(Big Data) Approaches to Designing Functional Molecules. Christof Schütte. Research Center Matheon Mathematics for key technologies

Transcription

1 (Big Data) Approaches to Designing Functional Molecules Christof Schütte Research Center Matheon Mathematics for key technologies

2 Different visual representations of a protein Christof Schütte, ZIB + FU Berlin 2 All atom pdf Secondäry structure Solvent accessible surface Helices as Cylinders

3 Docking Christof Schütte, FU Berlin 4

4 Christof Schütte, FU Berlin 5

5 The timescale problem Christof Schütte, FU Berlin + ZIB 6 Elastic vibrations of proteins α-helix folding β-hairpin folding Bond stretching Protein folding (fs) (ps) (ns) (μs) (ms) (s) MD Time It is still infeasible to compute rare event statistics using conventional MD methods

6 Christof Schütte, FU Berlin + ZIB 7 (ps) (ns) (ms) (ms) (s)

7 The timescale problem Christof Schütte, FU Berlin + ZIB 8 Elastic vibrations of proteins α-helix folding β-hairpin folding Bond stretching Protein folding (fs) (ps) (ns) (μs) (ms) (s) MD Time Reliable rare event statistics via long MD inappropriate! Instead: Extract statistics from many short MD simulations!!

8 Conformations and metastable sets Christof Schütte, FU Berlin + ZIB 9

9 Molecular Dynamics Christof Schütte, FU Berlin + ZIB 11 1 q M p q(0) q0 p grad V ( q) p(0) p 0 + Quantum corrections, Boundary conditions etc phase space: d 3 # atoms R 2d without overall translations and rotations (alignment)

10 Conformation Dynamics Christof Schütte, FU Berlin + ZIB 12 multiscale nature: + slow scale (conformation dynamics) + fast scale (oscillations/fluctuations/vibrations) conformations visualization by amiramol

11 Conformation Dynamics as Markov Process Christof Schütte, FU Berlin + ZIB 13 Time scale 1ps statistical weight metastability transition probabilities statistical weight statistical weight metastability metastability 0.930

12 Transfer Operators Christof Schütte, FU Berlin + ZIB 15

13 Transfer operator Christof Schütte, FU Berlin + ZIB 16

14 Transfer operator Christof Schütte, FU Berlin + ZIB 17

15 Transfer operator v 0 Markov process dynamics v T v 0 Markov operator (positive & norm preserving) spectrum contained in unit circle, 1 always eigenvalue Markov process reversible transfer operator self adjoint Schuette, Fischer, Huisinga, Deuflhard 98 Christof Schütte, FU Berlin + ZIB 18

16 Transfer Operators and Markov State Models Christof Schütte, FU Berlin + ZIB 20

17 Concept of MSMs Christof Schütte, FU Berlin + ZIB 21

18 Concept of MSMs Christof Schütte, FU Berlin + ZIB 22 discretization

19 Concept of MSMs Christof Schütte, FU Berlin + ZIB 23

20 Concept of MSMs Christof Schütte, FU Berlin + ZIB 24

21 Standard MSMs Christof Schütte, FU Berlin + ZIB 25

22 MSM as Galerkin projection Christof Schütte, FU Berlin 26

23 MSM as Galerkin projection Christof Schütte, FU Berlin 27

24 Main idea: (1) Discretize state space Christof Schütte, FU Berlin + ZIB 28 Folding mechanism

25 (2) Start short simulations from every discr. box Christof Schütte, FU Berlin + ZIB 29 Folding mechanism leads to stochastic matrix P with entries P kl = p(b k,b l, )

26 (2) Start short simulations from every discr. box Christof Schütte, FU Berlin + ZIB 30 Folding mechanism Main problems: How can we avoid an explosion of the number of boxes needed? How accurate is information about long timescales? leads to stochastic matrix P with entries P kl = p(b k,b l, )

27 Alternative 1: Markov State Models via Sparse Tensor Approximation Christof Schütte, FU Berlin 31

28 Sparse Tensor Approximation Approximation utilizing adaptive dimension coordinate frame identification low rank approximation polynomial and trigonometric ansatz functions Schuette et al 2014, Noe et al 2015 Christof Schütte, FU Berlin 32

29 Christof Schütte, FU Berlin 33 Alternative 2: Markov State Models via Core Sets Djurdjevac, Sarich, Schuette MMS 10 Schuette, Noe, Lu, Sarich, Vanden Eijnden, JCP 2011

30 Energy landscape with four main conformations Christof Schütte, FU Berlin 34 Example: Peptide MR121-GSGSW

31 Core sets Christof Schütte, FU Berlin 35 C3 C4 C2 C1

32 Problem-adapted ansatz function: Committors Christof Schütte, FU Berlin 36 C3 C4 C2 C1

33 Problem-adapted ansatz function: Committors Christof Schütte, FU Berlin 37 C3 C4 C2 C1

34 Problem-adapted ansatz function: Committors Christof Schütte, FU Berlin 38 C3 C4 C2 C1

35 Problem-adapted ansatz function: Committors Christof Schütte, FU Berlin 39 C3 C4 C2 C1

36 Committors=ansatz functions Christof Schütte, FU Berlin 40

37 Committors=ansatz functions Christof Schütte, FU Berlin 41

38 Approximation Quality Christof Schütte, FU Berlin 42

39 Approximation of Eigenvalues Djurdjevac, Sarich, Schuette 10 Christof Schütte, FU Berlin + ZIB 48

40 Estimation of the projection error Bovier et al. 09, Sarich, Schuette 13 Christof Schütte, FU Berlin 49

41 First Example: Drug design Christof Schütte, FU Berlin + ZIB 52

42 DPP4 with inhibitor in binding pocket Enzyme: Dipeptidyl peptidase 4 Inhibitor: Valine-Pyyrolidide Bujotzek, Weber 2009 Christof Schütte, FU Berlin + ZIB 53

43 DPP4: conformations within binding path Deuflhard, Sch. 04 / Pan, Roux 08/ Bujotzek, Weber 09 Christof Schütte, FU Berlin + ZIB 54

44 DPP4+inhibitor Deuflhard, Sch. 04 / Pan, Roux 08/ Bujotzek, Weber 09 Christof Schütte, FU Berlin + ZIB 55

45 DPP4+inhibitor Deuflhard, Sch. 04 / Pan, Roux 08/ Bujotzek, Weber 09 Christof Schütte, FU Berlin + ZIB 56

46 DPP4+inhibitor Deuflhard, Sch. 03 / Pan, Roux 08/ Bujotzek, Weber 09 / Schuette et al 14 Christof Schütte, FU Berlin + ZIB 57

47 Molecular Alchemy Christof Schütte, FU Berlin 58

48 From one molecule to another

49 Setting Dynamics MSM

50 From one molecule to another Dynamics Girsanov

51 Reiweighting trajectories Reweighting of path distributions Reweighting of transition probs:

52 MSM reweighting Schuette, Nielsen, Weber, Mol. Phys. 14

53 Second example: Pain relief drug Christof Schütte, FU Berlin + ZIB 64

54 Pain relief drugs: Opioids side effects respiratory depression constipation, tolerance, addiction pain relief effect Opioid Fentanyl (Fen), EUR 271 Mio. p.a. in Germany EUR 4 Mrd p.a. world-wide (mainly USA) prescription pharmaceuticals are now involved in more overdose deaths than either heroin or cocaine in North America B. Fischer, J. Rehm Deaths related to the use of prescription opioids CMAJ. Dec 8, 2009; 181(12):

55 Paw pressure test ph-dependent opioids MSM building & quantum chemistry side effects healthy tissue ph 7 F pain relief effect inflammation ph 5 F-Fentanyl ZIB, Charité in-vivo Injection into inflamed paw (i.pl.) * * * * mg/paw * * * * *

56 Application to Drug Design Christof Schütte, FU Berlin + ZIB 67 Docking position of a selective pain relief drug inactive in CNS active in inflammed tissue rational drug design, synthesis & preclinical testings two patents & spin-off MathPharm GmbH Cooperation: Ch. Stein, Charité

57 Third example: Multivalency Christof Schütte, FU Berlin + ZIB 68

58 Bivalent docking Ligand: bivalent ammonium-ion Receptor: bivalent rotaxane Solvent: water & methanol Ligand: tamoxifen with PEG bridge Receptor: a-estrogen receptor Solvent: water Bujotzek 13 / Weber, Fackeldey 13 Christof Schütte, FU Berlin + ZIB 69

59 Unbound Singly bound Doubly bound Weber, Fackeldey 13 Christof Schütte, FU Berlin + ZIB 70

60 Rebinding=Recrossing Christof Schütte, FU Berlin + ZIB 71

61 Rebinding=Recrossing Christof Schütte, FU Berlin + ZIB 72 Doubly bound Singly bound Unbound

62 Reactive Trajectory Christof Schütte, FU Berlin + ZIB 73 Doubly bound Singly bound Rebinding / Recrossing events Unbound

63 Committor functions = soft assignment Christof Schütte, FU Berlin + ZIB 74 Doubly bound Singly bound Unbound Committor probability= probability to hit set A next

64 Bivalent docking Ligand: tamoxifen with PEG bridge Receptor: a-estrogen receptor Solvent: water Bujotzek 13 / Weber, Fackeldey 13 Christof Schütte, FU Berlin + ZIB 75

65 Christof Schütte, FU Berlin + ZIB 76 Forth Example: Transformation Products High Throughput Screening

66 Binding Affinity MSM for ligand association process association constant Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni

67 Transformation Products Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni

68 Molecular Alchemy via MSMs 79

69 Comparison to Experiment Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni

70 Qualitative binding affinity estimation N4-Acetyl-SMZ Sulfamethoxazol (SMZ) and SMZ-TPs Potential target molecules Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni

71 Summary Christof Schütte, FU Berlin + ZIB 82

72 Extensions Christof Schütte, FU Berlin 83 Molecular Dynamics Combination with enhanced sampling techniques e.g. Bowman, Huang, Pande 09 / Prinz et al. 11 Generalization to non-equilibrium processes Wang, Sch. 15 Application to protein function e.g. Pande et al Sensitivity wrt. environmental parameters e.g. Enciso, Sch., Delle Site 13 Sparse approximation in high dimensions e.g. Schuette et al. 15 / Noe et al. 15 Software: EMMA, MSMBuilder, ZIBGridFree Beauchamp et al 11 / Senne et al. 11

73 Main Cooperations M. Sarich, C. Hartmann, R. Banisch, H. Wang, M. Fackeldey M. Weber / Computational Drug ZIB, Berlin E. Vanden Eijnden / Courant, NYU F. Noe / Computational Molecular Biology FU Berlin The End Thanks for your attention Christof Schütte, FU Berlin 84