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Modeling and optimization of hourglass-shaped aquaporins. (English) Zbl 1401.92074

Summary: This paper 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 S. Gravelle et al. [“Large permeabilities of hourglass nanopores: from hydrodynamics to single file transport”, J. Chem. Phys. 141, 18C526 (2014)], 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 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.

MSC:

92C40 Biochemistry, molecular biology
92C37 Cell biology
49Q10 Optimization of shapes other than minimal surfaces
76D05 Navier-Stokes equations for incompressible viscous fluids
92C35 Physiological flow
76Z05 Physiological flows

Software:

FreeFem++; BRENT
PDFBibTeX XMLCite
Full Text: DOI

References:

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