Our molecular simulations reveal that wild-type influenza fusion peptides are able to stabilize a highly fusogenic pre-fusion structure, i.e. a peptide bundle formed by four or more trans-membrane arranged fusion peptides. We rationalize that the lipid rim around such bundle has a non-vanishing rim energy (line-tension), which is essential to (i) stabilize… (More)
Motivated by mirror symmetry, we consider a Lagrangian fibra-tion X → B and Lagrangian maps f : L ֒→ X → B, when L has dimension 2, exhibiting an unstable singularity, and study how their caustic changes, in a neighbourhood of the unstable singularity, when slightly perturbed. The integral curves of ∇f x , for x ∈ B, where f x (y) = f (y) − x · y, called "… (More)
Motivated by mirror symmetry, we consider the Lagrangian fibration R 4 → R 2 and Lagrangian maps f : L ֒→ R 4 → R 2 , exhibiting an unstable singularity, and study how the bifurcation locus of gradient lines, the integral curves of ∇f x , for x ∈ B, where f x (y) = f (y) − x · y, changes when f is slightly perturbed. We consider the cases when f is the germ… (More)
The formation of an hourglass-shaped passage (stalk) connecting two apposed membranes is an essential initial step in membrane fusion. The most probable transition path from two separate membranes to a stalk, i.e., the minimum free-energy path (MFEP), is constructed using a combination of particle simulations and string method. For the reversible transition… (More)
Given the Lagrangian fibration T 4 → T 2 and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the " quantum " corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration.
Given any Morse function f on a Whitney stratified complex analytic variety of complex dimension n, we prove the existence of a stratified gradient-like vector field for f such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimension m(p) + n − s as was conjectured by Goresky and MacPherson.
Quantum corrections to the holomorphic structure of the mirror bundle along the caustic and the bifurcation locus Abstract. Given, in the Lagrangian torus fibration R 4 → R 2 , a Lagrangian submanifold L, endowed with a trivial flat connection, the corresponding mirror object is constructed on the dual fibration by means of a family of Morse homologies… (More)