Multi-Funnel Underestimation in Protein Docking

Transcription

1 Multi-Funnel Underestimation in Protein Docking Julie C. Mitchell Mathematics and Biochemistry University of Wisconsin - Madison January

2 Underestimation Schemes Fact Multiple minima = hard optimization problem Theory (Onuchic, Wolynes, Dill) The physics of protein folding and docking suggests and energy funnel. Idea (Dill, Rosen, Phillips) use local minima to construct surrogate functions. These surrogates capture large-scale details of the energy funnel 1

3 Underestimators If your function looks like a funnel then approximate it using a quadratic function. You can use local minima to estimate the shape of the energy landscape. 2

4 Underestimators 3

5 Underestimators 4

6 Underestimators 5

7 Underestimators 6

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14 Underestimators 13

15 Finding the CQU Solution Note that this is a linear programming problem when H is diagonal but requires non-linear or semi-definite programing when H is positive semi-definite!!!! 14

16 Prediction Hurdles There are four factors affecting docking optimization: Parameterization has the problem been formulated so that the correct solution is accessible and its nearby region explored? Scoring does the scoring model identify the correct solution as being the best one? Optimization can the optimal solution be reliably calculated? Speed can the optimal solution in a reasonable amount of time? 15

17 Project Evolution Simple Convex Global Underestimation (CGU) scheme for docking implemented Simple quadratic (diagonal H) Lennard-Jones and Electrostatics A General Convex Quadratic Approximation (GCQA) Full quadratic (semi-definite H) Better treatment of rotational variables Improved Energy Function Hydrogen Bonding Desolvation Multi-funnel Gaussian Underestimation Flexible docking prototype using normal modes 16

18 Scoring Functions for Docking Our energy function consists of electrostatics, Lennard- Jones, desolvation and hydrogen bonding terms. The energy function itself is of equal importance to finding a global minimum (or dominant basin). 17

19 Lennard-Jones Potentials Nearby atoms want to align their electron orbitals, creating a weak electrostatic force. At the same time, atoms repel when they get too close The attraction and repulsion are often modeled using a single function, a Lennard-Jones potential. 18

20 Hydrogen Bonding Hydrogen bonds are the strongest non-covalent bonds. Hydrogen bonds join DNA base pairs, and help proteins fold into their functional forms. The formation of hydrogen bonds is also important to protein interactions. 19

21 Electrostatics Classical Coulombic potentials vary as the reciprocal of distance. The average effects of temperature, water and ions lead to a Poisson-Boltzmann equation The Yukawa potentials solve a linearized PBE with constant dielectric. 20

22 Desolvation Energy When molecules bind in an aqueous environment, energy is required to break the molecule-solvent interactions at the binding site (desolvation penalty) We can approximate a (surface) solvation energy by This formula accounts for both polar and nonpolar contributions. The parameters are fitted to united atom radii. 21

23 1AVZ: Quadratic Underestimator 1AVZ: V-1 Nef protein in complex with wild type Fyn SH3 domain The interaction ensures long-term survival of infected T cells and the destruction of non-infected T cells by inducing apoptosis. 22

24 1TAB: Quadratic Underestimator 1TAB: Trypsin complex with the Bowman-Birk inhibitor Elevated levels of trypsin have been found in pancreatic tumors, and BBI has been shown to suppress this type of tumor in various animals. 23

25 Gaussian Underestimators What if our function has multiple prominent funnels/basins? We will divide and conquer our search space into prominent basins, and do convex underestimation in each region! Basin finding is performed by underfitting a Gaussian function to low-energy minima. We have nicknamed this scheme Gausster. 24

26 Finding the GU Solution 25

27 Gausster Scheme Use fast exhaustive search method to generate many favorable configurations. We often use ZDOCK* for this. Use low-resolution hits to initialize local optimization. Find basins using Gaussian Underestimation. Partition the space into low-energy basins. Perform GCQA underestimation in each basin. The prediction is taken as the best basin global minima. * Chen, Li, Weng (2003) 26

28 1AVZ: Gaussian Underestimation The use of a Gaussian underestimator to partition the space into four regions gives good convergence to a nearnative solution. 27

29 1TAB: Cluster Optimization Once again, the Gausster optimization scheme gives an improved prediction. 28

30 Gausster on ZDOCK Benchmark 29

31 Gausster Server A simple server allows users to run the first stage of Gausster and view the lowest-energy data points within each basin. 30

32 Future Work A hierarchical scheme for Gaussian underestimation Must implement faster flexible optimization Hello, threads!! 31

33 Acknowledgements Roummel Marcia, Duke University Engineering David Dynerman, UW-Madison Mathematics Erick Butzlaff, UW-Madison Mathematics and Physics Tess Anderson, UW-Madison Mathematics and Biochemistry Sarah Cunningham, UW-Madison Biophysics Steve Darnell, UW-Madison Biochemistry Omar Demerdash, UW-Madison Biophysics Raman Lall, University of Rochester Engineering Laura Legault, UW-Madison Computer Sciences Yinka Lesi, UW-Madison Engineering Jennifer Losaw, UW-Madison Mathematics Corina Prieto, Univ. of Arizona Biochemistry Sarah Springborn, UW-Madison Biochemistry Christina Carlson, UW-Madison Immunology J. Ben Rosen, UC San Diego Stephen J. Wright, UW-Madison Computer Sciences David Page, UW-Madison Biostatistics Ron Raines, UW-Madison Biochemistry F. Michael Hoffmann, UW-Madison Oncology Vijay Setaluri, UW-Madison Dermatology Tom Martin, UW-Madison Biochemistry $ US Department of Energy $ National Institutes of Health $ Sloan Foundation $ Vilas Foundation 32