quantum chemical modeling of photoexcitations in biology · quantum chemical modeling of...

Quantum chemical modeling of photoexcitations in biology

Ville R. I. Kaila Theoretical Biophysics Section @ Laboratory of Chemical Physics

NIDDK, National Institutes of Health, USA Ville R. I. Kaila

Winter School in Theoretical Chemistry, Helsinki, Dec. 13., 2011

Contents

Methodology Cluster modeling of proteins & enzymes Methods applicable for bio-modeling Benchmarking the methods on biochromophores

Short Introduction to Photobiology

Case-study Protein environment & photoexcitations in retinal

Phototrophs: Energy transduction

Chemotrophs: Photoreceptors/ Photosensors

= organisms using light as a primary energy source

Introduction to Photobiology

= organisms using chemical coumpounds as a primary energy source

Bioluminescence

Photobiology in energy transduction


Example I: Biological energy transduction Photosystem II converts the energy of the sunlight into electrochemical energy

Cardona et al. BBA (2012)


H2O → 2H+ + 2e- + ½O2

Q + 2H+ + 2e- → QH2


Example II: Biological energy transduction Bacteriorhodopsin (bR) converts light energy into an electrochemical proton gradient

Freier et al. PNAS 2011

all-trans → 13-cis

Photochemical reaction: all-trans retinal to 13-cis isomerization

Photoreceptors



Six main types of photoreceptors

Cryptochrome FAD

Blue-light sensing FAD (BLUF) FAD

Light, oxygen, voltage (LOV) FMN

Photoactive yellow protein (PYP) pCA

Rhodopsin retinal

Phytochrome bilin

Electron transfer/ “catalytic triplet state”

Photoisomerization

Chromophore Photoreceptor Photochemical process

Example III: Biological photoreseptors Rhodopsin is a G-protein coupled receptor


Sensor of visible light in vertebrates Photochemical reaction: 11-cis retinal to all-trans isomerization

Triggers vision process


Example IV: Biological sensors Photoactive yellow protein (PYP) is a blue-light receptor in chemotrophic bacteria

Ihee et al. PNAS 2008

Importance in phototaxis Photochemical reaction: Trans-cis isomerization of p-coumaric acid


Example V: Bioluminescense Green fluorescent protein (GFP) emits green light in Aequoria jellyfish

Fluorescence observed only in protein environment but not in solution

Function in nature unclear, biotechnology as a labeling tool

p-hydroxybenzylidene imidazolinone

Quantum chemical methodology

Quantum chemical cluster modeling of proteins and enzymes


Protein (X-rays) structure QM-model

Hydrogen atoms are not resolved Missing residues? Missing waters/ions/etc.?


How to construct a cluster model?

Residues based on proximity (to chromophore/site of interest) Physico-chemical aspects? Charged/polar/aromatic/non-polar/H-bonding residues?

How many atoms can we afford? Excited state DFT modeling 150 - 200 atoms

Bioinformatic consideration? Evoluationary conserved residues?

Where should I cut the residues? Proteins are polymers!

Where should I cut the residues? Where should I cut the residues?

Include protein backbone of residues n ± 1 if important for H-bonding

Model residue size: 33 atoms


Cut at Cα atom if conformational flexibility of side-chain is particularly important



Cut at Cβ atom minimial model where protein strain can easily be included



Cut at Cγ atom if model is otherwise too large



Simulating protein backbone strain - freezing terminal carbons

* *

*

*

*

*

*

*

*

*


The low dielectric environment of the protein (ε ~ 4) can be described by continuum solvation models e.g. the COnductor-like Screening MOdel (COSMO)

The “solvent” is approximated by a polarizable cavity, defined by the shape of the molecular cluster

A. Klamt & G. Schuurman J. Chem. Soc. Trans. Perkin Trans. 2 (1993)

The solvation effects are obtained from interaction between the charges polarized on the continuum shell and the charge distribution of the molecule

Quantum chemical approaches

X-ray structure

Active site + conserved surr.

~150-300 atoms

Freeze terminal carbons + optimize B3LYP/

def2-SVP

Properties: large basis sets, Dielectric constant

B3LYP/ def2-TZVP/ε=4


QM/MM approaches

MM

QM

An alternative approach: QM-model + full protein environment described by classical force fields (cf. Menucci’s talk)

link atoms

QM/MM approaches

Consideration for QM/MM: including large QM region might be important

JCTC (in press)

Protein shifts with classical non-polarizable forcefield not large enough


Methods applicable for biochemical modeling

Excited state properties

Linear-response Time-Dependent Density Functional Theory (cf. Norman’s lectures) (N4 scaling)

Solve:

To obtain: transition vectors, XY excitation energies, ω Where matrix elements,

a,b – occupied orbitals i,j – virtual orbitals

two-electron integrals exchange potential orbital energies of φa & φi


Example of drawbacks in LR-TDDFT: The charge transfer problem

CIS

BHLYP

B3LYP

SVWN LB94

Dreuw & Head-Gordon: Chem. Rev. 2005

Wrong charge-transfer excited states due to erranous 1/R behavior of TDDFT Underestimation of excitation energies


Example of drawbacks in LR-TDDFT: The charge transfer problem

Kaila et al. (in progress)

Particularly problematic in many biological systems, as they might comprise weakly interacting, non-covalently bound fragments

CCSD, N6


Approximate second order coupled cluster theory, CC2 (N5 scaling)

|ui> manifold of excitations from |HF> T1 single excitations T2 double excitations

F+U+V Hamiltonian, H F Fock operator V one-electron operator U fluctuation operator


Benchmarking the TDDFT and CC2 for biochromophores

Send, Kaila, Sundholm JCTC 7 (2011)



Retinal (rhodopsin) Lowest-excited states in agreement

0

1

1 2 3 4 5

f

2 2.5

3 3.5

4 4.5

5E

[eV]

DFTCC2




0 0.05

1 2 3 4 5

f

2 2.5

3 3.5

4 4.5

5E

[eV]

DFTCC2

TDDFT has problems in describing anionic molecules (pCA’’-, PYP chromophore) Send, Kaila, Sundholm JCTC 7 (2011)



0 0.05

1 2 3 4 5

f

2 2.5

3 3.5

4 4.5

5E

[eV]

DFTCC2

DFT pc

TDDFT has problems in describing anionic molecules (pCA’’-, PYP chromophore)

but can be resolved by stabilizing the chromophore with external point changes


Conclusions from benchmarking the TDDFT and CC2 for biochromophores

CC2 deviation (GFP and Rhodopsin chromophores) 0.15 eV

TD-B3LYP deviation (GFP and Rhodopsin chromophores) 0.2-0.3 eV

Avoid anionic DFT models (due to DFT-continuum problem?)

CC2 deviation (PYP chromophores) 0.3-0.4 eV

TD-B3LYP deviation (PYP chromophores) 0.1-0.5 eV



Frozen core-approximation in CC-methods saves computational time and has a small effect on the results


Restricted virtual space approximation

Send, Kaila, Sundholm JCP 134 (2011)

CP

U [h

] Error [eV

]

Freeze also virtual orbitals above a certain energy treshold


Restricted virtual space approximation has the same effect on the chromophore in gas-phase and embedded in the protein

Send, Kaila, Sundholm JCP 134 (2011)

Erro

r [eV

]

RVS treshold [eV]


Check also out: Laplace-transformed spin-opposite scaled CC2 (LT-SOS-CC2), N4 scaling

Algebraic diagrammatic correction ADC(2), ~3 x faster than CC2, (cf. Dreuw’s lecture)

The effect of protein environment on photoexcitation properties of retinal

Ville R. I. Kaila, Robert Send, and Dage Sundholm (in press)

Some abbreviations and concepts

SBH+ - protonated Schiff base retinal

SB - deprotonated Schiff base retinal

BC - blue-cone pigment

Rh - rhodopsin

Glu - will refer here to glutamate-113

For protein models SBH+ - will imply Glu- SB - will imply GluH

Some abbreviations and concepts

Blueshift Redshift

E E

Vertebrate vision

Human vision: rod pigment for dim-vision (498 nm)

Three cone pigments for color vision: pigments sensitive for blue (414 nm), green (553 nm), and red light (564 nm)

414 498 553 564

Vertebrate vision

How is the color-tuning achieved by the protein environment?

Gas-phase 610 nm (2.03 eV) Rhodopsin

498 nm (2.48 eV)

10.5 kcal/mol 0.45 eV

Bluecone 414 nm (3.00 eV)

11.6 kcal/mol 0.5 eV

We are not the first to address spectral tuning of retinal

Steric tuning mechanism: e.g. Blatz & Liebman 1973

Electrostatic tuning mechanism e.g. Honig et al. 1976 Photoexcitations leads to strong increase in retinal dipole moment

-

+

- hv

From experimental work on cyanines and polyenes:

Long λ → small bond lenght altenation → increased π-electron delocalization Short λ → large bond lenght altenation → decreased π-electron delocalization

QM/MM studies

Semi-empirical Warshel, A.; Chu, Z. T. J. Phys. Chem. B 2001, 105, 9857–9871. Hayashi, S.; Ohmine, I. J. Phys. Chem. B 2000, 104, 10678–10691. Matsuura, A. et al. J. Comp. Chem. 2006, 27, 1623–1630. Hoffmann, M.; et al. M. J. Am. Chem. Soc. 2006, 128, 10808–10818.

HF Yamada, A. et al. Chem. Phys. Letters 2002, 366, 670–675.

CIS Rajamani, R.; Gao, J. L. J. Comp. Chem. 2002, 23, 96–105. Trabanino, R. J.; et al. J. Phys. Chem. B 2006, 110, 17230–17239.

SAC-CI Fujimoto, K. et al. Chem. Phys. Letters 2005, 414, 239–242. Sakurai, M.; et al. J. Am. Chem. Soc. 2003, 125,3108–3112.

SORCI Hoffmann, M. et al. J. Am. Chem. Soc. 2006, 128, 10808–10818.

DFT/TDDFT Gascón, J. A. et al. Acc. Chem. Res. 2006, 39, 184–193. Röhrig, U. F.; Sebastiani, D. J. Phys. Chem. B 2008, 112, 1267–1274. Altun, A.; et al. J. Phys. Chem. A 2009, 113, 11685–11692.

CASSCF Hayashi, S.; et al. J. Phys. Chem. B 2001, 105, 10124–10131. Hayashi, S.; et al. Biophys. J. 2009, 96, 403–416.

CASPT2 Ferré, N.; Olivucci, M. J. Am. Chem. Soc. 2003, 125, 6868–6869. Andruniów, T.; et al. Proc. Natl. Acad. Sci. USA 2004, 101, 17908–17913.

MCQDPT2, MRCISD, MR-SORCI+Q, MR-DDCI+Q Altun, A.; et al. J. Phys. Chem. A 2009, 113, 11685–11692.

QM studies of retinal models

TDDFT/DFT Blomgren, F.; Larsson, S. J. Phys. Chem. B 2005, 109, 9104–9110. Send, R.; Sundholm, D. J. Phys. Chem. A 2007, 111, 27–33. Rostov, I. V.; et al. J. Phys. Chem. B 2010, 114, 5547–5555.

CC2 Send, R.; Sundholm, D. Phys. Chem. Chem. Phys. 2007, 9, 2862–2867. Szymczak, J. J. et al. J. Phys. Chem. A 2009, 113, 11907–11918.

Quantum Monte Carlo Valsson, O.; Filippi, C. J. Chem. Theory Comput. 2010, 6, 1275–1292.

CASSCF/CASPT2 Sekharan, S.; Weingart, O.; Buss, V. Biophys. J. 2006, 91, L07–L09. Andruniów, T.; et al. Proc. Natl. Acad. Sci. USA 2004, 101, 17908–17913.


What’s new?

Large QM models and chromophore-protein interactions treated at a QM-level


Methods

DFT cluster models of the rhodopsin (PDB ID: HZX) and blue-cone (PDB ID:1KPN)

Methods

DFT cluster models of the rhodopsin (PDB ID: HZX) and blue-cone (PDB ID:1KPN) Models comprised chromophore + 10 residues, terminated at Cβ, 160-171 atoms

Methods

DFT cluster models of the rhodopsin (PDB ID: HZX) and blue-cone (PDB ID:1KPN) Models comprised chromophore + 10 residues, terminated at Cβ, 160-171 atoms Two models: a) Schiff-base proton coordinated to retinal or b) Glu-113

Methods

DFT cluster models of the rhodopsin (PDB ID: HZX) and blue-cone (PDB ID:1KPN) Models comprised chromophore + 10 residues, terminated at Cβ, 160-171 atoms Two models: a) Schiff-base proton coordinated to retinal or b) Glu-113

B3LYP/def2-SVP optimized Single point and vertical excitation energies using: TD-B3LYP/def2-TZVP, TD-BHLYP/def2-TZVP, RVS20-ADC(2)/def2-TZVP First excited state optimized at the TD-B3LYP/def2-SVP level

Vertebrate vision

Results

Vertebrate vision

Bond-length alternations

Bond-length alternation

Bond length altenation of retinal in gas-phase

SB has stronger BLA relative to SBH+→ blueshifted in gas-phase?

Bond-length alternation

Protein increases the bond length altenation of retinal of SBH+ Smaller effect on SB

SBH+ more blueshifted by protein?

Vertebrate vision

Proton affinity of retinal embedded in the protein

Ground-state properties

Blue cone pigment: proton affinity of Schiff base ~ proton affinity of Glu-113

0 kcal/mol 0 kcal/mol

Glu-113

Ground-state properties

Rhodopsin: proton affinity of Schiff base 4 kcal mol-1 higher than for Glu-113

0 kcal/mol 4 kcal/mol

Glu-113

Vertebrate vision

Ground-state charge distributions

Ground-state charge distribution

Small protein polarization effect for protonated retinal (SBH+/Glu-)

BC

Qret = +0.97e

Qprot = -0.97e

Rh

Qret = +0.91e

Qprot = -0.91e

Ground-state charge distribution

Transfer of 0.5e upon proton transfer to Glu-113 (SB/GluH)

BC

Qret = +0.43e

Qprot = -0.44e

Rh

Qret = +0.44e

Qprot = -0.44e

Vertebrate vision

Vertical excitations

Vertical excitations at TD-B3LYP/def2-TZVP level

553 nm (1.12) gas-phase:

SBH+


553 nm (1.12)

491 nm (1.10)

gas-phase:

Rh

SBH+


553 nm (1.12)

491 nm (1.10) 485 nm (1.07)

gas-phase:

Rh BC

SBH+


553 nm (1.12)

491 nm (1.10) 485 nm (1.07)

gas-phase:

408 nm (1.47) gas-phase:

Rh BC

SBH+

SB


553 nm (1.12)

491 nm (1.10) 485 nm (1.07)

gas-phase:

408 nm (1.47)

454 nm (1.28)

Rh

gas-phase:

Rh BC

SBH+

SB


553 nm (1.12)

491 nm (1.10) 485 nm (1.07)

gas-phase:

408 nm (1.47)

454 nm (1.28) 441 nm (1.20)

Rh BC

gas-phase:

Rh BC

SBH+

SB

Excited-state charge distribution

+ hv -

Excitation leads to intra-molecular CT in retinal

gas-phase BC Rh

0.73e 0.74e 0.78e

0.08e 0.05e 0.07e

retinyl β-ionine gas-phase BC Rh

0.55e 0.53e 0.61e

0.26e 0.16e 0.25e

retinyl β-ionine


Charge-transfer in excited state for Rhodopsin (SBH+/Glu-)

BC

Qret = +0.94e

Qprot = -0.94e

Rh

Qret = +0.78e

Qprot = -0.78e

DFT artifacts?

Charge-transfers

1) Based on oscillator strengths, TD-B3LYP suggest that the second excited state has a strong intensity

System Model ES BC SBH+ 1

2

B3LYP [nm]/osc. 506 (0.00) 485 (1.07)

BHLYP [nm]/osc. 415 (1.58) 293 (0.25)

ADC(2) [nm]/osc. 420 (1.67) 300 (0.32)

2a) Based on osc. stregths, the order of the states are flipped when increasing the amount of HF exchange 2b) ES2 is significantly blueshifted at the BHLYP level (indicator of CT problem)

3) ADC(2) results support that the weak state at B3LYP has CT problems

DFT artifacts?

Support from flipping the order of states from dominant orbital contributions


2

B3LYP [nm]/osc. 506 (0.00) 485 (1.07)

BHLYP [nm]/osc. 415 (1.58) 293 (0.25)

ADC(2) [nm]/osc. 420 (1.67) 300 (0.32)


2

B3LYP orbital character |c|2 HOMO-1→LUMO 99.9

HOMO → LUMO 92.6

BHLYP orbital character |c|2 HOMO→LUMO 95.9

HOMO-3 → LUMO 90.1

1 2

ADC(2) orbital character |c|2 HOMO→LUMO 95.3

HOMO-3 → LUMO 89.4

1 2


What about Rh SBH+ with excited state charge transfer? TD-B3LYP artifact?

Rh

Qret = +0.78e

Qprot = -0.78e

DFT artifacts?

Similar charge-density distribution upon photoexcitation at B3LYP and BHLYP-levels

BHLYP/ES2

467 nm (0.08) 309 nm (0.02)

However, excitation energy shifts is blueshifted, possible CT problem ADC(2): 302 nm (0.32)

B3LYP/ES2

DFT artifacts?

ADC(2) calculations predict 25.5% orbital contributions from Trp-265 orbitals

Orbitals @ ADC(2) |c|2 HOMO-3 → LUMO 64.6 HOMO-1 →LUMO 25.5

Charge transfer to rhodopsin might be a ”real” effect

DFT artifacts?

Conformational vs. electrostatic tuning?

Approach:

Chromophore optimized in protein

Chromophore fixed in protein conformation

Chromophore optimized in gas-phase

“Electrostatic” “Strain”


Constructing a thermodynamic cycle

Electrostatics: 59.0-47.3 kcal/mol = 11.7 kcal/mol (protein blueshifts)

Vacuum

Energies in kcal/mol (eV)


Constructing a thermodynamic cycle

Vacuum

Electrostatics: 59.0-47.3 kcal/mol = 11.7 kcal/mol (protein blueshifts) Strain: 47.3-51.8 kcal/mol = -4.5 kcal/mol (protein redshifts)


BC Rh Electrostatic: 11.7 kcal/mol (0.51 eV) 8.0 kcal/mol (0.35 eV) Strain: -4.5 kcal/mol (0.20 eV) -1.5 kcal/mol (0.07 eV)


BC Rh Electrostatic: -4.8 kcal/mol (0.21 eV) -4.9 kcal/mol (0.21 eV) Strain: -0.4 kcal/mol (0.02 eV) -2.2 kcal/mol (0.10 eV)


Electrostatic effects blueshift SBH+ by ~8-12 kcal/mol (TDDFT) ~19 kcal/mol at ADC(2) level

Electrostatic effects redshift SB by ~5 kcal/mol (TDDFT) ~6 kcal/mol at ADC(2) level

Strain effects redshift SBH+ by ~2-5 kcal/mol (TDDFT) ~2-3 kcal/mol at ADC(2) level Strain effects redshift SB by ~0.4-2 kcal/mol (TDDFT) ~0.5-3.5 kcal/mol at ADC(2) level

Electrostatics: 70-80% Strain: 20-30%

Blueshift the bluecone pigment?

TDDFT calculations suggest that the blueshift in BC might be caused by a deprotonted Schiff base: 485 nm (SBH+)

441 nm (SB)

ADC(2) calculations: 423 nm (SBH+) 372 nm (SB)

TDDFT shift: 44 nm ADC(2) shift: 51 nm

Absolute spectra support SB for TDDFT and SBH+ for ADC(2) Exp. 414 nm

What happens upon relaxation of the excited state?

Excited state structure

The excited state structure

Smaller BLA → single bonded character → easier for isomerization?

Almost no change in dihedral angle (C10-C11-C12-C13) ~ 2 degrees


Thermal activation of rhodopsin is also possible

Dark-activation barrier comparable to the photon energy (ca. 60 kcal/mol) or early photo-intermediates (ca. 40 kcal/mol)?

Ea ~ 23 kcal mol-1

Baylor et al. 1980


Energy relaxation of the excited state ca. 30 kcal mol-1

Large scale TD-DFT cluster calculations correctly predict that the protein environment blueshifts the absorption spectra of retinal

Summary I

TD-DFT and ADC(2) calculation suggest that deprotonation of retinal in protein blushifts the absorption maximum by ca. 50 nm

Mechanism of spectral tuning: Electrostatics: 70-80% Strain: 20-30%

(Supported at both TD-B3LYP and ADC(2) levels)

Absolute TD-B3LYP spectra: Rh Glu-/SBH+ 491 nm (exp. 498 nm ) BC GluH/SB 441 nm (exp. 414 nm )

Absolute ADC(2) spectra: Rh Glu-/SBH+ 430 nm (exp. 498 nm ) BC Glu-/SBH+ 420 nm (exp. 414 nm )

Benefits and drawbacks with TD-DFT

Summary II

+ Large-scale cluster modeling possible - Charge-transfer problems

Low-order coupled-cluster method increasingly applicable for biomolecular simulations

Restricted virtual space approimation Laplace transformed SOS-CC2 ADC(2)

Acknowledgements

Dr. Robert Send BASF Germany

EMBO – Long Term Fellowship

Biowulf clusters at NIH and Center of Scientific Computing (CSC), Finland

Helsinki Bioenergetics Group, University of Helsinki

Department of Chemistry, University of Helsinki

Laboratory of Chemical Physics, US National Institutes of Health

Prof. Dage Sundholm Department of Chemistry, Uni. Helsinki, Finland

quantum chemical modeling of photoexcitations in biology · quantum chemical modeling of...

Documents