  Many native structures of proteins accomodate complex topological motifs such
as knots, lassos, and other geometrical entanglements. How proteins can fold
quickly even in the presence of such topological obstacles is a debated
question in structural biology. Recently, the hypothesis that energetic
frustration might be a mechanism to avoid topological frustration has been put
forward based on the empirical observation that loops involved in entanglements
are stabilized by weak interactions between amino-acids at their extrema. To
verify this idea, we use a toy lattice model for the folding of proteins into
two almost identical structures, one entangled and one not. As expected, the
folding time is longer when random sequences folds into the entangled
structure. This holds also under an evolutionary pressure simulated by
optimizing the folding time. It turns out that optmized protein sequences in
the entangled structure are in fact characterized by frustrated interactions at
the closures of entangled loops. This phenomenon is much less enhanced in the
control case where the entanglement is not present. Our findings, which are in
agreement with experimental observations, corroborate the idea that an
evolutionary pressure shapes the folding funnel to avoid topological and
kinetic traps.
