Cellular Fractionation, Centrifugation, and Chromatographic Purification

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Cellular Fractionation

1. Cellular Fractionation

Homogenization Techniques & Lysis Buffer Design — Foundations of Subcellular Isolation

1. Introduction to Cellular Fractionation

Cellular fractionation is a fundamental process in biochemistry and cell biology that involves breaking open cells (homogenization) and separating their individual organelles, membrane vesicles, and macromolecules based on physical characteristics such as size, shape, and buoyant density. To study metabolic pathways, organelle-specific enzyme activities, or macromolecular structures, the target components must first be isolated from the highly complex, crowded cellular interior — a two-stage process of first breaking the cell open, and then separating what spills out.

1.1 Mechanics of Cell Disruption (Homogenization)

The first critical step in cellular fractionation is homogenization: breaking open the plasma membrane while preserving the structural and functional integrity of the subcellular organelles. The choice of technique depends strictly on the source material — animal tissue, plant tissue, bacteria, yeast, or cultured cells each demand a different disruption strategy.

Dounce Homogenizer Manual shear through 0.05–0.1 mm gap Best for: Fragile animal tissue (liver, brain) French Press Extrusion through a valve at up to 20,000 psi (138 MPa) Best for: Tough bacterial walls (e.g. E. coli) Sonication Ultrasonic cavitation (20–50 kHz) — bubble implosion shear Best for: Bacteria & cultured mammalian cells Grinding (Abrasives) Friction with sand, alumina or glass beads Best for: Plant cells & yeast (rigid walls) Enzymatic Digestion Wall-degrading enzymes, then gentle osmotic lysis Best for: Protoplast / spheroplast generation

Figure: Five approaches to cell disruption. The physical or chemical strategy chosen for homogenization is dictated by the mechanical resilience of the starting material — from the delicate plasma membranes of animal tissue, which tolerate only gentle shear, to the rigid, wall-protected cells of bacteria, plants, and yeast, which require high pressure, abrasion, or targeted enzymatic digestion before they will lyse.

  1. Mechanical Shearing (Dounce Homogenizer): A glass pestle is manually moved up and down within a precision-bored glass cylinder. The clearance between the pestle and the cylinder is extremely small, typically 0.05 to 0.1 mm. As the pestle moves, the liquid suspension is forced through this narrow gap, subjecting the cells to high shear forces.
    This is the preferred method for fragile animal cells and soft tissues (such as liver or brain), because it breaks the plasma membrane while leaving the nuclei, mitochondria, and lysosomes intact.
  2. High-Pressure Extrusion (French Press): The French pressure cell forces a suspension of cells through a tiny, needle-valve orifice at extremely high pressures — up to 20,000 psi (138 MPa). As the cells pass through the valve into atmospheric pressure, they experience massive shear forces and a rapid drop in pressure, causing them to burst.
    Highly effective for breaking tough cell walls, such as those of Escherichia coli and other Gram-negative or Gram-positive bacteria.
  3. Sonication (Ultrasonic Cavitation): High-frequency sound waves (20 to 50 kHz), emitted from a metal probe immersed in the cell suspension, create localized high- and low-pressure zones. During the low-pressure cycle, microscopic vapor bubbles grow; during the high-pressure cycle, they implode violently — a process called cavitation. The resulting shockwaves and shear forces tear the cell membranes apart.
    Heat caution: sonication generates significant heat and can easily denature proteins, so the sample must be kept in an ice bath and sonicated in short pulses.
  4. Grinding with Abrasives (Mortar and Pestle): For plant tissues protected by rigid cellulose cell walls, or yeast cells protected by thick glucan/mannan walls, manual grinding in a mortar and pestle with dry abrasives — fine sand, alumina, or glass beads — is often required. The physical friction breaks the cell walls, releasing the intracellular contents into the buffer.
  5. Enzymatic Digestion (Protoplast Generation): Chemical or enzymatic pretreatments can selectively degrade the cell wall before lysis. Lysozyme hydrolyzes the β(1→4) glycosidic bonds of bacterial peptidoglycan; cellulases and pectinases digest plant cell walls; zymolyase or lyticase acts on yeast cells.
    Once the rigid wall is removed, the resulting fragile cell — a protoplast or spheroplast — can be easily lysed by gentle osmotic shock.
MethodPhysical mechanismTypical application
Dounce homogenizerManual shear through a 0.05–0.1 mm pestle–cylinder clearanceFragile animal tissue (liver, brain); preserves nuclei, mitochondria, lysosomes
French pressHigh-pressure extrusion through a needle-valve orifice (≤20,000 psi)Tough Gram-negative/positive bacterial walls (e.g. E. coli)
SonicationUltrasonic cavitation (20–50 kHz); bubble implosion shearBacteria, cultured mammalian cells; requires ice bath & pulsing
Grinding (abrasives)Mechanical friction with sand, alumina, or glass beadsPlant cells (cellulose walls), yeast (glucan/mannan walls)
Enzymatic digestionWall-degrading enzymes (lysozyme, cellulase/pectinase, zymolyase) + osmotic shockGenerating protoplasts/spheroplasts prior to gentle lysis

1.2 Osmotic, pH, and Chemical Composition of Lysis Buffers

Once the cells are disrupted, the released organelles must be stabilized in a specialized suspension medium called the homogenization buffer or lysis buffer. If the buffer composition is incorrect, the organelles will quickly swell, lyse, or aggregate. A standard homogenization buffer is built from five functional components layered together.

Homogenization Buffer pH 7.4, isotonic Osmotic Stabilizer Sucrose (~0.25 M), mannitol, sorbitol, or glycerol Prevents osmotic swelling & lysis of released organelles pH Buffer HEPES or Tris-HCl (10–50 mM) Holds pH at 7.4 despite acidic lysosomal/vacuolar release Chelating Agent EDTA (Ca²⁺/Mg²⁺) or EGTA (Ca²⁺-selective), 1–5 mM Blocks metalloprotease & nuclease activity Protease Inhibitors PMSF, leupeptin, pepstatin, aprotinin (fresh cocktail) Protects proteins from lysosomal protease attack Reducing Agent DTT or β-mercaptoethanol (0.1–1.0 mM) Keeps –SH groups reduced, blocks stray disulfide bonds

Figure: Anatomy of a homogenization buffer. Five functional components are combined around an isotonic, pH-controlled base: an osmotic stabilizer to prevent organelle swelling, a zwitterionic pH buffer to hold physiological pH, a chelating agent to disarm destructive metal-dependent enzymes, a protease-inhibitor cocktail to protect released proteins, and a reducing agent to preserve free thiol groups.

  1. Osmotic Stabilizers (Osmolytes): The intracellular fluid is highly concentrated and exerts significant osmotic pressure. In a hypotonic medium such as pure water, water rapidly diffuses into organelles by osmosis, causing them to swell and burst. Sucrose (typically 0.25 M) is the most widely used osmolyte because it is chemically inert, inexpensive, and does not easily cross organelle membranes; mannitol, sorbitol, or glycerol are alternatives, especially for plant or bacterial cells.
  2. Hydrogen Ion Buffers (pH Control): Biological membranes and enzymes are highly sensitive to pH fluctuations. Homogenization buffers are typically adjusted to physiological pH (7.4) using highly stable, non-reactive zwitterionic buffers such as HEPES or Tris-HCl (usually 10 to 50 mM), which maintain a stable pH despite the release of acidic compounds from damaged vacuoles or lysosomes.
  3. Chelating Agents: When cells are lysed, intracellular metalloproteases and nucleases are activated, and heavy metal contaminants can catalyze protein oxidation. EDTA or EGTA is added at 1 to 5 mM.
    EDTA vs. EGTA: EDTA chelates both Ca²⁺ and Mg²⁺, essential cofactors for many destructive enzymes (DNases, calcium-dependent proteases). EGTA is highly selective for Ca²⁺, making it ideal when Mg²⁺ must be preserved.
  4. Protease Inhibitors: To protect extracted proteins from degradation by lysosomal proteases (such as cathepsins) released during lysis, a cocktail is added immediately before homogenization.
    PMSF — irreversible inhibitor of serine proteases. Leupeptin / pepstatin — reversible inhibitors of lysosomal acid proteases. Aprotinin — inhibits trypsin and related serine proteases.
  5. Reducing Agents: The cytoplasm is a highly reducing environment that keeps protein sulfhydryl (–SH) groups reduced. On exposure to atmospheric oxygen during homogenization, these groups can oxidize and form incorrect intermolecular disulfide bonds, inactivating enzymes. Low concentrations (0.1 to 1.0 mM) of DTT (dithiothreitol) or β-mercaptoethanol are included to maintain a reducing environment.
ComponentPurposeCommon reagentsTypical concentration
Osmotic stabilizerKeeps medium isotonic/hypertonic to prevent organelle swelling & lysisSucrose, mannitol, sorbitol, glycerol~0.25 M (sucrose)
pH bufferMaintains physiological pH despite acidic lysosomal/vacuolar releaseHEPES, Tris-HCl10–50 mM, pH 7.4
Chelating agentSequesters Ca²⁺/Mg²⁺ that activate metalloproteases & nucleasesEDTA (broad), EGTA (Ca²⁺-selective)1–5 mM
Protease inhibitorsBlocks proteolytic degradation by released lysosomal proteasesPMSF, leupeptin, pepstatin, aprotininFresh cocktail, µM–mM range
Reducing agentPreserves –SH groups; prevents aberrant disulfide bondsDTT, β-mercaptoethanol0.1–1.0 mM
Physical Principles of Centrifugation

2. Physical Principles of Centrifugation

Force Balance, Sedimentation Theory & RCF Calculations — Quantitative Foundations of Centrifugal Separation

2. Physical Principles of Centrifugation

Centrifugation is a physical method that uses high-speed rotation to subject suspended particles to a radial centrifugal force. This force accelerates the natural sedimentation rate of particles — molecules, organelles, or whole cells — suspended in a liquid medium, allowing them to be separated based on their physical properties: mass, size, shape, and density.

2.1 Complete Force Balance Equations (Fc, Fb, Ff)

A particle suspended in a liquid medium inside a rotating centrifuge tube is subject to three primary, competing physical forces.

ω Axis of rotation r (radius) Centrifuge tube particle Fc Fb Ff

Figure: Force balance on a sedimenting particle. The centrifugal force (Fc) pushes the particle radially outward, away from the axis of rotation at angular velocity ω. Opposing it are the buoyant force (Fb), acting inward per Archimedes' principle, and the frictional/drag force (Ff), which opposes the particle's net motion through the fluid and grows with velocity until the three forces balance at terminal velocity.

  1. Centrifugal Force (Fc): Acts radially outward from the axis of rotation. It is directly proportional to the particle's mass, the square of the rotor's angular velocity, and the particle's distance from the axis.
    Fc = mω²r
    • m — actual mass of the particle (g)
    • ω — angular velocity of the rotor (rad/s)
    • r — radial distance from the axis to the particle (cm)
  2. Buoyant Force (Fb): By Archimedes' principle, any object immersed in a fluid experiences an upward (radially inward) force equal to the weight of fluid it displaces.
    Fb = m0ω²r

    Here m0 is the mass of displaced solvent. The displaced volume equals the particle's volume, expressible as mv, where v is the partial specific volume (mL of solvent displaced per gram of solute). Multiplying by solvent density ρ gives:

    m0 = mvρ

    Substituting back:

    Fb = mvρω²r
  3. Frictional Force (Ff): As the particle moves through the fluid it experiences hydrodynamic drag, opposing its net motion and proportional to its sedimentation velocity.
    Ff = fv
    • f — frictional coefficient (depends on size, shape, solvent viscosity)
    • v — sedimentation velocity of the particle (cm/s)

2.2 Mathematical Derivation of Sedimentation Velocity (v)

When the rotor starts spinning, Fc exceeds Fb and the particle accelerates outward. As velocity increases, the opposing Ff grows proportionally, until within microseconds the system reaches a dynamic equilibrium (terminal velocity) where the net force is zero.

  1. Set the forces in balance at terminal velocity:
    Ff = Fc − Fb
  2. Substitute the force equations from 2.1:
    fv = mω²r − mvρω²r
  3. Factor out the common terms (m, ω²r):
    fv = mω²r (1 − vρ)
  4. Re-express particle mass in macroscopic terms — molar mass M (g/mol) divided by Avogadro's number N (6.022×10²³ /mol):
    m = MN
  5. Substitute and solve for the terminal sedimentation velocity:
    fv = MNω²r (1 − vρ)
    v = Mω²r (1 − vρ)N f

This final equation reveals three governing physical factors:

FactorRelationshipPhysical meaning
Mass & sizev ∝ MLarger, heavier particles sediment faster than smaller, lighter ones
Viscosity & shapev ∝ 1/fCompact spherical particles (low f) sediment faster than elongated or denatured ones (high f) of the same mass
Density difference(1 − vρ) — the buoyancy factorSee the three cases below
ConditionBuoyancy factorOutcome
Particle denser than solvent (1/v > ρ)PositiveParticle sediments outward, toward the tube bottom
Particle less dense than solvent (1/v < ρ)NegativeParticle floats inward, toward the tube top
Densities equal (1/v = ρ)ZeroVelocity is zero — particle stays stationary regardless of rotor speed

2.3 Sedimentation Coefficient (s), Svedberg Units (S), and Non-Additivity in Complexes

The sedimentation coefficient is defined as sedimentation velocity per unit of centrifugal acceleration:

s = vω²r

Substituting the derived expression for v (from 2.2):

s = M (1 − vρ)N f
Svedberg unit: because biological macromolecules have extremely small s values (typically ~10⁻¹³ seconds), the Svedberg unit (S) was established in honor of Theodor Svedberg, the pioneer of ultracentrifugation: 1 S = 1×10⁻¹³ seconds.
Small subunit 40S Large subunit 60S + associate 80S ribosome buried interface (hidden from solvent)

Figure: Why sedimentation coefficients don't add. When the 40S and 60S ribosomal subunits associate, their masses simply sum — but the newly buried interface removes surface area that no longer contacts solvent, so the frictional coefficient of the 80S complex is smaller than the sum of the two individual coefficients. Since s ∝ M/f, a disproportionately smaller f alongside an additive M yields an 80S particle, not a 100S one.

SystemSubunitsComplexWhy not additive
Eukaryotic ribosome40S + 60S80SMass adds; buried surface area lowers f disproportionately
Bacterial ribosome30S + 50S70SSame principle — compact packing reduces total frictional drag

2.4 Thermodynamic & Hydrodynamic Standardization to s20,w

Because solvent density (ρ) and viscosity (η) are highly temperature- and salt-dependent, an experimentally measured sedimentation coefficient (sexp) must be converted to a standard reference state — pure water at 20°C — before it can be compared across laboratories.

s20,w = sexp × 1 − vρ20,w1 − vρexp × ηexpη20,w
  • sexp — sedimentation coefficient observed under experimental conditions
  • ηexp, η20,w — viscosity of the experimental solvent vs. water at 20°C
  • ρexp, ρ20,w — density of the experimental solvent vs. water at 20°C
  • v — partial specific volume of the macromolecule
This equation mathematically "corrects" the experimental value, stripping away the fluid-dynamic artifacts of the specific buffer and temperature used, and allowing direct comparison of structural properties across different laboratories.

2.5 Mathematical Relationship of RCF to rpm and Radius (r)

Earth's gravitational acceleration is roughly g = 980 cm/s². To sediment small biological molecules, a centrifuge must generate accelerations thousands of times stronger than gravity — this multiplier is the Relative Centrifugal Field (RCF), or g-force:

RCF = centrifugal accelerationgravitational acceleration = rω²g

To calculate RCF from standard instrument parameters — rotor radius r (cm) and rotational speed in rpm:

  1. Convert rpm to angular velocity ω (one revolution = 2π radians, one minute = 60 s):
    ω = 2π × rpm60 rad/s
  2. Substitute into the RCF equation:
    RCF = r (2π × rpm / 60)² / g
  3. Expand using g = 980 cm/s² and simplify the constants:
    RCF = r980 × 4π² × (rpm)²3600
RCF = 1.118 × 10⁻⁵ × r × (rpm)²

This is the practical working formula — the one used directly in the sample calculations below.

ω Axis of rotation Fixed-angle rotor tube rmin = 6 cm (top) 15,093 × g rmax = 12 cm (bottom) 30,186 × g

Figure: RCF varies with radial position. At 15,000 rpm in a fixed-angle rotor with rmin = 6 cm and rmax = 12 cm, a particle at the bottom of the tube experiences roughly twice the g-force of a particle at the top — RCF scales linearly with r. (In a real fixed-angle rotor the tube sits at an angle rather than perfectly vertical, but the radial distance — and therefore the g-force — still increases continuously from the top of the tube to the bottom.)

2.6 High-Yield Sample Calculations

Problem 1 — Calculating g-force (RCF)

A fixed-angle rotor has rmax = 12 cm and rmin = 6 cm, operated at 15,000 rpm. Find the RCF at the bottom and top of the tube.

At the bottom (rmax = 12 cm):

RCF = 1.118×10⁻⁵ × 12 × (15,000)² = 1.118×10⁻⁵ × 12 × 2.25×10⁸ = 1.118 × 12 × 2250
30,186 × g

At the top (rmin = 6 cm):

RCF = 1.118×10⁻⁵ × 6 × (15,000)² = 1.118 × 6 × 2250
15,093 × g
Takeaway: g-force varies linearly with distance from the axis of rotation — a particle at the bottom of the tube experiences roughly twice the sedimenting force of one at the top.
Problem 2 — Calculating Sedimentation Velocity

A spherical virus with s = 100 S sits in a rotor generating ω²r = 10⁷ cm/s² at the tube center. Find the sedimentation velocity in cm/hour.

Step 1 — convert S to seconds:

s = 100 × 10⁻¹³ s = 10⁻¹¹ s

Step 2 — use s = v / ω²r to solve for v:

v = s × (ω²r) = 10⁻¹¹ s × 10⁷ cm/s² = 10⁻⁴ cm/s

Step 3 — convert to cm/hour (1 hour = 3600 s):

v = 10⁻⁴ cm/s × 3600 s/hour
0.36 cm/hour
Centrifugation Instrumentation and Rotor Dynamics

3. Centrifugation Instrumentation and Rotor Dynamics

Rotor Geometry, Vacuum Engineering & Sedimentation Physics

3. Centrifugation Instrumentation and Rotor Dynamics

Centrifugation instruments are highly engineered devices capable of spinning rotors at extreme speeds. Because the forces generated are immense — in the largest ultracentrifuges, hundreds of thousands of times the force of gravity — rotor safety, aerodynamic friction, and temperature control are critical engineering challenges that shape every part of the instrument's design.

3.1 Structural and Operational Differences: Low-Speed, High-Speed, and Ultracentrifuges

Centrifuges are classified into three broad instrument classes based on the rotational speeds and forces they can safely generate.

ParameterLow-speed centrifugesHigh-speed centrifugesUltracentrifuges
Max rotational speed1,000–6,000 rpm10,000–25,000 rpm50,000–150,000 rpm
Max relative centrifugal field (RCF)up to 6,000 × gup to 60,000 × gup to 1,000,000 × g
Temperature controlAmbient (unrefrigerated) or simple coolingRefrigerated (4°C to 20°C)Precision refrigeration (0°C to 4°C)
Atmospheric chamberOpen to ambient airSealed, normal atmospheric pressureHigh vacuum (<0.13 Pa, or 10−3 torr)
Drive systemDirect-drive AC/DC motorHigh-torque brushless induction motorVariable-frequency induction or magnetic drive
Primary biological usesPelleting whole cells, red blood cells, large precipitatesHarvesting bacterial cells, yeast, nuclei, large chloroplastsIsolating proteins, ribosomes, nucleic acid conformations, lipid fractions

3.2 Why Does an Ultracentrifuge Require a Vacuum?

At speeds exceeding 30,000 rpm, the outer edge of a metal rotor travels faster than the speed of sound. The friction between the spinning rotor and surrounding air molecules generates extreme heat — enough to instantly cook and denature biological samples — while the air resistance itself places immense mechanical strain on the drive motor. To eliminate this aerodynamic drag and the heat it generates, ultracentrifuges are fitted with a heavy-duty vacuum pump that evacuates the rotor chamber to pressures below 10−3 torr before the run begins.

Without Vacuum With Vacuum (<10⁻³ torr) Air friction → heat → sample denatures PUMP No air molecules → no frictional heating

Figure: Why ultracentrifuges run under vacuum. In open air (left), rotor tip speeds above the speed of sound cause constant collisions with air molecules, generating heat that would denature the sample and straining the motor. Evacuating the chamber (right) removes the air molecules entirely, eliminating both the drag and the heat.

Threshold to remember: the vacuum requirement is a direct consequence of speed — below roughly 30,000 rpm the tip speed stays subsonic and a sealed, unevacuated chamber is sufficient, which is why only true ultracentrifuges (not high-speed centrifuges) need a vacuum pump.

3.3 Physics of Rotor Geometries: Swing-Bucket vs. Fixed-Angle vs. Vertical Rotors

The physical path a sedimenting particle takes, and the efficiency with which a pellet or gradient band forms, are dictated entirely by the geometry of the rotor.

Swing-Bucket Rotor AT REST SPINNING centrifugal force tubes swing to 90° Pellet forms symmetrically at tube bottom — straight radial path, no wall contact Fixed-Angle Rotor AT REST SPINNING angle constant (14–40°) short radial path to wall Particles strike the outer wall, then slide down — fastest pelleting, but wall contact Vertical Rotor AT REST SPINNING ~1–2 cm to wall tubes stay vertical Long thin pellet along the entire outer wall — fastest gradient separations

Figure: The three rotor geometries. A swing-bucket rotor's tubes hang vertically at rest and swing outward to a full 90° once spinning, so particles travel straight down the tube length. A fixed-angle rotor holds tubes rigidly at a permanent angle whether at rest or spinning, giving particles only a short radial distance to travel before hitting the wall. A vertical rotor holds tubes fully parallel to the spin axis at all times, so particles need to cross only the tube's diameter to reach the wall.

  1. Swing-Bucket Rotors (Horizontal Rotors): The rotor has individual hinges holding metal buckets. At rest the buckets hang vertically; as the rotor accelerates, centrifugal force swings them outward until they sit horizontally, at 90° to the vertical axis of rotation. Particles then travel along a straight path down the length of the tube, parallel to the tube walls, and the pellet forms symmetrically at the absolute center-bottom of the tube.
    Advantages: because particles never collide with the tube walls during their descent, there is no convective mixing or wall disturbance — this makes swing-bucket rotors ideal for density gradient centrifugation, both rate-zonal and isopycnic, where clean, discrete bands must be preserved.
    Disadvantages: the long sedimentation path means pelleting times are relatively slow, and the swung-out buckets create high aerodynamic drag, which limits the maximum achievable speed.
  2. Fixed-Angle Rotors: Centrifuge tubes sit in rigid cavities bored into a solid block of metal (aluminum or carbon fiber) at a permanent fixed angle, typically 14–40° from the central vertical axis. Particles travel only a short distance radially outward before striking the outer wall of the tube, lose their kinetic energy there, and slide down the wall to accumulate as a compact pellet at the bottom-side of the tube.
    Advantages: the sedimentation distance is often less than half that of a swing-bucket rotor, dramatically cutting the run time needed to form a pellet; the solid, aerodynamic block can also withstand much higher rotational speeds and forces.
    Disadvantages: particles sliding down the tube wall cause frictional heating and convective mixing, which makes fixed-angle rotors unsuitable for high-resolution rate-zonal gradients.
  3. Vertical Rotors: Tubes are held completely parallel to the vertical axis of rotation, at 0°. Because centrifugal force acts perpendicular to the tube's length, particles travel only a tiny distance — roughly the tube's diameter, about 1–2 cm — before reaching the outer wall, sliding down it to form a long, thin pellet along the entire outer wall of the tube.
    Advantages: the minimal sedimentation distance gives the fastest possible separation times, which makes vertical rotors especially useful for rapid plasmid DNA preparation in CsCl gradients.
    Disadvantages: as the rotor slows down, the bands that formed vertically along the width of the tube must reorient to a horizontal position under gravity, which can cause significant band-broadening and contamination.

3.4 Wall Effects, Thermal Convection, and Heat Generation

Beyond rotor geometry itself, several physical phenomena can degrade centrifugation efficiency if left unmanaged.

Wall Effect (Fixed-Angle / Vertical) particles pile up at the wall dense plume plunges through the gradient, disrupting bandsThermal Convection warm inner wall → mixing currents

Figure: Two failure modes of an unmanaged spin. Left — in fixed-angle and vertical rotors, particles striking the tube wall can stick and pile up into a locally concentrated, denser zone that plunges rapidly to the bottom in a convective plume, disrupting the carefully separated bands. Right — without adequate refrigeration, a temperature gradient develops across the tube; because fluid density falls as temperature rises, a warm zone at the inner radius sets up convective currents that mix and destroy the bands.

Wall effects: in fixed-angle and vertical rotors, particles striking the tube wall can stick or accumulate, creating localized zones that are denser than the surrounding fluid and so plunge rapidly to the tube bottom in convective plumes, disrupting the gradient separation.
Thermal convection: if the rotor chamber is not properly refrigerated, temperature gradients develop across the tube; since fluid density decreases with temperature, a warm zone at the inner radius creates convective currents that mix and destroy separated bands. Precision temperature sensors and microprocessors are required to keep the rotor isothermal to within ±0.1°C.

3.5 Rotor Selection at a Glance

GoalBest rotorWhy
Preserve clean gradient bands (rate-zonal or isopycnic)Swing-bucketNo wall contact; straight, parallel sedimentation path
Fastest pelleting of a crude sampleFixed-angleShortest radial path; withstands the highest speeds
Fastest possible gradient run (e.g. plasmid DNA prep)VerticalSedimentation distance is only the tube diameter
Routine bacterial or yeast harvestingHigh-speed fixed-angleBest balance of run time, capacity, and cost
Preparative and Analytical Centrifugation Techniques

4. Preparative and Analytical Centrifugation Techniques

Fractionation Cascades, Density Gradients & Isopycnic Equilibrium

4. Preparative and Analytical Centrifugation Techniques

Centrifugation techniques fall into two functional categories. Preparative centrifugation is designed to isolate and purify specific components for downstream use — the sample is physically separated into fractions that can be collected and studied further. Analytical centrifugation, by contrast, measures the physical properties of macromolecules — such as molecular weight or shape — directly during the run, using specialized optical detection systems built into the instrument. The remainder of this chapter focuses on the three workhorse preparative techniques: differential, rate-zonal, and isopycnic centrifugation.

4.1 Differential Centrifugation and the Pellet–Supernatant Fractionation Cascade

Differential centrifugation is the most common preparative method used to fractionate a complex cell homogenate. It separates organelles based on differences in their size and density, which translate into different sedimentation rates. The process consists of a sequential series of spins with increasing g-force and run duration, each one acting on the supernatant left over from the spin before it.

Homogenate 600 × g, 10 min supernatant carried forward ↓ Pellet 1 Nuclei, unbroken cells 15,000 × g, 5 min supernatant carried forward ↓ Pellet 2 Mitochondria, lysosomes, peroxisomes 100,000 × g, 60 min supernatant carried forward ↓ Pellet 3 Microsomes, ER, plasma membrane Final Supernatant Cytosol, soluble proteins

Figure: The differential centrifugation cascade. Each spin pellets everything above a certain size/density threshold while the supernatant — still containing everything smaller and less dense — is transferred to a fresh tube and spun again at higher force for longer. The threshold rises with each stage, so the pellets collected are, in order, progressively smaller and less dense organelles.

  1. Low-speed step (600 × g, 10 min): pellets the largest, densest structures — nuclei, intact unbroken cells, and large cytoskeletal elements.
  2. Medium-speed step (15,000 × g, 5 min): the supernatant from step 1 is transferred to a fresh tube and centrifuged to pellet intermediate organelles — mitochondria, lysosomes, peroxisomes, and chloroplasts.
  3. High-speed step (100,000 × g, 60 min): the supernatant from step 2 is centrifuged in an ultracentrifuge to pellet small membrane vesicles, microsomes (fragments of endoplasmic reticulum and Golgi), and plasma membrane sheets.
  4. Final supernatant: the remaining soluble fraction contains the cytosol, including soluble proteins, tRNA, and small metabolites.

4.2 The Co-pelleting Contamination Problem and the Necessity of Washing Steps

A fundamental limitation of differential centrifugation is that pellets are never 100% pure. At the start of centrifugation, all cellular components are distributed homogeneously throughout the tube.

1st Spin: Contaminated Pellet Nuclei pellet mitochondria trapped in the pellet zone Started near the tube bottom → pellet with the nucleiResuspend + Re-spin: Purified Nuclei pellet Redistributed evenly → most mitochondria stay in the supernatant

Figure: Why washing improves purity. Even though mitochondria sediment much more slowly than nuclei, any mitochondrion that happens to start out near the very bottom of the tube will still reach the pellet zone during the low-speed spin (left). Resuspending the pellet in fresh buffer randomizes the starting positions again, so on the second spin only the small fraction that happens to start closest to the bottom co-pellets (right) — repeating this cycle is called washing the pellet.

The contamination mechanism: even though mitochondria sediment much slower than nuclei, a mitochondrion that starts at the very bottom of the tube (adjacent to the pellet zone) will still reach the bottom and pellet during the low-speed 600 × g step.
The solution — washing: the supernatant is decanted and the contaminated pellet is resuspended in fresh homogenization buffer, then centrifuged again under the same conditions. The large particles (nuclei) pellet again, while the contaminating small particles (mitochondria), now starting from a homogeneous distribution, mostly remain in the supernatant. Repeating this resuspension-and-re-spin cycle is known as washing the pellet.

4.3 Rate-Zonal (Velocity) Centrifugation

To separate particles with similar densities but different sizes, rate-zonal centrifugation is used.

Before Spin sample layer shallow sucrose gradient (5–20%) Thin, concentrated band layered on top of the gradientAfter Short Spin Band B (slower) Band A (faster) Separated by sedimentation rate — neither band has pelleted yet

Figure: Rate-zonal separation. The sample is layered as a thin band on a preformed, shallow sucrose gradient whose density is lower than any of the particles throughout. Under centrifugal force, particles migrate down the tube at a rate set by their sedimentation coefficient (s — a function of mass, size, and shape); the gradient itself does not drive the separation, it simply increases density and viscosity down the tube to suppress convective mixing and keep the resolved bands from spreading.

Run time is critical: rate-zonal centrifugation is a time-dependent, non-equilibrium technique. Run it too long and every particle eventually migrates through the gradient and pellets at the bottom — the spin must be stopped while the bands of interest are still well resolved along the tube.

4.4 Isopycnic (Buoyant Density) Centrifugation

To separate particles based strictly on their chemical composition and buoyant density, isopycnic centrifugation is used.

Before: Homogeneous Mixture Sample pre-mixed evenly with CsCl solutionAfter: Equilibrium Reached Band A (low density) Band B (high density) Bands are static — longer runs will not move them further

Figure: Isopycnic separation. The sample is mixed homogeneously with a dense salt solution, typically caesium chloride (CsCl). At very high speed (>50,000 rpm) over 24–48 hours, the heavy Cs⁺ ions redistribute to establish a continuous, self-generated density gradient. Each molecule migrates until it reaches its isopycnic point — the position where the surrounding solution density exactly equals its own buoyant density — and then stops moving entirely.

Equilibrium, not kinetics: once molecules reach their isopycnic positions they stop moving altogether. Because the bands are defined by density rather than time, run time is not critical — spinning the rotor for longer will not alter where the bands sit.

4.5 Rate-Zonal vs. Isopycnic at a Glance

PropertyRate-zonal (velocity)Isopycnic (buoyant density)
Basis of separationSize and shape (sedimentation coefficient, s)Buoyant density only
Gradient mediumShallow, preformed sucrose gradient (5–20% w/v)Self-generating CsCl gradient
Technique typeTime-dependent, non-equilibrium (kinetic)Equilibrium (thermodynamic)
Run-time sensitivityCritical — must stop while bands are resolvedNot critical once equilibrium is reached
Typical runMinutes to a few hours24–48 hours at >50,000 rpm
Typical useSeparating particles of similar density but different size (e.g. ribosomal subunits)Separating molecules by density (e.g. plasmid DNA purification)
Practical Biological Applications of Centrifugation

5. Practical Biological Applications of Centrifugation

Density Gradients, DNA Conformation & Base-Composition Fractionation

5. Practical Biological Applications of Centrifugation

Centrifugation is highly versatile, enabling high-resolution purification of nucleic acid conformations, organelle populations, and macromolecular complexes. Which gradient medium to use, and how to interpret the bands it produces, both come down to the same underlying physics of buoyant density.

5.1 Density Gradient Media Selection: Cesium Chloride (CsCl) vs. Sucrose

The choice of gradient medium is dictated by the density of the target analytes and the physical mechanism of separation.

ParameterCesium chloride (CsCl)Sucrose
Chemical structureIonic salt (Cs+ Cl−)Non-ionic disaccharide (C12H22O11)
Aqueous viscosityExtremely low, even at high concentrationsHigh, rises exponentially with concentration
Max density in water∼1.91 g/cm3∼1.32 g/cm3
Osmotic activityExtremely high ionic strengthHigh osmotic pressure, non-ionic
Separation typeEquilibrium (isopycnic)Rate-zonal (velocity)
Primary target analytesDNA conformations, RNA, caesium-stable virusesIntact organelles, ribosomes, proteins, membrane fractions
Why can't sucrose be used for isopycnic separation of DNA? Double-stranded DNA has a buoyant density of about 1.70 g/cm3, but the maximum density sucrose can reach in water is only ∼1.32 g/cm3 (at its ∼65% w/v solubility limit). Because DNA is denser than the densest possible sucrose solution, it would simply sediment straight to the bottom of a sucrose gradient rather than finding an isopycnic point — a high-density salt like CsCl is required instead.

5.2 Conformational Separation of Nucleic Acids: EtBr Intercalation and Unwinding Kinetics

Isopycnic CsCl gradient centrifugation can separate different conformations of plasmid DNA — covalently closed circular (ccc) supercoiled DNA versus open circular or linear DNA — by adding ethidium bromide (EtBr) to the gradient.

LOW DENSITY HIGH DENSITY Linear / nicked circular dsDNA ∼1.55 g/cm³ — binds more EtBr, unwinds fully Supercoiled (ccc) dsDNA ∼1.59 g/cm³ — binds less EtBr, topologically constrained Unbound dsDNA reference (no EtBr): ∼1.70 g/cm³

Figure: Resolving plasmid DNA conformations in a CsCl–EtBr gradient. Both conformations become less dense than unbound DNA once EtBr intercalates, but supercoiled DNA can bind far less dye than linear or nicked DNA, so it stays denser and settles into a lower, distinct band at equilibrium.

  1. Mechanism of intercalation: ethidium bromide is a planar, hydrophobic, fluorescent molecule that inserts between adjacent base pairs of double-stranded DNA. Intercalation forces the base pairs apart, unwinding the double helix by 26° per intercalated molecule. This increases the DNA's length and physical volume far more than it increases its mass, so the net effect is a significant decrease in buoyant density.
  2. Linear and nicked circular DNA: free ends or a broken phosphodiester backbone let the molecule rotate freely, allowing the double helix to untwist completely and bind the maximum amount of EtBr.
    Density shift: extensive EtBr binding lowers buoyant density by about 0.125 g/cm³, from 1.70 g/cm³ down to ∼1.55 g/cm³.
  3. Covalently closed circular (ccc) supercoiled DNA: the double helix is continuous and topologically locked, with no free ends to relieve torsional stress. As EtBr intercalates and tries to unwind the helix, it introduces positive superhelical stress that resists further unwinding, so much less EtBr can bind overall.
    Density shift: the limited EtBr binding lowers buoyant density by only about 0.085 g/cm³, from 1.70 g/cm³ down to ∼1.59 g/cm³.
  4. Resolution: because supercoiled DNA binds less EtBr, it remains denser than linear or nicked circular DNA. When centrifuged to equilibrium in a CsCl–EtBr gradient, supercoiled DNA forms a distinct band lower in the tube (higher density) than the linear and nicked circular DNA, allowing it to be easily collected.

5.3 DNA Base Composition Separation: Buoyant Density vs. G+C Content

The buoyant density (ρ) of double-stranded DNA in a CsCl gradient is linearly proportional to its guanine–cytosine (G+C) base pair content.

ρ = 1.660 + 0.098 × (G+C) g/cm3

where (G+C) is the mole fraction of G–C base pairs in the DNA, from 0 (all A–T) to 1 (all G–C).

Buoyant density (g/cm³) G + C content (%)1.66 1.68 1.70 1.72 1.74 0 20 40 60 80 100 Mouse main band 42% G+C · 1.701 g/cm³ Mouse satellite (AT-rich) 30% G+C · ∼1.690 g/cm³

Figure: Buoyant density as a linear function of G+C content. Every 1% increase in G+C content raises buoyant density by roughly 0.00098 g/cm³. The mouse genome's two characteristic bands (marked) fall exactly on this line, since 1.660 + 0.098×0.42 = 1.701 and 1.660 + 0.098×0.30 ≈ 1.689.

Two physical properties of the G–C base pair explain why more of it means denser DNA:

Hydrogen bonding: G–C base pairs are held together by three hydrogen bonds, whereas A–T base pairs are held by only two.
Base stacking: G–C base pairs stack more tightly and compactly along the helix axis than A–T base pairs. This tighter packing reduces the partial specific volume (v̄) of G+C-rich DNA, making it denser than A+T-rich DNA of the same mass.

5.4 High-Resolution Purification of Satellite DNA

When genomic DNA is sheared into fragments of relatively uniform size and centrifuged to equilibrium in a CsCl gradient, the majority of fragments form a broad band at a density reflecting the average G+C content of the organism's genome — the main band. Highly repetitive, simple-sequence DNA, often found in centromeres and telomeres, can have a base composition biased enough from the genome average that it separates into its own satellite band.

LOW DENSITY HIGH DENSITY Satellite DNA band ∼30% G+C · 1.690 g/cm³ (centromeric / telomeric repeats) Main band ∼42% G+C (genome average) 1.701 g/cm³

Figure: Mouse genomic DNA in a CsCl gradient. The bulk of sheared genomic DNA bands at 1.701 g/cm³, matching the genome's ~42% average G+C content. The AT-rich satellite DNA (~30% G+C) is markedly less dense and resolves as a separate, lower-density band above the main band, allowing it to be isolated.

5.5 CsCl Gradient Applications at a Glance

TechniqueWhat it separatesBasisTypical density range
Conformational (CsCl–EtBr)Supercoiled vs. linear/nicked circular DNADifferential EtBr intercalation limited by DNA topology∼1.55–1.59 g/cm³
Base-composition (CsCl only)Main-band vs. satellite (AT-rich) genomic DNALinear ρ vs. G+C relationship (H-bonding + base stacking)∼1.68–1.74 g/cm³ (0–100% G+C)
General macromolecule banding (CsCl, no dye)RNA, caesium-stable viruses, other dsDNA speciesIntrinsic buoyant density differencesAnalyte-dependent, ∼1.3–1.9 g/cm³
Mechanisms of Chromatography

7. Mechanisms of Chromatography

Adsorption, Partition, and Planar Separation Chemistry

7. Mechanisms of Chromatography

Separations can be classified into four primary chemical mechanisms: adsorption, partition, ion exchange, and affinity. This chapter focuses on the two most common in practice — adsorption and partition — along with the planar (paper) technique that first made partition chromatography practical.

7.1 Adsorption Chromatography: Silica/Alumina Surfaces and Polar–Polar Interactions

Adsorption chromatography (liquid–solid chromatography) is based on direct electrostatic interactions between solute molecules and the active surface of a solid stationary phase. The most common stationary phases are polar inorganic solids — silica gel (SiO2·xH2O) or alumina (Al2O3) — whose surfaces are covered with highly polar silanol groups (–Si–OH). Solute molecules compete with mobile phase molecules for these active polar sites, binding through non-covalent dipole–dipole interactions, hydrogen bonding, and van der Waals forces.

Silica / Alumina (polar stationary phase) Non-polar (hydrocarbons) — elutes FIRST Polar (alcohols, amines, acids) elutes LASTCharcoal (non-polar stationary phase) Polar — elutes FIRST Non-polar (large, hydrophobic) — LAST

Figure: Elution order flips with stationary-phase polarity. On polar silica or alumina, non-polar compounds have little affinity for the silanol groups and wash straight through, while polar compounds bind tightly and elute last. Active charcoal is a non-polar solid, so the order reverses: polar molecules pass through quickly while large, hydrophobic molecules bind strongly and elute late.

7.2 Partition Chromatography: Normal-Phase vs. Reversed-Phase

Partition chromatography distributes solutes between two immiscible liquid phases based on their relative solubilities — much like a continuous liquid–liquid extraction.

Normal-Phase (NPC) Stationary: polar liquid (water/glycol) Mobile: non-polar solvent (hexane, CHCl₃) Non-polar elutes FIRST Polar elutes LASTReversed-Phase (RPC) Stationary: non-polar C18/C8 chains Mobile: polar solvent (water/MeCN) Polar elutes FIRST Non-polar elutes LASTReversed-phase is the most widely used configuration in modern biochemistry

Figure: Reversed-phase inverts the normal-phase elution order. In NPC the stationary film is polar, so polar solutes linger and non-polar ones wash out first. In RPC the stationary phase is a hydrophobic hydrocarbon layer instead, so the order flips: polar, hydrophilic molecules elute first and non-polar ones are retained longest.

  1. Normal-phase chromatography (NPC): the stationary phase is a polar liquid (e.g. water or glycol) immobilized on a solid support, and the mobile phase is a non-polar organic solvent (hexane, heptane, or chloroform). Non-polar molecules partition preferentially into the non-polar mobile phase and elute first; polar molecules dissolve into the polar stationary phase and elute late.
  2. Reversed-phase chromatography (RPC): the stationary phase is made non-polar by covalently bonding long hydrophobic hydrocarbon chains directly onto silica beads, while the mobile phase is a polar solvent — typically water mixed with a water-miscible organic solvent such as acetonitrile, methanol, or tetrahydrofuran. Polar, hydrophilic molecules elute first; non-polar, hydrophobic molecules interact with the hydrocarbon chains and elute late.
    C18 vs. C8: C18 (octadecylsilane) chains are 18 carbons long and highly hydrophobic, well suited to separating small, stable organic molecules. C8 (octylsilane) chains are only 8 carbons and moderately hydrophobic — gentler, and better suited to larger biomolecules like peptides and proteins.

7.3 Planar Sheet Chromatography: Paper Partitioning and Rf Calculations

Paper chromatography is a simple sheet-based form of partition chromatography. The stationary phase is water bound tightly to the polar cellulose fibers of the paper; the mobile phase is an organic solvent mixture that moves across the sheet, carrying the sample with it.

Solvent front Origin B A P Q RSolute A Solute B

Figure: Measuring Rf. P, Q, and R are all measured from the same origin. Solute A travelled distance P, solute B travelled the larger distance Q, and the solvent itself travelled the largest distance, R.

Rf = distance travelled by solute ⁄ distance travelled by solvent front

For the two solutes above: Rf(A) = P / R, and Rf(B) = Q / R. Because it is a ratio of two distances, Rf is always between 0.0 and 1.0.

Ascending solvent reservoir Capillary action works against gravityDescending solvent reservoir Capillary action is assisted by gravity

Figure: Ascending vs. descending mechanics. In ascending runs the paper's bottom edge dips into the solvent, which climbs upward by capillary action alone — gravity opposes the flow, so it slows and eventually stalls. In descending runs the reservoir sits above the paper, so gravity assists the capillary flow throughout the run.

Why descending is often preferred: gravity-assisted flow is significantly faster, especially for long runs, and it lets the solvent run completely off the bottom edge of the paper for an extended period — maximizing resolution for slow-moving bands with very small Rf values, which an ascending run could never fully resolve before stalling.

7.4 Chromatographic Mechanisms at a Glance

MechanismStationary phaseBasis of separationElution order
Adsorption (silica/alumina)Polar solid surface (silanol groups)Dipole–dipole, H-bonding, van der WaalsNon-polar first → polar last
Adsorption (charcoal)Non-polar solid surfaceHydrophobic interactionsPolar first → non-polar last
Partition (normal-phase)Polar liquid filmRelative solubility (polarity)Non-polar first → polar last
Partition (reversed-phase)Non-polar C18/C8 chainsHydrophobic interactionsPolar first → non-polar last
Planar (paper / TLC)Water on cellulose (paper) or an adsorbent layer (TLC)Partition or adsorptionQuantified as Rf (0.0–1.0)
Chromatography Techniques — Chapters 8–12

Chromatography Techniques

Chapters 8–12 · Separation Methods in Biochemistry

8. Size Exclusion Chromatography (Gel Filtration)

Size Exclusion Chromatography (SEC), also called gel filtration (aqueous mobile phases) or gel permeation (organic mobile phases), separates molecules strictly on the basis of their physical size and three-dimensional shape — no chemical interaction with the stationary phase is involved.

Sample Mixture large (O) + small (o) molecules Porous Gel Beads (Sephadex / Sepharose) o enters pores · O bypasses beads Large molecules (O) elute first — Void Volume V₀ Small molecules (o) elute last — Total Volume VT

Figure: Size-based separation on a gel filtration column. Large molecules are too big to enter the pores of the beads and travel only in the space between them, so they elute first, in the void volume (V₀). Small molecules diffuse into and out of the internal pore volume, slowing their progress, so they elute last.

8.1 Matrix Polymers and Gel Chemistry

The column is packed with porous, spherical beads composed of hydrated, cross-linked hydrophilic polymers. Pore size is carefully controlled by the degree of cross-linking.

  1. Dextran (Sephadex): composed of α(1→6)-linked glucose chains cross-linked with epichlorohydrin. Highly stable; used primarily for separating small-to-medium proteins and peptides.
  2. Polyacrylamide (Bio-Gel P): a synthetic polymer of acrylamide cross-linked with N,N′-methylenebisacrylamide. Chemically inert and resistant to microbial degradation.
  3. Agarose (Sepharose): a natural polysaccharide of alternating D-galactose and 3,6-anhydro-L-galactopyranose. Forms very large pore sizes, ideal for fractionating large protein complexes, nucleic acids, and viruses.

8.2 Complete Fractionation Range Reference

Molecular mass ranges below are calibrated for globular proteins.

Material & trade namePolymer typeFractionation range (Da)
Sephadex G-10Dextran0 – 700
Sephadex G-25Dextran1,000 – 5,000
Sephadex G-50Dextran1,500 – 30,000
Sephadex G-75Dextran3,000 – 70,000
Sephadex G-100Dextran4,000 – 150,000
Sephadex G-150Dextran5,000 – 300,000
Bio-Gel P-2Polyacrylamide100 – 1,800
Bio-Gel P-6Polyacrylamide1,000 – 6,000
Bio-Gel P-60Polyacrylamide3,000 – 60,000
Bio-Gel P-150Polyacrylamide15,000 – 150,000
Bio-Gel P-300Polyacrylamide60,000 – 400,000
Sepharose 2BAgarose2 × 106 – 25 × 106
Sepharose 4BAgarose3 × 105 – 3 × 106
Sepharose 6BAgarose1 × 105 – 20 × 106

8.3 Column Volume Mechanics

The total physical volume of the packed column bed is mathematically subdivided into three compartments:

VT = V0 + Vi + Vg
V₀ — Void volume: solvent outside the beads; measured experimentally with a huge, fully excluded molecule such as Blue Dextran (∼2 × 106 Da).
Vi — Internal pore volume: solvent trapped inside the porous channels of the beads.
Vg — Gel skeleton volume: the actual volume occupied by the solid polymer matrix.

8.4 Partition Coefficient and Elution Scenarios

The elution volume (Ve) needed to elute a solute relates to the column volumes and the partition coefficient σ (also written Kd), the fraction of internal pore volume accessible to that solute:

Ve = V0 + σVi      σ = (Ve − V0) / Vi
  1. Complete exclusion (σ = 0): the solute is larger than the largest pores and is carried entirely in the void volume, so Ve = V0. The molecular weight of the smallest molecule that cannot enter the pores is the exclusion limit of the gel.
  2. Complete inclusion (σ = 1): extremely small solutes (salts, water) have free access to the entire internal pore volume, so Ve = V0 + Vi. These elute last, in the total liquid volume of the column.
  3. Partial inclusion (0 < σ < 1): medium-sized molecules enter some of the larger pores but are excluded from smaller ones, eluting at intermediate volumes that depend on hydrodynamic size.

8.5 Molecular Weight Calibration

Within a gel's fractionation range, relative elution volume and the logarithm of solute molecular weight are linearly related:

Ve / V0 = A − B log M
By running a mixture of protein standards of known molecular weight, a calibration curve of log M against Ve/V0 is plotted. The elution volume of an unknown target protein is then measured against that line to estimate its molecular weight.

9. Ion Exchange Chromatography (IEX)

Ion exchange chromatography separates molecules based on their net surface charge, through reversible electrostatic interactions with a charged solid support.

Anion Exchanger (positive beads) + DEAE / Q resin − binds anions Cation Exchanger (negative beads) − CM / SP resin + binds cations

Figure: Anion vs. cation exchangers. A positively-charged matrix (e.g. DEAE-cellulose, Q-Sepharose) binds negatively-charged proteins; a negatively-charged matrix (e.g. CM-cellulose, SP-Sepharose) binds positively-charged proteins.

9.1 Ion Exchange Resin Chemistry

The matrix is an insoluble, hydrophilic polymer (cellulose, dextran, or agarose) covalently functionalized with charged chemical groups.

ResinClassFunctional groupCharge behavior
DEAE-celluloseWeak anion exchangerDiethylaminoethyl, –NH+(CH2CH3)2pKa ∼ 9.5; protonated at neutral/acidic pH, loses charge above pH 9.5
Q-SepharoseStrong anion exchangerQuaternary ammonium, –N+(CH3)3Permanent positive charge, pH 2–12
CM-celluloseWeak cation exchangerCarboxymethyl, –O–CH2–COO−pKa ∼ 4.0; loses charge below pH 4.0
SP-SepharoseStrong cation exchangerSulfopropyl, –SO3−Negative charge across nearly all of pH 2–14

9.2 Charge–pH Dynamics and the Isoelectric Point

Proteins are amphoteric, carrying both basic and acidic side chains. Net charge is set by buffer pH relative to the protein's isoelectric point (pI) — the pH at which net charge is exactly zero.

  1. pH > pI: the buffer accepts protons, the protein's acidic side chains lose H+, and it becomes net negatively charged (anionic) — it binds an anion exchanger (DEAE, Q).
  2. pH < pI: the buffer donates protons, the protein gains H+, and it becomes net positively charged (cationic) — it binds a cation exchanger (CM, SP).

9.3 Elution: Salt and pH Gradients

Salt gradient (ionic strength): a salt such as NaCl is passed through at increasing concentration; salt ions compete directly with bound proteins for charged sites. Weakly-charged proteins elute at low salt; highly-charged proteins require higher salt.
pH gradient: the mobile phase pH is moved toward the target protein's pI. As pH approaches pI, net charge falls to zero and the protein dissociates from the resin.

9.4 Buffer Selection Rules

With anion exchangers: use cationic buffers (Tris, imidazole, alkylamines) — their positive charge will not bind to the positive resin.
With cation exchangers: use anionic buffers (phosphate, acetate, citrate) — their negative charge will not bind to the negative resin.

9.5 Sequential Separation of DNA, RNA, and Proteins

Because the phosphodiester backbone of nucleic acids is highly acidic, both DNA and RNA carry a permanent, dense negative charge at physiological pH.

  1. Method: a cell extract is loaded onto an anion exchange column (e.g. DEAE-cellulose) at physiological pH.
  2. Elution: a gradient of increasing NaCl concentration is applied; molecules of lower charge density are displaced first.
MoleculeCharge densityElutes at
ProteinsRelatively low0.1 – 0.2 M NaCl
RNAIntermediate0.3 – 0.5 M NaCl
Genomic DNAHighest (double-stranded)> 0.7 M NaCl

10. Affinity Chromatography

Affinity chromatography is a highly selective purification technique that exploits unique, reversible biological interactions between a target molecule and a complementary ligand immobilized on a solid support.

10.1 High-Yield Ligand–Target Pairs

Immobilized ligandTarget / analytePrimary application
Monoclonal antibodyAntigenHigh-purity immunoaffinity purification of proteins
5′-AMP / NAD+Dehydrogenases, kinasesPurification of nucleotide-binding enzymes
Lectin (Concanavalin A)Glycoproteins, glycolipidsIsolation of membrane glycoproteins
Avidin / StreptavidinBiotinylated proteins/nucleic acidsUltra-strong affinity purification (Kd ≈ 10−15 M)
GlutathioneGST-tagged fusion proteinsIsolation of recombinant proteins
Oligo(dT)Poly(A)+ mRNASelective extraction of eukaryotic mRNA

10.2 Poly(A) mRNA Isolation via Oligo(dT)-Cellulose

Eukaryotic mRNAs uniquely carry a 3′ poly-A tail (50–200 adenines), which can be exploited to isolate mRNA from total cellular RNA (>95% of which is rRNA and tRNA).

Total RNA mRNA (poly-A) + rRNA + tRNA high salt Oligo(dT)-cellulose poly-A hybridizes (A=T) rRNA / tRNA no poly-A — wash through Purified mRNA eluted with low salt / water

Figure: mRNA purification by oligo(dT) affinity chromatography. Under high ionic strength, poly-A tails hybridize to the immobilized oligo-dT; rRNA and tRNA lack poly-A and wash through. Low-salt or water elution destabilizes the A=T pairing, releasing purified mRNA.

  1. Binding (high ionic strength): total RNA is loaded in ∼0.5 M NaCl. The high salt shields the negative phosphate backbones, letting poly-A tails hybridize to the oligo-dT ligand by A=T base pairing; rRNA and tRNA, lacking poly-A, pass straight through.
  2. Elution (low ionic strength): washing with very low-salt buffer or water removes the charge shielding, so electrostatic repulsion between phosphate backbones destabilizes the A=T bonds and releases pure mRNA.

10.3 Association and Dissociation Kinetics

Reversible binding of a macromolecule (M) to its ligand (L) is described by an association/dissociation equilibrium, quantified by the equilibrium dissociation constant:

Kd = [M][L] / [M·L] = koff / kon
Biological significance: Kd has units of concentration (M). A smaller Kd means less free reactant remains at equilibrium — i.e. higher binding affinity. High-affinity affinity-chromatography systems typically operate with Kd values from 10−6 to 10−11 M.

10.4 Sequence-Specific DNA Affinity Chromatography for Transcription Factors

  1. Preparation: synthetic double-stranded oligonucleotides carrying the target consensus sequence are covalently coupled to agarose beads.
  2. Binding: a nuclear extract containing a mixture of proteins is loaded; the target transcription factor binds specifically to the immobilized DNA sequence.
  3. Washing: weakly or non-specifically bound proteins are removed with moderate-salt washes.
  4. Elution: a high-salt buffer (> 0.5 M NaCl or KCl) weakens the electrostatic interaction between basic protein residues and the DNA backbone, releasing the purified transcription factor.

11. High-Performance Liquid Chromatography (HPLC)

HPLC is a highly instrumented column chromatography technique that uses high pressure to achieve rapid, high-resolution separations.

Solvent Reservoir A Solvent Reservoir B Gradient Controller High-Pressure Pump Sample Injector HPLC Column (micro-bead packing) Detector Data System / Chromatogram

Figure: HPLC system flow. Solvents from two reservoirs are combined in precise ratios by the gradient controller, driven at high pressure by the pump, mixed with the injected sample, resolved on the packed column, and read out by the detector into a chromatogram.

11.1 System Instrumentation

  1. High-pressure pumps: deliver a continuous, pulse-free flow of mobile phase at pressures up to 400 atmospheres (∼6,000 psi); dual-piston reciprocating pumps are common.
  2. Gradient mixer: mixes solvents from different reservoirs in precise, time-dependent ratios, enabling gradient elution (e.g. gradually increasing organic solvent in reversed-phase HPLC).
  3. Sample injector: a high-pressure loop valve (e.g. Rheodyne valve) introducing precise volumes (1–100 µL) into the pressurized stream without interrupting flow.
  4. Columns and guard columns: heavy-walled stainless steel or glass-lined tubing; a short guard column traps particulates and strongly-bound impurities ahead of the analytical column.
  5. Detectors: UV-Vis absorbance (diode-array detectors scan many wavelengths at once), fluorescence detectors (high sensitivity for fluorescent compounds), and mass spectrometers (LC-MS, giving mass-to-charge data for structural identification).

11.2 Resolving Power: The van Deemter Equation

High resolution comes from extremely small stationary-phase packing beads (3–10 µm). Column efficiency is described by plate height H (mobile-phase linear velocity u; smaller H means higher efficiency):

H = A + B/u + C·u
  1. A — Eddy diffusion: reflects the multiple paths solutes can take through the column (A = 2λdp, where dp is particle diameter). Smaller beads shorten and even out these paths, reducing A.
  2. B/u — Longitudinal diffusion: solute diffusing away from the center of its band along the column length; minimized by a faster mobile-phase flow rate.
  3. C·u — Mass transfer resistance: the time needed for a solute to equilibrate between phases (C ∝ dp²/Ds, where Ds is the stationary-phase diffusion coefficient). Smaller particles shorten this diffusion distance.

11.3 Why High Pressure Is Required

The trade-off: as packing bead size dp decreases, the spaces between beads shrink and resistance to flow rises sharply. By the Darcy equation, pressure drop ΔP ∝ 1/dp² — so maintaining a usable flow rate through columns packed with 3 µm beads requires high-pressure pumps to overcome that resistance.

12. Gas Chromatography (GC / GLC)

Gas Chromatography, typically run as Gas–Liquid Chromatography (GLC), separates volatile, thermally stable compounds by partitioning them between a gaseous mobile phase and a liquid stationary phase.

Carrier Gas Cylinder (He / N₂ / Ar) Flow Controller Injection Port (heated to vaporize, ∼250°C) Temperature-Programmed Oven Coiled Capillary Column Detector (FID / TCD / ECD)

Figure: GC system flow. An inert carrier gas is metered by the flow controller, sweeps the vaporized sample from the heated injection port through a coiled capillary column inside a temperature-programmed oven, and carries separated compounds into the detector.

12.1 System Configuration

  1. Carrier gas (mobile phase): an inert, dry gas — most commonly Helium, Nitrogen, or Argon; the choice depends on the detector used.
  2. Injection port: heated (often to 250°C) to instantly vaporize liquid samples injected via micro-syringe through a rubber septum into the carrier gas stream.
  3. Capillary columns (open tubular): long, thin, coiled fused-silica tubes (15–100 m long, 0.1–0.5 mm i.d.), interior-coated with a thin liquid polymer film (e.g. polydimethylsiloxane) for exceptionally high resolution.
  4. Packed columns: shorter (1–3 m), wider tubes packed with solid particles coated in the liquid stationary phase.
  5. Temperature programming: the oven can run isothermal or ramp gradually, letting low-boiling compounds separate quickly at low temperature while high-boiling compounds elute promptly as temperature rises.

12.2 Detectors: FID, TCD, and ECD

  1. Flame Ionization Detector (FID): effluent is mixed with hydrogen and air and burned in a micro-flame; pyrolysis produces carbon-containing ions collected across a potential difference, giving a current proportional to carbon content.
    Highly sensitive to organic molecules, but destructive to the sample; cannot detect inorganic compounds such as water or CO2.
  2. Thermal Conductivity Detector (TCD): measures thermal conductivity of the gas stream via a heated filament; an eluting analyte lowers conductivity, raising the filament's temperature and resistance.
    Universal (detects organic and inorganic compounds) and non-destructive, but less sensitive than FID.
  3. Electron Capture Detector (ECD): a radioactive source (typically Nickel-63) ionizes the carrier gas to generate free electrons; halogenated compounds (Cl, Br, F) capture these electrons, reducing measured current.
    Highly sensitive and selective for halogenated compounds, pesticides, and PCBs.

12.3 GC vs. HPLC

FeatureGas ChromatographyHPLC
Mobile phase stateGaseous (inert carrier gas: He, N2)Liquid (aqueous/organic mixtures)
Separation variablesVolatility and affinity for stationary phasePolarity, charge, size, or biological affinity
Thermal limitationSolutes must be volatile and stable to ∼300°CNone — separates thermally unstable proteins/DNA at ambient temperature
Column lengthVery long (15–100 m) coiled capillariesRelatively short (5–25 cm) packed columns
Sample recoveryTypically destructive (with FID)Completely non-destructive; samples can be recovered
Phase interactionSolutes interact only with the stationary phaseSolutes interact chemically with both phases

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