Cell stiffness is a sensitive indicator of physiological and pathological changes in cells, with many potential applications in biology and medicine. A new method, real-time deformability cytometry, probes cell stiffness at high throughput by exposing cells to a shear flow in a microfluidic channel, allowing for mechanical phenotyping based on single-cell deformability. However, observed deformations of cells in the channel not only are determined by cell stiffness, but also depend on cell size relative to channel size. Here, we disentangle mutual contributions of cell size and cell stiffness to cell deformation by a theoretical analysis in terms of hydrodynamics and linear elasticity theory. Performing real-time deformability cytometry experiments on both model spheres of known elasticity and biological cells, we demonstrate that our analytical model not only predicts deformed shapes inside the channel but also allows for quantification of cell mechanical parameters. Thereby, fast and quantitative mechanical sampling of large cell populations becomes feasible.

Significance: Morphogenesis, the emergence of shape and form in biological systems, is a process that is fundamentally mechanochemical: Shape changes of material are driven by active mechanical forces that are generated by chemical processes, which in turn can be affected by the deformations and flows that occur. We provide a framework that integrates these interactions between the geometry of deforming materials and active processes in them by introducing the shape dynamics of self-organized active surfaces. We show that the tight coupling between surface mechanics and active processes gives rise to the spontaneous formation of nontrivial shapes, shape oscillations, and directed peristaltic motion. Our simple yet general description lays the foundation to explore the regulatory role of shape in morphogenetic processes.