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Transient receptor potential vanilloid member 1 (TRPV1) is a heat and capsaicin receptor that allows cations to permeate and cause pain. As the molecular basis for temperature sensing, the heat capacity (Δ C p ) model [D. E. Clapham, C. Miller, Proc. Natl. Acad. Sci. U.S.A. 108 , 19492–19497 (2011).] has been proposed and experimentally supported. Theoretically, heat capacity is proportional to a variance in enthalpy, presumably related to structural fluctuation; however, the fluctuation of TRPV1 has not been directly visualized. In this study, we directly visualized single-molecule structural fluctuations of the TRPV1 channels in a lipid bilayer with the ligands resiniferatoxin (agonist, 1,000 times hotter than capsaicin) and capsazepine (antagonist) by high-speed atomic force microscopy. We observed the structural fluctuations of TRPV1 in an apo state and found that RTX binding enhances structural fluctuations, while CPZ binding suppresses fluctuations. These ligand-dependent differences in structural fluctuation would play a key role in the gating of TRPV1.

We study the bigraded vector space structure of Landau–Ginzburg orbifolds with the permutation symmetries of variables. We calculate the formula of the Poincare polynomial for a certain loop polynomial orbifoldized by a semidirect product of a diagonal symmetry group and cyclic permutation group and check that the generalization of Berglund–Hubsch transpose gives mirror symmetric pairs for these cases.