Microoptical characterization and modeling of positioning forces on drosophila embryos self-assembled in two-dimensional arrays

In this paper, we describe high-precision experimental and numerical characterization of the positioning forces acting on Drosophila embryos that have self-assembled onto 2-D arrays of hydrophobic sites on a silicon substrate in water. The forces measured using a surface micromachined optical-encoder force sensor operating in reflection, are in good agreement with numerical simulations based on an extended surface energy model for the oil-based fluidic system. The positioning forces of ellipsoidal embryos on flat sites show a linear-spring-like relationship between the force and displacement on rectangular as well as cross-shaped sites. An average detachment force of 8.9 μN±1.3 μN was found for the immobilized embryos on 250 μm×100 μm sites. The cross-shaped site has only 19.85% of the area of the rectangular site, but provides a comparable positioning force with a significant reduction in embryo clustering. In contrast, the positioning forces of flat silicon chips, similar in size to the embryos, are linear in the displacement only over a limited range (0∼40 μm), and are then constant up to the detachment force (25.0 μN±3.5 μN). Our measurements also show significant hysteresis in the force vs. displacement, indicating that variations in the surface properties play an important role in the self-assembly process.