Crowding Effects on the Unfolding of Ubiquitin*

Using a coarse-grained representation of polypeptide chains, we probed the mechanical stability of Ubiquitin (Ub) monomers and trimers ((Ub)$_3$) in the presence of monodisperse spherical crowding agents. Our findings indicate that crowding increases the volume fraction ($\Phi_c$)-dependent average force ($\langle f_u(\Phi_c) \rangle$), relative to the value at $\Phi_c = 0$, needed to unfold Ub and the polyprotein. Furthermore, we found that average unfolding forces increase with decreasing crowder diameter ($\sigma_c$). The average unfolding force $\langle f_u(\Phi_c) \rangle$ depends on the ratio $\frac{D}{R_g}$, where $D \approx \sigma_c (\frac{\pi}{6 \Phi_c})^{\frac{1}{3}}$ with $R_g$ being the radius of gyration of Ub (or (Ub)$_3$) in the unfolded state. Examination of the unfolding pathways shows that, relative to $\Phi_c = 0$, crowding promotes reassociation of ruptured secondary structural elements. Both the nature of the unfolding pathways and $\langle f_u(\Phi_c) \rangle$ for (Ub)$_3$ are altered in the presence of crowding particles with the effect being most dramatic for the subunit that unfolds last. We predict that $\langle f_u(\Phi_c) \rangle$ scales in a simple manner with $\Phi_c$.