Energy Landscape of Ubiquitin Is Weakly Multidimensional

Abstract

Single molecule pulling experiments report timedependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to onedimensional analytical models of the energy landscape, we can extract the hopping rates between the folded and unfolded states in two-state folders as well as the height and the location of the transition state (TS). Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one-dimensional, we simulated force-induced unfolding of ubiquitin (Ub) using the coarse-grained self-organized polymer−side chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD), governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi-1D X-dependent free energy profile. However, a granular analysis using the P fold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height and, more importantly, the location of the TS. The f-dependent TS location moves toward the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

Reconstruction of the Free Energy Profile for SUMO1 from Nonequilibrium Single-Molecule Pulling Experiments

“…In our previous work, only kinetic information was available, the spontaneous unfolding rate constant ( k u 0 ) was derived through Monte Carlo simulations (based on the Bell-like model), and the Δ G # value was obtained from the k u 0 value. , In this study, we have directly reconstructed free energy profile. Monte Carlo simulation based on the Bell-like model gives estimate of x u and k u 0 under the approximation that the free energy landscape is one-dimensional where pulling direction acts as the reaction coordinate. , It also assumes that the TS does not change its position along the reaction coordinate . We have used the x u obtained in our previous work to finally compute the Δ G u # value from the reconstructed free energy profile of stretching and unfolding SUMO1.…”

Recent Advances and Emerging Challenges in the Molecular Modeling of Mechanobiological Processes

“…At low forces, proteins can also refold, which represents an ever greater challenge for molecular dynamics approaches. Approaches based on coarse grained models in implicit solvent are of particular interest in that case, enabling the exploration of the conformational space faster, either by propagating SMD trajectories, or by determining the free-energy landscape under force using enhanced sampling techniques. − ,− Some other works have attempted to determine a multidimensional potential of mean force at zero force based on all-atom MD in explicit solvent, but these are currently limited to small and/or model proteins as the phase space sampling along all relevant folding/unfolding coordinates is not easily achieved. Moreover, even multidimensional PMFs require to make some assumptions and choices about the folding coordinates, which become highly non-trivial and not easily predicted for typical size proteins.…”

“…Moreover, even multidimensional PMFs require to make some assumptions and choices about the folding coordinates, which become highly non-trivial and not easily predicted for typical size proteins. These studies provide overwhelming evidence that the unfolding pathways at low and high forces are in many cases different (Figure ), with a variety of unfolding pathways and intermediates that cannot be observed under high forces. − ,, …”

Molecular interpretation of single-molecule force spectroscopy experiments with computational approaches

“…However, as will be detailed later, care should be taken when comparing experiments and simulations when the employed forces are very different, because the explored pathways on the free-energy landscape might be sensitive to force. 19–23…”

“…However, as will be detailed later, care should be taken when comparing experiments and simulations when the employed forces are very different, because the explored pathways on the free-energy landscape might be sensitive to force. [19][20][21][22][23] Interestingly, simulations employing enhanced sampling strategies specifically adapted to the study of biomolecules under force, such as infinite switch simulated tempering in force, 24 boxed molecular dynamics, 25 or accelerated steered molecular dynamics, 26 could offer the possibility to access conformational changes occurring at experimental forces but usually not in the limited timescale of unperturbed simulations. As recently argued, 27 another promising approach could be to combine SMD at experimental forces, with enhanced sampling algorithms designed for the estimation of kinetic rates.…”