Energy Transfer Processes

Question 1

Exciton

Definition

Answer 1

• an excited state can be considered to be a particle, an exciton, comprised of a linked electron-hole pair
• this exciton can be transferred from one molecule to another molecule WITHOUT radiation of a photon
• this is sometimes called transfer of a virtual photon
• the exciton can also be delocalised, spreading the exciton across the chlorophyll
• this makes energy transfer (across some distance easier)

Question 2

Forster Resonance Energy Transfer

Description

Answer 2

• non-radiative transfer of energy based on two molecules being physically close to each other
• the dipole oscillation associated with de-excitation in molecule 1 is coupled at close range to sympathetic oscillation in molecule 2
• this leads to excitation of molecule 2

Question 3

What does the rate of energy transfer between two pigments, ket, depend on?

Answer 3

• energetic overlap between the 2 pigments
• dipole-dipole coupling which includes:
• -relative orientation of 2 pigments (dipoles)
• -separation distance between pigments

Question 4

Fermi’s Golden Rule

General Case

Answer 4

kif = 2π/ħ |Vif|² δ(Ei-Ef)

• kif describes the rate of transition from one energy eigenstate to another in a continuum as a result of weak perturbation
• rate is proportional to the strength of coupling between initial and final states, V, and the density of states, related to δ

Question 5

Fermi’s Golden Rule

FRET

Answer 5

-exciton donor - acceptor is a quantum system where electromagnetic states are weak perturbations of the system:
ket = 2π/ħ |Vda|² δ(Ed-Ea)
-due to vibrational motion of the environment, replace δ with overlap between donor and acceptor spectra, J, which represents possible energy states:
ket = 2π/ħ |Vda|² Jda

Question 6

FRET

Spectral Overlap Integral

Answer 6

Jda = ∫ fd(E) εa(E) dE

• integrate from 0 to ∞
• where fd(E) is the fluorescence emission spectrum of the donor and εa(E) is the absorption spectrum of the acceptor
• J is in units of inverse energy

Question 7

FRET

Interaction Energy

Answer 7

-Vda is the interaction energy, in our system this is the dipole-dipole coupling
-the Coulombic interaction simplifies to:
Vda = keμdμa*κ / rda³
-where ke is the Coulomb constant
-μd and μa is the transition dipole strength of the donor or acceptor units
-κ accounts for the effect of orientation of energy transfer, it is averaged over all possible orientations of the dipoles givining κ²=2/3 if isotropic
-rda is the spatial separation between donor and acceptor

Question 8

Complete FRET Equation

Answer 8

-sub in expression for Vda and Jda:

ket = 2πke²/ħ * μd²*μa²/rda^6 * κ² * ∫ fd(E) εa(E) dE

Question 9

FRET Rate in Terms of Donor Excited State Lifetime

Answer 9

ket(r) = 1/τf * (Ro/r)^6

• where τf is the lifetime of the donor’s excited state in the absence of the aceptor
• r=rda, the interpigment distance between donor and acceptor
• Ro is the interpigment distance at which energy transfer probability is 50%

Question 10

FRET Rate in Terms of Donor Fluorescene Decay Rate

Answer 10

ket(r) = k_(f+nr) * (Ro/r)^6

• where k_(f+nr) is the combined decay rate of the donor excited state in the absence of the acceptor
• r=rda, the interpigment distance between donor and acceptor
• Ro is the interpigment distance at which energy transfer probability is 50%

Question 11

Forster Radius

Answer 11

-Ro is known as the Forster radius
-it is the inter-pigment distance at which energy transfer efficiency is 50%
Ro = (2πke²/ħ * μd²μa²κ²τfJda)^(1/6)

Question 12

FRET

Dependence on Distance

Answer 12

• rate of energy transfer has inverse sixth-power dependence on donor-acceptor separation r
• until the model breaks down at very short distances
• model predicts ket->∞ as r->0, which is not correct
• FRET gets less accurate for r<1nm and then breaks down dues to overlap of orbitals, repulsion etc.

Question 13

FRET

Efficiency

Answer 13

-efficiency of resonance energy transfer is the rate of energy transfer as a fraction fo the combined decay rates:
E = ket / (kf + ket + knr)

Question 14

FRET

Efficiency Dependence on Distance

Answer 14

E(r) = 1 / [1 + (r/Ro)^6]
= Ro^6 / [Ro^6 + r^6]
-so efficiency is 50% at Ro and changes deramatically at r slightly above/below this

Question 15

How can we calculate expected efficiency?

Answer 15

1) measure and analyse the spectral overlap of the donor and acceptor from steady-state spectroscopy to calculate Jda
2) measure τf from time-resolved spectroscopy of the donor molecule
3) assume κ²=2/3
4) calculate Forster radius Ro, this assumes you also know μd & μa
5) then calculate E(r)
6) compare with experiments on the donors and acceptors together and in different situations to test hypotheses

Question 16

How is FRET related to photosynthesis?

Answer 16

-the aim of photosynthesis is to maximise FRET efficiency between chlorophyll pigments

Question 17

Chlorophyll Chemical Structure and Delocalisation

Answer 17

• the structure of alternating double-bonds in a chlorophyll molecule leads to sharing of π-orbitals (hybridisation) across the macrocycle ring
• i.e. the π-electrons are delocalised across the molecule
• this allows the excited state to also delocalise, an advantage for transfering this energy across space, as delocalisation spreads this across a molecule

Question 18

Goal of an Antenna of Chlorophyll

Answer 18

i) chlorophyll π-bond network delocalisation spreads excitation energy beyond one atom, over ~1nm
ii) FRET is possible in single steps of 1-10nm; each chlorophyll should be close to the next one
iii) could assemble network of many chlorophylls - then by multiple FRET steps energy could hop across the system spreading out across tens or hundreds of nms
iv) this is the concept of an antenna/satellite of pigments to absorb photons and transfer excitons to where they are needed

Question 19

Antenna’s and Energy Collection

Answer 19

• the majority of pigments serve as an antenna within ‘Light Harvesting’ proteins
• they absorb photons and efficiently transfer (electronic) energy towards Reaction Centre (RC) proteins

Question 20

Absorption Cross-Section

Answer 20

σ(λ)
-if concentration is constant:
A(λ) ∝ ε(λ) ∝ σ(λ)
-can consider a spectral range:
∫ σ(λ) dλ
-integrate over spectral range

Question 21

What do light harvesting antenna polypeptides determine?

Answer 21

• the specific binding of the pigment molecules (type, number position, distance, orientation, pigment-pigment interactions for energy transfer - magnitude of absorbance, spectral shape and FRET
• the specific polypeptide environment of the pigments which tunes the site energies of the pigments - modulating absorption spectra
• the structural organisation of the pigment-protein complexes which determines the intramolecular organisation of polypeptides within the complex and intermolecular organisation of the complexes on the basis of protein-protein interactions

Question 22

What features should light harvesting proteins have to be effective at energy absorption and transfer?

Answer 22

• large spectral range - multiple broad absorption bands and different types of pigment
• high pigment concentration - closely packed together, <0.5Ro
• wide spatial cross-section - 10-100 pigment-protein complexes forming networks 50-300nm across
• minimise loss of excitation energy as heat and flourescence - well connected complexes
• modularity - assemble more antennae in low light, reduce the number in high light

Question 23

Which pigments do different organisms use for photosynthesis?

Answer 23

• plant & algae - Chlorophyll A, Chlorophyll B and carotenoids
• green and purple bacteria - bacteriochlorophyll and carotenoids

Question 24

What are the difference between types of chlorophyll and other pigments?

Answer 24

-the chemcial differences include different levels of pi-conjugation, different polar groups and lead to major shifts in the spectra

Question 25

Light Harvesting Complexes in Purple Bacteria

Answer 25

• Reaction centre surrounded by LH1 antenna which is in a ring shape around the RC
• LH2 antenna, also ring shaped, clustered around the LH1 antenna

Question 26

Purple Bacteria

Structure of LH2

Answer 26

• specific amino acids non-covalently bind the bacteriochlorophylls, arranging them into two concentric ring arrangements of overlapping, aligned pigment molecules
• 18 B850 BChls form an overlapping ring sandwiched between the inner LH2 α and the outer LH2 β transmembrane polypeptides
• the 9 B800 BChls lie towards the cytoplasmic face of the membrane, and almost parallel with the membrane slightly more towards the periphary, with greater separation between each pigment
• nine membrane-spanning carotenoids making close (<0.35nm) contacts with both the B850 and B800 BChls

Question 27

Purple Bacteria

Effect of Binding in LH2 Complex on BChl

Answer 27

• interactions between BChl and the amino acids in the LH2 structure alter its absorption spectrum
• this causes red shift to the BChl Qy transition

Question 28

Purple Bacteria

Effect of Binding in LH2 Complex on Carotenoids

Question 29

Purple Bacteria

FRET Between Different Pigments

Answer 29

• Electronic transitions can happen within each carotenoid, B800 and B850
• transitions also occur between pigment types
• S2 in carotenoid to Qx in B800 or Qx in B850
• S1 in carotenoid to Qy in B800 or Qy in B850

Question 30

Purple Bacteria

B800-B800

Answer 30

• the average distance is ~2.1nm

- energy transfer times of 1-3ps

Question 31

Purple Bacteria

B800-B850

Answer 31

• the average distance is 1.8nm

- energy transfer times of <1ps

Question 32

Purple Bacteria

B850-B850

Answer 32

• very close pigments, separation ~0.9nm

- energy transfer times of «1ps

Question 33

Purple Bacteria

Crt-BChl

Answer 33

• as the Crt molecules snake through the complex, very close contacts (0.3-0.5nm) are made with both B800 and B850
• extrememly rapid and efficient transfer «1ps

Question 34

What is the overall effect of all interactions within and between LH proteins?

Answer 34

• they allow the antenna system to work by:
• -increasing the spectral width of the antenna using different types of pigments and tuning the absorbance characteristics further by pigment-pigment and pigment-protein interactions
• -having an extensive network of repeating units that can be made smaller or larger depending on the amount of light available
• -making sure that the whole system forms an energy trap so harvested energy migrates to the RC, e.g. in purple bacteria highest energy pigments at the periphary and harvested energy migrates ‘downhill’ to where the RC is located

Question 35

Typical τf for Chl

Answer 35

5ns

Question 36

Typical φf for Chl

Answer 36

30%