title: Diffusion through thin membranes: Modeling across scales.
abstract: From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.
authors.affiliation: Department of Physics, and Nanoscience Center, P.O. Box 35, University of Jyväskylä, FI-40014 Jyväskylä, Finland.
authors.forename: Vesa
authors.initials: V
authors.lastname: Aho
authors.affiliation: Department of Physics, and Nanoscience Center, P.O. Box 35, University of Jyväskylä, FI-40014 Jyväskylä, Finland and Department of Physics, P.O. Box 692, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Keijo
authors.initials: K
authors.lastname: Mattila
authors.affiliation: Department of Applied Physics, P.O. Box 1627, University of Eastern Finland, FI-70211 Kuopio, Finland.
authors.forename: Thomas
authors.initials: T
authors.lastname: Kühn
authors.affiliation: Department of Chemistry, P.O. Box 55, University of Helsinki, FI-00014 Helsinki, Finland.
authors.forename: Pekka
authors.initials: P
authors.lastname: Kekäläinen
authors.affiliation: Department of Physics, P.O. Box 692, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Otto
authors.initials: O
authors.lastname: Pulkkinen
authors.affiliation: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
authors.forename: Roberta Brondani
authors.initials: RB
authors.lastname: Minussi
authors.affiliation: Department of Biological and Environmental Science, and Nanoscience Center, P.O. Box 35, University of Jyväskylä, FI-40014 Jyväskylä, Finland.
authors.forename: Maija
authors.initials: M
authors.lastname: Vihinen-Ranta
authors.affiliation: Department of Physics, and Nanoscience Center, P.O. Box 35, University of Jyväskylä, FI-40014 Jyväskylä, Finland and ITMO University, Kronverkskii Ave. 49, 197101, Saint Petersburg, Russia.
authors.forename: Jussi
authors.initials: J
authors.lastname: Timonen