Development of SCWRL4 for improved prediction of protein side-chain conformations In collaboration with Moscow Engineering & Physics Institute © George Krivov Georgii Krivov, Maxim Shapovalov and Roland L. Dunbrack Jr.

SCWRL ® program SCWRL Version 3 was written by Adrian A. Canutescu and Dr. Roland L. Dunbrack Jr. Main assumption: backbone  There is a finite set of possible conformations (called rotamers) for each amino acid residue. pair-wise interactions

1.Obtain spatial backbone structure and aminoacid sequence 2.For each residue build possible side-chain conformations (rotamers) using rotamer library 3.Build interaction graph –each vertex denotes a certain residue –an edge between vertices indicates that there is an interaction between some rotamers of the corresponding residues 4.Find optimal assignment of side-chain conformations by graph decomposition and dynamic programming 5.Save resolved structure into file SCWRL’s sidechains packing algorithm PDB Res 2 Res 1 Res 3 Res 4

Inproved dynamic programming A tree-decomposition of a graph is a pair, where  based on a tree-decomposition of the interaction graph – is a tree with a set of vertices I and a set of edges F – is a family of subsets of the set V, associated with the vertices of T, such that which satisfies the conditions: h kh k h lh l b c a c d b e g f d c e d e h i g e e g h a c b d e i f g h k l Res 2 Res 1 Res 3 Res 4 Hans L. Bodlaender. 1992

combinatorial complexity blows-up hardly feasible even with new algorithm  Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable Described combinatorial algorithm… resolves global optimum (avoids stochastics) accuracy of prediction entirely depends on rotamer library and energy potentials is capable of larger and denser graphs than one based on biconnected components SCWRL4 is capable of significantly larger proteins than SCWRL3 typically finishes pretty quicklyno coffee-breaks… However… However… a better accuracy is desired quick collision detection algorithm thermodynamic fluctuations via Flexible Rotamers Model

combinatorial complexity blows-up hardly feasible even with new algorithm  Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable Hierarchies of bounding boxes  enable efficient search for intersections between two groups of geometric figures 2. Check each combination for overlapping 4. Continue recursively on each clashing pair 1. If overlap then split each 3. Disregard boxes that don’t clash Given two groups of figures enclosed into k-dops… quick collision detection algorithm James T. Klosowski, et.al. 1998

Cubic (k = 3) Tetrahedral (k = 4) k = 2 k = 3 k = 4 examples: combinatorial complexity blows-up hardly feasible even with new algorithm  quick collision detection algorithm … works best in conjunction with k-Discrete Oriented Polytopes – a class of convex polytopes with 2k planes any plane is orthogonal to one of k basic axes which remain fixed – easy to enclose a ball – easy to merge – easy clash check – almost rotatable Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable

Cubic (k = 3) Tetrahedral (k = 4) k = 2 k = 3 k = 4 examples: combinatorial complexity blows-up hardly feasible even with new algorithm  basic axis x i min i max i i = 1..k simple projection onto all basic axes  easy to enclose a ball easy to merge easy clash check almost rotatable quick collision detection algorithm … works best in conjunction with k-Discrete Oriented Polytopes – a class of convex polytopes with 2k planes any plane is orthogonal to one of k basic axes which remain fixed Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable

Cubic (k = 3) Tetrahedral (k = 4) k = 2 k = 3 k = 4 examples: combinatorial complexity blows-up hardly feasible even with new algorithm  easy to enclose a ball  easy to merge easy clash check almost rotatable quick collision detection algorithm … works best in conjunction with k-Discrete Oriented Polytopes – a class of convex polytopes with 2k planes any plane is orthogonal to one of k basic axes which remain fixed Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable

Cubic (k = 3) Tetrahedral (k = 4) k = 2 k = 3 k = 4 examples: combinatorial complexity blows-up hardly feasible even with new algorithm  A doesn’t clash B if exists axis x i (1≤i ≤ k) such that easy to enclose a ball easy to merge  easy clash check almost rotatable k-DOP A k-DOP B ? quick collision detection algorithm … works best in conjunction with k-Discrete Oriented Polytopes – a class of convex polytopes with 2k planes any plane is orthogonal to one of k basic axes which remain fixed Involve more rotamers  more interaction to evaluate  more combinations to enumerate More realistic potentials  longer interaction range  more edges in the graph  less decomposable

More realistic potentials  longer interaction range  more edges in the graph  less decomposable Fast anisotropic hydrogen bond potential Fast anisotropic hydrogen bond potential

For more relevant comparison it make sense to predict a crystal not the ASU Amount of sidechains relative surface accessibility (%)

Extra percent in average accuracy due to crystal awareness Knowledge of crystal symmetry enables higher accuracy …

Tuning parameters of the Flexible Rotamer Model due to backbone and frame sample around rotamer library’s conformation due to sidechains’ interaction may be setup independently for each type of amino acid from rotamer library search for optimal values in high- dimensional space optimize one amino acid type in a time (and loop for all)

Optimizing expensive function in multidimensional space 1.Generate sample of arguments and evaluate function at these points 2.Assume that second order approximation works well 3.From the linear regression resolve coefficients and their covariance 4.Maximization of quadratic form is relatively simple, provided that we can resolve eigenvalues and eigenvectors 5.Hence, generate sample of quadratic forms, maximize each of them and aggregate robust for non-convex functions!

Traces through the optimization of the FRM parameters Training on 40 proteins ( ~ residues ) + 24 proteins more and continue ( ~ residues ) Testing on 130 proteins ( ~ residues )

Conditional accuracy (%) Confidence of side-chain placement (derived from experimental EDS maps) CYSASNASP ARG ILE GLN GLU HIS PHE LEU LYS METPRO SER THR TRP ALL TYRVAL sliding frame - 20% Measurement: Side chains with better electron density are easier to predict Shapovalov et.al. 2007

backbone PDB file SCWRL 3.exe rotamer library output PDB file functionality of SCWRL4 is available as library  enables direct manipulation of the model via C++ API class SCWRL { … }; SCWRL4.DLL all this good with Improved usability (coming soon)

Acknowledgements Dr. Roland Dunbrack Prof. Nickolai Kudryashov Colleagues: Adrian Canutescu Guoli Wang Maxim Shapovalov Qiang Wang Qifang Xu Questions, Comments, Suggestions ? Thanks for Your Attention! Have a Nice Day and welcome to our poster!