Protein folding in finite time despite combinatorial complexity

Establish how a newly translated protein achieves its native fold in finite time despite the exponentially large conformational space, identifying the physical principles and pathways that resolve Levinthal’s paradox in vivo.

Background

Protein folding remains a central challenge: the number of conformations grows exponentially with sequence length, yet folding occurs rapidly and reliably in cells.

Resolving this paradox requires integrating long-range interactions, solvent effects, and cellular factors beyond nearest-neighbor relaxation.

References

Such is the problem of protein folding where it is unknown how a newly-translated protein strand can relax into its optimal folded conformation in fixed time when the number of possible conformational states is exponentially large with respect to the protein sequence length, and explorations of the funnel-like conformational "landscape" are obstructed by numerous topological restrictions on folding [928].

— Physical Principles of Quantum Biology (2503.11747 - Babcock et al., 14 Mar 2025) in Chapter 12 - Molecular Forces: Solvent Effects & Dispersion