Mechanical behavior of cells in microinjection: A minimum potential energy study

Microinjection is a widely used technique to deliver foreign materials into biological cells. We propose a mathematical model to study the mechanical behavior of a cell in microinjection. Firstly, a cell is modeled by a hyperelastic membrane and interior cytoplasm. Then, based on the fact that the equilibrium configuration of a cell would minimize the potential energy, the energy function during microinjection is analyzed. With Lagrange multiplier and Rayleigh–Ritz technique, we successfully minimize the potential energy and obtain the equilibrium configuration. Upon this model, the injection force, the injection distance, the radius of the microinjector and the membrane stress are studied. The analysis demonstrates that the microinjector radius has a significant influence on the cell mechanical behavior: (1) the larger radius generates larger injection force and larger interior pressure at the same injection distance; (2) the radius determines the place where the membrane is most likely to rupture by governing the membrane stress distribution. For a fine microinjector with radius less than 20% of the cell radius, the most likely rupture point located at the edge of the contact area between the microinjector and the membrane; however, it may move to the middle of the equilibrium configuration as the radius increases. To verify our model, some experiments were conducted on zebrafish egg cells. The results show that the computational analysis agrees with the experimental data, which supports the findings from the theoretical model.