Microstructure-based Modeling of Primary Cilia Mechanics

A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load-bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure-based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip-anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium-length-dependent, we found the mechanical properties of the cilium are also highly deformation-dependent. More important, we found that the cilium membrane near the base is not under pure in-plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure-based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging-informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base

Numerical Modeling of Physical Cell Trapping in Microfluidic Chips

Microfluidic methods have proven to be effective in separation and isolation of cells for a wide range of biomedical applications. Among these methods, physical trapping is a label-free isolation approach that relies on cell size as the selective phenotype to retain target cells on-chip for follow-up analysis and imaging. In silico models have been used to optimize the design of such hydrodynamic traps and to investigate cancer cell transmigration through narrow constrictions. While most studies focus on computational fluid dynamics (CFD) analysis of flow over cells and/or pillar traps, a quantitative analysis of mechanical interaction between cells and trapping units is missing. The existing literature centers on longitudinally extended geometries (e.g., micro-vessels) to understand the biological phenomenon rather than designing an effective cell trap. In this work, we aim to make an experimentally informed prediction of the critical pressure for a cell to pass through a trapping unit as a function of cell morphology and trapping unit geometry. Our findings show that a hyperelastic material model accurately captures the stress-related softening behavior observed in cancer cells passing through micro-constrictions. These findings are used to develop a model capable of predicting and extrapolating critical pressure values. The validity of the model is assessed with experimental data. Regression analysis is used to derive a mathematical framework for critical pressure. Coupled with CFD analysis, one can use this formulation to design efficient microfluidic devices for cell trapping and potentially perform downstream analysis of trapped cells