Crowding effects on the mechanical stability and unfolding pathways of ubiquitin

The interiors of cells are 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 D/R(g), where D approximately sigma(c)(pi/6Phi(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)) approximately Phi(c)(1/3nu), where nu is the Flory exponent that describes the unfolded (random coil) state of the protein.