Coarse graining the soft-mode dynamics of a folding protein

Abstract

We introduce a coarse description of the peptide chain dynamics based on a topological representation of the ribbon model of the chain backbone. Our aim is to provide a coarsely defined solution to the protein folding problem based on a binary codification of the soft-mode dynamics. As a first step, a binary coding of local topological constraints associated with each secondary and tertiary structural motif is introduced, with each local topological constraint corresponding to a local torsional state. Our treatment enables us to adopt a relatively large computation time step of 64 ps, a value far larger than typical hydrodynamic drag timescales, without sacrificing accuracy within our level of description. Accordingly, the solvent can no longer be treated as the hydrodynamic drag medium, instead we incorporate its capacity for forming local conformation-dependent domains of different relative permittivities. Each evaluation of the matrix of local topological constraints (LTM) depends on the conformation-dependent local dielectric domains created by the confined solvent. Folding pathways are initially resolved as transitions between patterns of locally-encoded structural signals which change within the 10 µs–100 ms timescale range. These coarse folding pathways are generated by a parallel search for structural patterns in the LTM. Each pattern is evaluated, translated and finally recorded as a contact matrix (CM), an operation which is subject to a renormalization feedback loop. The renormalization operation periodically introduces long-range correlations on the LTM according to the latest CM generated by translation. Nucleation and cooperative effects are accounted for by means of the renormalization operation which warrants the persistence of seeding patterns or kernels upon successive LTM evaluations. The validity of our approach is tested vis-a-vis experimentally-probed folding pathways eventually generating tertiary interactions in proteins which recover their active structure under invitro renaturation conditions. As an illustration, we focus on determining significant folding intermediates and late kinetic bottlenecks which occur within the first 10 ms of the bovine pancreatic trypsin inhibitor (BPTI) renaturation process.