Distribution Of Unfolding Forces Research Articles

Unfolding rates of 1:1 and 2:1 complex of CX-5461 and c-MYC promoter G-quadruplexes revealed by single-molecule force spectroscopy.

CX-5461, also known as pidnarulex, is a strong G4 stabilizer and has received FDA fast-track designation for BRCA1- and BRCA2- mutated cancers. However, quantitative measurements of the unfolding rates of CX-5461-G4 complexes which are important for the regulation function of G4s, remain lacking. Here, we employ single-molecule magnetic tweezers to measure the unfolding force distributions of c-MYC G4s in the presence of different concentrations of CX-5461. The unfolding force distributions exhibit three discrete levels of unfolding force peaks, corresponding to three binding modes. In combination with a fluorescent quenching assay and molecular docking to previously reported ligand-c-MYC G4 structure, we assigned the ~69 pN peak corresponding to the 1:1 (ligand:G4) complex where CX-5461 binds at the G4's 5'-end. The ~84 pN peak is attributed to the 2:1 complex where CX-5461 occupies both the 5' and 3'. Furthermore, using the Bell-Arrhenius model to fit the unfolding force distributions, we determined the zero-force unfolding rates of 1:1, and 2:1 complexes to be (2.4 ± 0.9) × 10-8 s-1 and (1.4 ± 1.0) × 10-9 s-1 respectively. These findings provide valuable insights for the development of G4-targeted ligands to combat c-MYC-driven cancers.

High Mechanical Stability and Slow Unfolding Rates Are Prevalent in Parallel-Stranded DNA G-Quadruplexes.

Guanine-rich repeat sequences are known to adopt diverse G-quadruplex (G4) topologies. Determining the unfolding rates of individual G4 species is challenging due to the coexistence of multiple G4 conformations in a solution. Here, using single-molecule magnetic tweezers, we systematically measured the unfolding force distributions of 4 oncogene promoter G4s, 12 model sequences with two 1-nucleotide (nt) thymine loops that predominantly adopt parallel-stranded G4 structures, and 6 sequences forming multiple G4 structures. All parallel-stranded G4s reveal an unfolding force peak at 40-60 pN, which is associated with extremely slow unfolding rates on the order of 10-5-10-7 s-1. In contrast, nonparallel G4s and partially folded intermediate states reveal an unfolding force peak <40 pN. These results suggest a strong correlation between the parallel-stranded G4s folding topology and the slow unfolding rates and provide important insights into the mechanism that govern the stability and the transition kinetics of G4s.

Combined Force Ramp and Equilibrium High-Resolution Investigations Reveal Multipath Heterogeneous Unfolding of Protein G.

Over the past two decades, one of the standard models of protein folding has been the "two-state" model, in which a protein only resides in the folded or fully unfolded states with a single pathway between them. Recent advances in spatial and temporal resolution of biophysical measurements have revealed "beyond-two-state" complexity in protein folding, even for small, single-domain proteins. In this work, we used high-resolution optical tweezers to investigate the folding/unfolding kinetics of the B1 domain of immunoglobulin-binding protein G (GB1), a well-studied model system. Experiments were performed for GB1 both in and out of equilibrium using force spectroscopy. When the force was gradually ramped, simple single-peak folding force distributions were observed, while multiple rupture peaks were seen in the unfolding force distributions, consistent with multiple force-dependent parallel unfolding pathways. Force-dependent folding and unfolding rate constants were directly determined by both force-jump and fixed-trap measurements. Monte Carlo modeling using these rate constants was in good agreement with the force ramp data. The unfolding rate constants exhibited two different behaviors at low vs high force. At high force, the unfolding rate constant increased with increasing force, as previously reported by high force, high pulling speed force ramp measurements. However, at low force, the situation reversed and the unfolding rate constant decreased with increasing force. Taken together, these data indicate that this small protein has multiple distinct pathways to the native state on the free energy landscape.

Effect of concentration of molecular crowder on the unfolding force distribution: emergence of a long tail

We investigate the force induced unfolding transitions of a polymer in presence of crowding particles over a wide range of conditions. The polymer conformations are specified by the reaction coordinate i.e. end-to-end distance and the quality of the solvent. Crowding distribution is obtained through the percolation process, which gives rise to a distribution of clusters of different shapes and sizes starting from isolated disorder sites up to clusters with an extent spanning the entire system. It was shown here that the polymer structures are altered by such distributions and induces an array of structural changes in the form of intermediate states. It was found that the mechanical stability of polymer was insensitive at lower concentration, but increases at higher concentration. This is in accordance with experiments. Exact results based on a short polymer revealed that there is emergence of a long tail in the unfolding force distributions. This is less visible at lower concentration, but has significant contribution at higher concentration. This important feature either was overlooked or not explored so far, and therefore, needs further investigation.

Computing Average Passive Forces in Sarcomeres in Length-Ramp Simulations.

Passive forces in sarcomeres are mainly related to the giant protein titin. Titin’s extensible region consists of spring-like elements acting in series. In skeletal muscles these elements are the PEVK segment, two distinct immunoglobulin (Ig) domain regions (proximal and distal), and a N2A portion. While distal Ig domains are thought to form inextensible end filaments in intact sarcomeres, proximal Ig domains unfold in a force- and time-dependent manner. In length-ramp experiments of single titin strands, sequential unfolding of Ig domains leads to a typical saw-tooth pattern in force-elongation curves which can be simulated by Monte Carlo simulations. In sarcomeres, where more than a thousand titin strands are arranged in parallel, numerous Monte Carlo simulations are required to estimate the resultant force of all titin filaments based on the non-uniform titin elongations. To simplify calculations, the stochastic model of passive forces is often replaced by linear or non-linear deterministic and phenomenological functions. However, new theories of muscle contraction are based on the hypothesized binding of titin to the actin filament upon activation, and thereby on a prominent role of the structural properties of titin. Therefore, these theories necessitate a detailed analysis of titin forces in length-ramp experiments. In our study we present a simple and efficient alternative to Monte Carlo simulations. Based on a structural titin model, we calculate the exact probability distributions of unfolded Ig domains under length-ramp conditions needed for rigorous analysis of expected forces, distribution of unfolding forces, etc. Due to the generality of our model, the approach is applicable to a wide range of stochastic protein unfolding problems.

Direct Observation of Multimer Stabilization in the Mechanical Unfolding Pathway of a Protein Undergoing Oligomerization

Understanding how protein oligomerization affects the stability of monomers in self-assembled structures is crucial to the development of new protein-based nanomaterials and protein cages for drug delivery. Here, we use single-molecule force spectroscopy (AFM-SMFS), protein engineering, and computer simulations to evaluate how dimerization and tetramerization affects the stability of the monomer of Streptavidin, a model homotetrameric protein. The unfolding force directly relates to the folding stability, and we find that monomer of Streptavidin is mechanically stabilized by 40% upon dimerization, and that it is stabilized an additional 24% upon tetramerization. We also find that biotin binding increases stability by another 50% as compared to the apo-tetrameric form. We used the distribution of unfolding forces to extract properties of the underlying energy landscape and found that the distance to the transition state is decreased and the barrier height is increased upon multimerization. Finally, we inve...

Direct observation of multimer stabilization in the mechanical unfolding pathway of a protein undergoing oligomerization.

Understanding how protein oligomerization affects the stability of monomers in self-assembled structures is crucial to the development of new protein-based nanomaterials and protein cages for drug delivery. Here, we use single-molecule force spectroscopy (AFM-SMFS), protein engineering, and computer simulations to evaluate how dimerization and tetramerization affects the stability of the monomer of Streptavidin, a model homotetrameric protein. The unfolding force directly relates to the folding stability, and we find that monomer of Streptavidin is mechanically stabilized by 40% upon dimerization, and that it is stabilized an additional 24% upon tetramerization. We also find that biotin binding increases stability by another 50% as compared to the apo-tetrameric form. We used the distribution of unfolding forces to extract properties of the underlying energy landscape and found that the distance to the transition state is decreased and the barrier height is increased upon multimerization. Finally, we investigated the origin of the strengthening by ligand binding. We found that, rather than being strengthened through intramolecular contacts, it is strengthened due to the contacts provided by the biotin-binding loop that crosses the interface between the dimers.

Anti-Prion Ligand Binding Promotes Native PrP Folding Over Misfolding at the Single Molecule Level

Ligands that bind to the prion protein, PrP, and prevent the spread of the diseased state have been discovered, but their mechanism of action remains uncertain. Determining anti-prion mechanisms may provide insight into the still-unknown means by which native PrP is converted to the infectious form. To explore the effects of an anti-prion ligand at the molecular level, we used force spectroscopy to study how a tetrapyrrole known to have anti-prion activity, iron(III)meso-tetra(N-methyl-4-pyridyl-prophine) or Fe-TMPyP, alters the folding behavior of individual PrP molecules. Single PrP molecules were unfolded using optical tweezers in the presence and absence of Fe-TMPyP. Ligand binding to the native structure was found to significantly increase its unfolding force. Not only did Fe-TMPyP binding stabilize the native state as expected from ensemble binding studies, but analysis of the unfolding force distributions revealed that Fe-TMPyP binding altered the nature of the transition state for unfolding the native structure: the energy barrier moved closer to the native state, making the transition state more compact, and the barrier height increased. Unexpectedly, Fe-TMPyP was also able to bind to PrP when it was unfolded or only partially folded, thereby delaying the normally rapid refolding into the native state. Probing the effects of Fe-TMPyP on inter-molecular interactions by measuring PrP dimers revealed that ligand binding promoted the formation of the native structure in individual monomers, preventing the formation of a thermodynamically-stable misfolded dimeric state. The ligand thus promotes native folding by stabilizing the native state while at the same time suppressing interactions that drive the formation of stable aggregates. These results suggest parallels between pharmacological chaperones like Fe-TMPyP and cellular chaperones.

Transition Path Times for the Folding of Nucleic Acids and Proteins Determined from Experimentally-Reconstructed Energy Landscape Profiles

The transition path time for a folding reaction describes the time spent during the structural transition itself. In terms of the standard picture of folding as diffusion over a configurational free-energy landscape, it is the time required to cross over the barrier. Transition times are very brief and hence challenging to measure directly, but they may also be found indirectly from the shape of the landscape. We investigated the transition time for various nucleic acids and proteins by reconstructing the folding energy landscape profiles from high-resolution single-molecule force spectroscopy measurements using optical tweezers. Studying DNA hairpins, we first showed that landscapes reconstructed from the inverse Boltzmann transform of the extension probability distribution could be used to determine the diffusion constant for barrier crossing, D, via Kramers theory and the observed folding rates, before finding the transition time, τtp. We next showed that the same results could be found from a landscape parameterization obtained by fitting the distribution of unfolding forces, and applied this method to estimate τtp for several RNA pseudoknots and a riboswitch aptamer. Finally, we estimated τtp in the protein PrP both from the energy landscape reconstructed by the Hummer-Szabo formalism and from the landscape parameterization using unfolding force distributions. All the molecules had τtp on the order of 1-10 µs.

Spontaneous Dimerization of Titin Protein Z1Z2 Domains Induces Strong Nanomechanical Anchoring

Muscle elasticity strongly relies on the mechanical anchoring of the giant protein titin to both the sarcomere M-band and the Z-disk. Such strong attachment ensures the reversible dynamics of the stretching-relaxing cycles determining the muscle passive elasticity. Similarly, the design of biomaterials with enhanced elastic function requires experimental strategies able to secure the constituent molecules to avoid mechanical failure. Here we show that an engineered titin-mimicking protein is able to spontaneously dimerize in solution. Our observations reveal that the titin Z1Z2 domains are key to induce dimerization over a long-range distance in proteins that would otherwise remain in their monomeric form. Using single molecule force spectroscopy, we measure the threshold force that triggers the noncovalent transition from protein dimer to monomer, occurring at ∼700 piconewtons. Such extremely high mechanical stability is likely to be a natural protective mechanism that guarantees muscle integrity. We propose a simple molecular model to understand the force-induced dimer-to-monomer transition based on the geometric distribution of forces occurring within a dimeric protein under mechanical tension.

Reconstruction of the Energy Landscape Profile for Native Folding of Thepprion Protein from Single-Molecule Force Spectroscopy

Free energy landscapes drive protein folding phenomena but are difficult to measure directly. We measured the folding landscape of the prion protein PrP, a protein notable for its ability to form infectious non-native structures, using single molecule force spectroscopy with optical tweezers. Folding/unfolding trajectories of a single PrP molecule were observed directly by measuring the extension of the molecule under an applied tension, under both equilibrium constant-force and non-equilibrium force-ramp conditions. Native folding/unfolding was found to be a two-state process. The height and location of the energy barrier between the two states were determined from the distribution of unfolding forces in force-extension curves (FECs), and independently from the force-dependent lifetimes measured at constant force. The full profile of the landscape for native folding was then reconstructed from the FECs using the Hummer-Szabo method (Hummer and Szabo, 2001; Gupta A.N., et al., 2011). Because the landscape profile reconstructed this way is smoothed by the elastic compliance of the measurement set-up, we recovered the actual PrP folding landscape by using the measured point-spread function of the instrument to deconvolve the Hummer-Szabo result. The height and position of the barrier in the deconvolved landscape profile agreed well with the single reference point provided by the unfolding-force and force-dependent lifetime analyses, but the profile includes additional information about the width and shape of the potential wells and barriers. We found that the native folding pathway of PrP has an extended transition state, in agreement with mutational phi-analysis (Hart et al., 2009). These results show how protein folding landscapes can be recovered from non-equilibrium pulling experiments.

Order Statistics Theory of Unfolding of Multimeric Proteins

Dynamic force spectroscopy has become indispensable for the exploration of the mechanical properties of proteins. In force-ramp experiments, performed by utilizing a time-dependent pulling force, the peak forces for unfolding transitions in a multimeric protein (D)N are used to map the free energy landscape for unfolding for a protein domain D. We show that theoretical modeling of unfolding transitions based on combining the observed first (f1), second (f2), …, Nth (fN) unfolding forces for a protein tandem of fixed length N, and pooling the force data for tandems of different length, n1 <n2 < … <N, leads to an inaccurate estimation of the distribution of unfolding forces for the protein D, ψD(f). This problem can be overcome by using Order statistics theory, which, in conjunction with analytically tractable models, can be used to resolve the molecular characteristics that determine the unfolding micromechanics. We present a simple method of estimation of the parent distribution, ψD(f), based on analyzing the force data for a tandem (D)n of arbitrary length n. Order statistics theory is exemplified through a detailed analysis and modeling of the unfolding forces obtained from pulling simulations of the monomer and oligomers of the all-β-sheet WW domain.

Single-Molecule Unfolding Force Distributions Reveal a Funnel-Shaped Energy Landscape

The protein folding process is described as diffusion on a high-dimensional energy landscape. Experimental data showing details of the underlying energy surface are essential to understanding folding. So far in single-molecule mechanical unfolding experiments a simplified model assuming a force-independent transition state has been used to extract such information. Here we show that this so-called Bell model, although fitting well to force velocity data, fails to reproduce full unfolding force distributions. We show that by applying Kramers’ diffusion model, we were able to reconstruct a detailed funnel-like curvature of the underlying energy landscape and establish full agreement with the data. We demonstrate that obtaining spatially resolved details of the unfolding energy landscape from mechanical single-molecule protein unfolding experiments requires models that go beyond the Bell model.

Temperature Softening of a Protein in Single-molecule Experiments

Mechanical flexibility is crucial for the function of proteins. However, such material properties are not easily accessible experimentally. We used single-molecule force spectroscopy to study the stiffness of a single domain of Dictyostelium discoideum filamin (ddFLN4) in a temperature range from 5 degrees C to 37 degrees C. Analyzing the distributions of unfolding forces allowed us to extract transition barrier heights and positions of the underlying energy landscape. We found a marked narrowing of unfolding force distributions with increasing temperature. This narrowing reflects an increase in transition state position from 2.7 A to 7.8 A and thus a reduction of the molecular spring constant of the protein by a factor of 7. We suggest this temperature softening reflects a shift in the nature of the interactions responsible for mechanical stability from hydrogen bonds to hydrophobic interactions. This result has important consequences for all interpretations of protein mechanical studies if experimental results obtained at room temperature are to be transferred to physiological temperatures.

The unfolding kinetics of ubiquitin captured with single-molecule force-clamp techniques.

We use single-molecule force spectroscopy to study the kinetics of unfolding of the small protein ubiquitin. Upon a step increase in the stretching force, a ubiquitin polyprotein extends in discrete steps of 20.3 +/- 0.9 nm marking each unfolding event. An average of the time course of these unfolding events was well described by a single exponential, which is a necessary condition for a memoryless Markovian process. Similar ensemble averages done at different forces showed that the unfolding rate was exponentially dependent on the stretching force. Stretching a ubiquitin polyprotein with a force that increased at a constant rate (force-ramp) directly measured the distribution of unfolding forces. This distribution was accurately reproduced by the simple kinetics of an all-or-none unfolding process. Our force-clamp experiments directly demonstrate that an ensemble average of ubiquitin unfolding events is well described by a two-state Markovian process that obeys the Arrhenius equation. However, at the single-molecule level, deviant behavior that is not well represented in the ensemble average is readily observed. Our experiments make an important addition to protein spectroscopy by demonstrating an unambiguous method of analysis of the kinetics of protein unfolding by a stretching force.

Theoretical studies of the mechanical unfolding of the muscle protein titin: Bridging the time-scale gap between simulation and experiment

Brute-force, fully atomistic simulations of single molecule mechanical unfolding experiments are not feasible because current simulation time scales are about six orders of magnitude shorter than the time scales explored by experiments. To circumvent this difficulty, we have constructed a model, in which the unfolding dynamics of the I27 domain of the muscle protein titin is described as diffusive motion along a single unfolding coordinate R (equal to the domain extension) in the presence of an external driving potential and the potential of mean force G(R). The effect of the remaining degrees of freedom is described in terms of a viscous force with a friction coefficient η. The potential of mean force G(R) is computed from a series of equilibrium molecular dynamics trajectories performed with constrained values of R and η is extracted from a series of steered molecular dynamics simulations, in which R is increased at a constant rate and the mechanical response of the molecule is monitored as a function of time. The estimated G(R) allows us to calculate the force-dependent unfolding rate via transition-state theory and—by performing kinetic Monte Carlo simulations—to predict unfolding force distributions in experimentally relevant regimes. We compare the computed unfolding free energy profile with that deduced from atomic force microscopy studies of titin and find that, while the unfolding free energy barrier at zero force is nearly identical to the experimental value, the force dependence of the barrier is nonlinear, in contrast to most phenomenological models of titin unfolding. Because of this, the value ku(0) of the unfolding rate extrapolated to zero unfolding force, as well as the location of the unfolding transition state, differ from those previously estimated from experimental data. In particular, our estimate of ku(0) is several orders of magnitude lower than the unfolding rate measured in chemical denaturation experiments, suggesting that the two experimental techniques may probe different unfolding pathways. At the same time, the distribution of the unfolding force as well as its dependence on the pulling rate predicted by our simulations are found to be in agreement with atomic force microscopy experiments.