Size-Exclusion Chromatography (SEC): Native Stokes Radius & Oligomeric State Determination
Size-Exclusion Chromatography (SEC), also termed gel filtration, separates biological macromolecules strictly according to their hydrodynamic volume (effective Stokes radius, $R_s$), rather than molecular weight alone. The stationary phase consists of spherical, highly porous beads with a controlled pore size distribution.
When a sample is pumped through the column:
1. Large macromolecules whose Stokes radius exceeds the bead pore diameter are completely excluded from the internal pore volume and elute first in the Void Volume ($V_0$).
2. Very small molecules (salts, acetone) diffuse freely into the entire solvent volume of the column, eluting last in the Total Liquid Volume ($V_t$).
3. Intermediate proteins partition partially into the pores; larger proteins elute before smaller ones.
The retention of a solute is quantitatively parameterized by the partition coefficient ($K_{av}$):
$$K_{av} = frac{V_e – V_0}{V_t – V_0}$$
where $V_e$ is the elution volume corresponding to the peak maximum. Over the fractionation range of the gel, $K_{av}$ displays an inverse linear relationship with $log_{10}(M_r)$ or Stokes radius ($R_s$):
$$K_{av} = -a cdot log_{10}(M_r) + b$$
Oligomeric State Determination: While SDS-PAGE yields the denatured subunit molecular weight ($M_{r,text{subunit}}$), SEC reveals the native quaternary structure ($M_{r,text{native}}$). Comparing $M_{r,text{native}} / M_{r,text{subunit}}$ distinguishes monomeric, homodimeric, or higher-order multimeric quaternary architectures in solution.
- Chromatography System: รKTA Pure 25 FPLC system equipped with UV monitor ($280text{ nm}$ and $254text{ nm}$), conductivity flow cell, and automated fraction collector.
- Column: Superdex 75 Increase 10/300 GL ($24text{ mL}$ bed volume, fractionation range $3,000–70,000text{ Da}$, Cytiva).
- Calibration Standards:
- Blue Dextran 2000 ($M_r approx 2,000text{ kDa}$, $V_0$ void marker, $1.0text{ mg/mL}$)
- Bovine Serum Albumin ($66.2text{ kDa}$, $R_s = 3.48text{ nm}$)
- Ovalbumin ($44.3text{ kDa}$, $R_s = 3.05text{ nm}$)
- Carbonic Anhydrase ($29.0text{ kDa}$, $R_s = 2.43text{ nm}$)
- Ribonuclease A ($13.7text{ kDa}$, $R_s = 1.64text{ nm}$)
- Acetone ($0.5% v/v$, $V_t$ total permeation marker)
- Running Buffer: $20text{ mM Sodium Phosphate}$, $150text{ mM NaCl}$, $text{pH } 7.2$, filtered ($0.22 mutext{m}$) and degassed for 20 min.
Wash the Superdex 75 column with 1.5 column volumes (CV, ~36 mL) of degassed Milli-Q water, followed by 2.0 CV (~48 mL) of equilibration buffer at a constant flow rate of $0.8text{ mL/min}$ ($25^circtext{C}$). Monitor baseline UV at $280text{ nm}$ and conductivity to ensure flat, drift-free stability.
Load $100 mutext{L}$ of Blue Dextran ($1.0text{ mg/mL}$) mixed with $0.5%$ Acetone through the sample injection loop. Elute isocratically with 1.5 CV of buffer at $0.8text{ mL/min}$. Record $V_e$ of Blue Dextran peak ($A_{280}$) as $V_0$ and $V_e$ of Acetone peak ($A_{254}$) as $V_t$.
Inject $100 mutext{L}$ of protein standard mixture containing BSA, Ovalbumin, Carbonic Anhydrase, and Ribonuclease A ($1.5text{ mg/mL}$ each). Run isocratic elution over 1.2 CV. รKTA UNICORN software automatically integrates peak elution volumes ($V_e$). Calculate $K_{av}$ for each standard.
Centrifuge target protein solution ($1.5text{ mg/mL}$) at $14,000 times g$ for 10 min to remove subvisible aggregates. Inject $100 mutext{L}$ and elute under identical chromatographic conditions. Record peak elution volume and calculate native apparent molecular weight and Stokes radius from the standard curve.
| Standard Calibration Solute | M_r (Da) | Stokes Radius R_s (nm) | Elution Volume V_e (mL) | Partition Coeff K_av |
|---|---|---|---|---|
| Blue Dextran (V₀) | 2,000,000 | — | 7.85 mL (V₀) | 0.000 |
| Bovine Serum Albumin | 66,200 | 3.48 nm | 9.42 mL | 0.098 |
| Ovalbumin | 44,300 | 3.05 nm | 11.38 mL | 0.220 |
| Carbonic Anhydrase | 29,000 | 2.43 nm | 13.45 mL | 0.349 |
| Ribonuclease A | 13,700 | 1.64 nm | 16.12 mL | 0.515 |
| Acetone (V_t) | 58 | 0.25 nm | 23.90 mL (V_t) | 1.000 |
| Target Recombinant Protein | Native Calc | 3.12 nm | 11.10 mL | 0.202 |
Calculation of Native Molecular Weight:
Total available pore volume: $V_t – V_0 = 23.90 – 7.85 = 16.05text{ mL}$.
For Target Protein: $K_{av} = frac{11.10 – 7.85}{16.05} = mathbf{0.2025}$.
Regression fit: $K_{av} = -0.605 cdot log_{10}(M_r) + 3.018 quad (R^2 = 0.9972)$.
$$log_{10}(M_{r,text{native}}) = frac{3.018 – 0.2025}{0.605} = 4.654 implies M_{r,text{native}} = mathbf{45,100text{ Da}} approx mathbf{45.1text{ kDa}}$$
Quaternary Structure Conclusion: SDS-PAGE revealed a denatured subunit mass of $22.5text{ kDa}$. The native SEC mass of $45.1text{ kDa}$ demonstrates that the active protein exists in solution as a stable, monodisperse homodimer ($2 times 22.5text{ kDa} = 45.0text{ kDa}$).
