  Folding of Ubiquitin (Ub) is investigated at low and neutral pH at different
temperatures using simulations of the coarse-grained Self-Organized-Polymer
model with side chains. The calculated radius of gyration, showing dramatic
variations with pH, is in excellent agreement with scattering experiments. At
$T_m$ Ub folds in a two-state manner at low and neutral pH. Clustering analysis
of the conformations sampled in equilibrium folding trajectories at $T_m$, with
multiple transitions between the folded and unfolded states, show a network of
metastable states connecting the native and unfolded states. At low and neutral
pH, Ub folds with high probability through a preferred set of conformations
resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal
that Ub assembly at low pH occurs by multiple pathways involving a combination
of nucleation-collapse and diffusion collision mechanism. The mechanism by
which Ub folds is dictated by the stability of the key secondary structural
elements responsible for establishing long range contacts and collapse of Ub.
Nucleation collapse mechanism holds if the stability of these elements are
marginal, as would be the case at elevated temperatures. If the lifetimes
associated with these structured microdomains are on the order of hundreds of
$\mu sec$ then Ub folding follows the diffusion-collision mechanism with
intermediates many of which coincide with those found in equilibrium. Folding
at neutral pH is a sequential process with a populated intermediate resembling
that sampled at equilibrium. The transition state structures, obtained using a
$P_{fold}$ analysis, are homogeneous and globular with most of the secondary
and tertiary structures being native-like. Many of our findings are not only in
agreement with experiments but also provide missing details not resolvable in
standard experiments.
