Our simplest model surface appears to capture many of the most interesting features of the dynamical effects seen in clusters and proteins. Our results are also consistent with previous work framed within the language of spin-glass theory; for example increasing the barrier heights raises the glass temperature, Tg, without changing the folding temperature, Tf, and hence decreases the efficiency of relaxation to the global minimum.
We have also modelled kinetic bottlenecks and surfaces with multiple funnels. Multiple funnels can greatly reduce the relaxation efficiency and produce dynamics with both fast and slow time scales. In contrast the effects of kinetic bottlenecks appear to be more limited.
Our interest in this problem was first stirred by work which stressed the importance of the energy gap between the lowest and the next-lowest energy minima on the folding efficiency of model proteins. There immediately appeared to be an obvious analogy with `magic number' clusters such as the Mackay icosahedron, which are found in simulations and molecular beam experiments. Indeed, one could push the analogy further and consider magic number clusters as those which have survived a selection procedure in a molecular beam, just as proteins have apparently evolved to possess efficient `funneling' PES's. However, it now appears that factors other than the lowest energy gap are more important. Nevertheless, the analogies between `magic number' clusters in molecular beams and rapidly folding proteins are probably still valid and will continue to lead to new insights in the global analysis of PES's in terms of the interplay between structure, function, dynamics and thermodynamics.