Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins

The characterization of elastic properties of biopolymers is crucial to understand many molecular reactions determined by conformational bending fluctuations of the polymer. Direct measurement of such elastic properties using single‐molecule methods is usually hindered by the intrinsic tendency of such biopolymers to form high‐order molecular structures. For example, single‐stranded deoxyribonucleic acids (ssDNA) tend to form secondary structures such as local double helices that prevent the direct measurement of the ideal elastic response of the ssDNA. In this work, we show how to extract the ideal elastic response in the entropic regime of short ssDNA molecules by mechanically pulling two‐state DNA hairpins of different contour lengths. This is achieved by measuring the force dependence of the molecular extension and stiffness on mechanically folding and unfolding the DNA hairpin. Both quantities are fit to the worm‐like chain elastic model giving values for the persistence length and the interphosphate distance. This method can be used to unravel the elastic properties of short ssDNA and RNA sequences and, more generally, any biopolymer that can exhibit a cooperative two‐state transition between mechanically folded and unfolded states (such as proteins). © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1193–1199, 2014.     

Progressive stabilization of intermediate and transition states in protein folding reactions by introducing surface hydrophobic residues

It can be argued from the principle of solvent exclusion that the introduction of hydrophobic residues onto the surface of a protein will not destabilize the folded state because the nonpolar side chain will be at least as exposed in the unfolded state as it is when the protein chain is folded. A comparison of the folding pathway of wild type and 11 site-directed mutants of CD2.d1 shows this to be true. In fact, owing to partial burial of nonpolar groups as folding proceeds, we find that the rapidly formed intermediate state and, to a greater extent, the transition state are generally stabilized by hydrophobic surface mutations. This effect is slightly moderated in the folded state presumably by the perturbation of van der Waals' contacts and/or local electrostatic interactions that have a greater influence in this fully compact structure. The fact that in all but one case we find that stabilization of the rapidly collapsed intermediate is accompanied by a faster acquisition of the folded state refutes the argument that I states are generally "off pathway" conformations or ensembles that lead to the inhibition of otherwise more rapid folding trajectories.     

pH-induced conformation changes and equilibrium unfolding in yeast iso-2 cytochrome c

The relationship between pH-induced conformational changes in iso-2 cytochrome c from Saccharomyces cerevisiae and the guanidine hydrochloride induced unfolding transition has been investigated. Comparison of equilibrium unfolding transitions at acid, neutral, and alkaline pH shows that stability toward guanidine hydrochloride denaturation is decreased at low pH but increased at high pH. In the acid range the decrease in stability of the folded protein is correlated with changes in the visible spectrum, which indicate conversion to a high-spin heme state--probably involving the loss of heme ligands. The increase in stability at high pH is correlated with a pH-induced conformational change with an apparent pK near 8. As in the case of homologous cytochromes c, this transition involves the loss of the 695-nm absorbance band with only minor changes in other optical parameters. For the unfolded protein, optical spectroscopy and 1H NMR spectroscopy are consistent with a random coil unfolded state in which amino acid side chains serve as (low-spin) heme ligands at both neutral and alkaline pH. However, the paramagnetic region of the proton NMR spectrum of unfolded iso-2 cytochrome c indicates a change in the (low-spin) heme-ligand complex at high pH. Apparently, the folded and unfolded states of the (inactive) alkaline form differ from the corresponding states of the less stable native protein.     

How a vicinal layer of solvent modulates the dynamics of proteins

The dynamics of a folded protein is studied in water and glycerol at a series of temperatures below and above their respective dynamical transition. The system is modeled in two distinct states whereby the protein is decoupled from the bulk solvent at low temperatures, and communicates with it through a vicinal layer at physiological temperatures. A linear viscoelastic model elucidates the less-than-expected increase in the relaxation times observed in the backbone dynamics of the protein. The model further explains the increase in the flexibility of the protein once the transition takes place and the differences in the flexibility under the different solvent environments. Coupling between the vicinal layer and the protein fluctuations is necessary to interpret these observations. The vicinal layer is postulated to form once a threshold for the volumetric fluctuations in the protein to accommodate solvents of different sizes is reached. Compensation of entropic-energetic contributions from the protein-coupled vicinal layer quantifies the scaling of the dynamical transition temperatures in various solvents. The protein adapts different conformational routes for organizing the required coupling to a specific solvent, which is achieved by adjusting the amount of conformational jumps in the surface-group dihedrals.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.     

Characterization of the non-native trifluoroethanol-induced intermediate conformational state of the Shiga toxin B-subunit

The effect of increasing concentrations of 2,2,2-trifluoroethanol (TFE) on the conformational stability of the Shiga toxin B-subunit (STxB), a bacterial homopentameric protein involved in cell-surface binding and intracellular transport, has been studied by far-, near-UV circular dichroism (CD), intrinsic fluorescence, analytical ultracentrifugation, and differential scanning calorimetry (DSC) under equilibrium conditions. Our data show that the native structure of STxB is highly perturbed by the presence of TFE. In fact, at concentrations of TFE above 20% (v/v), the native pentameric conformation of the protein is cooperatively transformed into a helix-rich monomeric and partially folded conformational state with no significant tertiary structure. Additionally, no cooperative transition was detected upon a further increase in the TFE concentration (above 40% (v/v)). The thermal stability of STxB was investigated at several different TFE concentrations using DSC and CD spectroscopy. Thermal transitions at TFE concentrations of up to 20% (v/v) were successfully fitted to the two-state folding/unfolding coupled to oligomerization model consistent with the transition between a pentameric folded conformation to a monomeric state of the protein, which the presence of TFE stabilizes as a partially folded conformation.     

Energetic coupling between native-state prolyl isomerization and conformational protein folding

In folded proteins, prolyl peptide bonds are usually thought to be either trans or cis because only one of the isomers can be accommodated in the native folded protein. For the N-terminal domain of the gene-3 protein of the filamentous phage fd (N2 domain), Pro161 resides at the tip of a beta hairpin and was found to be cis in the crystal structure of this protein. Here we show that Pro161 exists in both the cis and the trans conformations in the folded form of the N2 domain. We investigated how conformational folding and prolyl isomerization are coupled in the unfolding and refolding of N2 domain. A combination of single-mixing and double-mixing unfolding and refolding experiments showed that, in unfolded N2 domain, 7% of the molecules contain a cis-Pro161 and 93% of the molecules contain a trans-Pro161. During refolding, the fraction of molecules with a cis-Pro161 increases to 85%. This implies that 10.3 kJ mol(-1) of the folding free energy was used to drive this 75-fold change in the Pro161 cis/trans equilibrium constant during folding. The stabilities of the forms with the cis and the trans isomers of Pro161 and their folding kinetics could be determined separately because their conformational folding is much faster than the prolyl isomerization reactions in the native and the unfolded proteins. The energetic coupling between conformational folding and Pro161 isomerization is already fully established in the transition state of folding, and the two isomeric forms are thus truly native forms. The folding kinetics are well described by a four-species box model, in which the N2 molecules with either isomer of Pro161 can fold to the native state and in which cis/trans isomerization occurs in both the unfolded and the folded proteins.     

Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes

Recently we have developed a normal-modes-based algorithm that predicts the direction of protein conformational changes given the initial state crystal structure together with a small number of pairwise distance constraints for the end state. Here we significantly extend this method to accurately model both the direction and amplitude of protein conformational changes. The new protocol implements a multisteps search in the conformational space that is driven by iteratively minimizing the error of fitting the given distance constraints and simultaneously enforcing the restraint of low elastic energy. At each step, an incremental structural displacement is computed as a linear combination of the lowest 10 normal modes derived from an elastic network model, whose eigenvectors are reorientated to correct for the distortions caused by the structural displacements in the previous steps. We test this method on a list of 16 pairs of protein structures for which relatively large conformational changes are observed (root mean square deviation >3 angstroms), using up to 10 pairwise distance constraints selected by a fluctuation analysis of the initial state structures. This method has achieved a near-optimal performance in almost all cases, and in many cases the final structural models lie within root mean square deviation of 1 approximately 2 angstroms from the native end state structures.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

A measure of conformational entropy change during thermal protein unfolding using neutron spectroscopy

Thermal unfolding of proteins at high temperatures is caused by a strong increase of the entropy change which lowers Gibbs free energy change of the unfolding transition (DeltaG(unf) = DeltaH - TDeltaS). The main contributions to entropy are the conformational entropy of the polypeptide chain itself and ordering of water molecules around hydrophobic side chains of the protein. To elucidate the role of conformational entropy upon thermal unfolding in more detail, conformational dynamics in the time regime of picoseconds was investigated with neutron spectroscopy. Confined internal structural fluctuations were analyzed for alpha-amylase in the folded and the unfolded state as a function of temperature. A strong difference in structural fluctuations between the folded and the unfolded state was observed at 30 degrees C, which increased even more with rising temperatures. A simple analytical model was used to quantify the differences of the conformational space explored by the observed protein dynamics for the folded and unfolded state. Conformational entropy changes, calculated on the basis of the applied model, show a significant increase upon heating. In contrast to indirect estimates, which proposed a temperature independent conformational entropy change, the measurements presented here, demonstrated that the conformational entropy change increases with rising temperature and therefore contributes to thermal unfolding.     

Three-dimensional domain swapping in the folded and molten-globule states of cystatins, an amyloid-forming structural superfamily

Cystatins, an amyloid-forming structural superfamily, form highly stable, domain-swapped dimers at physiological protein concentrations. In chicken cystatin, the active monomer is a kinetic trap en route to dimerization, and any changes in solution conditions or mutations that destabilize the folded state shorten the lifetime of the monomeric form. In such circumstances, amyloidogenesis will start from conditions where a domain-swapped dimer is the most prevalent species. Domain swapping occurs by a rearrangement of loop I, generating the new intermonomer interface between strands 2 and 3. The transition state for dimerization has a high level of hydrophobic group exposure, indicating that gross conformational perturbation is required for domain swapping to occur. Dimerization also occurs when chicken cystatin is in its reduced, molten-globule state, implying that the organization of secondary structure in this state mirrors that in the folded state and that domain swapping is not limited to the folded states of proteins. Although the interface between cystatin-fold units is poorly defined for cystatin A, the dimers are the appropriate size to account for the electron-dense regions in amyloid protofilaments.     

Analysis of a water mediated protein-protein interactions within RNase T1

Buried and well-ordered solvent molecules are an integral part of each folded protein. For a few individual water molecules, the exchange kinetics with solvent have been described in great detail. So far, little is known about the energetics of this exchange process. Here, we present an experimental approach to investigate water-mediated intramolecular protein-protein interactions by use of double mutant cycles. As a first example, we analyzed the interdependence of the contribution of two side chains (Asn9 and Thr93) to the conformational stability of RNase T1. In the folded state, both side chains are involved in the "solvation of the same water molecule WAT1. The coupling of the contributions of Asn9 and Thr93 to the conformational stability of RNase T1 was measured by urea unfolding and differential scanning calorimetry. The structural integrity of each mutant was analyzed by X-ray crystallography. We find that the effects of the Asn9Ala and the Thr93Ala mutations on the conformational stability are additive in the corresponding double mutant. We conclude that the free energy of the WAT1 mediated intramolecular protein-protein interaction in the folded state is very similar to solvent mediated protein-protein interaction in the unfolded state.     

States and transitions during forced unfolding of a single spectrin repeat

Spectrin is a vital and abundant protein of the cytoskeleton. It has an elongated structure that is made by a chain of so-called spectrin repeats. Each repeat contains three antiparallel alpha-helices that form a coiled-coil structure. Spectrin forms an oligomeric structure that is able to cross-link actin filaments. In red cells, the spectrin/actin meshwork underlying cell membrane is thought to be responsible for special elastic properties of the cell. In order to determine mechanical unfolding properties of the spectrin repeat, we have used single molecule force spectroscopy to study the states of unfolding of an engineered polymeric protein consisting of identical spectrin domains. We demonstrate that the unfolding of spectrin domains can occur in a stepwise fashion during stretching. The force-extension patterns exhibit features that are compatible with the existence of at least one intermediate between the folded and the completely unfolded conformation. Only those polypeptides that still contain multiple intact repeats display intermediates, indicating a stabilisation effect. Precise force spectroscopy measurements on single molecules using engineered protein constructs reveal states and transitions during the mechanical unfolding of spectrin. Single molecule force spectroscopy appears to open a new window for the analysis of transition probabilities between different conformational states.     

Multiple interactions of a DNA-binding protein in vivo. II. Effects of host mutations on DNA replication of phage T4 gene 32 mutants.

A quantitative analysis has been made of the kinetics of disulphide bond formation, breakage, and rearrangement which occur during the folding and unfolding of the pancreatic trypsin inhibitor. The results have been used to infer the energetics of the protein conformational transitions which accompany each step.The folding transition is shown to be a co-operative process in which all intermediate states with one or two disulphide bonds are unstable relative to the unfolded, reduced protein and that in the fully folded conformation with three disulphide bonds. The approximate two-state nature of the transition at equilibrium was demonstrated experimentally. The folding transition of the inhibitor which has been determined kinetically is therefore analogous to that observed generally with other globular proteins.     

Observing the osmophobic effect in action at the single molecule level

Protecting osmolytes are widespread small organic molecules able to stabilize the folded state of most proteins against various denaturing stresses in vivo. The osmophobic model explains thermodynamically their action through a preferential exclusion of the osmolyte molecules from the protein surface, thus favoring the formation of intrapeptide hydrogen bonds. Few works addressed the influence of protecting osmolytes on the protein unfolding transition state and kinetics. Among those, previous single molecule force spectroscopy experiments evidenced a complexation of the protecting osmolyte molecules at the unfolding transition state of the protein, in apparent contradiction with the osmophobic nature of the protein backbone. We present single-molecule evidence that glycerol, which is a ubiquitous protecting osmolyte, stabilizes a globular protein against mechanical unfolding without binding into its unfolding transition state structure. We show experimentally that glycerol does not change the position of the unfolding transition state as projected onto the mechanical reaction coordinate. Moreover, we compute theoretically the projection of the unfolding transition state onto two other common reaction coordinates, that is, the number of native peptide bonds and the weighted number of native contacts. To that end, we augment an analytic Ising-like protein model with support for group-transfer free energies. Using this model, we find again that the position of the unfolding transition state does not change in the presence of glycerol, giving further support to the conclusions based on the single-molecule experiments.     

Mapping molecular flexibility of proteins with site-directed spin labeling: a case study of myoglobin

Site-directed spin labeling (SDSL) has potential for mapping protein flexibility under physiological conditions. The purpose of the present study was to explore this potential using 38 singly spin-labeled mutants of myoglobin distributed throughout the sequence. Correlation of the EPR spectra with protein structure provides new evidence that the site-dependent variation in line shape, and hence motion of the spin label, is due largely to differences in mobility of the helical backbone in the ns time range. Fluctuations between conformational substates, typically in the μs-ms time range, are slow on the EPR time scale, and the spectra provide a snapshot of conformational equilibria frozen in time as revealed by multiple components in the spectra. A recent study showed that osmolyte perturbation can positively identify conformational exchange as the origin of multicomponent spectra ( López et al. ( 2009 ) , Protein Sci. 18 , 1637 ). In the present study, this new strategy is employed in combination with line shape analysis and pulsed-EPR interspin distance measurements to investigate the conformation and flexibility of myoglobin in three folded and partially folded states. The regions identified to be in conformational exchange in the three forms agree remarkably well with those assigned by NMR, but the faster time scale of EPR allows characterization of localized states not detected in NMR. Collectively, the results suggest that SDSL-EPR and osmolyte perturbation provide a facile means for mapping the amplitude of fast backbone fluctuations and for detecting sequences in slow conformational exchange in folded and partially folded protein sequences.     

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

The mechanical behavior of blood vessels is known to be viscoelastic rather than elastic. The functional role of viscoelasticity, however, has remained largely unclear. The hypothesis of this study is that viscoelasticity reduces the stresses and strains in the vessel wall, which may have a significant impact on the fatigue life of the blood vessel wall. To verify the hypothesis, the pulsatile stress in rabbit thoracic artery at physiological loading condition was investigated with a quasi-linear viscoelastic model, where the normalized stress relaxation function is assumed to be isotropic, while the stress-strain relationship is anisotropic and nonlinear. The artery was subjected to the same boundary condition, and the mechanical equilibrium equation was solved for both the viscoelastic and an elastic (which has a constant relaxation function) model. Numerical results show that, compared with purely elastic response, the viscoelastic property of arteries reduces the magnitudes and temporal variations of circumferential stress and strain. The radial wall movement is also reduced due to viscoelasticity. These findings imply that viscoelasticity may be beneficial for the fatigue life of blood vessels, which undergo millions of cyclic mechanical loadings each year of life.     

Dual energy landscape: the functional state of the β-barrel outer membrane protein G molds its unfolding energy landscape

We applied dynamic single-molecule force spectroscopy to quantify the parameters (free energy of activation and distance of the transition state from the folded state) characterizing the energy barriers in the unfolding energy landscape of the outer membrane protein G (OmpG) from Escherichia coli. The pH-dependent functional switching of OmpG directs the protein along different regions on the unfolding energy landscape. The two functional states of OmpG take the same unfolding pathway during the sequential unfolding of β-hairpins I-IV. After the initial unfolding events, the unfolding pathways diverge. In the open state, the unfolding of β-hairpin V in one step precedes the unfolding of β-hairpin VI. In the closed state, β-hairpin V and β-strand S11 with a part of extracellular loop L6 unfold cooperatively, and subsequently β-strand S12 unfolds with the remaining loop L6. These two unfolding pathways in the open and closed states join again in the last unfolding step of β-hairpin VII. Also, the conformational change from the open to the closed state witnesses a rigidified extracellular gating loop L6. Thus, a change in the conformational state of OmpG not only bifurcates its unfolding pathways but also tunes its mechanical properties for optimum function.     

Diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network normal mode analysis

We analyze the mechanical properties and putative dynamical fluctuations of a variety of viral capsids comprising different sizes and quasi-equivalent symmetries by performing normal mode analysis using the elastic network model. The expansion of the capsid to a swollen state is studied using normal modes and is compared with the experimentally observed conformational change for three of the viruses for which experimental data exist. We show that a combination of one or two normal modes captures remarkably well the overall translation that dominates the motion between the two conformational states, and reproduces the overall conformational change. We observe for all of the viral capsids that the nature of the modes is different. In particular for the T=7 virus, HK97, for which the shape of the capsid changes from spherical to faceted polyhedra, two modes are necessary to accomplish the conformational transition. In addition, we extend our study to viral capsids with other T numbers, and discuss the similarities and differences in the features of virus capsid conformational dynamics. We note that the pentamers generally have higher flexibility and propensity to move freely from the other capsomers, which facilitates the shape adaptation that may be important in the viral life cycle.