Energy Transfer Processes Flashcards
Exciton
Definition
- 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)
Forster Resonance Energy Transfer
Description
- 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
What does the rate of energy transfer between two pigments, ket, depend on?
- energetic overlap between the 2 pigments
- dipole-dipole coupling which includes:
- -relative orientation of 2 pigments (dipoles)
- -separation distance between pigments
Fermi’s Golden Rule
General Case
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
Fermi’s Golden Rule
FRET
-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
FRET
Spectral Overlap Integral
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
FRET
Interaction Energy
-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
Complete FRET Equation
-sub in expression for Vda and Jda:
ket = 2πke²/ħ * μd²*μa²/rda^6 * κ² * ∫ fd(E) εa(E) dE
FRET Rate in Terms of Donor Excited State Lifetime
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%
FRET Rate in Terms of Donor Fluorescene Decay Rate
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%
Forster Radius
-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)
FRET
Dependence on Distance
- 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.
FRET
Efficiency
-efficiency of resonance energy transfer is the rate of energy transfer as a fraction fo the combined decay rates:
E = ket / (kf + ket + knr)
FRET
Efficiency Dependence on Distance
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
How can we calculate expected efficiency?
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
How is FRET related to photosynthesis?
-the aim of photosynthesis is to maximise FRET efficiency between chlorophyll pigments
Chlorophyll Chemical Structure and Delocalisation
- 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
Goal of an Antenna of Chlorophyll
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
Antenna’s and Energy Collection
- 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
Absorption Cross-Section
σ(λ) -if concentration is constant: A(λ) ∝ ε(λ) ∝ σ(λ) -can consider a spectral range: ∫ σ(λ) dλ -integrate over spectral range
What do light harvesting antenna polypeptides determine?
- 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
What features should light harvesting proteins have to be effective at energy absorption and transfer?
- 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
Which pigments do different organisms use for photosynthesis?
- plant & algae - Chlorophyll A, Chlorophyll B and carotenoids
- green and purple bacteria - bacteriochlorophyll and carotenoids
What are the difference between types of chlorophyll and other pigments?
-the chemcial differences include different levels of pi-conjugation, different polar groups and lead to major shifts in the spectra
