Single molecule unzipping of coiled coils: sequence resolved stability profiles

Mechanical Unfolding and Refolding of NanoLuc via Single-Molecule Force Spectroscopy and Computer Simulations

A highly bioluminescent protein, NanoLuc (Nluc), has seen numerous applications in biological assays since its creation. We recently engineered a NanoLuc polyprotein that showed high bioluminescence but displayed a strong misfolding propensity after mechanical unfolding. Here, we present our single-molecule force spectroscopy (SMFS) studies by atomic force microscopy (AFM) and steered molecular dynamics (SMD) simulations on two new hybrid protein constructs comprised of Nluc and I91 titin domains, I91-I91-Nluc-I91-I91-I91-I91 (I91₂-Nluc-I91₄) and I91-Nluc-I91-Nluc-I91-Nluc-I91, to characterize the unfolding behavior of Nluc in detail and to further investigate its misfolding properties that we observed earlier for the I91₂-Nluc₃-I91₂ construct. Our SMFS results confirm that Nluc's unfolding proceeds similarly in all constructs; however, Nluc's refolding differs in these constructs, and its misfolding is minimized when Nluc is monomeric or separated by I91 domains. Our simulations on monomeric Nluc, Nluc dyads, and Nluc triads pinpointed the origin of its mechanical stability and captured interesting unfolding intermediates, which we also observed experimentally.

Engineered Molecular Therapeutics Targeting Fibrin and the Coagulation System: a Biophysical Perspective

The coagulation cascade represents a sophisticated and highly choreographed series of molecular events taking place in the blood with important clinical implications. One key player in coagulation is fibrinogen, a highly abundant soluble blood protein that is processed by thrombin proteases at wound sites, triggering self-assembly of an insoluble protein hydrogel known as a fibrin clot. By forming the key protein component of blood clots, fibrin acts as a structural biomaterial with biophysical properties well suited to its role inhibiting fluid flow and maintaining hemostasis. Based on its clinical importance, fibrin is being investigated as a potentially valuable molecular target in the development of coagulation therapies. In this topical review, we summarize our current understanding of the coagulation cascade from a molecular, structural and biophysical perspective. We highlight single-molecule studies on proteins involved in blood coagulation and report on the current state of the art in directed evolution and molecular engineering of fibrin-targeted proteins and polymers for modulating coagulation. This biophysical overview will help acclimatize newcomers to the field and catalyze interdisciplinary work in biomolecular engineering toward the development of new therapies targeting fibrin and the coagulation system.

Unraveling the Mechanics of a Repeat-Protein Nanospring: From Folding of Individual Repeats to Fluctuations of the Superhelix

Tandem-repeat proteins comprise small secondary structure motifs that stack to form one-dimensional arrays with distinctive mechanical properties that are proposed to direct their cellular functions. Here, we use single-molecule optical tweezers to study the folding of consensus-designed tetratricopeptide repeats (CTPRs), superhelical arrays of short helix-turn-helix motifs. We find that CTPRs display a spring-like mechanical response in which individual repeats undergo rapid equilibrium fluctuations between partially folded and unfolded conformations. We rationalize the force response using Ising models and dissect the folding pathway of CTPRs under mechanical load, revealing how the repeat arrays form from the center toward both termini simultaneously. Most strikingly, we also directly observe the protein's superhelical tertiary structure in the force signal. Using protein engineering, crystallography, and single-molecule experiments, we show that the superhelical geometry can be altered by carefully placed amino acid substitutions, and we examine how these sequence changes affect intrinsic repeat stability and inter-repeat coupling. Our findings provide the means to dissect and modulate repeat-protein stability and dynamics, which will be essential for researchers to understand the function of natural repeat proteins and to exploit artificial repeats proteins in nanotechnology and biomedical applications.

Unraveling the Mechanics of a Repeat-Protein Nanospring: From Folding of Individual Repeats to Fluctuations of the Superhelix

Tandem-repeat proteins comprise small secondary structure motifs that stack to form one-dimensional arrays with distinctive mechanical properties that are proposed to direct their cellular functions. Here, we use single-molecule optical tweezers to study the folding of consensus-designed tetratricopeptide repeats (CTPRs), superhelical arrays of short helix-turn-helix motifs. We find that CTPRs display a spring-like mechanical response in which individual repeats undergo rapid equilibrium fluctuations between partially folded and unfolded conformations. We rationalize the force response using Ising models and dissect the folding pathway of CTPRs under mechanical load, revealing how the repeat arrays form from the center toward both termini simultaneously. Most strikingly, we also directly observe the protein's superhelical tertiary structure in the force signal. Using protein engineering, crystallography, and single-molecule experiments, we show that the superhelical geometry can be altered by carefully placed amino acid substitutions, and we examine how these sequence changes affect intrinsic repeat stability and inter-repeat coupling. Our findings provide the means to dissect and modulate repeat-protein stability and dynamics, which will be essential for researchers to understand the function of natural repeat proteins and to exploit artificial repeats proteins in nanotechnology and biomedical applications.

Reconstruction of mechanical unfolding and refolding pathways of proteins with atomic force spectroscopy and computer simulations

Most proteins in proteomes are large, typically consist of more than one domain and are structurally complex. This often makes studying their mechanical unfolding pathways challenging. Proteins composed of tandem repeat domains are a subgroup of multi-domain proteins that, when stretched, display a saw-tooth pattern in their mechanical unfolding force extension profiles due to their repetitive structure. However, the assignment of force peaks to specific repeats undergoing mechanical unraveling is complicated because all repeats are similar and they interact with their neighbors and form a contiguous tertiary structure. Here, we describe in detail a combination of experimental and computational single-molecule force spectroscopy methods that proved useful for examining the mechanical unfolding and refolding pathways of ankyrin repeat proteins. Specifically, we explain and delineate the use of atomic force microscope-based single molecule force spectroscopy (SMFS) to record the mechanical unfolding behavior of ankyrin repeat proteins and capture their unusually strong refolding propensity that is responsible for generating impressive refolding force peaks. We also describe Coarse Grain Steered Molecular Dynamic (CG-SMD) simulations which complement the experimental observations and provide insights in understanding the unfolding and refolding of these proteins. In addition, we advocate the use of novel coiled-coils-based mechanical polypeptide probes which we developed to demonstrate the vectorial character of folding and refolding of these repeat proteins. The combination of AFM-based SMFS on native and CC-equipped proteins with CG-SMD simulations is powerful not only for ankyrin repeat polypeptides, but also for other repeat proteins and more generally to various multidomain, non-repetitive proteins with complex topologies.

Origin of the Surprising Mechanical Stability of Kinesin's Neck Coiled Coil

Kinesin-1 is a motor protein moving along a microtubule with its two identical motor heads dimerized by two neck linkers and a coiled-coil stalk. When both motor heads bind the microtubule, an internal strain is built up between the two heads, which is indispensable to ensure proper coordination of the two motor heads during kinesin-1's mechanochemical cycle. The internal strain forms a tensile force along the neck linker that tends to unwind the neck coiled coil (NCC). Experiments showed that the kinesin-1's NCC has a high antiunwinding ability compared with conventional coiled coils, which was mainly attributed to the enhanced hydrophobic pressure arising from the unconventional sequence of kinesin-1's NCC. However, hydrophobic pressure cannot provide the shearing force which is needed to balance the tensile force on the interface between two helices. To find out the true origin of the mechanical stability of kinesin-1's NCC, we perform a novel and detailed mechanical analysis for the system based on molecular dynamics simulation at an atomic level. We find that the needed shearing force is provided by a buckle structure formed by two tyrosines which form effective steric hindrance in the presence of tensile forces. The tensile force is balanced by the tensile direction component of the contact force between the two tyrosines which forms the shearing force. The hydrophobic pressure balances the other component of the contact force perpendicular to the tensile direction. The antiunwinding strength of NCC is defined by the maximum shearing force, which is finally determined by the hydrophobic pressure. Kinesin-1 uses residues with plane side chains, tryptophans and tyrosines, to form the hydrophobic center and to shorten the interhelix distance so that a high antiunwinding strength is obtained. The special design of NCC ensures exquisite cooperation of steric hindrance and hydrophobic pressure that results in the surprising mechanical stability of NCC.

Stick-slip kinetics in a bistable bar immersed in a heat bath

Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that 'stick-slip' kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.

Trimeric coiled coils expand the range of strength, toughness and dynamics of coiled coil motifs under shear

Coiled coils are widespread protein motifs in nature, and promising building blocks for bio-inspired nanomaterials and nanoscale force sensors. Detailed structural insight into their mechanical response is required to understand their role in tissues and to design building blocks for applications. We use all-atom molecular dynamics simulations to elucidate the mechanical response of two types of coiled coils under shear: dimers and trimers. The amino acid sequences of both systems are similar, thus enabling universal (vs. system-specific) features to be identified. The trimer is mechanically more stable - it is both stronger and tougher - than the dimer, withstanding higher forces (127 pN vs. 49 pN at v = 10-3 nm ns-1) and dissipating up to five times more energy before rupture. The deformation mechanism of the trimer at all pull speeds is dominated by progressive helix unfolding. In contrast, at the lowest pull speeds, dimers deform by unfolding/refolding-assisted sliding. The additional helix in the trimer thus both determines the stability of the structure and affects the deformation mechanism, preventing helix sliding. The mechanical response of the coiled coils is not only sensitive to the oligomerization state but also to helix stability: preventing helix unfolding doubles the mechanical strength of the trimer, but decreases its toughness to half. Our results show that coiled coil trimers expand the range of coiled coil responses to an applied shear force. Altering the stability of individual helices against deformation emerges as one possible route towards fine-tuning this response, enabling the use of these motifs as nanomechanical building blocks.

Molecular mechanics of coiled coils loaded in the shear geometry

Coiled coils are important nanomechanical building blocks in biological and biomimetic materials. A mechanistic molecular understanding of their structural response to mechanical load is essential for elucidating their role in tissues and for utilizing and tuning these building blocks in materials applications. Using a combination of single-molecule force spectroscopy (SMFS) and steered molecular dynamics (SMD) simulations, we have investigated the mechanics of synthetic heterodimeric coiled coils of different length (3-4 heptads) when loaded in shear geometry. Upon shearing, we observe an initial rise in the force, which is followed by a constant force plateau and ultimately strand separation. The force required for strand separation depends on the coiled coil length and the applied loading rate, suggesting that coiled coil shearing occurs out of equilibrium. This out-of-equilibrium behaviour is determined by a complex structural response which involves helix uncoiling, uncoiling-assisted sliding of the helices relative to each other in the direction of the applied force as well as uncoiling-assisted dissociation perpendicular to the force axis. These processes follow a hierarchy of timescales with helix uncoiling being faster than sliding and sliding being faster than dissociation. In SMFS experiments, strand separation is dominated by uncoiling-assisted dissociation and occurs at forces between 25-45 pN for the shortest 3-heptad coiled coil and between 35-50 pN for the longest 4-heptad coiled coil. These values are highly similar to the forces required for shearing apart short double-stranded DNA oligonucleotides, reinforcing the potential role of coiled coils as nanomechanical building blocks in applications where protein-based structures are desired.

Mechanical Folding and Unfolding of Protein Barnase at the Single-Molecule Level

The unfolding and folding of protein barnase has been extensively investigated in bulk conditions under the effect of denaturant and temperature. These experiments provided information about structural and kinetic features of both the native and the unfolded states of the protein, and debates about the possible existence of an intermediate state in the folding pathway have arisen. Here, we investigate the folding/unfolding reaction of protein barnase under the action of mechanical force at the single-molecule level using optical tweezers. We measure unfolding and folding force-dependent kinetic rates from pulling and passive experiments, respectively, and using Kramers-based theories (e.g., Bell-Evans and Dudko-Hummer-Szabo models), we extract the position of the transition state and the height of the kinetic barrier mediating unfolding and folding transitions, finding good agreement with previous bulk measurements. Measurements of the force-dependent kinetic barrier using the continuous effective barrier analysis show that protein barnase verifies the Leffler-Hammond postulate under applied force and allow us to extract its free energy of folding, ΔG0. The estimated value of ΔG0 is in agreement with our predictions obtained using fluctuation relations and previous bulk studies. To address the possible existence of an intermediate state on the folding pathway, we measure the power spectrum of force fluctuations at high temporal resolution (50 kHz) when the protein is either folded or unfolded and, additionally, we study the folding transition-path time at different forces. The finite bandwidth of our experimental setup sets the lifetime of potential intermediate states upon barnase folding/unfolding in the submillisecond timescale.

The physics of pulling polyproteins: a review of single molecule force spectroscopy using the AFM to study protein unfolding

One of the most exciting developments in the field of biological physics in recent years is the ability to manipulate single molecules and probe their properties and function. Since its emergence over two decades ago, single molecule force spectroscopy has become a powerful tool to explore the response of biological molecules, including proteins, DNA, RNA and their complexes, to the application of an applied force. The force versus extension response of molecules can provide valuable insight into its mechanical stability, as well as details of the underlying energy landscape. In this review we will introduce the technique of single molecule force spectroscopy using the atomic force microscope (AFM), with particular focus on its application to study proteins. We will review the models which have been developed and employed to extract information from single molecule force spectroscopy experiments. Finally, we will end with a discussion of future directions in this field.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Hierarchical cascades of instability govern the mechanics of coiled coils: helix unfolding precedes coil unzipping

Coiled coils are a fundamental emergent motif in proteins found in structural biomaterials, consisting of α-helical secondary structures wrapped in a supercoil. A fundamental question regarding the thermal and mechanical stability of coiled coils in extreme environments is the sequence of events leading to the disassembly of individual oligomers from the universal coiled-coil motifs. To shed light on this phenomenon, here we report atomistic simulations of a trimeric coiled coil in an explicit water solvent and investigate the mechanisms underlying helix unfolding and coil unzipping in the assembly. We employ advanced sampling techniques involving steered molecular dynamics and metadynamics simulations to obtain the free-energy landscapes of single-strand unfolding and unzipping in a three-stranded assembly. Our comparative analysis of the free-energy landscapes of instability pathways shows that coil unzipping is a sequential process involving multiple intermediates. At each intermediate state, one heptad repeat of the coiled coil first unfolds and then unzips due to the loss of contacts with the hydrophobic core. This observation suggests that helix unfolding facilitates the initiation of coiled-coil disassembly, which is confirmed by our 2D metadynamics simulations showing that unzipping of one strand requires less energy in the unfolded state compared with the folded state. Our results explain recent experimental findings and lay the groundwork for studying the hierarchical molecular mechanisms that underpin the thermomechanical stability/instability of coiled coils and similar protein assemblies.

Spring-loaded unraveling of a single SNARE complex by NSF in one round of ATP turnover

During intracellular membrane trafficking, N-ethylmaleimide-sensitive factor (NSF) and alpha-soluble NSF attachment protein (α-SNAP) disassemble the soluble NSF attachment protein receptor (SNARE) complex for recycling of the SNARE proteins. The molecular mechanism by which NSF disassembles the SNARE complex is largely unknown. Using single-molecule fluorescence spectroscopy and magnetic tweezers, we found that NSF disassembled a single SNARE complex in only one round of adenosine triphosphate (ATP) turnover. Upon ATP cleavage, the NSF hexamer developed internal tension with dissociation of phosphate ions. After latent time measuring tens of seconds, NSF released the built-up tension in a burst within 20 milliseconds, resulting in disassembly followed by immediate release of the SNARE proteins. Thus, NSF appears to use a "spring-loaded" mechanism to couple ATP hydrolysis and unfolding of substrate proteins.

Mutational analysis of dimeric linkers in peri- and cytoplasmic domains of histidine kinase DctB reveals their functional roles in signal transduction

Membrane-associated histidine kinases (HKs) in two-component systems respond to environmental stimuli by autophosphorylation and phospho-transfer. HK typically contains a periplasmic sensor domain that regulates the cytoplasmic kinase domain through a conserved cytoplasmic linker. How signal is transduced from the ligand-binding site across the membrane barrier remains unclear. Here, we analyse two linker regions of a typical HK, DctB. One region connects the first transmembrane helix with the periplasmic Per-ARNT-Sim domains, while the other one connects the second transmembrane helix with the cytoplasmic kinase domains. We identify a leucine residue in the first linker region to be essential for the signal transduction and for maintaining the delicate balance of the dimeric interface, which is key to its activities. We also show that the other linker, belonging to the S-helix coiled-coil family, plays essential roles in signal transduction inside the cell. Furthermore, by combining mutations with opposing activities in the two regions, we show that these two signalling transduction elements are integrated to produce a combined effect on the final activity of DctB.

Sequence-resolved free energy profiles of stress-bearing vimentin intermediate filaments

Intermediate filaments (IFs) are key to the mechanical strength of metazoan cells. Their basic building blocks are dimeric coiled coils mediating hierarchical assembly of the full-length filaments. Here we use single-molecule force spectroscopy by optical tweezers to assess the folding and stability of coil 2B of the model IF protein vimentin. The coiled coil was unzipped from its N and C termini. When pulling from the C terminus, we observed that the coiled coil was resistant to force owing to the high stability of the C-terminal region. Pulling from the N terminus revealed that the N-terminal half is considerably less stable. The mechanical pulling assay is a unique tool to study and control seed formation and structure propagation of the coiled coil. We then used rigorous theory-based deconvolution for a model-free extraction of the energy landscape and local stability profiles. The data obtained from the two distinct pulling directions complement each other and reveal a tripartite stability of the coiled coil: a labile N-terminal half, followed by a medium stability section and a highly stable region at the far C-terminal end. The different stability regions provide important insight into the mechanics of IF assembly.

Improving single molecule force spectroscopy through automated real-time data collection and quantification of experimental conditions

The benefits of single molecule force spectroscopy (SMFS) clearly outweigh the challenges which include small sample sizes, tedious data collection and introduction of human bias during the subjective data selection. These difficulties can be partially eliminated through automation of the experimental data collection process for atomic force microscopy (AFM). Automation can be accomplished using an algorithm that triages usable force-extension recordings quickly with positive and negative selection. We implemented an algorithm based on the windowed fast Fourier transform of force-extension traces that identifies peaks using force-extension regimes to correctly identify usable recordings from proteins composed of repeated domains. This algorithm excels as a real-time diagnostic because it involves <30 ms computational time, has high sensitivity and specificity, and efficiently detects weak unfolding events. We used the statistics provided by the automated procedure to clearly demonstrate the properties of molecular adhesion and how these properties change with differences in the cantilever tip and protein functional groups and protein age.

From mechanical folding trajectories to intrinsic energy landscapes of biopolymers

In single-molecule laser optical tweezer (LOT) pulling experiments, a protein or RNA is juxtaposed between DNA handles that are attached to beads in optical traps. The LOT generates folding trajectories under force in terms of time-dependent changes in the distance between the beads. How to construct the full intrinsic folding landscape (without the handles and beads) from the measured time series is a major unsolved problem. By using rigorous theoretical methods--which account for fluctuations of the DNA handles, rotation of the optical beads, variations in applied tension due to finite trap stiffness, as well as environmental noise and limited bandwidth of the apparatus--we provide a tractable method to derive intrinsic free-energy profiles. We validate the method by showing that the exactly calculable intrinsic free-energy profile for a generalized Rouse model, which mimics the two-state behavior in nucleic acid hairpins, can be accurately extracted from simulated time series in a LOT setup regardless of the stiffness of the handles. We next apply the approach to trajectories from coarse-grained LOT molecular simulations of a coiled-coil protein based on the GCN4 leucine zipper and obtain a free-energy landscape that is in quantitative agreement with simulations performed without the beads and handles. Finally, we extract the intrinsic free-energy landscape from experimental LOT measurements for the leucine zipper.

Single reconstituted neuronal SNARE complexes zipper in three distinct stages

Soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins drive membrane fusion by assembling into a four-helix bundle in a zippering process. Here, we used optical tweezers to observe in a cell-free reconstitution experiment in real time a long-sought SNARE assembly intermediate in which only the membrane-distal amino-terminal half of the bundle is assembled. Our findings support the zippering hypothesis, but suggest that zippering proceeds through three sequential binary switches, not continuously, in the amino- and carboxyl-terminal halves of the bundle and the linker domain. The half-zippered intermediate was stabilized by externally applied force that mimicked the repulsion between apposed membranes being forced to fuse. This intermediate then rapidly and forcefully zippered, delivering free energy of 36 k(B)T (where k(B) is Boltzmann's constant and T is temperature) to mediate fusion.

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.

Highly anisotropic stability and folding kinetics of a single coiled coil protein under mechanical tension

Coiled coils are one of the most abundant protein structural motifs and widely mediate protein interactions and force transduction or sensation. They are thus model systems for protein engineering and folding studies, particularly the GCN4 coiled coil. Major single-molecule methods have also been applied to this protein and revealed its folding kinetics at various spatiotemporal scales. Nevertheless, the folding energy and the kinetics of a single GCN4 coiled coil domain have not been well determined at a single-molecule level. Here we used high-resolution optical tweezers to characterize the folding and unfolding reactions of a single GCN4 coiled coil domain and their dependence on the pulling direction. In one axial and two transverse pulling directions, we observed reversible, two-state transitions of the coiled coil in real time. The transitions equilibrate at pulling forces ranging from 6 to 12 pN, showing different stabilities of the coiled coil in regard to pulling direction. Furthermore, the transition rates vary with both the magnitude and the direction of the pulling force by greater than 1000 folds, indicating a highly anisotropic and topology-dependent energy landscape for protein transitions under mechanical tension. We developed a new analytical theory to extract energy and kinetics of the protein transition at zero force. The derived folding energy does not depend on the pulling direction and is consistent with the measurement in bulk, which further confirms the applicability of the single-molecule manipulation approach for energy measurement. The highly anisotropic thermodynamics of proteins under tension should play important roles in their biological functions.

Single-molecule protein unfolding and refolding using atomic force microscopy

Over the past few years, atomic force microscopy (AFM) became a prominent tool to study the mechanical properties of proteins and protein interactions on a single-molecule level. AFM together with other mechanical, single-molecule manipulating techniques (Bustamante et al., Nat Rev Mol Cell Biol 1:130-136, 2000) made it possible to probe biological molecules in a way that is complementary to single-molecule methods using chemicals or temperature as a denaturant (Borgia et al., Annu Rev Biochem 77:101-125, 2008). For example, AFM offered new insights into the process of protein folding and unfolding by probing single proteins with mechanical forces. Since many proteins fulfill mechanical function or are exerted to mechanical forces in their natural environment, AFM allows to target physiologically relevant questions. Although the number of proteins unfolded with AFM continually increases (Linke and Grutzner, Pflugers Arch 456:101-115, 2008; Zhuang and Rief, Curr Opin Struct Biol 13:88-97, 2003; Clausen-Schaumann et al., Curr Opin Chem Biol 4:524-530, 2000; Rounsevell et al., Methods 34:100-111, 2004), the total number of proteins studied so far is still relatively small (Oberhauser and Carrion-Vazquez, J Biol Chem 283:6617-6621, 2008). This chapter aims at giving protocol-like instructions for people who are actually getting started using AFM to study mechanical protein unfolding or refolding. The instruction includes different approaches to produce polyproteins or modular protein chains which are commonly used to screen for true single-molecule AFM data traces. Also, the basic principles for data collection with AFM and the basic data analysis methods are explained. For people who want to study proteins that unfold at small forces or for people who want to study protein folding which also occurs typically at small forces (<30 pN), an averaging technique is explained, allowing to increase the force resolution in this regime. For topics that would go beyond the scope of this chapter - as, for example, the details about different cantilever calibration methods - references are provided.

Fast and forceful refolding of stretched alpha-helical solenoid proteins

Anfinsen's thermodynamic hypothesis implies that proteins can encode for stretching through reversible loss of structure. However, large in vitro extensions of proteins that occur through a progressive unfolding of their domains typically dissipate a significant amount of energy, and therefore are not thermodynamically reversible. Some coiled-coil proteins have been found to stretch nearly reversibly, although their extension is typically limited to 2.5 times their folded length. Here, we report investigations on the mechanical properties of individual molecules of ankyrin-R, beta-catenin, and clathrin, which are representative examples of over 800 predicted human proteins composed of tightly packed alpha-helical repeats (termed ANK, ARM, or HEAT repeats, respectively) that form spiral-shaped protein domains. Using atomic force spectroscopy, we find that these polypeptides possess unprecedented stretch ratios on the order of 10-15, exceeding that of other proteins studied so far, and their extension and relaxation occurs with minimal energy dissipation. Their sequence-encoded elasticity is governed by stepwise unfolding of small repeats, which upon relaxation of the stretching force rapidly and forcefully refold, minimizing the hysteresis between the stretching and relaxing parts of the cycle. Thus, we identify a new class of proteins that behave as highly reversible nanosprings that have the potential to function as mechanosensors in cells and as building blocks in springy nanostructures. Our physical view of the protein component of cells as being comprised of predominantly inextensible structural elements under tension may need revision to incorporate springs.

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.

Mechanical unfolding of an ankyrin repeat protein

Ankryin repeat proteins comprise tandem arrays of a 33-residue, predominantly alpha-helical motif that stacks roughly linearly to produce elongated and superhelical structures. They function as scaffolds mediating a diverse range of protein-protein interactions, and some have been proposed to play a role in mechanical signal transduction processes in the cell. Here we use atomic force microscopy and molecular-dynamics simulations to investigate the natural 7-ankyrin repeat protein gankyrin. We find that gankyrin unfolds under force via multiple distinct pathways. The reactions do not proceed in a cooperative manner, nor do they always involve fully stepwise unfolding of one repeat at a time. The peeling away of half an ankyrin repeat, or one or more ankyrin repeats, occurs at low forces; however, intermediate species are formed that are resistant to high forces, and the simulations indicate that in some instances they are stabilized by nonnative interactions. The unfolding of individual ankyrin repeats generates a refolding force, a feature that may be more easily detected in these proteins than in globular proteins because the refolding of a repeat involves a short contraction distance and incurs a low entropic cost. We discuss the origins of the differences between the force- and chemical-induced unfolding pathways of ankyrin repeat proteins, as well as the differences between the mechanics of natural occurring ankyrin repeat proteins and those of designed consensus ankyin repeat and globular proteins.

Force-driven separation of short double-stranded DNA

Short double-stranded DNA is used in a variety of nanotechnological applications, and for many of them, it is important to know for which forces and which force loading rates the DNA duplex remains stable. In this work, we develop a theoretical model that describes the force-dependent dissociation rate for DNA duplexes tens of basepairs long under tension along their axes ("shear geometry"). Explicitly, we set up a three-state equilibrium model and apply the canonical transition state theory to calculate the kinetic rates for strand unpairing and the rupture-force distribution as a function of the separation velocity of the end-to-end distance. Theory is in excellent agreement with actual single-molecule force spectroscopy results and even allows for the prediction of the rupture-force distribution for a given DNA duplex sequence and separation velocity. We further show that for describing double-stranded DNA separation kinetics, our model is a significant refinement of the conventionally used Bell-Evans model.

Designing the folding mechanics of coiled coils

Naturally occurring coiled coils are often not homogeneous throughout their entire structure but rather interrupted by sequence discontinuities and non-coiled-coil-forming subsegments. We apply atomic force microscopy to locally probe the mechanical folding/unfolding process of a well-understood model coiled coil when unstructured subsegments with different sizes are added. We find that the refolding force decreases from 7.8 pN with increasing size of the added unstructured subsegment, while the unfolding properties of the model coiled coil remain unchanged. We show that this behavior results from the increased size of the nucleation seed which has to form before further coiled-coil folding can proceed. Since the nucleation seed size is linked to the width of the energetic folding barrier, we are able to directly measure the dependence of folding forces on the barrier width. Our results allow the design of coiled coils with designated refolding forces by simply adjusting the nucleation seed size.

Full distance-resolved folding energy landscape of one single protein molecule

Kinetic bulk and single molecule folding experiments characterize barrier properties but the shape of folding landscapes between barrier top and native state is difficult to access. Here, we directly extract the full free energy landscape of a single molecule of the GCN4 leucine zipper using dual beam optical tweezers. To this end, we use deconvolution force spectroscopy to follow an individual molecule's trajectory with high temporal and spatial resolution. We find a heterogeneous energy landscape of the GCN4 leucine zipper domain. The energy profile is divided into two stable C-terminal heptad repeats and two less stable repeats at the N-terminus. Energies and transition barrier positions were confirmed by single molecule kinetic analysis. We anticipate that deconvolution sampling is a powerful tool for the model-free investigation of protein energy landscapes.

Length-dependent force characteristics of coiled coils

Coiled-coil domains within and between proteins play important structural roles in biology. They consist of two or more alpha helices that form a superhelical structure due to packing of the hydrophobic residues that pattern each helix. A recent continuum model showed that the correspondence between the chirality of the pack to that of the underlying hydrophobic pattern comes about because of the internal deformation energy associated with each helix in forming the superhelix. We have developed a coarse-grained atomistic model for coiled coils that includes the competition between the hydrophobic energy that drives folding and the cost due to deforming each helix. The model exhibits a structural transition from a non-coiled-coil to coiled-coil state as the contribution from the deformation energy changes. Our model is able to reproduce naturally occurring coiled coils and essential features seen in unzipping experiments. We explore the force-extension properties of these model coiled coils as a function helix length and find that shorter coils unfold at lower force than longer ones with the required unfolding force eventually becoming length independent.

Single molecule mechanics of the kinesin neck

Structural integrity as well as mechanical stability of the parts of a molecular motor are crucial for its function. In this study, we used high-resolution force spectroscopy by atomic force microscopy to investigate the force-dependent opening kinetics of the neck coiled coil of Kinesin-1 from Drosophila melanogaster. We find that even though the overall thermodynamic stability of the neck is low, the average opening force of the coiled coil is >11 pN when stretched with pulling velocities >150 nm/s. These high unzipping forces ensure structural integrity during motor motion. The high mechanical stability is achieved through a very narrow N-terminal unfolding barrier if compared with a conventional leucine zipper. The experimentally mapped mechanical unzipping profile allows direct assignment of distinct mechanical stabilities to the different coiled-coil subunits. The coiled-coil sequence seems to be tuned in an optimal way to ensure both mechanical stability as well as motor regulation through charged residues.

Free energies and forces in helix-coil transition of homopolypeptides under stretching

We show here that constant velocity steered molecular dynamics (SMD) simulations of alpha-helices in a vacuum present a well defined plateau in the force-extension relationship for homopolypeptides having more than (approximately) twenty residues. With the processes being far away from equilibrium, the energies strongly depend on the stretching velocity. Importantly, for a given velocity variation, the energy variation depends also on the helix sequence. Additionally, our observations show that homopolypeptides made of ten different amino acids (Ala, Cys, Gln, Ile, Leu, Met, Phe, Ser, Thr and Val) present a linear helix-coil transition.

Nonadiabatic simulation study of photoisomerization of azobenzene: detailed mechanism and load-resisting capacity

Nonadiabatic dynamical simulations were carried out to study cis-to-trans isomerization of azobenzene under laser irradiation and/or external mechanical loads. We used a semiclassical electron-radiation-ion dynamics method that is able to describe the coevolution of the structural dynamics and the underlying electronic dynamics in a real-time manner. It is found that azobenzene photoisomerization occurs predominantly by an out-of-plane rotation mechanism even under a nontrivial resisting force of several tens of piconewtons. We have repeated the simulations systematically for a broad range of parameters for laser pulses, but could not find any photoisomerization event by a previously suggested in-plane inversion mechanism. The simulations found that the photoisomerization process can be held back by an external resisting force of 90-200 pN depending on the frequency and intensity of the lasers. This study also found that a pure mechanical isomerization is possible from the cis-to-trans state if the azobenzene molecule is stretched by an external force of approximately 1250-1650 pN. Remarkably, the mechanical isomerization first proceeds through a mechanically activated inversion, and then is diverted to an ultrafast downhill rotation that accomplishes the isomerization. Implications of these findings to azobenzene-based nanomechanical devices are discussed.

Dynamic force spectroscopy: Analysis of reversible bond-breaking dynamics

The problem of diffusive bond dissociation in a double well potential under application of an external force is scrutinized. We compute the probability distribution of rupture forces and present a detailed discussion of the influence of finite rebinding probabilities on the dynamic force spectrum. In particular, we focus on barrier crossing upon extension, i.e., under linearly increased load, and upon relaxation starting from completely separated bonds. For large loading rates the rupture force and the rejoining force depend on the loading rate in the expected manner determined by the shape of the potential. For small loading rates the mean forces obtained from pull and relax modes approach each other as the system reaches equilibrium. We investigate the dependence of the rupture force distributions and mean rupture forces on external parameters such as cantilever stiffness and influence of a soft linker. We find that depending on the implementation of a soft linker the equilibrium rupture force is either unaffected by the presence of the linker or changes in a predictable way with the linker compliance. Additionally, we show that it is possible to extract the equilibrium constant of the on and off rates from the determination of the equilibrium rupture forces.

Elastic bond network model for protein unfolding mechanics

Recent advances in single molecule mechanics have made it possible to investigate the mechanical anisotropy of protein stability in great detail. A quantitative prediction of protein unfolding forces at experimental time scales has so far been difficult. Here, we present an elastically bonded network model to describe the mechanical unfolding forces of green fluorescent protein in eight different pulling directions. The combination of an elastic network and irreversible bond fracture kinetics offers a new concept to understand the determinants of mechanical protein stability.

Molecular basis of fibrin clot elasticity

Blood clots must be stiff to stop hemorrhage yet elastic to buffer blood's shear forces. Upsetting this balance results in clot rupture and life-threatening thromboembolism. Fibrin, the main component of a blood clot, is formed from molecules of fibrinogen activated by thrombin. Although it is well known that fibrin possesses considerable elasticity, the molecular basis of this elasticity is unknown. Here, we use atomic force microscopy (AFM) and steered molecular dynamics (SMD) to probe the mechanical properties of single fibrinogen molecules and fibrin protofibrils, showing that the mechanical unfolding of their coiled-coil alpha helices is characterized by a distinctive intermediate force plateau in the systems' force-extension curve. We relate this plateau force to a stepwise unfolding of fibrinogen's coiled alpha helices and of its central domain. AFM data show that varying pH and calcium ion concentrations alters the mechanical resilience of fibrinogen. This study provides direct evidence for the coiled alpha helices of fibrinogen to bring about fibrin elasticity.

Hydrophobic and Hofmeister effects on the adhesion of spider silk proteins onto solid substrates: an AFM-based single-molecule study

AFM-based single-molecule force spectroscopy has been used to study the effect of Hofmeister salts and protein hydrophobicity on the adhesion of recombinant spider silk proteins onto solid substrates. Therefore, a molecular probe consisting of a spider silk protein and an AFM tip has been developed, which (i) is a well-defined, small system that can be simulated by molecular dynamics simulations, (ii) allows access to the whole soluble concentration range for ions, and (iii) provides the distribution of desorption forces rather than just ensemble-averaged mean values. The measured desorption forces follow the Hofmeister series for anions (H2PO4-, Cl-, I-) with a stabilizing energy of more than 15 kBT for 5 M NaH2PO4. Moreover, this effect is influenced by the hydrophobicity of the spider silk protein, indicating that hydrophobic and Hofmeister effects are closely related.

Single-molecule dynamics of mechanical coiled-coil unzipping

We use atomic force microscopy (AFM) to mechanically unzip and rezip a double-stranded coiled-coil structure at varying pulling velocities. We find that force-extension traces exhibit hysteresis that grows with increasing pulling velocity. This shows that coiled-coil unzipping and rezipping do not occur in thermal equilibrium on our experimental time scale. We present a nonequilibrium simulation that fully reproduces the hysteresis effects, giving detailed insight into dynamics of coiled-coil folding. Using this model, we find that seed formation is responsible for the hysteresis. The seed consists of four alpha-helical turns on both strands of the coiled coil. To obtain equilibrium information from our nonequilibrium experiments, we used the Crooks fluctuation theorem (CFT) to calculate the equilibrium free energy of folding for all of the different pulling velocities. The paper presented here lays the groundwork for the study of self-assembly properties of many physiologically relevant coiled-coil structures at the single-molecule level.

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.

Direct observation of active protein folding using lock-in force spectroscopy

Direct observation of the folding of a single polypeptide chain can provide important information about the thermodynamic states populated along its folding pathway. In this study, we present a lock-in force-spectroscopy technique that improves resolution of atomic-force microscopy force spectroscopy to 400 fN. Using this technique we show that immunoglobulin domain 4 from Dictyostelium discoideum filamin (ddFLN4) refolds against forces of approximately 4 pN. Our data show folding of this domain proceeds directly from an extended state and no thermodynamically distinct collapsed state of the polypeptide before folding is populated. Folding of ddFLN4 under load proceeds via an intermediate state. Three-state folding allows ddFLN4 to fold against significantly larger forces than would be possible for a mere two-state folder. We present a general model for protein folding kinetics under load that can predict refolding forces based on chain-length and zero force refolding rate.

Nanoscale ion mediated networks in bone: osteopontin can repeatedly dissipate large amounts of energy

In the nanocomposite bone, inorganic material is combined with several types of organic molecules, and these complexes have been proposed to increase the bone strength. Here we report on a mechanism of how one of these components, human osteopontin, forms large mechanical networks that can repeatedly dissipate energy through work against entropy by breaking sacrificial bonds and stretching hidden length. The behavior of these in vitro networks is similar to that of organic components in bone, acting as an adhesive layer in between mineralized fibrils.

Print your atomic force microscope

Progress in scanning probe microscopy profited from a flourishing multitude of new instrument designs, which lead to novel imaging modes and as a consequence to innovative microscopes. Often these designs were hampered by the restrictions, which conventional milling techniques impose. Modern rapid prototyping techniques, where layer by layer is added to the growing piece either by light driven polymerization or by three-dimensional printing techniques, overcome this constraint, allowing highly concave or even embedded and entangled structures. We have employed such a technique to manufacture an atomic force microscopy (AFM) head, and we compared its performance with a copy milled from aluminum. We tested both AFM heads for single molecule force spectroscopy applications and found little to no difference in the signal-to-noise ratio as well as in the thermal drift. The lower E modulus seems to be compensated by higher damping making this material well suited for low noise and low drift applications. Printing an AFM thus offers unparalleled freedom in the design and the rapid production of application-tailored custom instruments.