  We consider two types of Go models of a protein (crambin) and study their
kinetics through molecular dynamics simulations. In the first model, the
residue -- residue contact interactions are selected based on a cutoff
distance, $R_c$, between the C$_\alpha$ atoms. The folding times depend on the
value of $R_c$ strongly and non-monotonically due to the interplay between
frustration and the free energy barrier for folding. This indicates a need for
a physically determined set of native contacts that takes into account all the
residual atoms. %%. One may accomplish it This can be accomplished by
considering the van der Waals radii of the atoms and checking if %%the atoms
overlap. they are found within a proper range of the van der Waals attraction.
In the second model, non-native attractive contacts are added to the system.
This leads to bad foldability. However, for a small number of such extra
contacts there is a slight acceleration in the kinetics of folding.
