Modeling and optimization of hourglass-shaped aquaporins

Matthieu Bonnivard, Florian Omnès, Yannick Privat
2018 Mathematical Models and Methods in Applied Sciences  
This article is concerned with aquaporins (AQPs), that are proteins playing the role of water-selective channels also called nanopores, involved in many biological systems. From a technological point of view, it is relevant to design systems enjoying as good filtration properties. Inspired by [?], we investigate in a quite general framework shape optimization issues related to the improvement of hourglass-shaped aquaporins performances, in terms of energy dissipated by the fluid through the
more » ... uid through the channel. After modeling this problem mathematically, we show that it is well-posed in some sense, and compute the so-called shape derivative of the cost functional in view of numerical simulations. Noting that our framework requires regularity properties of the free boundary, we introduce a dedicated numerical method, using in particular a proper shape gradient extension-regularization to adapt the mesh at each iteration, in an adequate way. Optimal shapes of aquaporins are then provided for relevant values of parameters, and we finally discuss the observed performances with respect to the existing results/literature.
doi:10.1142/s0218202518500422 fatcat:cvymm4zzdvde7gaiaesz55ryta