It has been proposed that proteins fold by a process called "Zipping and Assembly" (Z&A). Zipping refers to the growth of local substructures within the chain, and assembly refers to the coming together of already-formed pieces. Our interest here is in whether Z&A is a general method that can fold most of sequence space, to global minima, efficiently. Using the HP model, we can address this question by enumerating full conformation and sequence spaces. We find that Z&A reaches the global energy minimum native states, even though it searches only a very small fraction of conformational space, for most sequences in the full sequence space. We find that Z&A, a mechanism-based search, is more efficient in our tests than the replica exchange search method. Folding efficiency is increased for chains having: (a) small loop-closure steps, consistent with observations by Plaxco et al. 1998;277;985-994 that folding rates correlate with contact order, (b) neither too few nor too many nucleation sites per chain, and (c) assembly steps that do not occur too early in the folding process. We find that the efficiency increases with chain length, although our range of chain lengths is limited. We believe these insights may be useful for developing faster protein conformational search algorithms.

We develop a computer model for how two different chemical catalysts in solution, A and B, could be driven to form AB complexes, based on the concentration gradients of a substrate or product that they share in common. If A's product is B's substrate, B will be attracted to A, mediated by a common resource that is not otherwise plentiful in the environment. By this simple physicochemical mechanism, chemical reactions could spontaneously associate to become chained together in solution. According to the model, such catalyst self-association processes may resemble other processes of "stochastic innovation," such as Darwinian evolution in biology, that involve a search among options, a selection among those options, and then a lock-in of that selection. Like Darwinian processes, this simple chemical process exhibits cooperation, competition, innovation, and a preference for consistency. This model may be useful for understanding organizational processes in prebiotic chemistry and for developing new kinds of self-organization in chemically reacting systems.