8.1 Resolution and contrast #
8.1.1 The diffraction limit #
Magnification enlarges an image. Resolution decides whether two objects are recorded as two. The Abbe form of the lateral limit is
d โ ฮป / (2 NA), NA = n sin ฮธ
ฮป is wavelength, n the refractive index of the medium between specimen and lens, and ฮธ the half-angle of the cone of light the lens accepts. The Rayleigh form, 0.61 ฮป/NA, is a similar number. For green light near 550 nm and an oil lens of NA about 1.4, d is about 0.2 ยตm. Oil raises n, which is why a dry lens cannot match it. Axial resolution is poorer, typically around half a micrometre. A refractive-index mismatch between an aqueous cell, near 1.33, and an oil lens grows spherical aberration with depth and spoils the axial measurement first. Pixels much larger than about d/2 throw away resolution the lens had captured.
8.1.2 Where contrast comes from #
Cell Biology notes carry the organelle images and the chemistry of stains and fixation. The comparison here is only the origin of contrast.
| Method | Origin of contrast | Quantity in the image | Principal artefact |
|---|---|---|---|
| Bright field | absorption | transmitted amplitude | unstained cells barely absorb and disappear |
| Phase contrast | a phase shift converted to intensity (Zernike) | optical path difference | a halo around thick objects |
| DIC | interference of two close polarised beams | gradient of optical path, not height | birefringent plastic spoils it; not a height map |
| Dark field | only scattered light is collected | presence of a scatterer | detecting a point is not resolving its shape |
| Fluorescence | emission isolated from the excitation by filters | amount of fluorophore, within the limits of Chapter 3 | bleaching, phototoxicity, out-of-focus blur, spectral bleed-through |
Fluorescence makes a chosen molecule bright and everything else dark. The image reports the label. An antibody against the wrong protein, or a fusion that has altered its partner, gives a sharp and wrong localisation. A second method with a different artefact โ another antibody, a deletion, or a fraction with a marker enzyme โ is what turns a pattern into a location.
8.1.3 Confocal sectioning #
A wide-field image of a thick cell adds blurred light from above and below the focal plane. A confocal microscope scans a focused spot and places a pinhole in a conjugate plane so that out-of-focus light is rejected. The gain is an optical section, not a breach of the diffraction limit. A smaller pinhole sections more thinly and discards more photons, until noise dominates. Scanning concentrates light, so bleaching and phototoxicity limit the number of frames.
Two-photon excitation confines the event without a pinhole trick at the detector. Two infrared photons must arrive together, and that rate scales with intensity squared, which is significant only at the focus. Emission is ordinary fluorescence. Infrared excitation scatters less in tissue, so penetration improves. The diffraction limit on the emitted light remains. Two-photon microscopy confines excitation. It is not, by itself, a super-resolution method.
8.2 Measurements that use fluorescence #
The study of Measurements that use fluorescence provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.
Jablonski Of Fluorescence Only
8.2.1 FRET in an image #
The Fรถrster ruler of Chapter 3 applies pixel by pixel, with extra ways to be fooled. Sensitised emission records acceptor fluorescence during donor excitation. Acceptor photobleaching asks whether the donor brightens once the acceptor is destroyed. Lifetime imaging measures the donor lifetime, which shortens on transfer, and is less confused by how many fluorophores sit in the voxel. Donor bleed-through into the acceptor channel, and direct excitation of the acceptor, both imitate proximity. A loss of FRET does not prove two proteins moved apart: the dyes may have rotated, one may have quenched, or the acceptor may have bleached. A gain means r, Rโ, or ฮบยฒ changed, and the experiment has to say which.
Fret-Jablonski
8.2.2 FRAP and diffusion #
After a region is bleached, unbleached molecules move in and fluorescence returns. The mobile fraction is how much of the signal comes back. The rest is immobile on that timescale: bound to a large structure, cross-linked, or trapped in a compartment that does not exchange. The half-time, together with the size and shape of the bleached region, gives a diffusion coefficient. A half-time without the length scale is not a D, and the geometrical factor depends on the bleach profile.
If molecules spend most of their time bound and diffuse quickly between sites, recovery reports the off-rate, not the viscosity. Directed transport has a different curve shape from diffusion. Reversible photobleaching imitates fast diffusion: fluorophores return from a dark state without moving. A fixed sample, in which diffusion is impossible, is the control. Recovery there means the live-cell curve is not a mobility.
8.3 Past the limit, and cells one by one #
8.3.1 Super-resolution classes #
The Abbe limit applies when many fluorophores emit at once in a linear far-field microscope. Super-resolution changes one of those conditions. Betzig, Hell, and Moerner shared the 2014 Nobel prize for the two decisive approaches.
Stimulated emission depletion, from Hell, scans as a confocal microscope does and overlays a doughnut-shaped beam that returns fluorophores to the ground state everywhere except the centre. The emitting spot is smaller than the diffraction spot and shrinks as the depletion beam gets stronger. The cost is intensity and photodamage. Resolution is still the size of the region emitting during that visit of the scan.
Localisation methods switch fluorophores so that each frame contains only isolated diffraction spots. The centre of a spot can be found much more precisely than its width, improving roughly as that width divided by the square root of the number of photons, and worsening if the background is high. A molecule yielding about a thousand photons can be localised to a few nanometres. Many frames are stacked into one reconstruction. PALM and related methods switch fluorescent proteins; STORM and related methods switch organic dyes.
Precision is not the resolution of a structure. Two molecules emitting in the same frame, closer than the diffraction limit, become one misplaced spot. A fluorophore that blinks is counted twice unless the analysis recognises it. Labels must be dense enough to sample the structure, or a filament looks broken however precisely each dye is centred. A primary plus a secondary antibody can place the dye about 10โ15 nm from the epitope. That linkage error is a floor under any biological claim of nanometre resolution.
Structured illumination is the third class. Patterned excitation encodes finer detail into the pass-band of the lens. Linear forms improve resolution about twofold, use ordinary fluorophores, and are gentler. They do not reach the localisation regime. The choice is which assumption the specimen can bear.
8.3.2 Flow cytometry #
A flow cytometer does not make an image. Cells pass a laser one at a time. Forward scatter depends on size but also on refractive index and shape. Side scatter is sensitive to internal complexity. Fluorescence is recorded at chosen wavelengths. Thousands of events per second make a distribution, so a cell at one in a thousand is a cloud, which microscopy would count unfairly. The cytometer cannot say where in the cell the label sat.
Spectral overlap must be compensated or a bright channel paints a false signal into the next. A doublet of two cells looks large and double-positive; pulse width is the usual clue. Intensity is relative unless beads with a known dye load calibrate it. A threshold that ignores debris can also ignore small cells. Sorting deflects droplets that pass a gate; it is the same measurement plus a decision. Cell Biology and Immunology own the markers. The quantity here is scatter and fluorescence per event.
8.4 Key terms, summary, and self-check #
Key terms. Numerical aperture; Abbe limit; phase contrast; DIC; confocal pinhole; two-photon excitation; mobile fraction; STED; localisation precision; linkage error; forward scatter; compensation; doublet.
Summary. Lateral resolution is set by wavelength and numerical aperture and is about 0.2 ยตm at best in a conventional light microscope. Contrast comes from absorption, from a converted phase shift, or from filtered fluorescence. A confocal pinhole rejects out-of-focus light and does not break the diffraction limit. FRAP turns recovery into a mobile fraction and a diffusion coefficient unless dark states or binding dominate. STED shrinks the emitting spot; localisation methods find centres of isolated molecules; neither removes the distance between label and target. Flow cytometry counts scatter and fluorescence and never localises them inside the cell.
Self-check.
1. Two lenses magnify equally, with NA 0.3 and 1.4. Which resolves more, and what second quantity enters the formula?
2. What does a confocal pinhole remove, and why is two-photon excitation not itself super-resolution?
3. Why can two fluorophores 20 nm apart still appear as one object, and why does an antibody impose a further limit?
4. A FRAP curve is fast, and a fixed-cell control recovers too. What does the control expose?
5. Name one way a cytometer reports a double-positive population that is not a double-labelled cell, and state what it cannot say about location.
