Biophysical Techniques & Instrumentation: Chapter 6 — Separation methods

6.1 Chromatography #

6.1.1 Two phases and a gradient #

Species that spend more time in the mobile phase emerge first. The retention factor is k = (t_R − t₀) / t₀, with t_R the retention time and t₀ the time for a compound that does not interact. Resolution is

R_s = 2 (t_R2 − t_R1) / (w₁ + w₂)

where w is the base width. About 1.5 is baseline separation. Plate count N = 5.54 (t_R / w_½)², with w_½ the width at half height, describes narrowness. Extra-column volume and a large injection broaden peaks after the chemistry is finished.

Plate height depends on linear velocity u through the van Deemter relation H = A + B/u + C u. A is unequal paths through the packing, B is longitudinal diffusion, and C is slow transfer into the stationary phase. Very slow flow lets peaks spread by diffusion. Very fast flow leaves no time to equilibrate. Smaller particles raise N and raise the pressure required to push solvent through.

Capacity is how much solute the bed can bind before peaks distort. Analytical runs stay far below it so that retention reports partitioning. A gradient of salt, pH, or organic solvent exists because isocratic elution cannot do both jobs: conditions that resolve early peaks leave strongly retained ones to emerge late, broad, and dilute. Strengthening the mobile phase during the run is the general solution to that problem.

6.1.2 The modes #

An anion exchanger is positive and binds proteins above their pI. A cation exchanger binds them below the pI. At the pI the net charge is zero and ion exchange does not hold the protein. Elution order is not a strict pI order, because the pattern of charges matters as well as the sum.

A histidine tag binds immobilised nickel or cobalt and is displaced by imidazole. An antibody column binds its antigen. Other histidine-rich proteins also bind metal resins, harsh elution can destroy the fold, and the tag itself can change oligomeric state. Retention shows enrichment. A binding constant is a different experiment. Reversed phase is the separation in front of electrospray in proteomics. Peptides behave. Folded proteins often do not.

6.1.3 The shape assumption in gel filtration #

Pores exclude large molecules, which travel in the void volume V₀ and elute first. Small molecules explore the bead interior and elute later, near the total volume V_t. The partition coefficient

K_av = (V_e − V₀) / (V_t − V₀)

places the elution volume V_e between 0 and 1. K_av is not a dissociation constant. A plot of K_av against log mass for globular standards converts elution to an apparent mass only for that shape. An elongated protein is excluded from pores a sphere of the same mass could enter, elutes early, and looks heavier than it is. Gel filtration measures hydrodynamic size. The column also dilutes the sample, so a weak complex can dissociate on the way through. SEC-MALS, in Chapter 7, keeps the chromatography and replaces the calibration with a light-scattering mass.

6.2 Electrophoresis and blotting #

The study of Electrophoresis and blotting provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.

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6.2.1 Mobility #

A particle of charge q in a field E drifts at v = μ E, with mobility μ = q/f and f the frictional coefficient. In free solution this is a charge-to-size measurement. A gel adds sieving, so molecules of equal charge-to-mass still separate by whether they fit the pores. Agarose has large pores and is used for nucleic acids. Polyacrylamide has smaller pores and is used for proteins and short nucleic acids. A more concentrated gel sieves smaller molecules. That is the whole of the percentage decision.

6.2.2 Agarose and SDS-PAGE #

Each nucleotide brings one phosphate, so nucleic acids have nearly constant charge-to-mass and agarose separates them by length. Supercoiled, linear, and nicked circular DNA of the same sequence do not co-migrate, which spoils a length measurement and is itself a topology measurement. Very large DNA loses size resolution by reptation; pulsed fields reorient it so that size matters again.

Sodium dodecyl sulphate denatures proteins and binds at about 1.4 g per gram of protein, swamping the chain’s own charge. Charge-to-mass becomes roughly constant and the polyacrylamide sieve sorts by length. Log mass against relative mobility is approximately linear over a limited window, which is the only window in which the standards calibrate anything. Disulphide-linked chains stay linked unless a reductant breaks them, so a reduced versus non-reduced comparison reports inter-chain disulphides. Glycoproteins and some membrane proteins bind atypical amounts of SDS and run at the wrong apparent mass. A band is one mobility, not a proof of chemical purity, and not the mass of the native oligomer, which SDS took apart. Sharp zones in the usual discontinuous (Laemmli) buffer come from stacking the sample into a thin starting band. Stacking is why bands are narrow. It is not itself a mass.

6.2.3 Isoelectric focusing, two-dimensional gels, and native gels #

In a pH gradient a protein migrates until its net charge is zero, at its pI, and focuses there. A phosphate adds negative charge and typically moves the pI more acidic, which is a modification SDS-PAGE may miss on a large protein. A two-dimensional gel, associated with O’Farrell, pairs focusing with SDS-PAGE so that a spot has a pI and an apparent mass. Hydrophobic proteins are under-represented, one spot can hide several proteins, and the dynamic range does not match a cell. Liquid chromatography with tandem MS has taken over discovery catalogues. The orthogonal logic remains the clearest picture of a charge isoform.

Native gels omit SDS so the fold can survive. Mobility then mixes native charge, size, and shape, and a band is not a mass. Activity can be assayed in the gel. Blue-native electrophoresis adds a charged dye so that many membrane complexes still enter the gel and remain assembled. A stoichiometry still needs an independent mass from SEC-MALS, analytical ultracentrifugation, or native MS.

6.2.4 Blotting #

Blotting is transfer plus a probe. A Southern blot probes DNA with a nucleic acid, a Northern blot probes RNA, and a Western blot probes protein with an antibody. “Western” follows Southern’s name; it is not a direction. The gel supplies the separation and the probe supplies identity. The evidence is only as good as the antibody, and large proteins transfer poorly. A loading control asks whether lanes received comparable material. Immunology’s standard of antibody specificity applies. The logic, not a staining recipe, separates “a band is present” from “this molecule is present”.

6.2.5 Capillary electrophoresis #

The same mobility is measured in a capillary tens of micrometres wide. Heat dissipates, the field can be high, and plate counts are large. On bare fused silica the negative wall drags bulk solvent toward the cathode by electroosmotic flow, often faster than the analytes’ own electrophoresis, so cations, neutrals, and anions can pass one detector. Free solution separates by charge-to-friction. A sieving polymer restores size separation, which is how automated Sanger sequencing read labelled fragments. Wall adsorption changes the electroosmotic flow with pH and ionic strength, so migration times move even when the analyte has not.

6.3 Centrifugation #

6.3.1 Relative centrifugal force #

Centrifugal acceleration is ω²r, with ω the angular velocity and r the distance from the rotor axis. Divided by standard gravity, and with r in centimetres,

RCF = 1.118 × 10⁻⁵ × r(cm) × rpm²

The prefactor is (2π/60)²/g, converted to centimetres. Revolutions per minute without r do not specify a force, and the top and bottom of a tube sit at different r. Cell Biology notes carry the schedule that enriches nuclei, mitochondria, and microsomes, and the marker enzymes that identify those pellets. The physics below is what that schedule manipulates.

6.3.2 Three ways to separate #

Differential centrifugation enriches; it does not purify. Rate-zonal separation must be stopped on time, or every particle sits at its buoyant density and the rate information is gone. The gradient’s first job is to stop convection. Isopycnic separation cares only about density. DNA, buoyant density about 1.7 g mL⁻¹, bands in caesium chloride; proteins are less dense, near 1.3 g mL⁻¹. Meselson and Stahl shifted DNA with a heavy-nitrogen density label and so distinguished parental from new strands. The genetic conclusion belongs to Molecular Biology. The method conclusion is that a density label makes otherwise identical molecules separable. High salt denatures many proteins, and a gradient that is everywhere denser than the particle gives no band.

6.3.3 Svedberg units #

s = v / (ω² r) = M (1 − ρ v̄) / f

v is drift speed, M molar mass, ρ solvent density, v̄ partial specific volume, and f the frictional coefficient. The buoyancy term (1 − ρ v̄) is zero at the isopycnic density. One Svedberg is 10⁻¹³ seconds. Values corrected to water at 20 °C are written s₂₀,w, because an s measured in cold sucrose is not a property of the particle alone.

Svedberg units do not add. The 40S and 60S ribosomal subunits make an 80S ribosome, not a 100S particle. Mass adds, approximately, but f changes when two shapes become one. Quoting s as a mass is the same mistake as quoting a gel-filtration volume as a mass.

6.3.4 Analytical ultracentrifugation #

An analytical ultracentrifuge records concentration against radius during the run, by absorbance or by refractive-index interference. Absorbance sees the chromophore. Interference sees anything that changes refractive index. Nothing is collected as a pellet for later assay.

Sedimentation velocity, at high speed, moves a boundary whose speed gives s and whose spread contains the diffusion coefficient D. A distribution of s shows heterogeneity directly. The Svedberg equation removes shape because the same f sits in both s and D:

M = R T s / [D (1 − ρ v̄)]

R is the gas constant and T the absolute temperature. Sedimentation equilibrium, at lower speed, balances sedimentation against diffusion. For an ideal single species the profile gives molar mass with almost no shape dependence, and a reversible association can give a solution K_d. Non-ideality at high concentration curves the profile. Velocity asks how many species, and with what s. Equilibrium asks what mass, once transport has stopped.

A detergent-solubilised membrane protein sediments as a protein–detergent particle. Using v̄ of a soluble protein and reading M as polypeptide mass assigns the detergent to the protein. The artefact is a wrong buoyancy term.

6.4 Key terms, summary, and self-check #

Key terms. Retention factor; van Deemter equation; ion exchange; gel filtration; K_av; reversed phase; SDS-PAGE; isoelectric focusing; Western blot; electroosmotic flow; RCF; rate-zonal; isopycnic; Svedberg equation; sedimentation velocity; sedimentation equilibrium.

Summary. Chromatography separates by partition, and a gradient exists so that late peaks still emerge as peaks. Gel filtration reports hydrodynamic size and reports mass only for a calibrated shape. SDS-PAGE forces charge-to-mass nearly constant so that length dominates; focusing stops a protein at its pI; native gels keep the fold and lose the simple mass scale. Centrifugation separates by pelleting time, by s, or by density, and s does not add on assembly. Velocity and equilibrium analytical runs turn that physics into a distribution of s and a thermodynamic mass.

Self-check.

1. Why does a gradient solve a problem that isocratic elution cannot?

2. A protein elutes earlier than a globular standard of the same sequence mass. Give two physical explanations.

3. What does SDS do to charge-to-mass, and why can a glycoprotein still run at the wrong mass?

4. Which centrifugal experiment must be stopped while zones are still moving, and what did a density label allow Meselson and Stahl to separate?

5. Why do the 40S and 60S subunits not make a 100S ribosome? Which analytical experiment asks whether more than one species is present?

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