte participation in the unfolding transition state of a protein

Understanding the molecular mechanisms of osmolyte protection in protein stability has proved to be challenging. In particular, little is known about the role of osmolytes in the structure of the unfolding transition state of a protein, the main determinant of its dynamics. We have developed an experimental protocol to directly probe the transition state of a protein in a range of osmolyte environments. We use an atomic force microscope in force-clamp mode to apply mechanical forces to the protein I27 and obtain force-dependent rate constants of protein unfolding. We measure the distance to the unfolding transition state, Δx(u), along a 1D reaction coordinate imposed by mechanical force. We find that for the small osmolytes, ethylene glycol, propylene glycol, and glycerol, Δx(u) scales with the size of the molecule, whereas for larger osmolytes, sorbitol and sucrose, Δx(u) remains the same as that measured in water. These results are in agreement with steered molecular dynamics simulations that show that small osmolytes act as solvent bridges in the unfolding transition state structure, whereas only water molecules act as solvent bridges in large osmolyte environments. These results demonstrate that novel force protocols combined with solvent substitution can directly probe angstrom changes in unfolding transition state structure. This approach creates new opportunities to gain molecular level understanding of the action of osmolytes in biomolecular processes.

Contrasting the individual reactive pathways in protein unfolding and disulfide bond reduction observed within a single protein

Identifying the dynamics of individual molecules along their reactive pathways remains a major goal of modern chemistry. For simple chemical reactions, the transition state position is thought to be highly localized. Conversely, in the case of more complex reactions involving proteins, the potential energy surfaces become rougher, resulting in heterogeneous reaction pathways with multiple transition state structures. Force-clamp spectroscopy experimentally probes the individual reaction pathways sampled by a single protein under the effect of a constant stretching force. Herein, we examine the distribution of conformations that populate the transition state of two different reactions; the unfolding of a single protein and the reduction of a single disulfide bond, both occurring within the same single protein. By applying the recently developed static disorder theory, we quantify the variance of the barrier heights, σ(2), governing each distinct reaction. We demonstrate that the unfolding of the I27 protein follows a nonexponential kinetics, consistent with a high value of σ(2) ∼ 18 (pN nm)(2). Interestingly, shortening of the protein upon introduction of a rigid disulfide bond significantly modulates the disorder degree, spanning from σ(2) ∼ 8 to ∼21 (pN nm)(2). These results are in sharp contrast with the exponential distribution of times measured for an S(N)2 chemical reaction, implying the absence of static disorder σ(2) ∼ 0 (pN nm)(2). Our results demonstrate the high sensitivity of the force-clamp technique to capture the signatures of disorder in the individual pathways that define two distinct force-induced reactions, occurring within the core of a single protein.

Direct observation of multiple pathways of single-stranded DNA stretching

We observed multiple pathways of stretching single-stranded polydeoxynucleotides, poly(dA). Poly(dA) has been shown to undergo unique transitions under mechanical force, and such transitions were attributed to the stacking characteristics of poly(dA). Using single-molecule manipulation studies, we found that poly(dA) has two stretching pathways at high forces. The previously observed pathway has a free energy that is less than what is expected of single-stranded DNA with a random sequence, indicating the existence of a novel conformation of poly(dA) at large extensions. We also observed stepwise transitions between the two pathways by pulling the molecule with constant force, and found that the transitions are cooperative. These results suggest that the unique mechanical property of poly(dA) may play an important role in biological processes such as gene expression.

Hopping around an entropic barrier created by force

We use Langevin dynamics to investigate the role played by the recently discovered force-induced entropic energy barrier on the two-state hopping phenomena that has been observed in single RNA, DNA and protein molecules placed under a stretching force. Simple considerations about the free energy of a molecule readily show that the application of force introduces an entropic barrier separating the collapsed state of the molecule, from a force-driven extended conformation. A notable characteristic of the force induced barrier is its long distances to transition state, up to tens of nanometers, which renders the kinetics of crossing this barrier highly sensitive to an applied force. Langevin dynamics across such force induced barriers readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Such hopping is frequently interpreted as a manifestation of two-state folding/unfolding reactions observed in bulk experiments. However, given that such barriers do not exist at zero force these reactions do not take place at all in bulk.

Statistics of reversible bond dynamics observed in force-clamp spectroscopy

We present a detailed analysis of two-state trajectories obtained from force-clamp spectroscopy (FCS) of reversibly bonded systems. FCS offers the unique possibility to vary the equilibrium constant in two-state kinetics, for instance, the unfolding and refolding of biomolecules, over many orders of magnitude due to the force dependence of the respective rates. We discuss two different kinds of counting statistics, the event counting usually employed in the statistical analysis of two-state kinetics and additionally the so-called cycle counting. While in the former case all transitions are counted, cycle counting means that we focus on one type of transitions. This might be advantageous in particular if the equilibrium constant is much larger or much smaller than unity because in these situations the temporal resolution of the experimental setup might not allow to capture all transitions of an event-counting analysis. We discuss how an analysis of FCS data for complex systems exhibiting dynamic disorder might be performed yielding information about the detailed force dependence of the transition rates and about the time scale of the dynamic disorder. In addition, the question as to which extent the kinetic scheme can be viewed as a Markovian two-state model is discussed.

Water's role in the force-induced unfolding of ubiquitin

In atomic force spectroscopic studies of the elastomeric protein ubiquitin, the β-strands 1-5 serve as the force clamp. Simulations show how the rupture force in the force-induced unfolding depends on the kinetics of water molecule insertion into positions where they can eventually form hydrogen bonding bridges with the backbone hydrogen bonds in the force-clamp region. The intrusion of water into this region is slowed down by the hydrophobic shielding effect of carbonaceous groups on the surface residues of β-strands 1-5, which thereby regulates water insertion prior to hydrogen bond breakage. The experiments show that the unfolding of the mechanically stressed protein is nonexponential due to static disorder. Our simulations show that different numbers and/or locations of bridging water molecules give rise to a long-lived distribution of transition states and static disorder. We find that slowing down the translational (not rotational) motions of the water molecules by increasing the mass of their oxygen atoms, which leaves the force field and thereby the equilibrium structure of the solvent unchanged, increases the average rupture force; however, the early stages of the force versus time behavior are very similar for our "normal" and fictitious "heavy" water models. Finally, we construct six mutant systems to regulate the hydrophobic shielding effect of the surface residues in the force-clamp region. The mutations in the two termini of β-sheets 1-5 are found to determine a preference for different unfolding pathways and change mutant's average rupture force.

Full reconstruction of a vectorial protein folding pathway by atomic force microscopy and molecular dynamics simulations

During co-translational folding, the nascent polypeptide chain is extruded sequentially from the ribosome exit tunnel and is [corrected] under severe conformational constraints [corrected] dictated by the one-dimensional geometry of the tunnel. [corrected] How do such vectorial constraints impact the folding pathway? Here, we combine single-molecule atomic force spectroscopy and steered molecular dynamics simulations to examine protein folding in the presence of one-dimensional constraints that are similar to those imposed on the nascent polypeptide chain. The simulations exquisitely reproduced the experimental unfolding and refolding force extension relationships and led to the full reconstruction of the vectorial folding pathway of a large polypeptide, the 253-residue consensus ankyrin repeat protein, NI6C. We show that fully stretched and then relaxed NI6C starts folding by the formation of local secondary structures, followed by the nucleation of three N-terminal repeats. This rate-limiting step is then followed by the vectorial and sequential folding of the remaining repeats. However, after partial unfolding, when allowed to refold, the C-terminal repeats successively regain structures without any nucleation step by using the intact N-terminal repeats as a template. These results suggest a pathway for the co-translational folding of repeat proteins and have implications for mechanotransduction.

Molecular dynamics simulations suggest that electrostatic funnel directs binding of Tamiflu to influenza N1 neuraminidases

Oseltamivir (Tamiflu) is currently the frontline antiviral drug employed to fight the flu virus in infected individuals by inhibiting neuraminidase, a flu protein responsible for the release of newly synthesized virions. However, oseltamivir resistance has become a critical problem due to rapid mutation of the flu virus. Unfortunately, how mutations actually confer drug resistance is not well understood. In this study, we employ molecular dynamics (MD) and steered molecular dynamics (SMD) simulations, as well as graphics processing unit (GPU)-accelerated electrostatic mapping, to uncover the mechanism behind point mutation induced oseltamivir-resistance in both H5N1 “avian” and H1N1pdm “swine” flu N1-subtype neuraminidases. The simulations reveal an electrostatic binding funnel that plays a key role in directing oseltamivir into and out of its binding site on N1 neuraminidase. The binding pathway for oseltamivir suggests how mutations disrupt drug binding and how new drugs may circumvent the resistance mechanisms.

Oseltamivir (Tamiflu) is the main antiviral drug used to fight viral influenza outbreaks such as the recent swine flu (H1N1pdm) global pandemic and avian (H5N1) outbreak in Asia. Oseltamivir inhibits a protein on the surface of flu viruses called neuraminidase, which is responsible for releasing newly formed viruses. The rapid emergence of drug resistance in H5N1 avian flu (and recently the H1N1pdm strain) has already motivated numerous studies to understand how mutations render oseltamivir ineffective, but no focused investigation has yet elucidated the specific mechanism behind mutation-induced drug resistance. Here, large scale computer simulations are employed to study both H5N1 and H1N1pdm neuraminidase to answer the questions: how does N1-subtype neuraminidase bind oseltamivir, and how would mutations alter this process? The key finding revealed in our simulations is the discovery of oseltamivir binding to neuraminidase by a charged pathway on the protein surface. We suggest that point mutations may disrupt drug binding by interfering with this pathway. Our results explain the fundamental mechanism behind oseltamivir resistance and pave the way for the design of drugs that circumvent viral drug resistance.

Unravelling the design principles for single protein mechanical strength

In recent years single molecule manipulation techniques have improved to the extent that measurements of the mechanical strength of single proteins can now be undertaken routinely. This powerful new tool, coupled with theoretical frameworks to characterise the unfolding process, has enabled significant progress to be made in understanding the physical mechanisms that underlie protein mechanical strength. These design concepts have allowed the search for proteins with novel, mechanically strong folds to be automated and for previously mechanically characterised proteins to be engineered rationally. Methods to achieve the latter are diverse and include re-engineering of specific hydrophobic core residues, changing solvent conditions and the 'cross-linking' of side-chains that are separated in the rate-limiting unfolding transition. Predicting the mechanical behaviour of larger proteins and those with more complex structures remains a significant challenge while on-going instrument development is beginning to allow the examination of mechanical strength of protein across a wide range of force loading rates. The integral role of force in biology and the potential for exploitation of catalytic and structural proteins as functional bio-materials makes this a particularly important area of research.

Probing static disorder in Arrhenius kinetics by single-molecule force spectroscopy

The widely used Arrhenius equation describes the kinetics of simple two-state reactions, with the implicit assumption of a single transition state with a well-defined activation energy barrier DeltaE, as the rate-limiting step. However, it has become increasingly clear that the saddle point of the free-energy surface in most reactions is populated by ensembles of conformations, leading to nonexponential kinetics. Here we present a theory that generalizes the Arrhenius equation to include static disorder of conformational degrees of freedom as a function of an external perturbation to fully account for a diverse set of transition states. The effect of a perturbation on static disorder is best examined at the single-molecule level. Here we use force-clamp spectroscopy to study the nonexponential kinetics of single ubiquitin proteins unfolding under force. We find that the measured variance in DeltaE shows both force-dependent and independent components, where the force-dependent component scales with F(2), in excellent agreement with our theory. Our study illustrates a novel adaptation of the classical Arrhenius equation that accounts for the microscopic origins of nonexponential kinetics, which are essential in understanding the rapidly growing body of single-molecule data.

The relationship between water bridges and the polyproline II conformation: a large-scale analysis of molecular dynamics simulations and crystal structures

It has been suggested that denatured proteins are predisposed toward the left-handed polyproline II (P(II)) conformation. One possible source of P(II) stability in the denatured state is water bridges. Water bridges are networks of water molecules that link nearby hydrogen bond acceptors and/or donors on proteins. On the basis of the proposed behavior of P(II) and water bridges, the propensity of a residue to participate in water bridges should be correlated with its P(II) propensity. To test this hypothesis, we analyzed the following data sets: 2351 high-resolution crystal structures, and the native and denatured states of 188 different proteins from all-atom, explicit-solvent molecular dynamics (MD) simulations, which are part of our Dynameomics effort. We found that water bridges do not explain the high frequency of P(II) in denatured states; such bridges are less frequent around P(II) than around other conformations. Thus, this analysis casts doubt on water bridges as a dominant factor determining the residue-based P(II) propensities.

Understanding biology by stretching proteins: recent progress

Single molecule manipulation techniques combined with molecular dynamics simulations and protein engineering have enabled, during the last decade, the mechanical properties of proteins to be studied directly, thereby giving birth to the field of protein nanomechanics. Recent data obtained from such techniques have helped gain insight into the structural bases of protein resistance against forced unfolding, as well as revealing structural motifs involved in mechanical stability. Also, important technical developments have provided new perspectives into protein folding. Eventually, new and exciting data have shown that mechanical properties are key factors in cell signaling and pathologies, and have been used to rationally tune these properties in a variety of proteins.

Discovery through the computational microscope

All-atom molecular dynamics simulations have become increasingly popular as a tool to investigate protein function and dynamics. However, researchers are concerned about the short time scales covered by simulations, the apparent impossibility to model large and integral biomolecular systems, and the actual predictive power of the molecular dynamics methodology. Here we review simulations that were in the past both hotly disputed and considered key successes, namely of proteins with mainly mechanical functions (titin, fibrinogen, ankyrin, and cadherin). The simulation work covered shows how state-of-the-art modeling alleviates some of the prior concerns and how unrefuted discoveries are made through the "computational microscope."

Computational and single-molecule force studies of a macro domain protein reveal a key molecular determinant for mechanical stability

Resolving molecular determinants of mechanical stability of proteins is crucial in the rational design of advanced biomaterials for use in biomedical and nanotechnological applications. Here we present an interdisciplinary study combining bioinformatics screening, steered molecular dynamics simulations, protein engineering, and single-molecule force spectroscopy that explores the mechanical properties of a macro domain protein with mixed alpha + beta topology. The unique architecture is defined by a single seven-stranded beta-sheet in the core of the protein flanked by five alpha-helices. Unlike mechanically stable proteins studied thus far, the macro domain provides the distinct advantage of having the key load-bearing hydrogen bonds (H bonds) buried in the hydrophobic core protected from water attacks. This feature allows direct measurement of the force required to break apart the load-bearing H bonds under locally hydrophobic conditions. Steered molecular dynamics simulations predicted extremely high mechanical stability of the macro domain by using constant velocity and constant force methods. Single-molecule force spectroscopy experiments confirm the exceptional mechanical strength of the macro domain, measuring a rupture force as high as 570 pN. Furthermore, through selective deletion of shielding peptide segments, we examined the same key H bonds under hydrophilic environments in which the beta-strands are exposed to solvent and verify that the high mechanical stability of the macro domain results from excellent shielding of the load-bearing H bonds from competing water. Our study reveals that shielding water accessibility to the load-bearing strands is a critical molecular determinant for enhancing the mechanical stability of proteins.

Unfolding times for proteins in a force clamp

The escape process from the native valley for proteins subjected to a constant stretching force is examined using a model for a beta barrel. For a wide range of forces, the unfolding dynamics can be treated as one-dimensional diffusion, parametrized in terms of the end-to-end distance. In particular, the escape times can be evaluated as first passage times for a Brownian particle moving on the protein free-energy landscape, using the Smoluchowski equation. At strong forces, the unfolding process can be viewed as a diffusive drift away from the native state, while at weak forces thermal activation is the relevant mechanism. An escape-time analysis within this approach reveals a crossover from an exponential to an inverse Gaussian escape-time distribution upon passing from weak to strong forces. Moreover, a single expression valid at weak and strong forces can be devised both for the average unfolding time as well as for the corresponding variance. The analysis offers a possible explanation of recent experimental findings for the proteins ddFLN4 and ubiquitin.

Mechanical unfolding of bacterial flagellar filament protein by molecular dynamics simulation

Bacterial flagellum is a nano-scale motility device constructed by self-assembly. During construction of the cell-exterior filament (the 'propeller'), subunit proteins (called flagellin) are thought to be exported through the hollow flagellum to the growing filament tip in an unfolded state. To gain insight into the unfolded state preceding any force-spectroscopy experiments on flagellin, we employed force-probe molecular dynamics simulations. Two schemes to attain an unfolded state suitable for efficient transport were examined: (i) stretching flagellin along its length; (ii) unzipping flagellin from its adjacently placed termini. Atomic-level unfolding pathways and the mechanical efforts involved under each scheme were obtained for the four-domain flagellin from S. typhimurium. Flagellin appeared stiffer and required larger unfolding forces when stretched as the relative sliding of beta-strands require the breaking of multiple hydrogen bonds at once. In contrast, unzipping requires lower unfolding forces as it mainly involves unraveling beta-sheets by breaking hydrogen bonds one by one.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

Mechanical signaling on the single protein level studied using steered molecular dynamics

Efficient communication between the cell and its external environment is of the utmost importance to the function of multicellular organisms. While signaling events can be generally characterized as information exchange by means of controlled energy conversion, research efforts have hitherto mainly been concerned with mechanisms involving chemical and electrical energy transfer. Here, we review recent computational efforts addressing the function of mechanical force in signal transduction. Specifically, we focus on the role of steered molecular dynamics (SMD) simulations in providing details at the atomic level on a group of protein domains, which play a fundamental role in signal exchange by responding properly to mechanical strain. We start by giving a brief introduction to the SMD technique and general properties of mechanically stable protein folds, followed by specific examples illustrating three general regimes of signal transfer utilizing mechanical energy: purely mechanical, mechanical to chemical, and chemical to mechanical. Whenever possible the physiological importance of the example at hand is stressed to highlight the diversity of the processes in which mechanical signaling plays a key role. We also provide an overview of future challenges and perspectives for this rapidly developing field.

Mechanochemistry: one bond at a time

Single-molecule force-clamp spectroscopy offers a novel platform for mechanically denaturing proteins by applying a constant force to a polyprotein. A powerful emerging application of the technique is that, by introducing a disulfide bond in each protein module, the chemical kinetics of disulfide bond cleavage under different stretching forces can be probed at the single-bond level. Even at forces much lower than that which can rupture the chemical bond, the breaking of the S-S bond at the presence of various chemical reducing agents is significantly accelerated. Our previous work demonstrated that the rate of thiol/disulfide exchange reaction is force-dependent and well-described by an Arrhenius term of the form r = A(exp((FΔx(r) - E(a))/k(B)T)[nucleophile]). From Arrhenius fits to the force dependency of the reduction rate, we measured the bond elongation parameter, Δx(r), along the reaction coordinate to the transition state of the S(N)2 reaction cleaved by different nucleophiles and enzymes, never before observed by any other technique. For S-S cleavage by various reducing agents, obtaining the Δx(r) value can help depicting the energy landscapes and elucidating the mechanisms of the reactions at the single-molecule level. Small nucleophiles, such as 1,4-dl-dithiothreitol (DTT), tris(2-carboxyethyl)phosphine (TCEP), and l-cysteine, react with the S-S bond with monotonically increasing rates under the applied force, while thioredoxin enzymes exhibit both stretching-favored and -resistant reaction-rate regimes. These measurements demonstrate the power of the single-molecule force-clamp spectroscopy approach in providing unprecedented access to chemical reactions.

Mechanical characterization of protein L in the low-force regime by electromagnetic tweezers/evanescent nanometry

Mechanical manipulation at the single molecule level of proteins exhibiting mechanical stability poses a technical challenge that has been almost exclusively approached by atomic force microscopy (AFM) techniques. However, due to mechanical drift limitations, AFM techniques are restricted to experimental recordings that last less than a minute in the high-force regime. Here we demonstrate a novel combination of electromagnetic tweezers and evanescent nanometry that readily captures the forced unfolding trajectories of protein L at pulling forces as low as 10-15 pN. Using this approach, we monitor unfolding and refolding cycles of the same polyprotein for a period of time longer than 30 min. From such long-lasting recordings, we obtain ensemble averages of unfolding step sizes and rates that are consistent with single-molecule AFM data obtained at higher stretching forces. The unfolding kinetics of protein L at low stretching forces confirms and extends the observations that the mechanical unfolding rate is exponentially dependent on the pulling force within a wide range of stretching forces spanning from 13 pN up to 120 pN. Our experiments demonstrate a novel approach for the mechanical manipulation of single proteins for extended periods of time in the low-force regime.

Mechanical stability of proteins

A number of experiments and experimentally based simulations showed that beta-proteins are mechanically more stable than alpha-proteins. However, the theory that might explain this evidence is still lacking. In this paper we have developed a simple elastic theory, which allows to estimate critical forces for stretching both kinds of proteins. It has been shown that unfolding of beta-proteins does really require notably higher forces as compared to the stretching of alpha-proteins.

Single homopolypeptide chains collapse into mechanically rigid conformations

Huntington's disease is linked to the insertion of glutamine (Q) in the protein huntingtin, resulting in polyglutamine (polyQ) expansions that self-associate to form aggregates. While polyQ aggregation has been the subject of intense study, a correspondingly thorough understanding of individual polyQ chains is lacking. Here we demonstrate a single molecule force-clamp technique that directly probes the mechanical properties of single polyQ chains. We have made polyQ constructs of varying lengths that span the length range of normal and diseased polyQ expansions. Each polyQ construct is flanked by the I27 titin module, providing a clear mechanical fingerprint of the molecule being pulled. Remarkably, under the application of force, no extension is observed for any of the polyQ constructs. This is in direct contrast with the random coil protein PEVK of titin, which readily extends under force. Our measurements suggest that polyQ chains form mechanically stable collapsed structures. We test this hypothesis by disrupting polyQ chains with insertions of proline residues and find that their mechanical extensibility is sensitive to the position of the proline interruption. These experiments demonstrate that polyQ chains collapse to form a heterogeneous ensemble of conformations that are mechanically resilient. We further use a heat-annealing molecular dynamics protocol to extensively search the conformation space and find that polyQ can exist in highly mechanically stable compact globular conformations. The mechanical rigidity of these collapsed structures may exceed the functional ability of eukaryotic proteasomes, resulting in the accumulation of undigested polyQ sequences in vivo.

Osmolyte-induced separation of the mechanical folding phases of ubiquitin

Solvent molecules play key roles in the conformational dynamics of proteins. Here we use single molecule force-clamp spectroscopy to probe the role played by the stabilizing osmolyte glycerol on the conformational ensembles visited by a single ubiquitin protein folding after mechanical extension. Using a variety of force-pulse protocols, we find that glycerol stabilizes the native state of ubiquitin, making it more resistant to mechanical unfolding. We also find that although glycerol enhanced the hydrophobic collapse of unfolded and highly extended ubiquitins, it had no effect on the resulting collapsed states that are essential precursors of the folded state. These disparate effects of glycerol may be the result of distinct structural roles played by solvent molecules at the transition state of each folding ensemble. Our results open the way for a detailed analysis of the transition state structures that form along the folding trajectory of a mechanically extended protein.

Sequence-specific size, structure, and stability of tight protein knots

Approximately 1% of known protein structures display knotted configurations in their native fold, but the function of these configurations is not understood. It has been speculated that the entanglement may inhibit mechanical protein unfolding or transport, e.g., as in cellular threading or translocation processes through narrow biological pores. Protein knot manipulation, e.g., knot tightening and localization, has become possible in single-molecule experiments. Here, we investigate tight peptide knot (TPK) characteristics in detail by pulling selected 3(1) and 4(1)-knotted peptides using all-atom molecular dynamics computer simulations. We find that the 3(1)- and 4(1)-TPK lengths are typically Deltal approximately 47+/- 4 A and 69 +/- 4 A, respectively, for a wide range of tensions (0.1 nN less, similarF less, similar 1.5 nN). The 4(1)-knot length is in agreement with recent atomic force microscopy pulling experiments. Calculated TPK radii of gyration point to a pore diameter of approximately 20 A, below which a translocated knotted protein might get stuck. TPK characteristics, however, may be sequence-specific: we find a different size and structural behavior in polyglycines, and, strikingly, a strong hydrogen bonding and water trapping capability of hydrophobic TPKs. Water capture and release is found to be controllable by the tightening force in a few cases. These mechanisms result in a sequence-specific "locking" and metastability of TPKs, which might lead to a blocking of knotted peptide transport at designated sequence positions. We observe that macroscopic tight 4(1)-knot structures are reproduced microscopically ("figure of eight" versus the "pretzel") and can be tuned by sequence, in contrast to mathematical predictions. Our findings may explain a function of knots in native proteins, challenge previous studies on macromolecular knots, and prove useful in bio- and nanotechnology.

A single-molecule perspective on the role of solvent hydrogen bonds in protein folding and chemical reactions

We present an array of force spectroscopy experiments that aim to identify the role of solvent hydrogen bonds in protein folding and chemical reactions at the single-molecule level. In our experiments we control the strength of hydrogen bonds in the solvent environment by substituting water (H(2)O) with deuterium oxide (D(2)O). Using a combination of force protocols, we demonstrate that protein unfolding, protein collapse, protein folding and a chemical reaction are affected in different ways by substituting H(2)O with D(2)O. We find that D(2)O molecules form an integral part of the unfolding transition structure of the immunoglobulin module of human cardiac titin, I27. Strikingly, we find that D(2)O is a worse solvent than H(2)O for the protein I27, in direct contrast with the behaviour of simple hydrocarbons. We measure the effect of substituting H(2)O with D(2)O on the force dependent rate of reduction of a disulphide bond engineered within a single protein. Altogether, these experiments provide new information on the nature of the underlying interactions in protein folding and chemical reactions and demonstrate the power of single-molecule techniques to identify the changes induced by a small change in hydrogen bond strength.

An experimentally guided umbrella sampling protocol for biomolecules

We present a simple method for utilizing experimental data to improve the efficiency of numerical calculations of free energy profiles from molecular dynamics simulations. The method involves umbrella sampling simulations with restraining potentials based on a known approximate estimate of the free energy profile derived solely from experimental data. The use of the experimental data results in optimal restraining potentials, guides the simulation along relevant pathways, and decreases overall computational time. In demonstration of the method, two systems are showcased. First, guided, unguided (regular) umbrella sampling simulations and exhaustive sampling simulations are compared to each other in the calculation of the free energy profile for the distance between the ends of a pentapeptide. The guided simulation use restraints based on a simulated "experimental" potential of mean force of the end-to-end distance that would be measured by fluorescence resonance energy transfer (obtained from exhaustive sampling). Statistical analysis shows a dramatic improvement in efficiency for a 5 window guided umbrella sampling over 5 and 17 window unguided umbrella sampling simulations. Moreover, the form of the potential of mean force for the guided simulations evolves, as one approaches convergence, along the same milestones as the extensive simulations, but exponentially faster. Second, the method is further validated by replicating the forced unfolding pathway of the titin I27 domain using guiding umbrella sampling potentials determined from actual single molecule pulling data. Comparison with unguided umbrella sampling reveals that the use of guided sampling encourages unfolding simulations to converge faster to a forced unfolding pathway that agrees with previous results and produces a more accurate potential of mean force.