TD!DFT applied to biological problems. Marcus Elstner TU Braunschweig

Transcription

1 TD!DFT applied to biological problems Marcus Elstner TU Braunschweig

2 0) biological structures

3 Biological structures: proteins, DNA, lipids N lipids Amino acids: 20 DNA bases: 4 (A,C,G,T)

4 Proteins - contain (mainly) H, C, N, O and S - units: amino acids N

5 Proteins - contain (mainly) H, C, N, O and S - units: amino acids N

6 Proteins

7 Proteins

8 Proteins

9 Different representations of backbone br Aquaporin Photosynthetic Reaction Center Photochemistry

10 DNA

11 1) Intro

12 Optical properties in biological systems: examples bioenergetics: photosynthesis vision avoiding radiation damage: DNA protection and repair biological fluorescence: from jellyfish to biological markers

13 Vision Three pigments, same chromopor: what determines the color?

14 Vision two different types of cells involved in vision rod cells for dim-light vision (500 nm, rhodopsin) cone cells (425nm, 533 nm, 560 nm) for color discrimination

15 Vision 7-helix proteins G-protein coupled receptors (GPCR s) cone cells (425nm, 533 nm, 560 nm) for color discrimination differ in amino acid composition

16 After photon absorption: cis trans Reaction coordinate efficiency alcohol not specific 10 ps 0.1 Rh cis-trans <0.5 ps intiates structural response => signalling state

17 Questions: can we calculate the excitation energy of Rhodopsins? can we describe the isomerization process? cis trans

18 Answers: Rh exp: 500 nm TD-B3LYP: 505 nm (JPCB ) (also Biophys J ) DFT-QM/MM simulation of isomerization process: JACS cis trans

19 Retinal has different absorption properties in different protein environments Spectral tuning over 300 nm Mechanism of color tuning: What about other rhodopsins? from Kusnetzow et al. Biochemistry 2001, 40, 7832

20 e.g. Bacteriorhodopsin transmembrane protein 7 a-helices retinal chromophor

21 e.g. Bacteriorhodopsin transmembrane protein 7 a-helices retinal chromophor

22 Bioenergetics br is simplest light driven proton pump

23 absorbs at 570 nm, e.g. 70 red-shifted with respect to Rh br photocycle

24 SRII absorbs as Rh at 500 nm, i.e. 70 red-shifted with respect to br and one more: SRII

25 Is TD-DFT color blind? TD-DFT (B3LYP) exp. br 2.57 ev 2.18 ev (570nm) SRII 2.58 ev 2.48 ev (500nm) Rh 2.52 ev 2.49 ev (498nm) JCTC 3 (2007) 605 JPCB Theor Chem Acc (2003) 109:125

26 Further DFT-QM/MM simulation of isomerization process: JACS why did they heat the chromophore to 690K? cis trans

27 Some other interesting systems bioenergetics: photosynthesis vision Avoiding radiation damage: DNA protection and repair Biological fluorescence: from jellyfish to biological markers

28 Bacterial Photosynthesis 1! light absorption 2! proton transfer 3! ATP synthesis " bacterial reaction center " bacteriorhodopsin

29 Bacterial Photosynthesis bacteriorhodopsin bacterial reaction center

30 - photon absorption - energy transfer - electron transfer - proton transfer - Q B movement: large structural transitions Bacterial Reaction Center

31 Special pair special pair: chlorophyll

32 Light Harvesting LH1 and LH2 complexes

33 LH2 - Antenna complex - BChl800 (green) - BChl850 (red) - carotenoids (yellow) from Sundström ARPC 2007

34 Chromophors Mg! porphyrene polyenes

35 Green fluorescent protein (GFP) - Shomomura discovered GFP from Aequorea victoria - Similar proteins exist in a big number of jellyfish with different wavelenghts of emission - GFP can be expressed by bacteria - chromophore build from amino acids: good marker for molecular biology

36 - green fluorescence 508 nm - dual absorption: 395 nm (neutral form) A 475 nm (anionic form) B 4:1 fraction (A:B) - Conversion via PT and structural change of Thr 203

37 DNA how does it avoid radiation damage? - rapid radiationless de-excitation via conical intersections - N-H stretch coordinate - out-of-plane motion - transport of radical cations over large distcances

38 2) simulating biological structures

39 simulating biological structures complexity has 2 dimensions: 1) size: number of atoms 2) time scale of processes: need MD to sample conformational space environment of acitve site looks caotic, but is highly structured from a functional perspective => do not neglect environment, otherwise you loose the most important point!

40 The computational problem Size: atoms (water) actives site: atoms excited states, chemical reactions => QM size, ns MD simulations => MM active site: chromophore + X

41 models in theoretical chemistry/biophysics fs ps ns time HF, DFT Approximative Methods Force Fields:MM Continuum Electrostatics Coarse graining CI, MP CASPT2 nm 10"" 100 " 1000"" " atoms Length scale

42 Molecular Mechanics: MM

43 Quelle: Grubmüller MPI Göttingen

44 Molecular Mechanics: MM For Protein- and DNA ok! Problems.: - Polarization - Charge transfer - no reactions! k b k! k " q i q j fixed point charges

45 models in theoretical chemistry/biophysics fs ps ns time HF, DFT Approximative Methods Force Fields:MM Continuum Electrostatics Coarse graining CI, MP CASPT2 nm 10"" 100 " 1000"" " atoms Length scale

46 Continuum electrostatics!#?0!"#$%&'()*&+$#+#,-.$/&+0)1+%$0",##$ 0#,2%3!"1%$/&+0,145*&+$/")+-#%$)''$6,&6#,*#%7$'18# #+#,-1#%7$9&,/#%$:1;#;$-#&2#0,.<7$(14;$9,#=5#+/1#%$>$

47 Continuum electrostatics &(#,$%5,9)/#$),#)%$D 1 $ &9$)0&2%

48 Continuum electrostatics E+0#,)/*&+$&9$2&'#/5'),$/"),-#%$C10"$#'#/0,&%0)*/$6&0#+*)'$F:,

49 Continuum electrostatics G&(#$0&$9,##$#+#,-.$%5,9)/#$4.$H%)26'1+-I$&(#,$6&%%14'#$%&'(#+0$ L,##$#+0")'6.3

50 Continuum electrostatics O/"1#(#2#+03$ G&(#$0&$9,##$#+#,-.$%5,9)/#$4.$H%)26'1+-I$&(#,$6&%%14'#$%&'(#+0$ L,##$#+0")'6.3

51 Continuum electrostatics

52 Continuum electrostatics

53 Continuum electrostatics 1 $)+@$/"),-#$= 1

54 Poisson Boltzmann (PB) vs. Generalized Born (GB) #?0#+%1(#'.$)'&+-$GX$%125')*&+% 1++#,$,#-1&+ )$4)%1%$%#0$9&,$0"#$1++#,$,#-1&+ 2&*&+$&9$0"#$&50#,$6),0

55 !"#$%&'()#*+,% calculate reaction field with and without external dielectric rescale charges in order to reproduce solvent reaction field solvent exposed charges are nearly zeroed out!

56 3) QM/MM

57 simulating biological structures complexity has 2 dimensions: 1) size: number of atoms 2) time scale of processes: need MD to sample conformational space environment of acitve site looks caotic, but is highly structured from a functional perspective => do not neglect environment, otherwise you loose the most important point!

58 Computational problem I: number of atoms! chemical reaction which needs QM treatment! immediate environment: electrostatic and steric interactions! solution, membrane: polarization and structural effects on protein and reaction! " several atoms

59 combining models in multi-scale approaches fs ps ns time HF, DFT Approximative Methods Force Fields:MM Continuum Electrostatics Coarse graining CI, MP CASPT2 nm 10"" 100 " 1000"" " atoms Length scale

60 Combined QM/MM methods QM ~ atoms ~ ns MD simulations (MD, umbrella sampling) - chemical reactions - excited states, spectroscopy In many cases, the site of interest is localized " apply QM locally Recent review: Senn & Thiel, Top Curr Chem #2007! 268: 173

61 Combined QM/MM methods 1976 Warshel und Levitt 1986 Singh und Kollman 1990 Field, Bash und Karplus QM semi-empirical methods quantum chemistry : DFT, HF, MP2, LMP2 DFT plane wave codes: CPMD MM CHARMM, AMBER, GROMOS, SIGMA,TINKER,... Recent review: Senn & Thiel, Top Curr Chem #2007! 268: 173

62 !=80 Combined QM-MM methods QM region Molecular Mechanics (MM) region Effects: - polarization of QM region through MM - steric interactions Main effect e.g. for catlytic efficiency of proteins Recent review: Senn & Thiel, Top Curr Chem #2007! 268: 173

63 QM/MM Methods! Mechanical embedding: only steric effects! Electrostatic embedding: polarization of QM due to MM! Electrostatic embedding + polarizable MM QM MM

64 QM/MM Methods! Mechanical embedding: only steric effects! Electrostatic embedding: polarization of QM due to MM! Electrostatic embedding + polarizable MM! Larger environment: - box + Ewald summ. - continuum electrostatics - coarse graining?? QM MM

65 Subtractive vs. additive models - subtractive: several layers: QM-MM doublecounting on the regions is subtracted - additive: different methods in different regions + interaction between the regions QM MM

66 Subtractive QM/MM: ONIOM Morokuma and co.: GAUSSIAN total energy = MM + QM MM -

67 Additive QM/MM total energy = QM + MM + interaction QM MM

68 Additive QM/MM: linking

69 Additive QM/MM:

70 Additive QM/MM: Elecrostatic mechanical embedding

71 Combined QM/MM Bonds: a) take force field terms b) - link atom - pseudo atoms - frontier bonds Nonbonding: - VdW - electrostatics Amaro, Field, Chem Acc. 2003

72 Combined QM/MM Bonds: a) from force field Reuter et al, JPCA 2000

73 Combined QM/MM: link atom a) constrain or not? (artificial forces) relevant for MD b) Electrostatics - QM-MM: exclude MM-host exclude MM-hostgroup - DFT, HF: gaussian broadening of MM point charges, pseudopotentails (e spill out) - J. Chem. Phys. 2002, 117, J. Phys. Chem. B 2005, 109, 9082

74 Combined QM/MM: frozen orbitals Reuter et al, JPCA 2000 Warshel, Levitt 1976 Rivail + co Gao et al 1998

75 Combined QM/MM: Pseudoatoms Amaro & Field,T Chem Acc Pseudobond- connection atom Zhang, Lee, Yang, JCP 110, 46 Antes&Thiel, JPCA X No link atom: parametrize C! H 2 as pseudoatom

76 Combined QM/MM Nonbonding terms: VdW - take from force field - reoptimize for QM level Amaro & Field,T Chem Acc Coulomb: which charges?

77 Combined QM/MM Tests: - C-C bond lengths, vib. frequencies - C-C torsional barrier - H-bonding complexes - proton affinities, deprotonation energies

78 Subtractive vs. additive QM/MM - parametrization of methods for all regions required e.g. MM for Ligands SE for metals + QM/QM/MM conceptionally simple and applicable

79 Local Orbital vs. plane wave approaches: PW implementations (most implementations in LCAO) - periodic boundary conditions and large box! lots of empty space in unit cell - hybride functionals have better accuracy: B3LYP, PBE0 etc. + no BSSE + parallelization (e.g. DNA with ~1000 Atoms)

80 Problems QM and MM accuracy QM/MM coupling model setup: solvent, restraints PES vs. FES: importance of sampling All these factors CAN introduce errors in similar magnitude

81 -,.&$(/#,.+,%'/"&'#)01,'12'&,345&(6 78#$("&*9'O++5;$Y#(;$Q1&6".%;$Q1&2&';$D0,5/0;$TUU_;$_T3`Tab`_: '#%%$126&,0)+03 [$%0#,1/$#J#/0%$$[$$$+#),$)\)/$/&+9&,2)*&+$:]OM<

82 Example br: 1st step, excited states dynamics

83 2nd step: proton transfer

84 How the protein shapes the barrier Retinal direct proton transfer Thr89 Asp212 Asp85 w402 MM: CHARMM QM: DFT-B3LYP and semi-empirical SCC-DFTB Minimum Energy Path (MEP)

85 Example 2: vision Three pigments with same chromophore: what determines absorption maximum?

86 Spectral tuning Absorption over 300 nm Tuning by protein environment (opsin-shift) [$steric interactions: twist - interaction with polar groups in environment - H-bonding with counterions

87 Spectral tuning Absorption over 300 nm Tuning by protein environment (opsin-shift) [$steric interactions: twist - interaction with polar groups in environment - H-bonding with counterions -nearby amino acids have functional role: a single mutation can have drastic effects

88 Long range forces in Biology << Solvation of whole protein can be important: ;< => a) periodic boundary: box filled with water b) continuum electrostatic c) charge scaling

89 Multi-scale methods: QM 1 /QM 2 /MM/continuum!=80!=2!linearized PB eq.

90 Computational problem II: sampling with MD!$flexibility: not one global minimum " conformational entropy! solvent relaxation " ps ns timescale (timestep ~ 1fs)

91 Problem of potential energy Different energy profiles for different protein conformations c")+-$#0$)'$dwmq$rue$:tuu_<$```as

92 Problem of potential energy Different energy profiles for different protein conformations A) One always has to average over the different conformations of the environment : Total energy" inner energy E" U B) Entropy is often as important as accurate total energy : U" F c")+-$#0$)'$dwmq$rue$:tuu_<$```as

93 Molecular Dynamics: MD $ G&'#/5'),$X.+)21/%$:GX<3$ ]52#,1/)'$1+0#-,)*&+$&9$]#C0&+%$$#=5)*&+$&9$2&*&+$Lf2g)$$C10"$ *2#%0#63$hR9% "$0,)i#/0&,1#% "$R6%$@.+)21/%3$RUUU$9&,/#$#()'5)*&+%

94 First Molecular Dynamics Simulation (MD) of a protein: 9.2 ps G/$M)22&+7$V#'1+j$k),6'5%7$])05,#$Tle7$=>?? QW!E :4&(1+#$6)+/,#)*/$0,.6%1+$ 1+"1410&,< am$)21+&$)/1@%

95 First Molecular Dynamics Simulation (MD) of a protein: 9.2 ps G/$M)22&+7$V#'1+j$k),6'5%7$])05,#$Tle7$=>?? QW!E :4&(1+#$6)+/,#)*/$0,.6%1+$ 1+"1410&,< am$)21+&$)/1@%,&&.&.6 )$4(/#*'(/$@)/@$&

96 n#(1\$j$d"),&+7$w]od$ma7$=>aab BPTI: 210ps and water

97 BPTI: 210ps and water n#(1\$j$d"),&+7$w]od$ma7$=>aab /1.#46''C=DDBDDD'#/15( ''''C=DE=DD',(

98 Multi-scale models in theoretical biophysics M&+*+552$o'#/0,&%0)*/%$ pm&),%#$-,)1+1+-q ''''''''''2(''''''''''''''''G(''''''''''''''''''',('''''''''''''''05& ME7$GW MODW!T rl7$xl! O66,&?12)*(# +2 =D' ' =DD' ' =DDD'' =DBDDD' #/15( F&,%/"'()#*&

99 Multi-scale models in theoretical biophysics M&+*+552$o'#/0,&%0)*/%$ pm&),%#$-,)1+1+-q ''''''''''2(''''''''''''''''G(''''''''''''''''''',('''''''''''''''05& ME7$GW MODW!T rl7$xl! O66,&?12)*(# +2 =D' ' =DD' ' =DDD'' =DBDDD' #/15( problem: time step~ 1fs s: energy + forces min h: energy + forces h days: energy + forces F&,%/"'()#*&