Foldara: Levinthal's Paradox

Physics of Life & Earth arc, page 192 of 193. Back to The Pixelated Physics Universe

Who they are

Foldara's ribbon does not search every shape. It slides down a funnel and drops into its fold.

Foldara is a character of the Physics of Life & Earth arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

Cyrus Levinthal pointed out in a 1969 talk that a protein cannot find its folded shape by random search. Take illustrative numbers: 100 residues, 3 shapes each, 10⁻¹³ s per try. That is 3¹⁰⁰ ≈ 5 × 10⁴⁷ shapes, and a blind search would take about 10²⁷ years. Real proteins fold in milliseconds to seconds.

$$ \begin{gathered} 3^{100} \approx 5\times10^{47} \ \text{shapes} \\ 5\times10^{47} \times 10^{-13}\ \mathrm{s} \approx 10^{27}\ \text{years} \end{gathered} $$

Honest caveat: The numbers are a textbook illustration, not measurements or figures from Levinthal's talk. AlphaFold predicts structures; the paradox is about folding kinetics. How much folding follows specific pathways versus a broad funnel is still discussed.

Sources

• Zwanzig, Szabo & Bagchi (1992) Levinthal's paradox, Proc. Natl. Acad. Sci. USA 89, 20
• Bryngelson & Wolynes (1987) Spin glasses and the statistical mechanics of protein folding, Proc. Natl. Acad. Sci. USA 84, 7524
• Dill & Chan (1997) From Levinthal to pathways to funnels, Nat. Struct. Biol. 4, 10

Crossovers

Foldara meets Barrierwyn (Kramers Escape Rate). Foldara's protein slides down a funnel instead of searching every shape. Barrierwyn's barriers along the way set how fast folding happens.

Foldara meets Vitressa (Glass Transition). Foldara's funnel leads to one fold. Vitressa's rugged landscape traps a glass in many states. A smooth funnel is how a protein avoids getting stuck.

Wear the lore

• Foldara – Levinthal's Paradox Physics T-Shirt

Concept keywords: Levinthal's Paradox, Foldara, Physics of Life & Earth, physics lore, Pixelated Physics