Applying Motion Planning Techniques to Molecular Docking Mark Moll Physical and Biological Computing Group Computer Science Department Rice University 1
Molecular Docking Goal: quickly determine ‘good fit’ between ligand (shown in green) and receptor. HIV-1 protease 2
Molecular Docking Problem: receptor is flexible, and has thousands of degrees of freedom molecular dynamics of HIV-1 protease, simulated in water; 2ns takes about 1 week on cluster of 16 machines, 9360 DOF 3
Motivation Important problem in computational drug design. Used in virtual screening of ligand databases. Current docking methods only allow for limited flexibility 4
Related Work on Flexible Receptor Docking Soft potentials: modify energy function, so that ligand fits more easily in binding site (Jiang & Kim 1991; Schnecke et al. 1998; Apostolakis et al. 1998) Selection of a few critical degrees of freedom in receptor binding site (Leach 1994; Leach & Lemon 1998) Use multiple receptor conformations (Pang & Kozikowski 1994; Knegtel et al. 1997; Sudbeck et al. 1998) Modified molecular dynamics methods (Di Nola et al. 1994; Mangoni et al. 1999; Nakajima et al. 1997) Collective degrees of freedom (Levy & Karplus 1979; Levitt et al. 1983; Garcia 1992; Teodoro et al. 2003) 5
Outline Capturing the essential degrees of freedom Biased expansive search using molecular energy Evaluating search results Simulation results Discussion 6
Capturing the Essential Degrees of Freedom Motions of atoms are not independent Find the main modes of motion by performing Principal Component Analysis (PCA) on molecular dynamics trajectory Use first couple principal components to represent the essential degrees of freedom Potential drawbacks: Molecular motions are mainly rotations, whereas PCA is linear decomposition Overfitting: we do not want to model random loop fluctuations 7
Capturing the Essential Degrees of Freedom 8
Capturing the Essential Degrees of Freedom First essential degree of freedom: Over 60% of variability in data captured by 5 degrees of freedom! 9
Capturing the Essential Degrees of Freedom For systems with approximate symmetry (like HIV-1 protease) can impose constraints to extract more robust modes of motion. Sorensen & Shah, our collaborators in the Comp. & Applied Math. Dept., have developed a symmetry preserving version of SVD. Using symmetry constraint averages out some random fluctuations, but preserves essential motions. Robustness verified by looking at how well other known crystal structures are approximated by symmetry preserving major modes. (Very recent results; not yet used for results presented today!) 10
Expansive Search (based on Hsu & Latombe’s algorithm) Search only conformational space of receptor Sample conformations along principal components ⇒ use local energy minimization to compensate for distortion Create new conformations with an expansive search: Randomly select previously generated conformation Perturb it to generate a new conformation Search strategy should have the following properties: Biased towards low-energy conformations Biased towards unexplored parts of the search space 11
Expansive Search Pick conformation i with probability inversely proportional to its weight: � � w i = 1 . 1 − exp ( − γ ( E i − E min )) · c i /( 1 + d i ), where where γ = a constant controlling the sensitivity to energy, E i = the energy of conformation i , E min = i = 1 ,..., n E i , min c i = number of times conformation i has been selected, and d i = sum of distances to k nearest neighbors. 12
Neighbor Selection Instead of simply perturbing conformation q to generate q new , we can potentially do better with a random walk: high energy low energy q new q high energy Energy barrier at min( Eq + E rel, E abs) 13
Evaluating Search Results Evaluation of a search is non-trivial. Need to consider several criteria: Number of distinct low-energy conformations (low energy ≡ energy of crystal structs. + small tolerance or lower) how well are we doing within the model? Distance to other crystal structures how does it compare to experimental data? Diameter of set of conformations is the search expansive? 14
Simulation Results Experimental setup: Tested docking program on two systems: HIV-1 protease, 3120 atoms, ~110 crystal structures available, rotationally symmetric FK506 binding protein, 1663 atoms, ~70 crystal structures available, very flexible Use 5 principal components, computed from molecular dynamics simulation Compare regular neighbor selection with random bounce walk Vary parameters for random bounce walk: energy thresholds, number of steps Take average over 5 runs 15
Simulation Results: Number of Distinct Low-Energy Confs. Low-energy conformations that are at least 1Å RMSD apart: regular perturbation 10 step random walk 20 step random walk 400 385 361 300 200 172 166 100 40 0 25 HIV-1 protease (4hvp) FK binding protein (1fkr17) Results measured after 20 hours. 16
Simulation Results: Percentage of Distinct Low-Energy Confs. Low-energy conformations that are at least 1Å RMSD apart, measured as percentage of total #conformations generated: regular perturbation 10 step random walk 20 step random walk 8% 7.7% 7.2% 6.9% 6.6% 6% 4% 2% 0% 0.4% 0.3% HIV-1 protease (4hvp) FK binding protein (1fkr17) Results measured after 20 hours. 17
Simulation Results: Energy average crystal structs. min (cal/mol) regular -3968 4hvp 10 steps -3436 -2000 20 steps -3413 regular -1885 1fkr17 10 steps -1725 -1000 20 steps -1813 Energy is higher on average with random bounce walk, which is to be expected. 18
Discussion Energy-guided expansive search effective at finding low-energy conformations But search is not expanding much towards crystal structures Can potentially improve results by using free energy (i.e., include entropic effects) using more (weighted) principal components 19
Acknowledgements Physical & Biological Computing Group: Lydia Kavraki David Schwartz Allison Heath Comp. & Applied Math. Dept.: @ Rice University Danny Sorensen Mili Shah Chemistry Department: Cecilia Clementi Funding: NSF, Whitaker Foundation 20
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