The measurement of cell stiffness is an important part of biological research with diverse applications in biology, biotechnology and medicine. Real-time deformability cytometry (RT-DC) is a new method to probe cell stiffness at high throughput by flushing cells through a microfluidic channel where cell deformation provides an indicator for cell stiffness (Otto et al. Real-time deformability cytometry: on-the-fly cell 725 mechanical phenotyping. Nat. Methods 2015, 12, 199−202). Here, we propose a full numerical model for single cells in a flow channel to quantitatively relate cell deformation to mechanical parameters. Thereby the cell is modeled as a viscoelastic material surrounded by a thin shell cortex, subject to bending stiffness and cortical surface tension. For small deformations our results show good agreement with a previously developed analytical model that neglects the influence of cell deformation on the fluid flow (Mietke et al.

Cell shape changes are vital for many physiological processes such as cell proliferation, cell migration and morphogenesis. They emerge from an orchestrated interplay of active cellular force generation and passive cellular force response -both crucially influenced by the actin cytoskeleton. To model cellular force response and deformation, cell mechanical models commonly describe the actin cytoskeleton as a contractile isotropic incompressible material. However, in particular at slow frequencies, there is no compelling reason to assume incompressibility as the water content of the cytoskeleton may change. Here we challenge the assumption of incompressibility by comparing computer simulations of an isotropic actin cortex with tunable Poisson ratio to measured cellular force response. Comparing simulation results and experimental data, we determine the Poisson ratio of the cortex in a frequency-dependent manner. We find that the Poisson ratio of the cortex decreases with frequency likely due to actin cortex turnover leading to an over-proportional decrease of shear stiffness at larger time scales. We thus report a trend of the Poisson ratio similar to that of glassy materials, where the frequency-dependence of jamming leads to an analogous effect. arXiv:1912.04927v2 [physics.bio-ph] 14 Dec 2019 2 Side view x z shear dilation C o rtical sh e ll a) b) c) 0 h 0 =14 μm h 0 =12 μm h 0 h 0 =8 μm 0 0.5 1 area shear area dilation area shear h 0 =10 μm h 1 reference shape deformed shapeFigure 1. Elastic uniaxial compression of a cortical shell. a) Cell-mechanical model. b) Left panel: a square-shaped surface element (green) in the elastic reference shape of the shell. Right panel: after a small amount of uniaxial compression through reduction of shell height, the surface element is deformed (deformation is exaggerrated here for illustration purposes). c) Elastic deformation of model cells exhibit a decreasing ratio of area shear to area dilation at decreasing reference cell heights (simulation parameters as in Fig. 2). INTRODUCTIONThe actin cytoskeleton, a cross-linked meshwork of actin polymers, is a key structural element that crucially influences mechanical properties of cells [1]. In fact, for rounded mitotic cells, the mitotic actin cortex, a thin actin cytoskeleton layer attached to the plasma membrane, could be shown to be the dominant mechanical structure in whole-cell deformations [6].In the past, cell mechanical models have been developed to rationalize cell deformation in different biological systems [3, 4]. Commonly, these models describe the actin cytoskeleton as a contractile isotropic incompressible material [5]. The assumption of incompressibility implies a Poisson ratio of 0.5. Incompressibility of the actin cytoskeleton is motivated by incompressibility of water and high water content in the actin cytoskeleton [6]. This assumption is justified for high-frequency deformations as in this case substantial water movement past the elastic scaffold of the polymerized actin meshwork would give rise to strong fri...

The dynamics of membranes, shells and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel ALE method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions which are present in a wide range of biophysical problems. We formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. We show in several numerical test cases that accurate results can be achieved at computational times on the order of minutes on a single core CPU. We demonstrate two state-of-the-art applications which to our knowledge cannot be simulated with any other numerical method so far: We present first simulations of the observed shape oscillations of novel microswimming shells and the uniaxial compression of the cortex of a biological cell during an AFM experiment.

Continuous-flow microreactors are an important development in chemical engineering technology, since pharmaceutical production needs flexibility in reconfiguring the synthesis system rather than large volumes of product yield. Microreactors of this type have a special vessel, in which the convective vortices are organized to mix the reagents to increase the product output. We propose a new type of micromixer based on the intensive relaxation oscillations induced by a fundamental effect discovered recently. The mechanism of these oscillations was found to be a coupling of the solutal Marangoni effect, buoyancy and diffusion. The phenomenon can be observed in the vicinity of an air–liquid (or liquid–liquid) interface with inhomogeneous concentration of a surface-active solute. Important features of the oscillations are demonstrated experimentally and numerically. The periodicity of the oscillations is a result of the repeated regeneration of the Marangoni driving force. This feature is used in our design of a micromixer with a single air bubble inside the reaction zone. We show that the micromixer does not consume external energy and adapts to the medium state due to feedback. It switches on automatically each time when a concentration inhomogeneity in the reaction zone occurs, and stops mixing when the solution becomes sufficiently uniform.

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