In-Silico -Versuche für die Human- und Ökotoxikologie. Vedat Durmaz Zuse Institute Berlin Computational Molecular Design

Transkript

1 In-Silico -Versuche für die Human- und Ökotoxikologie Vedat Durmaz Zuse Institute Berlin Computational Molecular Design

2 BMBF-Projekt TransRisk: Risikocharakterisierung Molecular Modelling & molecular simulation Economic/ecological/toxicological aspects of Waste/drinkingwater treatment Investigation of new stages (ozone) & focussing on transformation products Communication with educators and polluters (citizens, hospitals, industry) 2

3 Molecular Dynamics Simulations

4 Molecular Dynamics MD Simulations Mimicking the behaviour (dynamics) of molecular systems 3D representation & time development of molecular systems Insight into molecular mechanics on the atomistic (microscopic) level Thermodynamic (macroscopic) quantities through statistical mechanics Simulation box & solvent molecules 4

5 MD: applications Virtual screening & drug design Structure refinement & protein design Conformational analysis & kinetics Structure prediction 5

6 MD: history 6

7 MD: ZIB supercomputer Fibreglass-connected supercomputer twin system in Hannover & Berlin (ZIB) Identical infrastructure (Cray XC3) per site: 45 Compuing cores 1.4 PFLOP/s 117 TB RAM 4.4 PB hard drive space 7

8 Classical Molecular Mechanics Force Fields

9 Empirical force fields: atom type assignment Atom type definition depending on hybridization state & bindung partners 9

10 Empirical force fields: covalent bond representation Parameters for harmonic bond representation between atoms i and j : Reference bond length rij Force constant Kij Origin of parameters: X-ray cristallography Spectroscopic methods Quantum chemical calculations 1

11 Empirical force fields: harmonic potential f ( x ) =a ( x b ) bond Bonds: V Bond angles: V angle ( θ )= ( r )= 2 K ij 2 r r ij ) ( 2 K ijk cos θ cos θijk ) 2 ( 2 11

12 Empirical force fields: torsional potential Torsional angles Pijk i k V l Pjkl torsion ( φ )= K ijkl 1+cos ( n φ γijkl ) ) 2 ( φijkl =arccos ( rij r jk,r jk r kl r ij r jk r jk r kl ) j "Improper dihedrals" =18, n =3 + =18, n =1 =18, n =3 =18, n =1 j i k l 12

13 Empirical force fields: nonbonded potentials Lennard-Jones potential (van der Waals forces) Coulomb potential (electronic interactions) Repulsive term: 1/r12 Charges with same sign: (zizj > ) Repulsion With opposing signs: (zizj < ) Attraction Attractive term: -1/r6 LJ V ( r ) = 4 εij [( σij r ) ( )] 12 σ ij r 6 V Coul z i z ij (r) = ε ε r 13

14 Empirical force fields: potential energy qy qz Potential energy V (q ) of a molecular geometry (conformer) with coordinates q : qx angles bonds V ( q) = Bonds K ij r r ij ) 2 + ( 2 Angles K ijk cosθ cos θ ijk ) 2 + ( 2 dihedrals Dihedrals K ijkl (1+cos ( n φ γ ijkl ) ) + 2 nonbonded i< j [( Aij 12 B ij 6 z i z j + r r εε r ) ( ) ] Potential energy V ( q) 14

15 Empirical force fields: potential energy qy qz Potential energy V (q ) of a molecular geometry (conformer) with coordinates q : qx angles bonds V ( q) = Bonds K ij 2 r r ij ) + ( 2 Angles dihedrals K ijk 2 cosθ cos θ ijk ) + ( 2 Dihedrals K ijkl 1+cos ( n φ γ ijkl ) ) + 2 ( Potential energy V ( q) nonbonded Partial derivatives i< j [( Aij 12 B ij 6 z i z j + r r εε r ) ( ) Force F = qv (q ) = { ] V ( q ) q } 15

16 Empirical force fields: potential energy qy qz Potential energy V (q ) of a molecular geometry (conformer) with coordinates q : qx angles bonds V ( q) = Bonds Conformation q K ij 2 r r ij ) + ( 2 Angles dihedrals K ijk 2 cosθ cos θ ijk ) + ( 2 Dihedrals K ijkl 1+cos ( n φ γ ijkl ) ) + 2 ( Potential energy V ( q) nonbonded Partial derivatives i< j [( Aij 12 B ij 6 z i z j + r r εε r ) ( ) Force F = q V ( q ) = { ] V ( q ) q } Numerical mathematics 16

17 Empirical force fields: potential energy qy qz Potential energy V (q ) of a molecular geometry (conformer) with coordinates q : qx angles bonds V ( q) = Bonds K ij 2 r r ij ) + ( 2 Conformation q Angles dihedrals K ijk 2 cosθ cos θ ijk ) + ( 2 Dihedrals K ijkl 1+cos ( n φ γ ijkl ) ) + 2 ( Potential energy Force field V ( q) nonbonded Partial derivatives i< j [( Aij 12 B ij 6 z i z j + r r εε r ) ( ) Force F = qv (q ) = { ] V ( q ) q } Numerical mathematics 17

18 Numerical Integration of the Equation of motion

19 MD: numerical time integration with velocity Verlet N conformations qi N potential energies V (qi ) Time 19

20 MD: numerical time integration with velocity Verlet New positions: New momenta: N conformations qi N potential energies V (qi ) Time 2

21 MD: time step & trajectory in phase space New positions: New momenta: How to choose? N conformations qi N potential energies V (qi ) Time 21

22 MD: time step & trajectory in phase space N conformations qi N potential energies V (qi ) 22

23 MD: time step & trajectory in phase space That's it: = 1-15s N conformations qi N potential energies V (qi ) 23

24 MD: time scaling problem = 1-15s N conformations qi N potential energies V (qi ) 24

25 MD: "trapping" problem & convergence Conformational changes are rare events Long simulations required for exhaustive sampling of the conformational space Convergence check recommended (visually or according to Gelman & Rubin) 25

26 MD: potential energy surface & Boltzmann distribution gauche/anti eclipsed/eclipsed anti/anti Energy distribution in the conformational space (potential energy surface) Distribution of states at particular temperature (Boltzmann distribution) 26

27 MD: "trapping" problem & convergence Sufficient convergence at 5 steps, 3 K No convergence at 5 steps, 3 K Apparently sufficient convergence at 5 steps, 8 K wrong distribution! 27

28 Statistical thermodynamics: Boltzmann distribution V A B q ZA = A exp ( β V ( q ) ) Δ AB A = k B T ln ZB = B exp ( β V ( q ) ) ZB n k B T ln B ZA na ( ) ( ) Helmholtz free energy difference between conformations A and B Most thermodynamic variables (macroscopic view) can be derived from the partition function Z or its derivatives (microscopic view). 28

29 Some Practical Applications of MD Simulations

30 Application: probabilistic model for polymer assembly GCR GCA GCB GCX dentritic P = ( GCL S ' ( t ) = S ( ) P t ) P hyper = ( ) [Durmaz, JCAM 215 ] 31

31 Application: computational drug design ph-dependent analgesic: effective only in inflamed tissue reduced side effects Paw pressure test Injection into inflamed paw (i.pl.) 16 * 12 * 8 * * * * * * * * 8 * 4 Intravenous injection (i.v.) * * * * * * * * g/paw g/kg [Stein, Weber, Scharkoi, Deuflhard: EU patent 213 ] 32

32 Application: conformational clustering Minit df1 M1 df6 M2 df5 Mfinal F C1 = F1 F2 2.4 df df df df df df6.8.4 df df min() min() min() df df df6 2.5 C3 = F5 3.3 df C2 = F6 F7.3 df df df1.3 F8 2.2 df df df5 2. k = 2π d max ( ) N f (1 α )

33 Application: prediction of the HPLC elution order [Durmaz, JMM 212 ] 34

34 Application: conformational entropy estimation rmax qref rmax qref Monte Carlo-based conformational entropy estimation: variance of coordinates during MD [Weber, MATCH 21 ] 35

35 Binding Affinity and Toxicity Estimation for Transformation Products

36 Toxicity estimation for transformation products TP Sulfamethoxazole 37

37 Toxicity estimation for transformation products TP Abiotic Biotic Sulfamethoxazole? 38

38 Thermodynamics: free energy of binding G RL R + L First-order reaction of a host guest system at thermodynamic equlibrium 39

39 Thermodynamics: free energy of binding G RL R + L First-order reaction of a host guest system at thermodynamic equlibrium Association constant Ka = 1/Kd (equals inverse dissociation constant Kd) 4

40 Thermodynamics: free energy of binding G Gibbs free energy difference between bound and unbound RL R + L First-order reaction of a host guest system at thermodynamic equlibrium Association constant Ka = 1/Kd (equals inverse dissociation constant Kd) 41

41 Binding free energy G : enthalpy & entropy Enthalpy H Entropy S 42

42 Binding free energy G : enthalpy & entropy Enthalpy H Entropy S 43

43 Binding free energy G : enthalpy & entropy Enthalpy H Entropy S 44

44 Human estrogen receptor & 17- -estradiol hormone Transcription factor ER (gene regulation) PDB data base entry "1GWR" Crystal structure including hormone 17- -estradiol (E2) Amber force field parameterization Explicit solvent MD with Gromacs Calculation of interaction energies & conformational entropy 45

45 Binding mode & affinity prediction: estrogen receptor Parameter fitting using training data (molecules) with known binding affinity: Experimental affinities Simulated energies/entropies Weights x=? [Durmaz, JCIM 213 ] 46

46 Relative affinity prediction: cytochrom P45 Abschätzung der Interaktion von CBZ-TP mit Enzymklasse Cytochrom P45 ohne Trainingsdaten ("x " unbekannt) Vergleich mit Muttersubstanz CBZ möglich 47

47 Relative affinity prediction: dihydropteroatsynthase Abschätzung der Interaktion von SMZ-TP mit Enzym Dihydropteroatsynthase ohne Trainingsdaten ("x " unbekannt) Vergleich mit Muttersubstanz SMZ möglich 48

48 Thanks for your attention!