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

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

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

Docking Christof Schütte, FU Berlin 4

Christof Schütte, FU Berlin 5

The timescale problem Christof Schütte, FU Berlin + ZIB 6 Elastic vibrations of proteins α-helix folding β-hairpin folding Bond stretching Protein folding 10-15 10-12 10-9 10-6 10-3 10 0 (fs) (ps) (ns) (μs) (ms) (s) MD Time It is still infeasible to compute rare event statistics using conventional MD methods

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

The timescale problem Christof Schütte, FU Berlin + ZIB 8 Elastic vibrations of proteins α-helix folding β-hairpin folding Bond stretching Protein folding 10-15 10-12 10-9 10-6 10-3 10 0 (fs) (ps) (ns) (μs) (ms) (s) MD Time Reliable rare event statistics via long MD inappropriate! Instead: Extract statistics from many short MD simulations!!

Conformations and metastable sets Christof Schütte, FU Berlin + ZIB 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)

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

Conformation Dynamics as Markov Process Christof Schütte, FU Berlin + ZIB 13 Time scale 1ps statistical weight 0.510 metastability 0.937 0.031 0.064 transition probabilities 0.065 0.032 0.005 0.005 statistical weight 0.243 statistical weight 0.247 metastability 0.931 metastability 0.930

Transfer Operators Christof Schütte, FU Berlin + ZIB 15

Transfer operator Christof Schütte, FU Berlin + ZIB 16

Transfer operator Christof Schütte, FU Berlin + ZIB 17

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

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

Concept of MSMs Christof Schütte, FU Berlin + ZIB 21

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

Concept of MSMs Christof Schütte, FU Berlin + ZIB 23

Concept of MSMs Christof Schütte, FU Berlin + ZIB 24

Standard MSMs Christof Schütte, FU Berlin + ZIB 25

MSM as Galerkin projection Christof Schütte, FU Berlin 26

MSM as Galerkin projection Christof Schütte, FU Berlin 27

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

(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, )

(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, )

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

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

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

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

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

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

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

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

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

Committors=ansatz functions Christof Schütte, FU Berlin 40

Committors=ansatz functions Christof Schütte, FU Berlin 41

Approximation Quality Christof Schütte, FU Berlin 42

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

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

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

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

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

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

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

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

Molecular Alchemy Christof Schütte, FU Berlin 58

From one molecule to another

Setting Dynamics MSM

From one molecule to another Dynamics Girsanov

Reiweighting trajectories Reweighting of path distributions Reweighting of transition probs:

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

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

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): 881 882.

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.) 180 160 140 120 100 80 60 40 20 0 * * * * 0 0.5 1 1.5 2 mg/paw * * * * *

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

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

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

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

Rebinding=Recrossing Christof Schütte, FU Berlin + ZIB 71

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

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

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

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

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

Binding Affinity MSM for ligand association process association constant Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni 2013 77

Transformation Products Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni 2013 78

Molecular Alchemy via MSMs 79

Comparison to Experiment Christof Scientific Schütte, Advisory FU Board Berlin ZIB + ZIB Christof Schuette Juni 2013 80

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 2013 81 81

Summary Christof Schütte, FU Berlin + ZIB 82

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. 08-13 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

Main Cooperations M. Sarich, C. Hartmann, R. Banisch, H. Wang, M. Fackeldey M. Weber / Computational Drug Design @ ZIB, Berlin E. Vanden Eijnden / Courant, NYU F. Noe / Computational Molecular Biology Group @ FU Berlin www.biocomputing-berlin.de www.zib.de The End Thanks for your attention Christof Schütte, FU Berlin 84