3.1 After a photon is absorbed #
3.1.1 The Jablonski scheme #
Most organic molecules have a singlet ground state S₀. Absorption, in about 10⁻¹⁵ s, promotes the molecule to S₁ or S₂. Vibrational energy leaves into the solvent in about 10⁻¹² s, and any S₂ population converts to S₁ by internal conversion. Emission therefore almost always leaves from the lowest vibrational level of S₁. That regularity is Kasha’s rule: the shape of the emission spectrum usually does not depend on the exciting wavelength, provided the same electronic state is reached.
Fret Jablonski
From S₁ three paths compete. Fluorescence is the radiative return to S₀, spin-allowed, typically nanoseconds. Internal conversion returns the energy as heat. Intersystem crossing flips a spin and populates the triplet T₁. Phosphorescence, the return from T₁ to S₀, is spin-forbidden and slow, microseconds to seconds, and in aerated solution at room temperature the triplet is usually quenched before it emits. Room-temperature biological fluorescence is a singlet experiment. A bright fluorophore is not simply one that absorbs. It is one whose radiative path wins.
Fret-Jablonski
3.1.2 Quantum yield, lifetime, and the Stokes shift #
The quantum yield is the fraction of absorbed photons re-emitted:
Φ = k_r / (k_r + k_nr)
where k_r is the radiative rate constant and k_nr is the sum of every non-radiative rate, including quenching. The lifetime is τ = 1 / (k_r + k_nr). A new non-radiative path lowers both Φ and τ. Brightness in an experiment is εΦ, so a dye that absorbs intensely and wastes the energy as heat can be dimmer than a dye with modest ε and Φ near 1. Tryptophan in water sits toward the low end, with Φ often well below 0.2, and that value swings widely inside a protein.
The Stokes shift is the gap between the absorption maximum and the emission maximum. Vibrational relaxation has already shed energy as heat, and the solvent reorganises around the excited-state dipole, lowering that state before the photon leaves. Emission is therefore at longer wavelength than absorption. A large shift lets filters reject the exciting beam. A small shift lets excitation leak into the emission channel and look exactly like fluorescence. The shift is set by the fluorophore and the polarity of its surroundings, not by the slit widths.
3.1.3 Intrinsic fluorophores and the environment #
Tryptophan absorbs near 280 nm and, in water, emits near 350 nm. Buried in a non-polar core, the emission typically moves toward 320–330 nm and the yield usually rises. Nearby disulphides, protonated histidine, and electron acceptors quench it. A change in tryptophan fluorescence means the local environment of that side chain changed. It does not, alone, mean the global fold changed, and several tryptophans report only a sum. NADH and flavins are the main autofluorescence of cells, useful as a metabolic signal and troublesome under a label. Dyes such as ANS fluoresce weakly in water and strongly in non-polar pockets.
The inner-filter artefact sits underneath. If the sample absorbs a large fraction of the exciting light, the beam never reaches the centre of the cuvette, and emitted light can be reabsorbed on the way out. Intensity then stops rising linearly with concentration. Dilute samples keep the reading inside the range where it reports concentration and quantum yield rather than optical thickness.
3.2 Quenching and distance #
3.2.1 Collisional and static quenching #
Collisional quenching is a collision during the lifetime that opens an extra non-radiative path. The Stern–Volmer relation is
F₀ / F = 1 + k_q τ₀ [Q]
F₀ and F are intensities without and with quencher, [Q] is quencher concentration, τ₀ is the unquenched lifetime, and k_q is the bimolecular rate constant. Intensity falls and the lifetime falls in proportion. Higher temperature usually increases collisional quenching because encounters are more frequent.
Static quenching is a non-fluorescent ground-state complex. Intensity falls because fewer free fluorophores absorb, but the lifetime of those that remain is unchanged, and the absorption spectrum often changes. Higher temperature often weakens static quenching by dissociating the complex. If τ falls with F, the quenching is dynamic. If τ is unchanged while F falls, it is static. An upward-curving Stern–Volmer plot usually means both. Treating every dark molecule as a binding complex confuses the two.
3.2.2 FRET and the Förster radius #
Förster resonance energy transfer is a non-radiative, dipole–dipole hand-off from a donor fluorophore to an acceptor chromophore. It is not the donor emitting a photon that the acceptor then absorbs; that trivial reabsorption has a different dependence on geometry. Transfer needs spectral overlap between donor emission and acceptor absorption, a useful donor quantum yield, and transition dipoles that are neither too far apart nor unhelpfully oriented.
Fret Paths
E = 1 / (1 + (r / R₀)⁶)
r is the distance between the dipoles and R₀, the Förster radius, is the distance at which E = 0.5. R₀ gathers the overlap, the donor quantum yield, the refractive index, and an orientation factor κ². Efficiency is also E = 1 − τ_DA/τ_D, which is less confused by concentration than a raw intensity ratio.
The sixth power packs almost all of the change in E into a band around R₀. At r = R₀, E = 0.5. At r = 2 R₀, (r/R₀)⁶ = 64 and E falls to about 0.015. At r = 0.5 R₀, E is already above 0.98. For the dye pairs used on proteins, that informative band is about 2–10 nm: the width of a protein or a complex, not a bond length and not a cell. Anything that changes R₀ — spectra, donor yield, or orientation — changes E at fixed r.
κ² equals 2/3 only if both dipoles randomise quickly relative to the lifetime. Fixed dyes can take κ² from 0 (perpendicular, no transfer) to 4 (collinear). A distance calculated with 2/3 is then wrong, and a change in E may be an angle rather than a distance. High fluorescence anisotropy means the fluorophore did not tumble during the excited state, so the isotropic assumption is unsafe. FRET is a ruler with a stated assumption about orientation.
3.2.3 Genetically encoded fluorophores #
Green fluorescent protein from Aequorea victoria folds as a β-barrel whose chromophore forms autocatalytically from serine–tyrosine–glycine at residues 65–67. The barrel holds that chromophore rigid and is required for the fluorescence. Mutation shifts the spectra, the pH sensitivity, and, in some variants, makes the protein photoactivatable. Shimomura isolated the protein, Chalfie showed that other organisms can make it from the gene, and Tsien developed much of the colour range.
In this course these proteins are fluorophores a cell can be instructed to make, with a defined spectrum, ε, and Φ. They are about 27 kDa, so the label is not a point, and they photobleach. Cell Biology owns their use in imaging. FRET between colour variants is the same sixth-power physics as for a small dye, including the κ² caveat.
3.3 Infrared and Raman #
3.3.1 Dipole and polarisability #
A vibration absorbs infrared light if the dipole changes. Carbonyl, O–H, N–H, and phosphate stretches are strong. It appears in the Raman spectrum if the polarisability changes, so symmetrical stretches of less polar bonds are often strong in Raman and weak in the infrared. The wavenumber of a stretch behaves approximately as a Hooke’s-law oscillator,
ν̄ = (1 / 2πc) √(k / μ)
where k is the force constant, μ the reduced mass, and c the speed of light. Stiffer bonds and lighter atoms vibrate higher, which is why C–H and O–H stretches lie near and above 3000 cm⁻¹. In a protein a shift of tens of cm⁻¹ usually means hydrogen bonding or the local dielectric has changed k. A shift of 1 cm⁻¹ needs a repeated spectrum before it is interpreted.
3.3.2 The amide I band #
Amide I, about 1600–1700 cm⁻¹, is mainly the peptide C=O stretch. Helices often lie near 1650 cm⁻¹ and sheets often lower, toward 1620–1640 cm⁻¹, with turns and unordered chain in the same window. The bands are broader than the gaps between them. A secondary-structure fraction from curve fitting is not unique, for the same reason a far-ultraviolet CD decomposition is not unique. Amide II, near 1550 cm⁻¹, mixes N–H bending and C–N stretching and shifts on deuteration. Amide III, about 1200–1300 cm⁻¹, is stronger in Raman. A protected amide that fails to shift has not exchanged. Structural Biology reads protection patterns; the measurement here is the frequency change.
Resonance Raman is the selective version. A laser tuned to a haem, retinal, or flavin absorption enhances that chromophore’s vibrations by orders of magnitude and the rest of the protein drops out. Fluorescence is the practical enemy, because emission is far brighter than Raman scatter. A longer-wavelength laser usually reduces fluorescence and also reduces Raman intensity, which scales roughly as 1/λ⁴.
3.3.3 Why water defeats transmission infrared #
The water bend near 1640 cm⁻¹ overwhelms a millimolar protein in any centimetre cell. Three arrangements follow from that absorbance, and none is a recipe for a particular protein. The path can be shortened to micrometres. The beam can meet the sample as an evanescent wave at a high-refractive-index crystal (attenuated total reflectance), penetrating on the order of a micrometre. Or the solvent can be D₂O, whose bend has moved, at the cost of deuterating exchangeable protons and slightly shifting the amide bands themselves. Raman sidesteps most of this because water is a weak Raman scatterer, at the price of a weaker signal and fluorescence background. A Fourier-transform infrared instrument records all wavelengths at once through a Michelson interferometer. The gain is throughput. The transform does not remove water’s absorbance.
Surface plasmon resonance also shines light at a surface and records a dip in reflectance when bound mass changes the refractive index. That is a binding measurement, treated in Chapter 7, not a vibrational spectrum.
3.4 Key terms, summary, and self-check #
Key terms. Jablonski scheme; internal conversion; intersystem crossing; quantum yield; lifetime; Stokes shift; Stern–Volmer constant; Förster radius; κ²; amide I; attenuated total reflectance.
Summary. An absorbed photon returns as fluorescence, as heat, or, after a spin flip, as phosphorescence, and the quantum yield is the radiative share. Collisional quenching shortens the lifetime; static quenching does not. FRET efficiency falls with the sixth power of distance and is informative only within about 2–10 nm, and only if orientation is accounted for. Infrared and Raman report vibrations under complementary selection rules; water’s bend buries amide I in transmission infrared and is a minor nuisance in Raman.
Self-check.
1. Why does emission almost always leave from S₁, and why is the emitted photon of lower energy than the absorbed one?
2. A quencher lowers intensity but not lifetime. Which mechanism is that, and what should a higher temperature do to it?
3. For R₀ = 5 nm, what is E at 5 nm and, approximately, at 10 nm? Why is 50 nm invisible to FRET?
4. Why is κ² = 2/3 an assumption, and what does a high anisotropy say about it?
5. Why is a 1 cm aqueous sample incompatible with transmission amide I, and which of infrared or Raman is less troubled by water?
