Unfolding times for proteins in a force clamp

Exposure of Von Willebrand Factor Cleavage Site in A1A2A3-Fragment under Extreme Hydrodynamic Shear

Von Willebrand Factor (vWf) is a giant multimeric extracellular blood plasma involved in hemostasis. In this work we present multi-scale simulations of its three-domains fragment A1A2A3. These three domains are essential for the functional regulation of vWf. Namely the A2 domain hosts the site where the protease ADAMTS13 cleavages the multimeric vWf allowing for its length control that prevents thrombotic conditions. The exposure of the cleavage site follows the elongation/unfolding of the domain that is caused by an increased shear stress in blood. By deploying Lattice Boltzmann molecular dynamics simulations based on the OPEP coarse-grained model for proteins, we investigated at molecular level the unfolding of the A2 domain under the action of a perturbing shear flow. We described the structural steps of this unfolding that mainly concerns the β-strand structures of the domain, and we compared the process occurring under shear with that produced by the action of a directional pulling force, a typical condition of single molecule experiments. We observe, that under the action of shear flow, the competition among the elongational and rotational components of the fluid field leads to a complex behaviour of the domain, where elongated structures can be followed by partially collapsed melted globule structures with a very different degree of exposure of the cleavage site. Our simulations pose the base for the development of a multi-scale in-silico description of vWf dynamics and functionality in physiological conditions, including high resolution details for molecular relevant events, e.g., the binding to platelets and collagen during coagulation or thrombosis.

Thermal versus mechanical unfolding in a model protein

Force spectroscopy techniques are often used to learn about the free energy landscape of single biomolecules, typically by recovering free energy quantities that, extrapolated to zero force, are compared to those measured in bulk experiments. However, it is not always clear how the information obtained from a mechanically perturbed system can be related to the information obtained using other denaturants since tensioned molecules unfold and refold along a reaction coordinate imposed by the force, which is not likely to be meaningful in its absence. Here, we explore this dichotomy by investigating the unfolding landscape of a model protein, which is unfolded first mechanically through typical force spectroscopy-like protocols and next thermally. When unfolded by nonequilibrium force extension and constant force protocols, we recover a simple two-barrier landscape as the protein reaches the extended conformation through a metastable intermediate. Interestingly, folding-unfolding equilibrium simulations at low forces suggested a totally different scenario, where this metastable state plays little role in the unfolding mechanism, and the protein unfolds through two competing pathways [R. Tapia-Rojo et al., J. Chem. Phys. 141, 135102 (2014)]. Finally, we use Markov state models to describe the configurational space of the unperturbed protein close to the critical temperature. The thermal dynamics is well understood by a one-dimensional landscape along an appropriate reaction coordinate, however it is very different from the mechanical picture. In this sense, the results of our protein model for the mechanical and thermal descriptions provide incompatible views of the folding/unfolding landscape of the system, and the estimated quantities to zero force result are hard to interpret.

Periodic forces trigger knot untying during translocation of knotted proteins

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process, jamming the pore, since the diameter of the pore is smaller than the size of maximally tightened knot. The jamming probability dramatically increases as the magnitude of the driving force exceeds a critical value, F_c. In this numerical study, we show that for deep knots F_c lies below the force range over which molecular import motors operate, which suggest that in these cases the knots will tighten and block the pores. Next, we show how such topological traps might be prevented by using a pulling protocol of a repetitive, on-off character. Such a repetitive pulling is biologically relevant, since the mitochondrial import motor, like other molecular motors transforms chemical energy into directed motions via nucleotide-hydrolysis-mediated conformational changes, which are cyclic in character.

Protein unfolding by biological unfoldases: insights from modeling

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.

Mechanical unfolding of a simple model protein goes beyond the reach of one-dimensional descriptions

We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition-path theory we also provide a quantitative description of the unfolding pathways followed by the system. Our study shows a complex dynamical scenario. In particular, we see that the usual one-dimensional picture: free-energy vs end-to-end distance representation, gives a misleading description of the process. Unfolding can occur following different pathways and configurations which seem to play a central role in one-dimensional pictures are not the intermediate states of the unfolding dynamics.

Evolution of the potential energy landscape with static pulling force for two model proteins

The energy landscape is analyzed for off-lattice bead models of protein L and protein G as a function of a static pulling force. Two different pairs of attachment points (pulling directions) are compared in each case, namely, residues 1/56 and 10/32. For the terminal residue pulling direction 1/56, the distinct global minimum structures are all extended, aside from the compact geometry that correlates with zero force. The helical turns finally disappear at the highest pulling forces considered. For the 10/32 pulling direction, the changes are more complicated, with a variety of competing arrangements for beads outside the region where the force is directly applied. These alternatives produce frustrated energy landscapes, with low-lying minima separated by high barriers. The calculated folding pathways in the absence of force are in good agreement with previous work. The N-terminal hairpin folds first for protein L and the C-terminal hairpin for protein G, which exhibits an intermediate. However, for a relatively low static force, where the global minimum retains its structure, the folding mechanisms change, sometimes dramatically, depending on the protein and the attachment points. The scaling relations predicted by catastrophe theory are found to hold in the limit of short path lengths.

Protein high-force pulling simulations yield low-force results

All-atom explicit-solvent molecular dynamics simulations are used to pull with extremely large constant force (750–3000 pN) on three small proteins. The introduction of a nondimensional timescale permits direct comparison of unfolding across all forces. A crossover force of approximately 1100 pN divides unfolding dynamics into two regimes. At higher forces, residues sequentially unfold from the pulling end while maintaining the remainder of the protein force-free. Measurements of hydrodynamic viscous stresses are made easy by the high speeds of unfolding. Using an exact low-Reynolds-number scaling, these measurements can be extrapolated to provide, for the first time, an estimate of the hydrodynamic force on low-force unfolding. Below 1100 pN, but surprisingly still at extremely large applied force, intermediate states and cooperative unfoldings as seen at much lower forces are observed. The force-insensitive persistence of these structures indicates that decomposition into unfolded fragments requires a large fluctuation. This finding suggests how proteins are constructed to resist transient high force. The progression of helix and sheet unfolding is also found to be insensitive to force. The force-insensitivity of key aspects of unfolding opens the possibility that numerical simulations can be accelerated by high applied force while still maintaining critical features of unfolding.

Direction-dependent mechanical unfolding and green fluorescent protein as a force sensor

An Ising-like model of proteins is used to investigate the mechanical unfolding of the green fluorescent protein along different directions. When the protein is pulled from its ends, we recover the major and minor unfolding pathways observed in experiments. Upon varying the pulling direction, we find the correct order of magnitude and ranking of the unfolding forces. Exploiting the direction dependence of the unfolding force at equilibrium, we propose a force sensor whose luminescence depends on the applied force.

Discrete breathers in a realistic coarse-grained model of proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small β-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

Cooperativity at different space and time scales in multiscale protein dynamics

A method proposed by Matsunaga [Phys. Rev. Lett. 99, 238103 (2007)] is applied to simple stochastic models and two model proteins composed of 46 amino beads with three different kinds of residues. The method, which is based on the combination of the principal component analysis and the finite size Lyapunov exponent, characterize the coarse-grained dynamics in different spatiotemporal hierarchies in protein dynamics. The application of the method to model proteins reveals that the low-indexed (large-variance) principal components carry less-divergent, regularized dynamics at the coarse-grained scales on a less-frustrated energy landscape, whereas this less-divergent nature is less pronounced for a protein model with a more frustrated energy landscape. It is also revealed that our technique can differentiate the collective motions on the projected principal component space inherent to the system and the apparent collective behavior which can appear even in high-dimensional stochastic systems.