Foldara

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

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.

Levinthal's own point was that folding must follow pathways. The modern picture is a funnel-shaped energy landscape that biases the chain downhill, so it never samples most states. Zwanzig, Szabo and Bagchi (1992) showed that a small energy bias shrinks the search time enormously.

3¹⁰⁰ ≈ 5 × 10⁴⁷ shapes × 10⁻¹³ s ≈ 10²⁷ years

• 100: residues (illustrative)
• 3: shapes per residue (illustrative)
• 10⁻¹³ s: time per trial (illustrative)

Levinthal, “How to fold graciously” (1969 talk); Bryngelson & Wolynes, PNAS 84, 7524 (1987); Dill & Chan, Nat. Struct. Biol. 4, 10 (1997).

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.

On the shirt

Front: Foldara, the pixel-art character, with “LEVINTHAL'S PARADOX”. Back: the 3¹⁰⁰ count, the 10²⁷-year blind search, the real folding times, the funnel and the 1969, 1987 and 1997 sources. Printed on a unisex tee.