99
TD ! DFT applied to biological problems Marcus Elstner TU Braunschweig
TD!DFT applied to biological problems
Marcus ElstnerTU Braunschweig
0) biological structures
N
Biological structures: proteins, DNA, lipids
Amino acids: 20DNA bases: 4 (A,C,G,T)
lipids
- contain (mainly) H, C, N, O and S
- units: amino acids
N
Proteins
- contain (mainly) H, C, N, O and S
- units: amino acids
N
Proteins
Proteins
Proteins
Proteins
Photosynthetic Reaction CenterAquaporin
Photochemistry
bR
Different representations of backbone
DNA
1) Intro
Optical properties in biological systems: examples
• bioenergetics: photosynthesis
• vision
• avoiding radiation damage: DNA protection and repair
• biological fluorescence: from jellyfish to biological markers
Three pigments, same chromopor: what determines the color?
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
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
Vision
Reaction coordinate efficiencyalcohol not specific 10 ps 0.1
Rh cis-trans <0.5 ps 0.65
- intiates structural response => signalling state
cis trans
After photon absorption:
Questions:
cis trans
can we calculate the
excitation energy of
Rhodopsins?
can we describe the
isomerization
process?
Answers:
cis trans
Rh exp: 500 nm
TD-B3LYP: 505 nm
(JPCB 112 2007 6814)
(also Biophys J. 87 2004 2931)
DFT-QM/MM simulation
of isomerization
process:
JACS 126 2004 15328
Spectral tuning over 300 nmMechanism of color tuning:
Retinal has different absorption properties in different protein environments
What about other rhodopsins?
from Kusnetzow et al. Biochemistry
2001, 40, 7832
e.g. Bacteriorhodopsin
• transmembrane protein
• 7 a-helices
• retinal chromophor
e.g. Bacteriorhodopsin
• transmembrane protein
• 7 a-helices
• retinal chromophor
Bioenergetics
bR is simplest light driven proton pump
bR photocycle
absorbs at 570 nm, e.g. 70 red-shifted with respect to Rh
and one more: SRII
SRII absorbs as Rh at 500 nm, i.e. 70 red-shifted with respect to bR
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 112 2007 6814
Theor Chem Acc (2003) 109:125
Is TD-DFT color blind?
cis trans
Further
DFT-QM/MM simulation
of isomerization
process:
JACS 126 2004 15328
why did they heat the
chromophore to
690K?
Some other interesting systems
• bioenergetics: photosynthesis
• vision
• Avoiding radiation damage: DNA protection and repair
• Biological fluorescence: from jellyfish to biological markers
1! light absorption
2! proton transfer
3! ATP synthesis
Bacterial Photosynthesis
" bacterial reaction center" bacteriorhodopsin
bacteriorhodopsin bacterial reaction center
Bacterial Photosynthesis
- photon absorption- energy transfer- electron transfer- proton transfer
- QB movement:
large structural transitions
Bacterial Reaction Center
Special pair
special pair: chlorophyll
Light Harvesting LH1 and LH2 complexes
- Antenna complex
- BChl800 (green)- BChl850 (red) - carotenoids (yellow)
LH2
from Sundström ARPC 2007
Chromophors
Mg ! porphyrenepolyenes
- 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
Green fluorescent protein (GFP)
- 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
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
2) simulating biological structures
simulating biological structures
complexity has 2 dimensions:
1) size: number of atoms2) 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!
active site: chromophore + X
• Size: 4000-15000 atoms (water)
• actives site:50-100 atoms
• excited states, chemical reactions => QM
• size, ns MD simulations => MM
The computational problem
models in theoretical chemistry/biophysics
CI, MPCASPT2
Length scale
Continuum Electrostatics “Coarse graining”
Force Fields:MM
f
s
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ApproximativeMethods
HF, DFT
nm10"" 100"" 1000"" 10.000 " atoms
© Grubmüller
Molecular Mechanics: MM
Quelle: GrubmüllerMPI Göttingen
For Protein- and DNA ok!
Problems.:
- Polarization
- Charge transfer
- no reactions!
kb
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fixed point charges
Molecular Mechanics: MM
models in theoretical chemistry/biophysics
CI, MPCASPT2
Length scale
Continuum Electrostatics “Coarse graining”
Force Fields:MM
f
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ps
ns
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ApproximativeMethods
HF, DFT
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Continuum electrostatics
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Continuum electrostatics
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Poisson Boltzmann (PB) vs. Generalized Born (GB)
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• calculate reaction field with and without external dielectric
• ‘rescale’ charges in order to reproduce solvent reaction field
• solvent exposed charges are nearly zeroed out!
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3) QM/MM
simulating biological structures
complexity has 2 dimensions:
1) size: number of atoms2) 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!
! chemical reaction which needs QM treatment
! immediate environment: electrostatic and steric interactions
! solution, membrane: polarization and structural effects on protein and reaction!
" 10.000... - several 100.000 atoms
Computational problem I: number of atoms
combining models in multi-scale approaches
CI, MPCASPT2
Length scale
Continuum Electrostatics “Coarse graining”
Force Fields:MM
f
s
ps
ns
tim
e
ApproximativeMethods
HF, DFT
nm10"" 100"" 1000"" 10.000 " atoms
~ 1.000-100.000 atoms
~ ns MD simulations
(MD, umbrella sampling)
- chemical reactions
- excited states, spectroscopy
QM
Combined QM/MM methods
In many cases, the site of interest is localized" apply QM locally
Recent review: Senn & Thiel, Top Curr Chem #2007! 268: 173
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, ...
Combined QM/MM methods
Recent review: Senn & Thiel, Top Curr Chem #2007! 268: 173
!=80
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
Combined QM-MM methods
MM
QM
! Mechanical embedding: only steric effects
! Electrostatic embedding: polarization of QM due to MM
! Electrostatic embedding + polarizable MM
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
MM
QM
? ?
QM/MM Methods
- subtractive: several layers: QM-MM
doublecounting on the regions is subtracted
- additive: different methods in different regions +
interaction between the regions
MM
QM
Subtractive vs. additive models
total energy
QM
MM=
-+ MM
Subtractive QM/MM: ONIOM Morokuma and co.: GAUSSIAN
total energy QM= +
QM+
MM
MM
interaction
Additive QM/MM
Additive QM/MM: linking
Additive QM/MM:
Additive QM/MM:
Elecrostatic mechanical embedding
Combined QM/MM
Amaro , Field , Chem Acc. 2003Bonds:
a) take force field terms
b) - link atom
- pseudo atoms
- frontier bonds
Nonbonding:
- VdW
- electrostatics
Combined QM/MM
Reuter et al, JPCA 2000
Bonds:
a)
from force field
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, 10534 J. Phys. Chem. B 2005, 109, 9082
Combined QM/MM: frozen orbitals
Warshel, Levitt 1976
Rivail + co. 1996-2002
Gao et al 1998
Reuter et al, JPCA 2000
Combined QM/MM: Pseudoatoms
Amaro & Field ,T Chem Acc. 2003
Pseudobond- connection atom
Zhang, Lee, Yang, JCP 110, 46
Antes&Thiel, JPCA 103 9290
No link atom: parametrize C! H2 as pseudoatom
X
Nonbonding terms:
VdW
- take from force field
- reoptimize for QM level
Coulomb:
which charges?
Combined QM/MM
Amaro & Field ,T Chem Acc. 2003
Tests:
- C-C bond lengths, vib. frequencies
- C-C torsional barrier
- H-bonding complexes
- proton affinities, deprotonation
energies
Combined QM/MM
- parametrization of methods for all regions required
e.g. MM for Ligands
SE for metals
+ QM/QM/MM conceptionally simple and applicable
Subtractive vs. additive QM/MM
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)
Local Orbital vs. plane wave approaches:
• 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
Problems
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Example bR: 1st step, excited states dynamics
2nd step: proton transfer
Retinal
Asp85
Thr89
Asp212
w402
direct proton transfer
How the protein shapes the barrier
•MM: CHARMM
•QM: DFT-B3LYP and semi-empirical SCC-DFTB
• Minimum Energy Path (MEP)
Example 2: vision
Three pigments with same chromophore: what determines absorption maximum?
Absorption over 300 nm“Tuning” by protein environment(opsin-shift)
‘Spectral tuning’
[$steric interactions: twist
- interaction with polar groups in environment
- H-bonding with counterions
Absorption over 300 nm“Tuning” by protein environment(opsin-shift)
‘Spectral tuning’
[$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
;<
Long range forces in Biology
<<
Solvation of whole protein can be important:
=> a) periodic boundary: box filled with waterb) continuum electrostatic c) charge scaling
Multi-scale methods:QM1/QM2/MM/continuum
!linearized PB eq.
!=80
!=2
Computational problem II: sampling with MD
!$flexibility: not one global minimum
" conformational entropy
! solvent relaxation
" ps – ns timescale (timestep ~ 1fs)
Different energy profiles for different
protein conformations
‘Problem’ of potential energy
c")+-$#0$)'$dWMQ$RUe$:TUU_<$```aS
Different energy profiles for different
protein conformations
‘Problem’ of potential energy
c")+-$#0$)'$dWMQ$RUe$:TUU_<$```aS
A) One always has to average over the different conformations of the environment :
Total energy" inner energyE" U
B) Entropy is often as important as accurate total energy : U" F
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Molecular Dynamics: MD
First Molecular Dynamics Simulation (MD) of a protein: 9.2 ps
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First Molecular Dynamics Simulation (MD) of a protein: 9.2 ps
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BPTI: 210ps and water
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Multi-scale models in theoretical biophysics
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Multi-scale models in theoretical biophysics
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problem: time step~ 1fs
s: energy + forces
min – h: energy + forces
h – days: energy + forces
