Topography of the free-energy landscape probed via mechanical unfolding of proteins

Abstract

Single-molecule experiments in which proteins are unfolded by applying mechanical stretching forces generally force unfolding to proceed along a reaction coordinate that is different from that in chemical or thermal denaturation. Here we simulate the mechanical unfolding and refolding of a minimalist off-lattice model of the protein ubiquitin to explore in detail the slice of the multidimensional free-energy landscape that is accessible via mechanical pulling experiments. We find that while the free-energy profile along typical "chemical" reaction coordinates may exhibit two minima, corresponding to the native and denatured states, the free energy G(z) is typically a monotonic function of the mechanical coordinate z equal to the protein extension. Application of a stretching force along z tilts the free-energy landscape resulting in a bistable (or multistable) free energy G(z)-fz probed in mechanical unfolding experiments. We construct a two-dimensional free-energy surface as a function of both chemical and mechanical reaction coordinates and examine the coupling between the two. We further study the refolding trajectories after the protein has been prestretched by a large force, as well as the mechanical unfolding trajectories in the presence of a large stretching force. We demonstrate that the stretching forces required to destabilize the native state thermodynamically are larger than those expected on the basis of previous experimental estimates of G(z). This finding is consistent with the recent experimental studies, indicating that proteins may refold even in the presence of a substantial stretching force. Finally, we show that for certain temperatures the free energy of a polyprotein chain consisting of multiple domains is a linear function of the chain extension. We propose that the recently observed "slow phase" in the refolding of proteins under mechanical tension may be viewed as downhill diffusion in such a linear potential.

The molecular elasticity of the insect flight muscle proteins projectin and kettin

“…32), and ubiquitin (can refold at forces of up to 40 pN) (33). In addition, recent molecular dynamics simulations (41,42) demonstrate that refolding can occur at high forces (Ϸ40 pN).…”

Two-dimensional fluorescence resonance energy transfer as a probe for protein folding: A theoretical study

“…64,65 Fernandez and Li 64 studied the refolding of a multidomain polyubiquitin chain by monitoring the decrease in the overall extension of the chain. As was shown by subsequent theoretical studies, 65,66 the dynamics of the chain extension is similar regardless of whether or not each domain folds independently. This makes differentiating between the cooperative and noncooperative scenarios difficult.…”

Communication: Coordinate-dependent diffusivity from single molecule trajectories

“…Despite the remarkable success of this model in describing many experimental observations, 12 theoretical studies have highlighted its limitations. [13][14][15][16][17] Recent experimental work has also brought possible shortcomings of this model into a) Email: makarov@cm.utexas.edu spotlight: although its predictions 18,19 seem to fit well the observed distributions of transition path times for biomolecular folding, 3 the barrier height estimates obtained from such fits were inconsistent with the measured potentials of mean force and transition rates, 3 motivating several theoretical proposals to account for this discrepancy. [20][21][22] Perhaps the most straightforward improvement of the one-dimensional diffusion model is to allow the diffusion coefficient to be a coordinate-dependent function D(x) (for a justification of the position dependence of the diffusivity, see the discussion in Ref.…”