A model for the force exerted on a primary cilium by an optical trap and the resulting deformation

Cilia are slender flexible structures extending from the cell body; genetically similar to flagella. Although their existence has been long known, the mechanical and functional properties of non-motile ("primary") cilia are largely unknown. Optical traps are a non-contact method of applying a localized force to microscopic objects and an ideal tool for the study of ciliary mechanics. We present a method to measure the mechanical properties of a cilium using an analytic model of a flexible, anchored cylinder held within an optical trap. The force density is found using the discrete-dipole approximation. Utilizing Euler-Bernoulli beam theory, we then integrate this force density and numerically obtain the equilibrium deformation of the cilium in response to an optical trap. The presented results demonstrate that optical trapping can provide a great deal of information and insight about the properties and functions of the primary cilium.