Computational methods for the incorporation of protein unfolding pathways and kinetics in protein design

Abstract

If proteins achieved their native structure through a random search of every potential conformation, the first proteins would still be folding today. However, most proteins fold on the timescale of milliseconds to a few seconds. It has therefore been suggested that proteins fold along a pathway, gaining structure in an ordered fashion. Knowledge of these pathways can provide insight into both disease and protein design, but they are difficult to elucidate experimentally via φ-value analysis or hydrogen deuterium exchange. To quickly calculate the folding pathway, or rather its inverse, the unfolding pathway, we have created a program called GeoFold. GeoFold simulates the unfolding pathway via recursively partitioning the folded structure of a protein into unfolded substructures based on geometric operations, constructing a directed acyclic graph (DAG) between these states. Energies of folding and unfolding between these states are calculated and used in a finite elements simulation to elucidate the maximum traffic pathway and produce an unfolding rate. While it has successfully recapitulated experimental observations for the effects of disulfides in a small case study, GeoFold has yet to accurately predict unfolding rates and may not accurately model the folding of β-barrel proteins.

In addition to GeoFold, the Rosetta suite of protein engineering software has been applied to the problem of designing a protein ligand for the detection of paranemic crossover DNA (PX) in vivo based on T7 endonuclease I (T7 endoI). To achieve this, a starting structure was generated with each potential active site of PX superimposed over the active site of a Holliday junction complexed with T7 endoI (PDB 2PFJ). Constraints were added to retain active site contacts and a protein-DNA docking simulation was per- formed in PyRosetta. The resulting structures were used to generate a final model of PX bound to 4 molecules of T7 endoI. To further enhance the affinity of T7 endoI for PX, it has been proposed to change the length of the linker region between the two active sites on T7 endoI. To achieve this, a novel protocol called INDEL has been designed for InteractiveROSETTA allowing for the insertion of variable length loops in a protein. This new protocol is benchmarked for its ability to reconstruct native loop conformations for variable length loop, consistently outputting low RMSD loops.

In software design, usability is integral to utility. To simplify the interpretation of GeoFold pathway results, a new interface was designed for InteractiveROSETTA allowing for the direct visualization of unfolding transition and intermediate structures on the protein’s 3-dimensional structure. Additionally, InteractiveROSETTA has been expanded to allow constraints to be implemented in multiple protocols. To further enhance GeoFold’s accuracy, a parameter determining what unfolding step will be taken was adjusted, allowing for the accurate prediction of folding intermediates in two proteins. A new entropy term has also been introduced to GeoFold, but has little impact on both kinetic and pathway output. Finally, the viability a disulfide-engineered leave-one-out GFP (LOO-GFP) as a biosensor candidate is explored.

β-barrel proteins are those consisting of β strands where the strands form a single β-sheet structure that wraps around itself, forming the eponymous barrel structure. These are among the most common protein folds with the 10% of the PDB falling into the TIM-barrel subclass of β-barrel alone. Initially, GeoFold could not adequately unfold these proteins, unrealistically peeling off β strands and breaking hydrogen bonds on both sides of the strand. To remedy this shortcoming, a new unfolding move, seam, was created which operates by breaking the hydrogen bonds between a pair of β-strands in a barrel, allowing the protein to unfold more naturally. This algorithm successfully distinguishes barrel proteins from nonbarrels and recaptured folding intermediates seen in the pathways of three different β-barrels.

Hydrophobic collapse is one of the main driving forces of protein folding. As such, accurately modeling solvation effects and electrostatics is a key component of any energy function. This can be achieved through explicitly modeling each solvent water molecule or by implicitly modeling the bulk solvent as a continuum. GeoFold utilizes a solvent accessible surface area (SAS) based implicit solvation model; however, it does not adequately capture the impact of exposure to solvent of hydrophobic vs hydrophilic residues. In this work, the WZS model is implemented, demonstrating improved accuracy in the prediction of unfolding rates in an 86-protein case study.