Macromolecular Crowding & Protein Folding

Cellular Environment

Crowder volume fraction φ 20%

Crowder radius r_c 2.5 nm

Protein

Chain length N 150 aa

Intrinsic stability ΔG₀ +1.0 kcal/mol

Live State

Unfolded (coil)

ΔΔG crowding

0.00 kcal/mol

Fraction folded

Chain radius of gyration (live)

0.00 nm

How it works

A folded (compact) protein has a much smaller effective radius than its unfolded (coil) form. Squeezing a sphere of radius a into a bath of hard-sphere crowders of radius R at volume fraction φ costs a free energy given by scaled-particle theory (Minton):

βμ(a,R,φ) = −ln(1−φ) + 3q·t + [3q²t + 4.5q²t²] + q³t
  where q = a/R,  t = φ/(1−φ)

Because the unfolded coil's radius is bigger, inserting it costs more free energy than inserting the compact folded state — crowding entropically favours the folded state. The stabilisation is:

ΔΔG_crowd = RT · [μ(a_folded) − μ(a_unfolded)]   (kcal/mol, always ≤ 0)
ΔG_total  = ΔG_intrinsic + ΔΔG_crowd
K_fold    = exp(−ΔG_total / RT),   fraction folded = K_fold / (1 + K_fold)

Radii are estimated from chain length N (residues) with standard scaling laws: folded R_g ≈ 0.224·N^0.38 nm (compact globule), unfolded R_g ≈ 0.193·N^0.598 nm (Flory random coil). Temperature is fixed at 310 K (body temperature).

φ slider — how much of the cytoplasm volume is occupied by other macromolecules (crowders, translucent spheres). Real cells run ~20–40%.
r_c slider — crowder size (e.g. small ions vs. BSA-sized proteins). Smaller crowders pack more excluded volume per φ, so they stabilise folding more strongly.
N slider — protein chain length; sets both bead-chain length on screen and the two physical radii above.
ΔG₀ slider — the protein's own intrinsic folding stability in dilute buffer, before crowding is added (many real proteins are only marginally stable, ±3 kcal/mol).
Every few seconds the chain attempts a folding/unfolding transition, sampled from the live equilibrium probability above — this is the same excluded-volume argument used to explain why proteins that barely fold in a test tube fold reliably inside a real, crowded cell.

Crowder molecules Protein chain

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