Protein Regge Trajectories, Phase Coexistence and Physics of Alzheimers Disease

Alzheimer’s disease causes severe neurodegeneration in the brain that leads to a certain death. The defining factor is the formation of extracellular senile amyloid plaques in the brain. However, therapeutic approaches to remove them have not been effective in humans, and so our understanding of the cause of Alzheimer’s disease remains incomplete. Here we investigate physical processes that might relate to its onset. Instead of the extracellular amyloid, we scrutinize the intracellular domain of its precursor protein. We argue for a phenomenon that has never before been discussed in the context of polymer physics: Like ice and water together, the intracellular domain of the amyloid precursor protein forms a state of phase coexistence with another protein. This leads to an inherent instability that could well be among the missing pieces in the puzzle of Alzheimer’s disease.

💡 Research Summary

The paper “Protein Regge Trajectories, Phase Coexistence and Physics of Alzheimer’s Disease” proposes a novel physical mechanism that may underlie the onset of Alzheimer’s disease (AD). While the conventional view focuses on extracellular Aβ42 plaques, the authors shift attention to the intracellular domain of the amyloid precursor protein (APP), specifically the APP intracellular domain (AICD), and its interaction with the nuclear adaptor protein Fe65.

The authors begin by treating proteins as polymers and invoking the well‑known scaling law for the radius of gyration (Rg) of a polymer chain: Rg ≈ R0·N^ν, where N is the number of residues, ν is the compactness (inverse fractal) exponent, and R0 is a prefactor that depends weakly on chemistry. They argue that, because protein sequences become chemically uniform as N grows, R0 takes on only a few discrete values, giving rise to distinct “Regge trajectories” in the (N, Rg) plane – an analogy to Regge trajectories in high‑energy physics.

Four universal polymer phases are identified: (i) a collapsed, space‑filling phase with ν≈1/3, (ii) the Θ‑point with ν≈1/2, (iii) the self‑avoiding random‑walk (Flory) phase with ν≈3/5, and (iv) a one‑dimensional rod‑like phase with ν≈1 (e.g., straight α‑helices or β‑strands). By mining the Protein Data Bank (PDB) for high‑resolution, low‑homology structures, the authors show that the vast majority of single‑chain proteins lie on the ν≈1/3 trajectory, while a few oligomeric complexes populate two additional ν≈1 trajectories (R(2)g≈0.48·N^0.973 and R(3)g≈1.02·N^0.94).

Crucially, a small subset of oligomers displays “phase coexistence”: one chain follows a Θ‑point trajectory (ν≈1/2) while another follows a ν≈1 trajectory. The authors identify two classes of such complexes. The first consists of a single protein that, due to multiple sub‑chains, occupies different phases. The second class – the focus of the paper – comprises heteromeric complexes where distinct proteins occupy distinct phases. Among these, the AICD/Fe65 complex (PDB entry 3DXC, chain B for AICD) is highlighted as Alzheimer‑relevant.

Structural analysis of AICD reveals two tightly packed loops separated by a short β‑strand. The backbone bond (ψ) and torsion (θ) angles of each loop are fitted to soliton solutions of the nonlinear Schrödinger equation, providing an analytical description of the loops. The loops are anchored by proline residues at positions 669 and 685. By virtually sliding the first loop along the backbone toward Pro‑669, the authors compute the resulting change in Rg. The radius of gyration increases monotonically, and when the loop reaches the proline, the AICD configuration shifts from the ν≈1 Regge trajectory R(2)g to the slightly different ν≈1 trajectory R(3)g. This demonstrates that two distinct, yet energetically comparable, conformations exist for AICD when bound to Fe65.

The authors argue that this bistability constitutes a “genetic switch”. In the cellular context, the AICD/Fe65 complex may toggle between the two ν≈1 conformations, or, upon dissociation, AICD may undergo a rapid phase transition to the collapsed ν≈1/3 state. Such a transition could facilitate γ‑secretase cleavage, generate Aβ peptides, or otherwise perturb normal cellular processes, thereby contributing to plaque formation and neurodegeneration.

The paper concludes that (1) protein structures can be classified by Regge‑type trajectories, revealing rare phase‑coexistence phenomena; (2) the AICD/Fe65 complex exemplifies such a phenomenon and may provide a missing physical link in AD pathology; and (3) experimental validation (e.g., NMR, single‑molecule force spectroscopy, mutagenesis of the anchoring prolines) and more sophisticated molecular dynamics simulations are essential to test the hypothesis.

Overall, the work introduces an interdisciplinary framework that merges polymer physics, high‑energy theory concepts, and neurobiology. While the theoretical analysis is intriguing and the identification of phase coexistence is novel, the study currently lacks direct experimental evidence linking the proposed structural instability to Alzheimer’s disease progression. Future work that quantifies the energetics of the two AICD conformations, measures their prevalence in neuronal cells, and assesses the impact on Aβ production will be critical to determine whether the proposed mechanism is biologically significant.