Zinc Finger Dna Complex
9.1 Electron microscopes #
9.1.1 TEM and SEM #
Electrons accelerated through 100–300 kV have a de Broglie wavelength of a few picometres. Biological electron microscopy does not reach the resolution that wavelength would allow. Electrons interact strongly, so the specimen must be thin and the column under vacuum, and the same interaction that gives contrast breaks bonds. Dose, not wavelength, is the limit. Lenses are magnetic. Light atoms scatter weakly.
Transmission electron microscopy images electrons that pass through the specimen. Conventional resin sections are about 50–100 nm thick because thicker specimens do not transmit. Scanning electron microscopy scans a surface and collects secondary electrons. The image is topography, the interior is hidden unless the sample is opened, and biological resolution is typically a few nanometres on a dry, conductively coated specimen. Cell Biology owns what stained sections showed about organelles. A stained section is a map of heavy metal in a prepared specimen: membranes look dark because the stain scatters, not because the microscope photographs lipid. Negative stain surrounds an isolated particle with dense salt so the particle appears light in projection. In unstained work a small defocus creates phase contrast and also a contrast-transfer function that passes some spatial frequencies and zeroes others. A raw cryo image looks modulated for that reason, and a data set uses many defocus values so that the missing frequencies can be filled.
9.1.2 Cryo-EM as an average #
Water frozen faster than it crystallises is vitreous ice, and the macromolecule stays hydrated without stain, which is Dubochet’s contribution. The dose must stay low, so each image is noisy. Single-particle analysis aligns large numbers of copies in different orientations and reconstructs a three-dimensional map of the scattering potential. The averaging is the method. One particle is not a structure.
A mixture of conformations, averaged together, blurs or invents a state that never existed. Classification into subsets fails when each subset is too sparse to align. Preferred orientation, particles that sit on the ice in only one or two ways, leaves a missing wedge and an anisotropic map. The air–water interface can unfold particles before they freeze, so the average is of what survived preparation. A resolution quoted as a consistency statistic between halves of the data is not a promise that every side chain is correctly built. Structural Biology judges what the map supports. The measurement statement is that the map is an average of surviving particles, weighted by how they were oriented, at a dose they could tolerate.
9.2 Diffraction #
9.2.1 Bragg’s law #
A crystal scatters X-rays coherently because its molecules repeat. Constructive interference occurs only at angles given by Bragg’s law,
n λ = 2 d sin θ
λ is the X-ray wavelength, d the spacing of a family of planes, θ the glancing angle between the beam and those planes, and n the integer order. The beam is deflected by 2θ. Copper Kα radiation, wavelength 0.154 nm, is comparable to interatomic spacings, so the angles are large enough to measure. Spot position gives the unit-cell geometry. Intensity is the square of the scattered amplitude from that set of planes.
The detector records intensity and does not record phase. Without phases a Fourier map of the electron density cannot be computed. This missing information is the phase problem. Phases are recovered by molecular replacement from a related structure, by anomalous scattering from a heavy atom or from selenomethionine, or by isomorphous replacement. Kendrew’s myoglobin and Perutz’s haemoglobin showed that phased protein diffraction can become an atomic model. Building and judging that model is Structural Biology.
“Resolution” here means the smallest d whose intensities were used. A 3 Å data set is a set of reflections from planes at least 3 Å apart, not a photograph with 3 Å pixels. The crystal averages every unit cell, and the time of the exposure, into the conformation that was able to pack. Contacts can distort loops. Cryocooling slows radiation damage and does not abolish it. The quantity actually measured is a list of intensities.
9.2.2 Solution scattering #
Small-angle X-ray scattering records interference from a macromolecule in solution: a continuous curve, not Bragg spots. With q = (4π/λ) sin θ, and 2θ the angle between the incident beam and the scattered ray, the Guinier approximation at low q is
ln I(q) = ln I(0) − q² R_g² / 3
so the slope of ln I against q² gives the radius of gyration R_g. It holds only while q R_g is small, below about 1.3 for a globular particle. I(0) gives a molar mass if concentration and contrast are known. The wider curve gives a distribution of internal distances and a maximum dimension. An envelope built from it is a low-resolution shape, not an atomic model.
The signal averages every molecule in the beam. A mixture produces an R_g that belongs to no species present and an envelope that looks like a molecule and is a blend. Monodispersity has to be shown by light scattering, analytical ultracentrifugation, or scattering during chromatography before a shape is believed. Solution scattering checks that a Structural Biology model has the right size in solvent. It does not supply atomic coordinates.
9.3 Force at single molecules #
9.3.1 Atomic force microscopy #
Deflection x of a cantilever with spring constant k gives the force by Hooke’s law, F = −k x. A reflected laser reads the deflection. Biological cantilevers are soft, often well below 1 N m⁻¹, so that piconewton-to-nanonewton forces move them detectably. An uncalibrated nominal k makes the force only a relative deflection.
Contact mode drags the tip and shears soft samples. Tapping mode oscillates and touches once per cycle, which is the usual choice for biomolecules. Imaging in liquid means the sample need not enter a vacuum. Individual proteins can be seen on a flat membrane. The height is a height under the tip force, and a soft object is flattened. It is not an atomic structure.
If a protein is held between tip and surface, retraction stretches it. The classic record is titin. Rief, Gaub and colleagues pulled immunoglobulin-like domains and saw a sawtooth: each tooth is one domain unfolding, the force drops as the chain lengthens, and the curve that follows is the stretching of polypeptide already unfolded. The extra contour length, a few tens of nanometres, matches that domain extended. Membrane proteins pulled from a bilayer give a related fingerprint. The force is not an equilibrium constant. Unfolding here is escape over a barrier, and the force rises approximately with the logarithm of the loading rate. A number without a rate cannot be compared with another number. Nonspecific adhesion at the start of a pull is not domain unfolding. Structural Biology supplies the domain boundaries that make the sawtooth readable.
9.3.2 Optical tweezers #
A tightly focused laser holds a dielectric bead at the focus by the momentum of refracted rays. For small displacements the trap is a spring, F = −κ x, with stiffness κ. Equipartition calibrates it, κ = k_B T / ⟨x²⟩, if the position detector is calibrated and filtering has not hidden part of the motion. Forces of a few piconewtons are accessible, below typical titin unfolding forces and in the range of a cytoskeletal motor.
Attached so that kinesin walks a microtubule against the trap, the bead reports steps of about 8 nm, the spacing of tubulin dimers, under loads of a few piconewtons, as resolved by Svoboda, Block and colleagues. The stall force is a few piconewtons. The record is displacement and force of one motor, not an image of the cycle. Cell Biology owns the motor’s place in transport. The measurement artefact is compliance: bead, molecular handle, and surface attachment are springs in series with the motor, so a molecular step looks rounded unless the handle is stiff. The laser also heats the trap. A step size is trusted when it matches a structural repeat and survives a change of bead and handle.
9.4 Key terms, summary, and self-check #
Key terms. De Broglie wavelength; negative stain; contrast-transfer function; vitreous ice; single-particle average; preferred orientation; Bragg’s law; phase problem; Guinier plot; radius of gyration; loading rate; optical trap; trap stiffness.
Summary. Electron wavelength is not the biological limit; dose, contrast, and preparation are. Cryo-EM averages many noisy particles in vitreous ice, and heterogeneity or preferred orientation enters that average. Bragg’s law turns crystal spacings into angles, intensities are measured, and phases are not. Solution scattering gives R_g and a low-resolution envelope of a pure sample. AFM turns cantilever deflection into a force curve whose unfolding peaks depend on loading rate. Optical tweezers turn bead displacement into piconewton forces and resolve motor steps, filtered by linkage compliance.
Self-check.
1. Why is routine biological TEM resolution far worse than the electron wavelength, and what does a heavy-metal stain contribute?
2. What does averaging do to a mixture of two conformations, and what is preferred orientation?
3. Write Bragg’s law, define the symbols, and state what the detector does not record.
4. Why can the Guinier R_g of a mixture belong to none of the species present?
5. Why is a titin unfolding force incomplete without a loading rate, and what does an optical trap measure on kinesin that an AFM height image does not?
