Xiaojing ZHANG^*, Chung-Chu CHEN¹, Matthew P. SCOTT² and Olav SOLGAARD¹

Media Laboratory, Massachusetts Institute of Technology, MA 02139, U.S.A.
¹Ginzton Laboratory, Department of Electrical Engineering, Stanford University, CA 94305, U.S.A.
²Department of Developmental Biology, and of Genetics, Stanford University, CA 94305, U.S.A.

(Received November 4, 2004; Accepted June 15, 2005)

We describe high precision experimental and numerical characterization of the positioning forces acting on Drosophila embryos that have self-assembled onto two-dimensional 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 pads show a linear-spring-like relationship between the force and displacement on rectangular as well as cross-shaped pads. 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, and are then constant up to the detachment force. The optical force characterization method and the associated surface energy model for the self-assembly process can potentially be used for design optimization of fluidic self-assembly for a wide range of applications in biology.

Key words: optical encoder, force sensor, Drosophila, embryo, self-assembly

^*E-mail address: xjzhang@stanfordalumni.org