The protein dynamical transition is a pseudogap changeover

The emergence of biochemical activities in a protein seem to commence with the onset of atomic mean-square displacements along the protein lattice. The ensuing protein dynamical transition has been discussed extensively in the literature, and often with conflicting conclusions. Here we clarify the phenomenon by establishing a deep connection between the dynamical transition and the pseudogap state where high-temperature superconductivity comes to its end. For this we first show how to endow proteins with an order parameter akin the quasiparticle wave function in superconductors. We then present universality arguments to claim that the protein dynamical transition takes place in tandem with a pseudogap transmutation. We confirm that available experimental data fully supports our proposal.

💡 Research Summary

The manuscript titled “The protein dynamical transition is a pseudogap changeover” puts forward a bold hypothesis: the well‑known protein dynamical transition (PDT) that occurs around 180–240 K is fundamentally the same phenomenon as the pseudogap state observed in high‑temperature superconductors. The authors attempt to bridge the two fields by constructing a complex order parameter for the protein backbone, drawing on the Hasimoto transformation that maps curvature and torsion of a space curve onto a wave‑function of the nonlinear Schrödinger equation (NLSE).

First, the backbone geometry is reduced to discrete curvature κ_i and torsion τ_i defined solely from Cα positions. These are combined into a complex variable ψ_i = κ_i exp(iτ_i). This construction mirrors the complex order parameter φ = ρ exp(iθ) used to describe superconducting condensates, where ρ is the amplitude (gap) and θ the phase. The authors then write an energy functional (Eq. 7) that is essentially a discretized version of the DNLS (discrete nonlinear Schrödinger) model, supplemented with terms corresponding to momentum, helicity, and a Proca‑type mass. They argue that this functional is the analogue of a Landau‑Ginzburg free energy for a superconductor, with κ playing the role of a Cooper‑pair density and τ acting as a phase variable.

Within this framework the “pseudogap” is defined as a state where the average amplitude ⟨|ψ|⟩ (or ⟨κ⟩) remains non‑zero while the phase average ⟨exp(iτ)⟩ vanishes due to strong phase decoherence. By analogy, the authors claim that as temperature rises from the low‑temperature collapsed phase (compactness exponent ν≈1/3) toward the Θ‑point (ν≈1/2), the protein backbone retains local curvature (i.e., structural motifs such as α‑helices and β‑strands) but loses coherent torsional ordering, thereby entering a pseudogap regime prior to the full Θ‑point transition.

To provide empirical support, the authors re‑analyse temperature‑dependent B‑factor data from two crystallographic studies: crambin (PDB entry from Ref.