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Subject: modeling × WGL Institute: INM ×

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    Analytical and numerical results for the elasticity and adhesion of elastic films with arbitrary Poisson’s ratio and confinement
    (London [u.a.] : Taylor & Francis, 2022) Müller, Christian; Müser, Martin H.
    We present an approximate, analytical treatment for the linearly elastic response of a film with arbitrary Poisson's ratio (Formula presented.), which is indented by a flat cylindrical punch while resting on a rigid foundation. Our approach is based on a simple scaling argument allowing the vast changes of the elastomer’s effective modulus (Formula presented.) with the ratio of film height (Formula presented.) and indenter radius (Formula presented.) to be described with a compact, analytical expression. This yields exact asymptotics for large and small reduced film heights (Formula presented.), whereby it also reproduces the observation that (Formula presented.) has a pronounced minimum for (Formula presented.) at (Formula presented.). Using Green’s function molecular dynamics (GFMD), we demonstrate that the predictions for (Formula presented.) are reasonably correct and generate accurate reference data for effective modulus and pull-off force. GFMD also reveals that the nature of surface instabilities occurring during stable crack growth as well as the crack initiation itself depend sensitively on the way how continuum mechanics is terminated at small scales, that is, on parameters beyond the two dimensionless numbers (Formula presented.) and (Formula presented.) defining the continuum problem.
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    Mathematical modeling of drug-induced receptor internalization in the HER2-positive SKBR3 breast cancer cell-line
    (Berlin : Springer Nature, 2019) Fehling-Kaschek, M.; Peckys, D.B.; Kaschek, D.; Timmer, J.; Jonge, N.
    About 20% of breast cancer tumors over-express the HER2 receptor. Trastuzumab, an approved drug to treat this type of breast cancer, is a monoclonal antibody directly binding at the HER2 receptor and ultimately inhibiting cancer cell growth. The goal of our study was to understand the early impact of trastuzumab on HER2 internalization and recycling in the HER2-overexpressing breast cancer cell line SKBR3. To this end, fluorescence microscopy, monitoring the amount of HER2 expression in the plasma membrane, was combined with mathematical modeling to derive the flux of HER2 receptors from and to the membrane. We constructed a dynamic multi-compartment model based on ordinary differential equations. To account for cancer cell heterogeneity, a first, dynamic model was expanded to a second model including two distinct cell phenotypes, with implications for different conformational states of HER2, i.e. monomeric or homodimeric. Our mathematical model shows that the hypothesis of fast constitutive HER2 recycling back to the plasma membrane does not match the experimental data. It conclusively describes the experimental observation that trastuzumab induces sustained receptor internalization in cells with membrane ruffles. It is also concluded that for rare, non-ruffled (flat) cells, HER2 internalization occurs three orders of magnitude slower than for the bulk, ruffled cell population. © 2019, The Author(s).