VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS

We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler–Lagrange equation of the Chern–Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern–Federer submanifolds in Riemannian space forms

The first variational formulae for integral invariants of degree two of the second fundamental form of a map between pseudo-Riemannian manifolds

東京都立大学Tokyo Metropolitan University博士（理学）doctoral thesi

Moving toward generalizable NZ-1 labeling for 3D structure determination with optimized epitope-tag insertion

タンパク質の抗体ラベリング技術を改良し、構造解析をアシスト --電子顕微鏡やX線結晶解析による構造決定を加速化--. 京都大学プレスリリース. 2021-04-20.Antibody labeling has been conducted extensively for structure determination using both X-ray crystallography and electron microscopy (EM). However, establishing target-specific antibodies is a prerequisite for applying antibody-assisted structural analysis. To expand the applicability of this strategy, an alternative method has been developed to prepare an antibody complex by inserting an exogenous epitope into the target. It has already been demonstrated that the Fab of the NZ-1 monoclonal antibody can form a stable complex with a target containing a PA12 tag as an inserted epitope. Nevertheless, it was also found that complex formation through the inserted PA12 tag inevitably caused structural changes around the insertion site on the target. Here, an attempt was made to improve the tag-insertion method, and it was consequently discovered that an alternate tag (PA14) could replace various loops on the target without inducing large structural changes. Crystallographic analysis demonstrated that the inserted PA14 tag adopts a loop-like conformation with closed ends in the antigen-binding pocket of the NZ-1 Fab. Due to proximity of the termini in the bound conformation, the more optimal PA14 tag had only a minor impact on the target structure. In fact, the PA14 tag could also be inserted into a sterically hindered loop for labeling. Molecular-dynamics simulations also showed a rigid structure for the target regardless of PA14 insertion and complex formation with the NZ-1 Fab. Using this improved labeling technique, negative-stain EM was performed on a bacterial site-2 protease, which enabled an approximation of the domain arrangement based on the docking mode of the NZ-1 Fab

Mechanistic insights into intramembrane proteolysis by E. coli site-2 protease homolog RseP

細胞膜の中ではたらく特殊なタンパク質分解酵素の構造を解明 --細菌感染症の新たな治療法の開発へ期待--. 京都大学プレスリリース. 2022-08-25.Site-2 proteases are a conserved family of intramembrane proteases that cleave transmembrane substrates to regulate signal transduction and maintain proteostasis. Here, we elucidated crystal structures of inhibitor-bound forms of bacterial site-2 proteases including Escherichia coli RseP. Structure-based chemical modification and cross-linking experiments indicated that the RseP domains surrounding the active center undergo conformational changes to expose the substrate-binding site, suggesting that RseP has a gating mechanism to regulate substrate entry. Furthermore, mutational analysis suggests that a conserved electrostatic linkage between the transmembrane and peripheral membrane-associated domains mediates the conformational changes. In vivo cleavage assays also support that the substrate transmembrane helix is unwound by strand addition to the intramembrane β sheet of RseP and is clamped by a conserved asparagine residue at the active center for efficient cleavage. This mechanism underlying the substrate binding, i.e., unwinding and clamping, appears common across distinct families of intramembrane proteases that cleave transmembrane segments

VARIATIONAL PROBLEMS FOR INTEGRAL INVARIANTS OF THE SECOND FUNDAMENTAL FORM OF A MAP BETWEEN PSEUDO-RIEMANNIAN MANIFOLDS

We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler–Lagrange equation of the Chern–Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern–Federer submanifolds in Riemannian space forms