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.

We have used the SOP-SC model, 1,2 which is a native-centric coarse-grained protein model in which each amino acid is represented by two beads to model cSrc-SH3 and Aβ 9−40 . The backbone atoms of an amino acid are represented by a bead positioned at the center of C α atom, and the side chain atoms are represented by a bead positioned at the center of mass of the side-chain. SOP-SC model for monomeric cSrc-SH3, domain swapped cSrc-SH3 and Aβ 9−40 are constructed using the structures in the protein data bank (PDB) with PDB ID: 1SRL, 3 3FJ5 4 and 2LMN, 5 respectively. Missing hydrogen atoms are added to the structures using the program visual molecular dynamics (VMD) 6 before calculating the centre of mass of the side chain. The Hamiltonian corresponding to the SOP-SC model is described in terms of bonded (E B ) and non-bonded (E N B ) interactions. Covalently connected beads interact via a bonded potential (E B ). Non-bonded interactions (E N B ) consist of native (N) and non-native (NN) interactions. Interactions between two beads are considered native, if they are separated by at least three bonds and are within a cut-off distance (R c ) in the SOP-SC model of the PDB structure. Any other non-covalent interactions are considered as non-native interactions (E N N ). Native interactions between neighboring side-chain beads

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Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, the hopping rates between the folded and unfolded states in two-state folders, the height and the location of the transition state (TS) can be extracted. 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 Pfold 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 towards 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 in order to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

Cosolvents modulate the stability of protein conformations and exhibit contrasting effects on the kinetics of aggregation by globular proteins and intrinsically disordered proteins (IDPs). The growth of ordered protein aggregates, after the initial nucleation step is believed to proceed through a dock-lock mechanism. We have studied the effect of two denaturants (guanidinium chloride (GdmCl) and urea) and four protective osmolytes (trimethylamine N-oxide (TMAO), sucrose, sarcosine, and sorbitol) on the free energy surface (FES) of the dock-lock growth step of protein aggregation using a coarse-grained protein model and metadynamics simulations. We have used the proteins cSrc-SH3 and Aβ 9−40 as model systems representing globular proteins and IDPs, respectively. The effect of cosolvents on protein conformations is taken into account using the molecular transfer model (MTM). The computed FES shows that protective osmolytes stabilize the compact aggregates, while denaturants destabilize them for both cSrc-SH3 and Aβ 9−40 . However, protective osmolytes increase the effective energy barrier for the multi-step domain swapped dimerization of cSrc-SH3, which is critical to the growth of protein aggregates by globular proteins, thus slowing down overall aggregation rate. Contrastingly, denaturants decrease the effective barrier height for cSrc-SH3 dimerization, and hence enhances the aggregation rate in globular proteins.The simulations further show that cSrc-SH3 monomers unfold before dimerization and the barrier to monomer unfolding regulates the effective rate of agrgegation. In the case of IDP, Aβ 9−40 , protective osmolytes decrease and denaturants increase the effective barriers in the dock-lock mechanism of fibril growth, leading to faster and slower growth kinetics, respectively.