Background: Functionally useful proteins are sequences of amino acids
that fold rapidly under appropriate conditions into their native state
s. It is believed that rapid folders are sequences for which the foldi
ng dynamics entail the exploration of restricted conformations - the p
hase space can be thought of as a folding funnel. While there are many
experimentally accessible predictions pertaining to the existence of
such funnels and a coherent picture of the kinetics of folding has beg
un to emerge, there have been relatively few simple studies in the con
trolled setting of well-characterized lattice models. Results: We desi
gn rapidly folding sequences by assigning the strongest couplings to t
he contacts present in a target native state in a two-dimensional mode
l of heteropolymers. Such sequences have large folding transition temp
eratures and low grass transition temperatures. The dependence of medi
an folding times on temperature is investigated. The pathways to foldi
ng and their dependence on the temperature are illustrated via a study
of the cell dynamics - a mapping of the dynamics into motion within t
he space of the maximally compact cells.Conclusions: Folding funnels c
an be defined operationally in a coarse-grained sense by mapping the s
tates of the system into maximally compact conformations and then by i
dentifying significant connectivities between them.