SDS-PAGE Relative Molecular Weight ($M_r$) Determination & Ferguson Plot Analysis
In Sodium Dodecyl Sulfate Polyacrylamide Gel Electrophoresis (SDS-PAGE), the anionic detergent SDS binds to unfolded polypeptide backbones at a constant stoichiometric ratio of approximately $1.4text{ g SDS per 1.0 g protein}$ (roughly one SDS molecule per two amino acid residues). This imparts a uniform, high negative net charge density that overwhelms intrinsic protein charges, producing a constant charge-to-mass ratio ($q/m$).
Consequently, electrophoretic separation occurs solely on the basis of hydrodynamic sieving through the polyacrylamide gel pore matrix, governed by the Ferguson relationship:
$$log_{10}(R_f) = log_{10}(Y_0) – K_R cdot %T$$
where $R_f$ is relative mobility, $Y_0$ is free electrophoretic mobility, $K_R$ is the retardation coefficient (proportional to molecular weight), and $%T$ is total acrylamide concentration. In a fixed-percentage resolving gel ($12%T$), electrophoretic mobility is inversely proportional to the logarithm of molecular mass:
$$log_{10}(M_r) = -m cdot R_f + b$$
where relative mobility $R_f$ is defined as:
$$R_f = frac{text{Distance migrated by protein band (mm)}}{text{Distance migrated by Bromophenol Blue dye front (mm)}}$$
Isotachophoresis Stacking Mechanism: The discontinuous Laemmli system employs a two-gel architecture with differing $text{pH}$ and pore sizes:
1. Stacking Gel ($4%T$, $text{pH } 6.8$ Tris-HCl): Chloride ions ($text{Cl}^-$) possess high mobility and act as the leading ions. Glycine, whose isoelectric point is $text{pI } = 5.97$, exists predominantly as a zwitterion ($>99%$) with very low electrophoretic mobility at $text{pH } 6.8$, acting as the trailing ion. Protein-SDS complexes have intermediate mobilities and are compressed into an ultra-sharp ($<0.1text{ mm}$) starting band between the leading chloride and trailing glycine fronts.
2. Resolving Gel ($12%T$, $text{pH } 8.8$ Tris-HCl): At $text{pH } 8.8$, glycine fully ionizes into glycinate ($text{Gly}^-$), speeding past the proteins directly behind chloride. The unstacked proteins then resolve purely according to molecular sieve sieving.
- Electrophoresis Apparatus: Bio-Rad Mini-PROTEAN Tetra Cell with casting stands, $1.0text{ mm}$ glass plates, and 10-well combs. PowerPac Basic power supply.
- Acrylamide Stock: $30% (w/v)$ Acrylamide / Bis-acrylamide solution ($29:1$ crosslinking ratio).
- Gel Buffers: $1.5text{ M Tris-HCl}$ ($text{pH } 8.8$) for resolving gel; $0.5text{ M Tris-HCl}$ ($text{pH } 6.8$) for stacking gel.
- Running Buffer ($1times$): $25text{ mM Tris}$, $192text{ mM Glycine}$, $0.1% (w/v)text{ SDS}$, $text{pH } 8.3$.
- Sample Loading Buffer ($4times$): $200text{ mM Tris-HCl}$ ($text{pH } 6.8$), $8% (w/v)text{ SDS}$, $40% (v/v)text{ Glycerol}$, $20% (v/v) betatext{-mercaptoethanol}$, $0.04% (w/v)text{ Bromophenol Blue}$.
- Protein Molecular Weight Ladder: Broad-range prestained marker ($14.4–116.0text{ kDa}$: β-galactosidase $116.0text{ kDa}$, BSA $66.2text{ kDa}$, Ovalbumin $45.0text{ kDa}$, Carbonic Anhydrase $29.0text{ kDa}$, Lysozyme $14.4text{ kDa}$).
- Staining & Destaining Solutions: Coomassie Brilliant Blue R-250 ($0.1%$ in $40%$ methanol, $10%$ acetic acid); Destain: $20%$ methanol, $10%$ acetic acid.
Assemble $1.0text{ mm}$ glass plates in casting frames. Prepare $10text{ mL}$ of $12%$ resolving gel solution: $4.0text{ mL}$ $30%$ Acrylamide/Bis, $2.5text{ mL}$ $1.5text{ M Tris}$ ($text{pH } 8.8$), $100 mutext{L}$ $10%$ SDS, $3.3text{ mL}$ $text{ddH}_2text{O}$. Initiate polymerization with $100 mutext{L}$ $10%$ freshly prepared APS and $10 mutext{L}$ TEMED. Pour into cassette leaving $1.5text{ cm}$ at top; overlay immediately with isopropanol to exclude atmospheric $text{O}_2$. After 30 minutes, wash overlay, pour $4%$ stacking gel with comb inserted, and polymerize for 20 minutes.
Mix $15 mutext{L}$ of protein sample ($1.0text{ mg/mL}$) with $5 mutext{L}$ of $4times$ Laemmli sample buffer in microcentrifuge tubes. Heat samples in a dry block at $95^circtext{C}$ for precisely 5 minutes to fully disrupt tertiary/secondary structures and reduce all disulfide bonds via $beta$-mercaptoethanol. Pulse-spin in microcentrifuge.
Place gel cassette into tank and fill inner and outer chambers with $1times$ Tris-Glycine-SDS running buffer. Load $10 mutext{L}$ of protein ladder into Lane 1 and $15 mutext{L}$ of denatured samples into remaining wells. Run at constant voltage of $80text{ V}$ through the stacking gel (~20 min) until the blue dye front enters resolving gel, then increase to $120text{ V}$. Terminate run when the Bromophenol Blue dye front reaches $2text{ mm}$ above the bottom plate (~75 min).
Disassemble plates and immerse gel in Coomassie R-250 staining solution for 45 minutes with gentle orbital shaking ($50text{ rpm}$). Transfer to destaining solution, replacing destain every hour until gel background is completely clear. Image gel using a calibrated transilluminator / flatbed scanner and measure migration distances with digital calipers ($pm 0.05text{ mm}$).
| Protein Marker Band | Actual M_r (Da) | log₁₀(M_r) | Migration d (mm) | Dye Front d_front (mm) | Relative Mobility R_f |
|---|---|---|---|---|---|
| β-Galactosidase | 116,000 | 5.064 | 10.4 | 65.0 | 0.160 |
| Bovine Serum Albumin | 66,200 | 4.821 | 18.9 | 65.0 | 0.291 |
| Ovalbumin | 45,000 | 4.653 | 30.6 | 65.0 | 0.471 |
| Carbonic Anhydrase | 29,000 | 4.462 | 41.6 | 65.0 | 0.640 |
| Lysozyme | 14,400 | 4.158 | 54.0 | 65.0 | 0.831 |
| Unknown Target Band | Calculated | 4.680 | 28.0 | 65.0 | 0.431 |
Regression Equation:
$$log_{10}(M_r) = -1.350 cdot R_f + 5.281 quad (R^2 = 0.9984)$$
Calculation for Unknown:
$$log_{10}(M_r) = -1.350(0.431) + 5.281 = 4.699 implies M_r = 10^{4.699} = mathbf{50,020text{ Da}} approx mathbf{50.0text{ kDa}}$$
Conclusion: The calculated subunit molecular weight of $50.0text{ kDa}$ matches the predicted open reading frame translation of the target recombinant monomer with $<1.5%$ experimental error.
