  Deviations from linearity in the dependence of the logarithm of protein
unfolding rates, $\log k_u(f)$, as a function of mechanical force, $f$,
measurable in single molecule experiments, can arise for many reasons. In
particular, upward curvature in $\log k_u(f)$ as a function of $f$ implies that
the underlying energy landscape must be multidimensional with the possibility
that unfolding ensues by parallel pathways. Here, simulations using the SOP-SC
model of a wild type $\beta$-sandwich protein and several mutants, with
immunoglobulin folds, show upward curvature in the unfolding kinetics. There
are substantial changes in the structures of the transition state ensembles as
force is increased, signaling a switch in the unfolding pathways. Our results,
when combined with previous theoretical and experimental studies, show that
parallel unfolding of structurally unrelated single domain proteins can be
determined from the dependence of $\log k_u(f)$ as a function of force (or
$\log k_u[C]$ where $[C]$ is the denaturant concentration).
