theory of cd spectroscopy - welcome to the … refractive index • passage of light through any...
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1
Theoretical Studies of
Protein Circular Dichroism
Jonathan Hirst
School of Chemistry
http://comp.chem.nottingham.ac.uk
Theory of CD
Spectroscopy
Outline
• Light + dichroism
• Electronic structure:
– 1
– 2
– Many
• Applications
• Charge transfer (deep-UV)
Let there be light
• Beam of unpolarized
light (viewed end-on)
• Beam of polarized
light (viewed end-on)
To put it planely
• plane polarized light - an
oscillation of the electric field
vector intensity in a plane that
has the same direction of the
beam (red light).
• the intensity of the electric
field vector (magenta) varies
from a positive maximum (t1)
to a negative minimum (t3)
over time.
On the other hand
• Decompose the magenta vector in two green vectors of equal intensity.
• Change in intensity of the magenta electric field vector causes these two green vectorsto rotate in opposite directions round the circumference.
• A beam of polarized light is described by the set of each of the two green vectors along the original plane polarized light direction.
• a plane polarized light can be seen as resulting from a right (clockwise) and left (anticlockwise) circularly polarized beams of light.
2
Refractive index
• Passage of light through any medium is characterized by medium’s refractive index, η
• Optically active compounds have different refractive indices for left and right circularly polarized light
• ηL ≠ ηR
• Leads to a rotation of the plane of polarization
Refractive index
• Passage of light through any medium is characterized by medium’s refractive index, η
• Optically active compounds have different refractive indices for left and right circularly polarized light
• ηL ≠ ηR
• Leads to a rotation of the plane of polarization
Dichroism – two colours (Gk.)
• Linear polarized light
– superposition of opposite
circular polarized light of
equal amplitude and
phase.
• different absorption of
the left- and right-hand
polarized component
– ellipticity (CD)
– optical rotation (OR)
• Actual effect is minute
Ellipticity
• The ratio of the minor to the major axis of the ellipse is the tangent of the angle θ (blue). This angle is called ellipticity; angle OR is called optical rotation.
• θ = 32.98 ∆ε
• To remove the dependence on cuvette path length and solute concentration, use molar ellipticity, defined as:
• [θ] = 100 θ / C l
• where C is the solute molarity and l the cuvette path length. The factor 100 as l in cm.
• Dimensions of molar ellipticity are:
• 100 deg dm3 mol-1 cm-1 = 100 deg cm3/1000 mol-1
cm-1 = deg cm2/10 mol-1 = deg cm2 dmol-1
Traditional electronic absorption spectroscopy
Selection rule: electric dipole allowed and magnetic dipole forbidden or magnetic dipole allowed and electric dipole forbidden
Intensity (oscillator strength, f )
Circular dichroism – differential absorption of left and right circularly polarised light
Selection rule: transitions are electric and magnetic dipole allowed
Intensity (rotational strength, R)
Electric dipole allowed = translation of charge
Magnetic dipole allowed = rotation of charge
Translation + rotation = helix
Circular Dichroism (CD)
2µ∝
mµ∝
Electronic excited states of amides
3
Amide electronic structure
πb
πnb
n’
n
π*
σ*
NO
NO
NO
NO
NO
nπ* transition @ 220 nm
πb
πnb
n’
n
π*
σ*
NO
NO
ππ* transition @ 190 nm
πb
πnb
n’
n
π*
σ*
NO
NO
ππ* transition
• Electric dipole allowed
• Electric transition moment
• Translation of charge
O O O+
+
µ
Molecular orbital diagram
monoamides
Gas phase Condensed phase
Pre-1996
πb
πnb
n’
n
π*σ*
Current
n’πb
πnb
n
Rydberg s/p
π*
Rydberg d
πb
πnb
n
Rydberg
π*
n’
Molecular orbital diagrams
n
πnb
π*
n
πnb
π*
Monomer 1 Monomer 2Dimer
Eππ∗ + V12
Eππ∗ - V12
πb
πnb
n
Rydberg
π*
n’
Monomer
4
Diamide Hamiltonian matrix
=
2
*
22
**
21
**
21
**
22
**
2
*
21
**
21
**
12
**
12
**
1
*
11
**
12
**
12
**
11
**
1
*
ππππππππππππ
πππππππππ
ππππππππππππ
πππππππππ
EVVV
VEVV
VVEV
VVVE
H
nn
nnnnn
nn
nnnnn
Moffitt’s dipole-dipole interaction
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
∑ ∑∫∫ ≈=s t
st
ts
r
rV
12
2
*
1
* ππππ ρρ
Dimer of interacting monomers
• Hamiltonian: kinetic + potential energies
• H = H1 + H2 + V12
• V12 - potential energy of interaction
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
Dimer of interacting monomers
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
µµµµ1 µµµµ2r
mu dot r ?
µµµµ r
θ
00cos)(90
1cos)(0
cos
22
=•⇒=⇒=
=•⇒=⇒=
+=
=•
rlarperpendicu
rrparallel
rrr
rr
yx
µθθ
µµθθ
θµµ
Dimer energies & intensities
• E+ = E0 + V12
• E- = E0 - V12
π* π*
Eππ∗ + V12
Eππ∗ - V12
• D+ = D0 + D0cosθ
• D- = D0 - D0cosθ
• D0 = µ2
Angle
between
dipoles
5
Parallel dimers
N
N
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
V = µ1µ2/r3 – 3µ1rµ2r/r5
V = µ1µ2/r3 – 3µ1µ2/r
3
V = –2µ1µ2/r3 = –2µ2/r3 = –2D0/r
3
D+ = D0 + D0cos0 = 2D0
D- = D0 - D0cos0 = 0
Shift
not split
Stacked dimers
N
N
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
V = µ1µ2/r3 = D0/r
3
D+ = D0 + D0cos0 = 2D0
D- = D0 - D0cos0 = 0
Anti-parallel dimers
N
5
21
3
21 )()(3
r
rr
rV
••−
•=
µµµµ
V = –µ1µ2/r3 + 3µ1rµ2r/r5
V = –µ1µ2/r3 + 3µ1µ2/r
3
V = 2µ1µ2/r3 = 2µ2/r3 = 2D0/r
3
D+ = D0 + D0cos180 = D0 - D0 = 0
D- = D0 - D0cos180 = D0 + D0 = 2D0
Anti-parallel,
stacked dimers
N
Orthogonal,
stacked dimers
N
θ = 90°
Orthogonal,
in-plane dimers
N
Angle between
dipoles is 90°; angle
between dipole and r
is 45°.
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Combinations of monomer ππ* transitions
• In phase combination
– parallel polarisation
• Out-of-phase combination
– perpendicular polarisation
1
2
34
1
Idealised α-helix (1968)
Reproduced in Cantor &
Schimmel
Textbook calculation
Ribonuclease A, Kurapkat et al. (1997)
Don’t trust textbooks
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CD – probe of protein 2° structure
Kemp – peptides with >100% helicity!
Previous
Ab initio
side chains
Errors over 30 proteins
JACS, 1999; JPCB, 2003
Angew Chemie, 2001; Biochemistry, 2004
Protein ECD
Protein ECD
47 proteins
Near-quantitative correlation between calculated & exptl intensity at 222 nm
- Key wavelength, reflecting helix content
- Backbone only
Highly helical, e.g. myoglobin
No helix, e.g. plastocyanin
Kemp – peptides with >100% helicity!
Previous
Ab initio
side chains
Errors over 30 proteins
JACS, 1999; JPCB, 2003
Angew Chemie, 2001; Biochemistry, 2004
Protein ECD
r ~ 0.9
Protein ECD126 excised helices – only possible in silico
“Cooperativity” – residues in longer helices contribute more per residue to [θ]222
End effect – k ~ 3;
Infinite helix [θ]222 ~-40,000
Unfolding a helix by fraying ends reduces [θ]222 less than breaking in the middle
Kemp – peptides with >100% helicity!
Previous
Ab initio
side chains
Errors over 30 proteins
JACS, 1999; JPCB, 2003
Angew Chemie, 2001; Biochemistry, 2004
Protein ECDk ~ 3;
[θ]-inf ~-40000r ~ 0.9
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Kemp – peptides with >100% helicity!
Protein ECD
[θ]222 for infinite helix ~ -40,000
Kemp peptides show -55,000 !?
Exptl conditions (solvent, low T) favour short h-bonds?
Test in silico –build models, compute CD
Variation of computed [θ]222
for different regular helices (310, α and π)
Kemp – peptides with >100% helicity!
Previous
Ab initio
side chains
Errors over 30 proteins
JACS, 1999; JPCB, 2003
Angew Chemie, 2001; Biochemistry, 2004
Protein ECDk ~ 3;
[θ]-inf ~-40000r ~ 0.9
H-bond distance important
Previous
Ab initio
side chains
Errors over 30 proteinsCASSCF/CASPT2 studies of aromatic side chains �parameters for matrix method, which improve accuracy in near-UV
Protein near-UV ECD
Origin of band @165 nm?
• πσ*? nσ*? n’π*?
Matsuo et al. J Biochem (2004) Oakley & Hirst J Am Chem Soc 128 12414 (2006)
Bulheller et al. J Phys Chem B 112 1866 (2008)
Charge Transfer
φ ψN
O
NO
NO
CASSCF/CASPT2 calculations on dipeptides with 10 important geometries from across the Ramachandran plot
Protein deep-UV ECD
Serrano-Andres & Fulscher J Am Chem Soc 1998120, 10912; Tozer et al. Mol Phys 1999, 97, 859
Protein deep-UV ECD
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Charge transfer in the matrix method
Protein deep-UV ECD
Gilbert ATB & Hirst JD J Mol Struct (THEOCHEM) 2004, 675, 53
Protein deep-UV ECD
Correlation between computed and exptl intensity for a set of 71
structurally diverse proteins;
Exptal data from Bonnie Wallace
(Birkbeck)
πnb1-π*2 excitation important in the β-sheet / PP-II region.
N-lobe of the πnb1 orbital and C-lobe of the π*2 orbital are in close proximity.
Key transitions
The n1-π*2 transition occurs at low energy and is fairly strong in the α-helical region.
The n1 orbital and the C-lobe of the π*2 orbital are in close proximity and good alignment.
Protein CD - Summary
• Semi-quantitative – more to
do, but can …
• Probe structure-spectra
relationships computationally
– Helices
– Conformational dynamics
• Sidechains – near UV
• Charge transfer – deep UV
http://comp.chem.nottingham.ac.uk/dichrocalc
Bulheller BM, Rodger A & Hirst JD. Phys Chem Chem Phys, 9, 2020 (2007).
Further reading
• Fasman Circular dichroism and the
conformational analysis of biomolecules
• Charney The molecular basis of optical
activity
• Cantor & Schimmel Biophysical Chemistry
Part II Techniques for the study of
biological structure and function
Acknowledgments
Ben BulhellerLilianna Bryjko