How Do Chemical Denaturants Affect the Mechanical Folding and Unfolding of Proteins?

A pressure-jump EPR system to monitor millisecond conformational exchange rates of spin-labeled proteins

Site-directed spin labeling electron paramagnetic resonance (SDSL-EPR) using nitroxide spin labels is a well-established technology for mapping site-specific secondary and tertiary structure and for monitoring conformational changes in proteins of any degree of complexity, including membrane proteins, with high sensitivity. SDSL-EPR also provides information on protein dynamics in the time scale of ps-µs using continuous wave lineshape analysis and spin lattice relaxation time methods. However, the functionally important time domain of µs-ms, corresponding to large-scale protein motions, is inaccessible to those methods. To extend SDSL-EPR to the longer time domain, the perturbation method of pressure-jump relaxation is implemented. Here, we describe a complete high-pressure EPR system at Q-band for both static pressure and millisecond-timescale pressure-jump measurements on spin-labeled proteins. The instrument enables pressure jumps both up and down from any holding pressure, ranging from atmospheric pressure to the maximum pressure capacity of the system components (~3500 bar). To demonstrate the utility of the system, we characterize a local folding-unfolding equilibrium of T4 lysozyme. The results illustrate the ability of the system to measure thermodynamic and kinetic parameters of protein conformational exchange on the millisecond timescale.

Tuning Protein Hydrogel Mechanics through Modulation of Nanoscale Unfolding and Entanglement in Postgelation Relaxation

Globular folded proteins are versatile nanoscale building blocks to create biomaterials with mechanical robustness and inherent biological functionality due to their specific and well-defined folded structures. Modulating the nanoscale unfolding of protein building blocks during network formation (in situ protein unfolding) provides potent opportunities to control the protein network structure and mechanics. Here, we control protein unfolding during the formation of hydrogels constructed from chemically cross-linked maltose binding protein using ligand binding and the addition of cosolutes to modulate protein kinetic and thermodynamic stability. Bulk shear rheology characterizes the storage moduli of the bound and unbound protein hydrogels and reveals a correlation between network rigidity, characterized as an increase in the storage modulus, and protein thermodynamic stability. Furthermore, analysis of the network relaxation behavior identifies a crossover from an unfolding dominated regime to an entanglement dominated regime. Control of in situ protein unfolding and entanglement provides an important route to finely tune the architecture, mechanics, and dynamic relaxation of protein hydrogels. Such predictive control will be advantageous for future smart biomaterials for applications which require responsive and dynamic modulation of mechanical properties and biological function.

Molecular homogeneity of GB1 revealed by single molecule force spectroscopy

In single molecule studies, the ergodic hypothesis is inherently assumed, which states that the time average of a physical quantity of a single member of an ensemble is the same as the average of the same quantity on the whole ensemble at a given time. This hypothesis implies the homogeneity of a molecular ensemble of a system of interest. However, it is difficult to test the validity of the ergodic hypothesis experimentally. Recent theoretical work suggested that heterogeneity may be widely present in single molecule force spectroscopy studies. Here we used atomic force microscope based single molecule force spectroscopy to examine the molecular homogeneity/heterogeneity of a small globular protein GB1 in its mechanical unfolding reaction. Using a polyprotein (GB1)₄, we directly measured the ensemble average and time average for a single molecule of the mechanical unfolding force and kinetic parameters that characterize the mechanical unfolding free energy profile of GB1. Our results showed that the ensemble averages of these physical quantities are indeed the same as the time averages for single molecules, and individual molecules did not show any differences amongst them in these physical quantities. These results are consistent with the expectation of the ergodic hypothesis and indicate that GB1 is a homogeneous molecular ensemble in its mechanical unfolding reaction on the time scale of our force spectroscopy experiments.

Nonpolar hydrophobic amino acids tune the enzymatic activity of lysozyme

We have used five different hydrophobic L-amino acids (Gly, Ala, Val, Leu, Ile) as molecular crowders to investigate their role on the enzymatic activity of lysozyme towards Micrococcus lysodeikticus (M. lys.)cell as substrate. We found that except Ile, all other amino acids show a bell like profile of catalytic efficiency (k_cat/K_m) with their increasing concentration whereas for Ile, the value is gradually increasing. The trend of activation energy (E_a) is also well correlated with the catalytic efficiency of lysozyme. At low concentration of amino acids, soft interaction predominates whereas at higher concentration range, excluded volume, viscosity, hydrophobicity combinedly decrease the activity of lysozyme.

Engineering shape memory and morphing protein hydrogels based on protein unfolding and folding

Engineering shape memory/morphing materials have achieved considerable progress in polymer-based systems with broad potential applications. However, engineering protein-based shape memory/morphing materials remains challenging and under-explored. Here we report the design of a bilayer protein-based shape memory/morphing hydrogel based on protein folding-unfolding mechanism. We fabricate the protein-bilayer structure using two tandem modular elastomeric proteins (GB1)₈ and (FL)₈. Both protein layers display distinct denaturant-dependent swelling profiles and Young’s moduli. Due to such protein unfolding-folding induced changes in swelling, the bilayer hydrogels display highly tunable and reversible bidirectional bending deformation depending upon the denaturant concentration and layer geometry. Based on these programmable and reversible bending behaviors, we further utilize the protein-bilayer structure as hinge to realize one-dimensional to two-dimensional and two-dimensional to three-dimensional folding transformations of patterned hydrogels. The present work will offer new inspirations for the design and fabrication of novel shape morphing materials.

Engineering shape memory and morphing materials achieved considerable progress in polymer-based systems, but protein-based shape memory and morphing materials remain less investigated. Here, the authors report the engineering of protein-based shape memory and morphing hydrogels using protein folding-unfolding as a general mechanism to trigger shape morphing in protein-bilayer structures.

Hidden Intermediate State and Second Pathway Determining Folding and Unfolding Dynamics of GB1 Protein at Low Forces

Atomic force microscopy experiments found that GB1, a typical two-state model protein used for study of folding and unfolding dynamics, can sustain forces of more than 100 pN, but its response to low forces still remains unclear. Using ultrastable magnetic tweezers, we discovered that GB1 has an unexpected nonmonotonic force-dependent unfolding rate at 5-160 pN, from which a free energy landscape with two main barriers and a hidden intermediate state was constructed. A model combining two separate models by Dudko et al. with two pathways between the native state and this intermediate state is proposed to rebuild the unfolding dynamics over the full experimental force range. One candidate of this transient intermediate state is the theoretically proposed molten globule state with a loosely collapsed conformation, which might exist universally in the folding and unfolding processes of two-state proteins.

Environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by atomic force microscopy-based single-molecule force spectroscopy and the implications for advanced polymer materials

"The Tao begets the One. One begets all things of the world." This quote from Tao Te Ching is still inspiring for scientists in chemistry and materials science: The "One" can refer to a single molecule. A macroscopic material is composed of numerous molecules. Although the relationship between the properties of the single molecule and macroscopic material is not well understood yet, it is expected that a deeper understanding of the single-chain mechanics of macromolecules will certainly facilitate the development of materials science. Atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS) has been exploited extensively as a powerful tool to study the single-chain behaviors of macromolecules. In this review, we summarize the recent advances in the emerging field of environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by means of AFM-SMFS. First, the single-chain inherent elasticities of several typical linear macromolecules are introduced, which are also confirmed by one of three polymer models with theoretical elasticities of the corresponding macromolecules obtained from quantum mechanical (QM) calculations. Then, the effects of the external environments on the single-chain mechanics of synthetic polymers and biomacromolecules are reviewed. Finally, the impacts of single-chain mechanics of macromolecules on the development of polymer science especially polymer materials are illustrated.

Harvesting Mechanical Work From Folding-Based Protein Engines: From Single-Molecule Mechanochemical Cycles to Macroscopic Devices

Mechanochemical coupling cycles underlie the work-generation mechanisms of biological systems and are realized by highly regulated conformational changes of the protein machineries. However, it has been challenging to utilize protein conformational changes to do mechanical work at the macroscopic level in biomaterials, and it remains elusive to construct macroscopic mechanochemical devices based on molecular-level mechanochemical coupling systems. Here, the authors demonstrate that protein folding can be utilized to realize protein’s mechanochemical cycles at both single-molecule and macroscopic levels. Our results demonstrate, for the first time, the successful harnessing of mechanical work generated by protein folding in a macroscopic protein hydrogel device, and the work generated by protein folding compares favorably with the energy output of molecular motors. Our work bridges a gap between single-molecule and macroscopic levels, and paves the way to utilizing proteins as building blocks to design protein-based artificial muscles and soft actuators.

Force-Clamp Rheometry for Characterizing Protein-based Hydrogels

Here, we describe a force-clamp rheometry method to characterize the biomechanical properties of protein-based hydrogels. This method uses an analog proportional-integral-derivative (PID) system to apply controlled-force protocols on cylindrical protein-based hydrogel samples, which are tethered between a linear voice-coil motor and a force transducer. During operation, the PID system adjusts the extension of the hydrogel sample to follow a predefined force protocol by minimizing the difference between the measured and set-point forces. This unique approach to protein-based hydrogels enables the tethering of extremely low-volume hydrogel samples (< 5 µL) with different protein concentrations. Under force-ramp protocols, where the applied stress increases and decreases linearly with time, the system enables the study of the elasticity and hysteresis behaviors associated with the (un)folding of proteins and the measurement of standard elastic and viscoelastic parameters. Under constant-force, where the force pulse has a step-like shape, the elastic response, due to the change in force, is decoupled from the viscoelastic response, which comes from protein domain unfolding and refolding. Due to its low-volume sample and versatility in applying various mechanical perturbations, force-clamp rheometry is optimized to investigate the mechanical response of proteins under force using a bulk approach.

Probing Small Molecule Binding to Unfolded Polyprotein Based on its Elasticity and Refolding

Unfolded protein, a disordered structure found before folding of newly synthesized protein or after protein denaturation, is a substrate for binding by many cellular factors such as heat-stable proteins, chaperones, and many small molecules. However, it is challenging to directly probe such interactions in physiological solution conditions because proteins are largely in their folded state. In this work we probed small molecule binding to mechanically unfolded polyprotein using sodium dodecyl sulfate (SDS) as an example. The effect of binding is quantified based on changes in the elasticity and refolding of the unfolded polyprotein in the presence of SDS. We show that this single-molecule mechanical detection of binding to unfolded polyprotein can serve, to our knowledge, as a novel label-free assay with a great potential to study many factors that interact with unfolded protein domains, which underlie many important biological processes.

On the indirect relationship between protein dynamics and enzyme activity

The behaviors of simple thermal systems have been well studied in physical chemistry and the principles obtained from such studies have been applied to complex thermal systems, such as proteins and enzymes. But the simple application of such principles is questionable and may lead to mistakes under some circumstances. In enzymology, the transition state theory of chemical reactions has been accepted as a fundamental theory, but the role of protein dynamics in enzyme catalysis is controversial in the context of transition state theory. By studying behaviors of complex thermal systems, we have revised the Arrhenius equation and transition state theory and our model is validated in enzymology. Formally speaking, the revised Arrhenius equation is apparently similar to a conventional Arrhenius equation, but the physical meanings of its parameters differ from that of traditional forms in principle. Within this model, the role of protein dynamics in enzyme catalysis is well defined and quantified.

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.

How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory

It is currently the consensus belief that protective osmolytes such as trimethylamine N-oxide (TMAO) favor protein folding by being excluded from the vicinity of a protein, whereas denaturing osmolytes such as urea lead to protein unfolding by strongly binding to the surface. Despite there being consensus on how TMAO and urea affect proteins as a whole, very little is known as to their effects on the individual mechanisms responsible for protein structure formation, especially hydrophobic association. In the present study, we use single-molecule atomic force microscopy and molecular dynamics simulations to investigate the effects of TMAO and urea on the unfolding of the hydrophobic homopolymer polystyrene. Incorporated with interfacial energy measurements, our results show that TMAO and urea act on polystyrene as a protectant and a denaturant, respectively, while complying with Tanford-Wyman preferential binding theory. We provide a molecular explanation suggesting that TMAO molecules have a greater thermodynamic binding affinity with the collapsed conformation of polystyrene than with the extended conformation, while the reverse is true for urea molecules. Results presented here from both experiment and simulation are in line with earlier predictions on a model Lennard-Jones polymer while also demonstrating the distinction in the mechanism of osmolyte action between protein and hydrophobic polymer. This marks, to our knowledge, the first experimental observation of TMAO-induced hydrophobic collapse in a ternary aqueous system.

Single-molecule chemo-mechanical unfolding reveals multiple transition state barriers in a small single-domain protein

A fundamental question in protein folding is whether proteins fold through one or multiple trajectories. While most experiments indicate a single pathway, simulations suggest proteins can fold through many parallel pathways. Here, we use a combination of chemical denaturant, mechanical force and site-directed mutations to demonstrate the presence of multiple unfolding pathways in a simple, two-state folding protein. We show that these multiple pathways have structurally different transition states, and that seemingly small changes in protein sequence and environment can strongly modulate the flux between the pathways. These results suggest that in vivo, the crowded cellular environment could strongly influence the mechanisms of protein folding and unfolding. Our study resolves the apparent dichotomy between experimental and theoretical studies, and highlights the advantage of using a multipronged approach to reveal the complexities of a protein's free-energy landscape.

Although most protein folding experiments can be explained by a single pathway, theoretical evidence suggests the presence of multiple pathways. Here, the authors resolve this using a combination of force, chemical denaturation and mutagenesis to modulate the flux between parallel pathways.

Mechanical stability analysis of the protein L immunoglobulin-binding domain by full alanine screening using molecular dynamics simulations

This article is the first to study the mechanical properties of the immunoglobulin-binding domain of protein L (referred to as protein L) and its mutants at the atomic level. In the structure of protein L, each amino acid residue (except for alanines and glycines) was replaced sequentially by alanine. Thus, 49 mutants of protein L were obtained. The proteins were stretched at their termini at constant velocity using molecular dynamics simulations in water, i.e. by forced unfolding. 19 out of 49 mutations resulted in a large decrease of mechanical protein stability. These amino acids were affecting either the secondary structure (11 mutations) or loop structures (8 mutations) of protein L. Analysis of mechanical unfolding of the generated protein that has the same topology as protein L but consists of only alanines and glycines allows us to suggest that the mechanical stability of proteins, and specifically protein L, is determined by interactions between certain amino acid residues, although the unfolding pathway depends on the protein topology. This insight can now be used to modulate the mechanical properties of proteins and their unfolding pathways in the desired direction for using them in various biochips, biosensors and biomaterials for medicine, industry, and household purposes.

Experimental and theoretical studies of mechanical unfolding of different proteins

Mechanical properties of proteins are important for a wide range of biological processes including cell adhesion, muscle contraction, and protein translocation across biological membranes. It is necessary to reveal how proteins achieve their required mechanical stability under natural conditions in order to understand the biological processes and also to use the knowledge for constructing new biomaterials for medical and industrial purposes. In this connection, it is important to know how a protein will behave in response to various impacts. Theoretical and experimental works on mechanical unfolding of globular proteins will be considered in detail in this review.

Protein Folding Under Mechanical Forces: A Physiological View

Mechanical forces regulate the function of numerous proteins relevant to physiology. The functions and folding of proteins have been under scrutiny for decades, but it was not until recently that mechanical forces have been considered. Here, we review different techniques for studying protein folding, highlighting their physiological significance.

Low folding cooperativity of HP35 revealed by single-molecule force spectroscopy and molecular dynamics simulation

Some small proteins, such as HP35, fold at submicrosecond timescale with low folding cooperativity. Although these proteins have been extensively investigated, still relatively little is known about their folding mechanism. Here, using single-molecule force spectroscopy and steered molecule dynamics simulation, we study the unfolding of HP35 under external force. Our results show that HP35 unfolds at extremely low forces without a well-defined unfolding transition state. Subsequently, we probe the structure of unfolded HP35 using the persistence length obtained in the force spectroscopy. We found that the persistence length of unfolded HP35 is around 0.72 nm, >40% longer than typical unstructured proteins, suggesting that there are a significant amount of residual secondary structures in the unfolded HP35. Molecular dynamics simulation further confirmed this finding and revealed that many native contacts are preserved in HP35, even its two ends have been extended up to 8 nm. Our results therefore suggest that retaining a significant amount of secondary structures in the unfolded state of HP35 may be an efficient way to reduce the entropic cost for the formation of tertiary structure and increase the folding speed, although the folding cooperativity is compromised. Moreover, we anticipate that the methods we used in this work can be extended to the study of other proteins with complex folding behaviors and even intrinsically disordered ones.

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.

Effects of pH on proteins: predictions for ensemble and single-molecule pulling experiments

Protein conformations change among distinct thermodynamic states as solution conditions (temperature, denaturants, pH) are altered or when they are subjected to mechanical forces. A quantitative description of the changes in the relative stabilities of the various thermodynamic states is needed to interpret and predict experimental outcomes. We provide a framework based on the Molecular Transfer Model (MTM) to account for pH effects on the properties of globular proteins. The MTM utilizes the partition function of a protein calculated from molecular simulations at one set of solution conditions to predict protein properties at another set of solution conditions. To take pH effects into account, we utilized experimentally measured pK(a) values in the native and unfolded states to calculate the free energy of transferring a protein from a reference pH to the pH of interest. We validate our approach by demonstrating that the native-state stability as a function of pH is accurately predicted for chymotrypsin inhibitor 2 (CI2) and protein G. We use the MTM to predict the response of CI2 and protein G subjected to a constant force (f) and varying pH. The phase diagrams of CI2 and protein G as a function of f and pH are dramatically different and reflect the underlying pH-dependent stability changes in the absence of force. The calculated equilibrium free energy profiles as functions of the end-to-end distance of the two proteins show that, at various pH values, CI2 unfolds via an intermediate when subjected to f. The locations of the two transition states move toward the more unstable state as f is changed, which is in accord with the Hammond-Leffler postulate. In sharp contrast, force-induced unfolding of protein G occurs in a single step. Remarkably, the location of the transition state with respect to the folded state is independent of f, which suggests that protein G is mechanically brittle. The MTM provides a natural framework for predicting the outcomes of ensemble and single-molecule experiments for a wide range of solution conditions.

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

The emergence of single-molecule force measurement experiments has facilitated a better understanding of protein folding pathways and the thermodynamics involved. Computational methods such as steered molecular dynamics (SMD) simulations are helpful in providing atomistic level information on the unfolding pathways. Recent experimental studies have showed that combinations of single-molecule experiments with traditional methods such as chemical and/or thermal denaturation yield additional insights into the folding phenomenon. In this study, we report results from extensive computations (a total of about 60 SMD simulations with a total length of about 0.4 μs) that address the effect of thermal perturbation on the mechanical stability of the I27 domain of the protein titin. A wide range of temperatures (280-340 K) were considered for the pulling, which was done at both constant velocity and constant force using SMD simulations. Good agreement with experimental data, such as for the trends in changes in average force and the maximum force with respect to the temperature, was obtained. This study identifies two competing pathways for the mechanical unfolding of I27, and illustrates the significance of combining various techniques to examine protein folding.

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.

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.

Inhibitor binding increases the mechanical stability of staphylococcal nuclease

Staphylococcal nuclease (SNase) catalyzes the hydrolysis of DNA and RNA in a calcium-dependent fashion. We used AFM-based single-molecule force spectroscopy to investigate the mechanical stability of SNase alone and in its complex with an SNase inhibitor, deoxythymidine 3',5'-bisphosphate. We found that the enzyme unfolds in an all-or-none fashion at ∼26 pN. Upon binding to the inhibitor, the mechanical unfolding forces of the enzyme-inhibitor complex increase to ∼50 pN. This inhibitor-induced increase in the mechanical stability of the enzyme is consistent with the increased thermodynamical stability of the complex over that of SNase. Because of its strong mechanical response to inhibitor binding, SNase, a model protein folding system, offers a unique opportunity for studying the relationship between enzyme mechanics and catalysis.

Optical trapping with high forces reveals unexpected behaviors of prion fibrils

Amyloid fibrils are important in diverse cellular functions, feature in many human diseases and have potential applications in nanotechnology. Here we describe methods that combine optical trapping and fluorescent imaging to characterize the forces that govern the integrity of amyloid fibrils formed by a yeast prion protein. A crucial advance was to use the self-templating properties of amyloidogenic proteins to tether prion fibrils, enabling their manipulation in the optical trap. At normal pulling forces the fibrils were impervious to disruption. At much higher forces (up to 250 pN), discontinuities occurred in force-extension traces before fibril rupture. Experiments with selective amyloid-disrupting agents and mutations demonstrated that such discontinuities were caused by the unfolding of individual subdomains. Thus, our results reveal unusually strong noncovalent intermolecular contacts that maintain fibril integrity even when individual monomers partially unfold and extend fibril length.

Composition-based effective chain length for prediction of protein folding rates

Folding rate prediction is a useful way to find the key factors affecting folding kinetics of proteins. Structural information is more or less required in the present prediction methods, which limits the application of these methods to various proteins. In this work, an "effective length" is defined solely based on the composition of a protein, namely, the number of specific types of amino acids in a protein. A physical theory based on a minimalist model is employed to describe the relation between the folding rates and the effective length of proteins. Based on the resultant relationship between folding rates and effective length, the optimal sets of amino acids are found through the enumeration over all possible combinations of amino acids. This optimal set achieves a high correlation (with the coefficient of 0.84) between the folding rates and the optimal effective length. The features of these amino acids are consistent with our model and landscape theory. Further comparisons between our effective length and other factors are carried out. The effective length is physically consistent with structure-based prediction methods and has the best predictability for folding rates. These results all suggest that both entropy and energetics contribute importantly to folding kinetics. The ability to accurately and efficiently predict folding rates from composition enables the analysis of the kinetics for various kinds of proteins. The underlying physics in our method may be helpful to stimulate further understanding on the effects of various amino acids in folding dynamics.

Naturally occurring osmolytes modulate the nanomechanical properties of polycystic kidney disease domains

Polycystin-1 (PC1) is a large membrane protein that is expressed along the renal tubule and exposed to a wide range of concentrations of urea. Urea is known as a common denaturing osmolyte that affects protein function by destabilizing their structure. However, it is known that the native conformation of proteins can be stabilized by protecting osmolytes that are found in the mammalian kidney. PC1 has an unusually long ectodomain with a multimodular structure including 16 Ig-like polycystic kidney disease (PKD) domains. Here, we used single-molecule force spectroscopy to study directly the effects of several naturally occurring osmolytes on the mechanical properties of PKD domains. This experimental approach more closely mimics the conditions found in vivo. We show that upon increasing the concentration of urea there is a remarkable decrease in the mechanical stability of human PKD domains. We found that protecting osmolytes such as sorbitol and trimethylamine N-oxide can counteract the denaturing effect of urea. Moreover, we found that the refolding rate of a structurally homologous archaeal PKD domain is significantly slowed down in urea, and this effect was counteracted by sorbitol. Our results demonstrate that naturally occurring osmolytes can have profound effects on the mechanical unfolding and refolding pathways of PKD domains. Based on these findings, we hypothesize that osmolytes such as urea or sorbitol may modulate PC1 mechanical properties and may lead to changes in the activation of the associated polycystin-2 channel or other intracellular events mediated by PC1.

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.

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.

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.

Multiple Unfolding Intermediates Obtained by Molecular Dynamic Simulations under Stretching for Immunoglobulin-Binding Domain of Protein G

We have studied the mechanical properties of the immunoglobulin-binding domain of protein G at the atomic level under stretching at constant velocity using molecular dynamics simulations. We have found that the unfolding process can occur either in a single step or through intermediate states. Analysis of the trajectories from the molecular dynamic simulations showed that the mechanical unfolding of the immunoglobulin-binding domain of protein G is triggered by the separation of the terminal beta-strands and the order in which the secondary-structure elements break is practically the same in two- and multi-state events and at the different extension velocities studied. It is seen from our analysis of 24 trajectories that the theoretical pathway of mechanical unfolding for the immunoglobulin-binding domain of protein G does not coincide with that proposed in denaturant studies in the absence of force.

Temperature and chemical denaturant dependence of forced unfolding of titin I27

Single-molecule force measurement opens a new door for investigating detailed biomolecular interactions and their thermodynamic properties by pulling molecules apart while monitoring the force exerted on them. Recent advances in the nonequilibrium work theorem allows one to determine the free-energy landscapes of these events. Such information is valuable for understanding processes such as protein and RNA folding and receptor-ligand binding. Here, we used force as a physical parameter under the traditional chemical and temperature denaturing environment to alter the protein folding energy landscape and compared the change in the unfolding free-energy barrier of the I27 domain of human cardiac titin. We found that the trends in protein unfolding free-energy barriers are consistent for single-molecule force measurements and bulk chemical and temperature studies. The results suggest that the information from single-molecule pulling experiments are meaningful and useful for understanding the mechanism of folding of titin I27.

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.

The effect of temperature on mechanical resistance of the native and intermediate states of I27

We investigated the effect of temperature on the mechanical unfolding of I27 from human cardiac titin, employing a custom-built temperature control device for single-molecule atomic force microscopy measurement. A sawtooth pattern was observed in the force curves where each force peak reports on the unfolding of an I27 domain. In early unfolding events, we observed a "hump-like" deviation due to the detachment of beta-strand A from each I27 domain. The force at which the humps appear was approximately 130 pN and showed no temperature dependence, at least in the temperature range of 2 degrees C-30 degrees C. The hump structure was successfully analyzed with a two-state worm-like chain model, and the Gibbs free energy difference of the detachment reaction was estimated to be 11.6 +/- 0.58 kcal/mol and found to be temperature independent. By contrast, upon lowering the temperature, the mean unfolding force from the partly unfolded intermediate state was found to markedly increase and the unfolding force distribution to broaden significantly, suggesting that the distance (x(u)) between the folded and transition states in the energy landscape along the pulling direction is decreased. These results suggest that the local structure of beta-strand A are stabilized by topologically simple local hydrogen-bond network and that the temperature does not affect the detachment reaction thermodynamically and kinetically, whereas the interaction between the beta-strands A' and G, which is a critical region for its mechanical stability, is strongly dependent on the temperature.