Crowding effects on the mechanical stability and unfolding pathways of Ubiquitin

The interior of cells is crowded thus making it important to assess the effects of macromolecules on the folding of proteins. Using the Self-Organized Polymer (SOP) model, which is a coarse-grained representation of polypeptide chains, we probe the mechanical stability of Ubiquitin (Ub) monomers and trimers ((Ub)$_3$) in the presence of monodisperse spherical crowding agents. Crowding increases the volume fraction ($\Phi_c$)-dependent average force ($<f_u(\Phi_c)>$), relative to the value at $\Phi_c = 0$, needed to unfold Ub and the polyprotein. For a given $\Phi_c$, the values of $<f_u(\Phi_c)>$ increase as the diameter ($\sigma_c$) of the crowding particles decreases. The average unfolding force $<f_u(\Phi_c)>$ depends on the ratio $\frac{D}{R_g}$, where $D \approx \sigma_c (\frac{\pi}{6 \Phi_c})^{{1/3}}$ 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 $<f_u(\Phi_c)>$ 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, based on SOP simulations and theoretical arguments, that $<f_u(\Phi_c) > \sim \Phi_c^{\frac{1}{3\nu}}$, where $\nu$ is the Flory exponent that describes the unfolded (random coil) state of the protein.