0.8 Motion planning for proteins: biophysics and applications  (Page 9/10)

The variance of the distribution of the folding time for each node provides an estimate of the error. If at each stage of simulation instead of choosing a node at random to start the next simulation, we select the node with the greatest contribution to our estimate of the error in folding time, we effectively focus our efforts where they will decrease the error most. In this way, MSMs with less overall error may be generated with using simulations.

Protein-ligand docking pathways and kinetics

So far, we have looked at applications of roadmap methods that deal with the single-body problem of protein folding. The first use of roadmaps in molecular modeling, however, was to study the two-body system of protein-ligand docking. The docking problem itself is, given a small molecule and a protein, to predict whether they will bind to form a complex, and if so, what will be the geometry and stability (binding affinity) of this complex. This problem is path-independent, and so does not lend itself to motion planning approaches. Roadmaps can be used, however, to study the question of how a ligand reaches or exits the binding pocket of a protein, what the energy profile of this process looks like, and the rate at which the ligand binds and dissociates.

Typically, in modeling protein-ligand docking with a roadmap, the protein is held rigid and induces a force field in which the ligand is free to rotate, translate, and change conformation. The first work in this area, by Latombe, Singh, and Brutlag , led a few years later to the SRS framework. An SRS for ligand docking pathways can be constructed be starting with the ligand in the bound state, and generating samples for its conformation, location, and orientation in, around, and outside the binding pocket of the protein. These paths can then be studied individually to examine features of the binding process, or as an aggregate to get properties such as binding affinity or escape time, which is represented in an SRS by the weight of paths away from the bound state.

To validate their method for studying docking, the developers of SRS showed that the escape times (in Monte Carlo steps) calculated for ligands leaving proteins with particular mutations in their binding sites were consistent with the expected effect of the mutations: Mutations expected to increase the binding affinity led to longer escape times, and mutations expected to decrease the binding affinity led to shorter escape times. They also showed that SRS could be used to distinguish between the binding site of the protein and other pockets on its surface. Ligands had significantly greater estimated escape times from the true binding site than from spurious ones.

Cortes et al. developed a tree-based sampling method for studying protein-ligand docking pathways. The algorithm is based on the dynamic-domain RRT planner (see Robotic Path Planning and Protein Modeling for an introduction to RRTs and other tree-based motion planners), in which, when sampling a random point toward which to expand, the location of that point is restricted to be within some distance of the existing tree, rather than anywhere in the whole space. The sampling method is based on the geometry of the system being studied: The major factors contributing to the energy of a conformation are reduced to geometric criteria. Hydrogen bonds and hydrophobic interactions are modeled by distance constraints. Steric clash is handled by treating atoms as hard spheres and performing collision checks using a fast collision checker called BioCD, developed by the same research group. Only structures satisfying all geometric constraints are subjected to an energy minimization procedure. The geometric constraints help ensure that structures to be added to the tree are already fairly low-energy, ensuring that the minimization can be done quickly, and that time is not wasted minimizing unrealistic structures.