Reversible mechanical unfolding of single ubiquitin molecules

Single-molecule manipulation techniques have enabled the characterization of the unfolding and refolding process of individual protein molecules, using mechanical forces to initiate the unfolding transition. Experimental and computational results following this approach have shed new light on the mechanisms of the mechanical functions of proteins involved in several cellular processes, as well as revealed new information on the protein folding/unfolding free-energy landscapes. To investigate how protein molecules of different folds respond to a stretching force, and to elucidate the effects of solution conditions on the mechanical stability of a protein, we synthesized polymers of the protein ubiquitin and characterized the force-induced unfolding and refolding of individual ubiquitin molecules using an atomic-force-microscope-based single-molecule manipulation technique. The ubiquitin molecule was highly resistant to a stretching force, and the mechanical unfolding process was reversible. A model calculation based on the hydrogen-bonding pattern in the native structure was performed to explain the origin of this high mechanical stability. Furthermore, pH effects were studied and it was found that the forces required to unfold the protein remained constant within a pH range around the neutral value, and forces decreased as the solution pH was lowered to more acidic values.     

Tracking unfolding and refolding of single GFPmut2 molecules

The unfolding and refolding kinetics of >600 single GFPmut2 molecules, entrapped in wet nanoporous silica gels, were followed by monitoring simultaneously the fluorescence emission of the anionic and neutral state of the chromophore, primed by two-photon excitation. The rate of unfolding, induced by guanidinium chloride, was determined by counting the number of single molecules that disappear in fluorescence images, under conditions that do not cause bleaching or photoinduced conversion between chromophore protonation states. The unfolding rate is of the order of 0.01 min(-1), and its dependence on denaturant concentration is very similar to that previously reported for high protein load gels. Upon rinsing the gels with denaturant-free buffer, the GFPmut2 molecules refold with rates >10 min(-1), with an apparently random distribution between neutral and anionic states, that can be very different from the preunfolding equilibrium. A subsequent very slow (lifetime of approximately 70 min) relaxation leads to the equilibrium distribution of the protonation states. This mechanism, involving one or more native-like refolding intermediates, is likely rate limited by conformational rearrangements that are undetectable in circular dichroism experiments. Several unfolding/refolding cycles can be followed on the same molecules, indicating full reversibility of the process and, noticeably, a bias of denaturated molecules toward refolding in the original protonation state.     

Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.     

Folding and unfolding of gammaTIM monomers and dimers

Kinetic simulations of the folding and unfolding of triosephosphate isomerase (TIM) from yeast were conducted using a single monomer gammaTIM polypeptide chain that folds as a monomer and two gammaTIM chains that fold to the native dimer structure. The basic protein model used was a minimalist Gō model using the native structure to determine attractive energies in the protein chain. For each simulation type--monomer unfolding, monomer refolding, dimer unfolding, and dimer refolding--thirty simulations were conducted, successfully capturing each reaction in full. Analysis of the simulations demonstrates four main conclusions. First, all four simulation types have a similar "folding order", i.e., they have similar structures in intermediate stages of folding between the unfolded and folded state. Second, despite this similarity, different intermediate stages are more or less populated in the four different simulations, with 1), no intermediates populated in monomer unfolding; 2), two intermediates populated with beta(2)-beta(4) and beta(1)-beta(5) regions folded in monomer refolding; 3), two intermediates populated with beta(2)-beta(3) and beta(2)-beta(4) regions folded in dimer unfolding; and 4), two intermediates populated with beta(1)-beta(5) and beta(1)-beta(5) + beta(6) + beta(7) + beta(8) regions folded in dimer refolding. Third, simulations demonstrate that dimer binding and unbinding can occur early in the folding process before complete monomer-chain folding. Fourth, excellent agreement is found between the simulations and MPAX (misincorporation proton alkyl exchange) experiments. In total, this agreement demonstrates that the computational Gō model is accurate for gammaTIM and that the energy landscape of gammaTIM appears funneled to the native state.     

Folding and unfolding characteristics of short beta strand peptides under different environmental conditions and starting configurations

We analyze the effect of different environmental conditions, sequence lengths and starting configurations on the folding and unfolding pathways of small peptides exhibiting beta turns. We use chignolin and a sequence of peptide G as examples. A variety of different analysis tools allows us to characterize the changes in the folding pathways. It is observed that different harmonic modes dominate not only for different conditions but also for different starting points. The modes remain essentially very similar but their relative importance varies. A detailed analysis from diverse viewpoints including the influence of the particular amino acid sequence, conformational aspects as well as the associated motions yields a global picture that is consistent with experimental evidence and theoretical studies published elsewhere. Patterns of modes that remain stable over a range of temperatures might serve as an additional diagnostic to identify conformations that have reliably adopted a native fold. This could aid in reconstructing the folding process of a complete protein by identifying conformationally determined regions.     

Molecular beacons as probes of RNA unfolding under native conditions

Hybridization of fluorescent molecular beacons provides real-time detection of RNA secondary structure with high specificity. We used molecular beacons to measure folding and unfolding rates of the Tetrahymena group I ribozyme under native conditions. A molecular beacon targeted against 15 nt in the 5′ strand of the P3 helix specifically hybridized with misfolded forms of the ribozyme, without invading the native tertiary structure. The beacon associated with the misfolded ribozyme 300 times more slowly than with an unstructured oligonucleotide containing the same target sequence, suggesting that the misfolded ribozyme core remains structured in the absence of Mg²⁺. The rate of beacon hybridization under native conditions revealed a linear relationship between the free energy of unfolding and Mg²⁺ concentration. A small fraction of the RNA population unfolded very rapidly, suggesting parallel unfolding in one step or through misfolded intermediates.     

Freezing shortens the lifetime of DNA molecules under tension

DNA samples are commonly frozen for storage. However, freezing can compromise the integrity of DNA molecules. Considering the wide applications of DNA molecules in nanotechnology, changes to DNA integrity at the molecular level may cause undesirable outcomes. However, the effects of freezing on DNA integrity have not been fully explored. To investigate the impact of freezing on DNA integrity, samples of frozen and non-frozen bacteriophage lambda DNA were studied using optical tweezers. Tension (5–35 pN) was applied to DNA molecules to mimic mechanical interactions between DNA and other biomolecules. The integrity of the DNA molecules was evaluated by measuring the time taken for single DNA molecules to break under tension. Mean lifetimes were determined by maximum likelihood estimates and variances were obtained through bootstrapping simulations. Under 5 pN of force, the mean lifetime of frozen samples is 44.3 min with 95% confidence interval (CI) between 36.7 min and 53.6 min while the mean lifetime of non-frozen samples is 133.2 min (95% CI: 97.8–190.1 min). Under 15 pN of force, the mean lifetimes are 10.8 min (95% CI: 7.6–12.6 min) and 78.5 min (95% CI: 58.1–108.9 min). The lifetimes of frozen DNA molecules are significantly reduced, implying that freezing compromises DNA integrity. Moreover, we found that the reduced DNA structural integrity cannot be restored using regular ligation process. These results indicate that freezing can alter the structural integrity of the DNA molecules.     

Force unfolding single RNAs

We develop a continue time Monte Carlo algorithm to simulate single RNAs unfolded by a time-dependent external force on the secondary structure level. Two recent unfolding RNA experiments carried out by Bustamante group are mainly investigated. We find that, in contrast to popular two-state assumption about the RNAs free energy landscape along the molecular extension, the molecules used in the experiments do not present apparent energy barriers. The strong cooperative folding and unfolding transitions of the RNAs observed in the experiments and in our simulations arise from the interaction of the molecules and the light trap. In addition, we also investigate the properties of Jarzynski's remarkable equality, whose experimental test has received considerable attention.     

Measuring the folding transition time of single RNA molecules

We describe a new, time-apertured photon correlation method for resolving the transition time between two states of RNA in folding--i.e., the time of the transition between states rather than the time spent in each state. Single molecule fluorescence resonance energy transfer and fluorescence correlation spectroscopy are used to obtain these measurements. Individual RNA molecules are labeled with fluorophores such as Cy3 and Cy5. Those molecules are then immobilized on a surface and observed for many seconds during which time the molecules spontaneously switch between two conformational states with different levels of flourescence resonance energy transfer efficiency. Single photons are counted from each fluorophore and cross correlated in a small window around a transition. The average of over 1000 cross correlations can be fit to a polynomial, which can determine transition times as short as the average photon emission interval. We applied the method to the P4-P6 domain of the Tetrahymena group I self-splicing intron to yield the folding transition time of 240 micros. The unfolding time is found to be too short to measure with this method.     

Mechanically probing the folding pathway of single RNA molecules

We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating the experimentally determined free energy rules for RNA secondary structure, whereas exterior single-stranded regions are modeled as freely jointed chains. For exemplary RNA sequences (hairpins and the Tetrahymena thermophila group I intron), we compute the quasiequilibrium fluctuations in the end-to-end distance as the molecule is unfolded by pulling on opposite ends. Unlike the average quasiequilibrium force-extension curves, these fluctuations reveal clear signatures from the unfolding of individual structural elements. We find that the resolution of these signatures depends on the spring constant of the force-measuring device, with an optimal value intermediate between very rigid and very soft. We compare and relate our results to recent experiments by Liphardt et al. (2001).     

Folding and unfolding mechanism of highly stable full-consensus ankyrin repeat proteins

Full-consensus designed ankyrin repeat proteins were designed with one to six identical repeats flanked by capping repeats. These proteins express well in Escherichia coli as soluble monomers. Compared to our previously described designed ankyrin repeat protein library, randomized positions have now been fixed according to sequence statistics and structural considerations. Their stability increases with length and is even higher than that of library members, and those with more than three internal repeats are resistant to denaturation by boiling or guanidine hydrochloride. Full denaturation requires their heating in 5 M guanidine hydrochloride. The folding and unfolding kinetics of the proteins with up to three internal repeats were analyzed, as the other proteins could not be denatured. Folding is monophasic, with a rate that is nearly identical for all proteins (∼ 400-800 s^− 1), indicating that essentially the same transition state must be crossed, possibly the folding of a single repeat. In contrast, the unfolding rate decreases by a factor of about 10⁴ with increasing repeat number, directly reflecting thermodynamic stability in these extraordinarily slow denaturation rates. The number of unfolding phases also increases with repeat number. We analyzed the folding thermodynamics and kinetics both by classical two-state and three-state cooperative models and by an Ising-like model, where repeats are considered as two-state folding units that can be stabilized by interacting with their folded nearest neighbors. This Ising model globally describes both equilibrium and kinetic data very well and allows for a detailed explanation of the ankyrin repeat protein folding mechanism.     

Folding of branched RNA species

The global structures of branched RNA species are important to their function. Branched RNA species are defined as molecules in which double-helical segments are interrupted by abrupt discontinuities. These include helical junctions of different orders, and base bulges and loops. Common helical junctions are three- and four-way junctions, often interrupted by mispairs or additional nucleotides. There are many interesting examples of functional RNA junctions, including the hammerhead and hairpin ribozymes, and junctions that serve as binding sites for proteins. The junctions display some common structural properties. These include a tendency to undergo pairwise helical stacking and ion-induced conformational transitions. Helical branchpoints can act as key architectural components and as important sites for interactions with proteins. Copyright 1999 John Wiley & Sons, Inc.     

Mechanical unfolding of single filamin A (ABP-280) molecules detected by atomic force microscopy

Filamin A (ABP-280), which is an actin-binding protein of 560 kDa as a dimer, can, together with actin filaments, produce an isotropic cross-linked three-dimensional network (actin/filamin A gel) that plays an important role in mechanical responses of cells in processes such as maintenance of membrane stability and translational locomotion. In this study, we investigated the mechanical properties of single filamin A molecules using atomic force microscopy. In force-extension curves, we observed sawtooth patterns corresponding to the unfolding of individual immunoglobulin (Ig)-fold domains of filamin A. At a pulling speed of 0.37 microm/s, the unfolding interval was sharply distributed around 30 nm, while the unfolding force ranged from 50 to 220 pN. This wide distribution of the unfolding force can be explained by variation in values of activation energy and the width of activation barrier of 24 Ig-fold domains of the filamin A at the unfolding transition. This unfolding can endow filamin A with great extensibility. The refolding of the unfolded chain of filamin A occurred when the force applied to the protein was reduced to near zero, indicating that its unfolding is reversible. Based on these results, we discuss here the physiological implications of the mechanical properties of single filamin A molecules.