Coarse semiempirical solution to the protein folding problem

We introduce a semiempirical theory leading to the ab initio prediction of conducive folding pathways and coarsely resolved native backbone geometries of proteins suddenly exposed to in vitro renaturation conditions. The underlying model incorporates a discrete codification of local steric hindrances of the peptide backbone. We first determine a time-evolving finite set of local torsional constraints upon which large-scale organization is built. Thus, the torsional state of the chain is topologically represented by viewing the (Φ,Ψ)-state of each residue modulo the basin of attraction to which it belongs in the Ramachandran plot. A grammar to combine such coarsely defined torsional states (topologies) and translate them into meaningful patterns of long-range interactions is developed. An algorithm for structure prediction is shown to emerge once this grammar is combined with prescriptions for the time evolution of topological patterns. This algorithm is rooted in the fact that local contributions to the potential energy may be subsumed into time-evolving conformational constraints coarsely defining sets of restricted backbone geometries responsible for framing the patterns of nonbonded interactions. The predictive power of the algorithm is established by obtaining stable topologies of small proteins, which prove to be compatible with their native folds, and computing ab-initio folding pathways for mammalian ubiquitin that ultimately yield a stable structural pattern reproducing its native features.