Biological Spectroscopy

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Biological Spectroscopy

• Absorption
• (Einstein coefficients for absorption, stimulated
  emission, spontaneous emission, transition
  dipole, symmetry, linear dichroism, Franck-Condon
  principle, line broadening)
• Time-resolved absorption spectroscopy
• (ultrashort laser pulses, modelocking, pump-probe
  spectrsocopy, early events in vision and
  photosynthesis)
• Fluorescence
• (radiationless decay, fluorescence lifetime,
  polarized fluorescence, depolarization due to
  molecular dynamicssingle molecule fluorescence,
  resonance energy transfer, photosynthetic
  light-harvesting

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Light, Spectrum and Absorption
f
I0(n)
l
I(n)
I0(n)
C concentration
i
Beer-Lamberts law
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Absorption
When a beam of light impinges on a sample of
(bio)molecules, part of the light may be
absorbed, the precise amount depending on the
wavelength. For instance, chlorophyll, the
pigment of plants displays two major transitions
around 670 nm (red) and 430 nm (blue). In
addition several weaker transitions are visible.
The quantity that determines the probability of a
transition to take place is the transition dipole
moment
For a single molecule
Where is a lineshape function
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The transition dipoles of chlorophyll
The transition dipole , which determines
the probability of a light-induced transition
between two energy levels, has a well-defined
orientation in the molecular frame. can
be calculated if the molecular wavefunctions are
known, and experimentally obtained from polarized
spectroscopic experiments on crystals
670nm
630nm
Chlorophyll a
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The Einstein Coefficients
Thermal equilibrium
When the light field interacts with
the molecular system, here represented as a
2-level system, three processes can be induced
stimulated absorption, stimulated emission and
spontaneous emission. The first two only operate
in the presence of the light, spontaneous
emission also in the dark. Spontaneous emission
is responsible for the return to thermal
equilibrium in the dark.
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Relating the dipole strength to the absorption
properties of a molecule
Then it follows
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Vibronic transitions
For a (bio)molecule the vibronic wave- function
is given by
Electrons
Nuclei
Light induces transitions between vibronic states
of the molecule. These transitions are
vertical, because the nuclei do not move on the
timescale of the transition. For a vibronic
transition the transition dipole is
With the dipole moment operator. For
only dependent on r, the transition dipole has
the following form
f
Electronic transition dipole
Franck-Condon factor
Note that the transition probability form the
lowest vibronic level to one of the vibronic
levels of the excited state depends on the
overlap between the ground state and shifted
excited state vibrational wavefunctions.
i
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Selection rules for electronic transitions in a
simple molecule formaldehyde
Formaldehyde, CH2O, is a small molecule, the
C-atom is sp2-hybridized (2px, 2py, 2s), the
O-atom is sp-hybridized (2px, 2s). Two of the
C-sp2 hybrids are used to form s-bonds with the
1s AOs of the H-atoms the third C-sp2 hybrid
forms a s-bond with one of the O-sp hybrids. A
p-MO is formed between the 2pz of C and the 2pz
of O and both C and O add one electron to this
p-MO. The remaining electrons of the O-atom are
in O-1s (2 el), the other O-sp hybrid (2el) and
the O-2py (2el). Thus the final electronic
configuration for formaldehyde is
(1sO)2.(1sC)2.(s1sH,sp2C)2. (s1sH,sp2C)2.(ssp2C,s
pO)2.(spO)2.(spy,O)2.(p2pzC,2pzO)2. The electron
pairs in spO and spy,O are called non-bonding
(symbol n) the electrons do not participate in
the covalent structure of the molecule. The upper
energy levels of the molecule are p and n. The
lowest unoccupied molecular orbital (LUMO) is p.
Electronic transitions may occur between p and p
and n and p. Symmetry considerations show that
only p-gtp transitions can occur and that these
transitions are polarized along the x-axis of the
molecule
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Formaldehyde
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Symmetry forbidden transitions
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Linear dichroism (1)
Since the transition dipole moment has a well
defined and known orientation in the frame of the
molecule, one can use polarized light to find out
how (bio)molecules and even complex molecular
aggregates are organized in space. Suppose you
have a DNA molecule and suppose that it would be
possible to measure the absorption of this DNA
molecule with a light beam that is polarized
parallel to the helix axis and with a lightbeam
that is polarized perpendicular to the helix
axis. In case the DNA bases are truly
perpendicular to the helix axis, the first beam
would be transmitted for 100, while the second
beam would be partially absorbed. This is due to
the fact that the transition dipoles of all the
DNA bases are in the plane of the base, and
consequently perpendicular to the helix axis. In
a sample that contains a random distribution of
DNA molecules this effect would be lost, because
DNA molecules occur with all possible
orientations. However, if one would be able to
orient the DNA molecules in some known manner,
then, depending on how well one could orient the
DNA molecules, a difference in the absorption
between light polarized parallel and light
polarized perpendicular to some orientation axis
would be measured. This phenomenon is called
linear dichroism and the amount of linear
dichroism is a direct measure for the three
dimensional structure of a biomolecule containing
light absorbing groups. DNA can be oriented in
many ways. One can apply an electric field and
the DNA will orient along the electric field
lines, largely due to a large induced dipole
moment, DNA can be oriented in a hydrodynamic
flow, DNA can be oriented in a compressed gel,
etc.
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Linear dichroism (2)
Perfectly oriented DNA
Epar
Eperp
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Linear Dichroism (5)
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Linear Dichroism (3) How to orient biomolecules?
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Linear Dichroism (4)
The amount of absorption for light incident along
the y-axis and polarized along the x-axis is
given by
In case there is no net order in the system
Then
With Aiso the absorption of an isotropic sample
measured with unpolarized light.
With the light incident along the y-axis we can
define the amount of dichroism as
And the reduced dichroism as
For a disordered sample we find of course
,while for a
sample with all the transition dipoles perfectly
oriented along the z-axis we find
Thus LDr is the quantity of interest and contains
the information about the molecule that is being
studied. In principle the angle between the
transition dipole and the symmetry-axis of the
particle can be obtained. The unknown parameter
is the degree of orientation, for which some
model must be developed.
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Linear Dichroism Perfectly ordered rods (6)
z
m12
We have a sample of perfectly ordered rod-shaped
molecules. The molecules contain one coloured
group, a chromophore, which has its transition
dipole m12 at an angle q with the long axis of
the molecule.
q
m12
q
q
m12
x
j
y
Then we have
Thus, for the reduced linear dichroism
Note that there exists an angle qM for which
LDr0, in spite of the fact that the sample is
perfectly ordered!!

or
The magic angle
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Linear Dichroism (6) The a-helix
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Elements of secundary structure the a-helix
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Linear Dichroism (7) The degree of orientation
In general one can not obtain a perfect
orientation of the molecule under study. For
instance in a pressed gel one typically reaches
about 10-20, DNA in a flow cell gt50, membranes
spread out on a surface 30 etc. In that case it
is useful to define a function F which represents
the degree of orientation and investigate by
independent means how large F is. In general we
have In which lt....gt indicates the
averaging of the angles that occur in one
particle, and F is a function that rangs between
0 (no orientation) and 1 (perfect
orientation). An example for a gel which is
compressed in both the x and y direction with a
factor and expands in the z-direction with
a factor n one can derive that
For instance, gels can be compressed so much
that their length in the z-axis increases by
about a factor of 2.
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The Franck-Condon Principle
According to the Franck-Condon principle, the
most intense vibronic transition is from the
ground vibrational state to the vibrational state
lying vertically above it. Transitions to other
vibrational levels also occur but with lower
intensity
In the QM version of the FC-principle, the
molecule undergoes a transition to the upper
vibrational state that most closely resembles
the vibrational wavefunction of the vibrational
ground state of the lower electronic state. The
two wavefunctions shown herehave the greatest
overlap integral of all the vibrational states of
the upper electronic state
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The Franck-Condon Principle (2)
The overall state of the molecule consists of an
electronic part, , and a vibrational part,
. Therefore, within the Born-Oppenheimer
approximation, the transition dipole moment
factorizes as follows
The second term on the right of the second row is
zero, because for two
different electronic states (they are
orthogonal). Therefore,
The matrix element is the
electronic transition dipole moment. The factor
is the overlap
integral between the vibrational state
in the initial electronic state of the
molecule, and the vibrational state in
the final state of the molecule.
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Calculating a Franck-Condon factor
Consider the transition from one electronic state
to another, their equilibrium bond lengths being
and and their force constants equal.
To calculate the Franck-Condon factor for the 0-0
transition, we need to calculate the overlap
integral of the two ground-state
vibrational wavefunctions, and then take its
square. We will use the harmonic oscillator
wavefunctions.
Then
Note The FC-factor equals 1 when
And the Franck-Condon factor is
And decreases as the equilibrium bond lengths
diverge
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Line broadening
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Line broadening (2)
Spectral lines are not infinitely narrow, but
show a certain width. A large variety of
phenomena contribute to the observed linewidths.
In principle we distinguish homogeneous and
inhomogeneous broadening. In the first case all
molecules that contribute to the absorption line
suffer from the same broadening. In the second
case different molecules absorb at slightly
different frequencies due to small variations in
their direct environment
For the homogeneous contribution to the linewidth
we have
T1Excited state lifetime
T2pure dephasing time
For the inhomogeneous contribution the
transition frequencies are taken from some
distribution Inhomogeneous distribution function
(IDF)
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LH2 is a disordered excitonically coupled ring
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Time-resolved spectroscopy
Isomerisation of Retinal in Rhodopsin Excitation
Energy Transfer in photosynthesis Electron
Transfer in Photosynthesis Proton Transfer
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The Primary Donor in Bacterial Reaction Centers
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Dispersed Pump-Probe
Experimental Setup

• Measure pump induced changes in the sample
• Energy Transfer
• Reaction Dynamics
• Internal Conversion
• Intersystem Crossing
• Solvation Dynamics
• Vibrational Relaxation
• Proton Transfer
• Electron Transfer

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Amplified TiSapphire Laser
1 mJ 40 fs 3khz
NOPA

Sapphire
1 mm 3 fs
Optical Delay Line
Spinning cell

Grating
Diode Array
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Modelocking (1)
Many laser modes are amplified simultaneously
spectrally broad gain medium (dye, TiSapph)
All the modes are forced in phase. In reality
the only stable way for the laser to operate is
in a pulsed fashion
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Modelocking (2)
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Schematic of the organization of the
photosynthetic units. Based on the X-ray
structures of the components.
AFM topography of LH2 on mica in buffer solution.
Scale bar is 5 nm Stahlberg et al. (2001) FEBS
Lett 504, 166
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Normalized one-color isotropic pump-probe
kinetics measured for LH2 of Rs. molischianum at
77K, excitation in the 800 nm region. Note that
the decay of the 800 nm band bleaching is
accompanied by formation of excited-state
absorption (ESA) of the 850 nm band.
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Three Pulse Photon Echo Measures Spectral
Diffusion
k1-k2k3
k2-k1k3
t
T
Coherence time
Population time
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Three Pulse Echo Peak Shift
Maximum of echo not at ? 0 peak shift
frequency grating by pulses 12
frequency changes during T
grating disappears
gt Peak shift decay with T probes

• Vibrational relaxation
• Solvent/protein relaxation
• Underdamped vibrations
• Energy transfer among the same Chlorophylls

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3PEPS B800 Rs. molischianum Rps. acidophila