# How the Venus Flytrap snaps

### How the Venus Flytrap Sanos

Yoël Forterre, Jan M. Skotheim, Jacques Dumais & L. Mahadevan

Nature 433, 421-425 (27 January 2005)

## Keywords

elastic deformation, instability

## Summary

Although people rarely think about plant movement, there are examples of rapid behavior in the plant kingdom. Some examples include dispersing seeds or pollen and capturing prey. The Venus Fly Trap is one dramatic examples. Previous researcher have searched for a purely biological basis for the rapid motion of the plant, such as "acid-induced wall loosening" or a loss of turgor pressure inside special motor cells. However, much of the behavior can be understood just in terms of elastic deformation. The leaves are curved outwards (convex) in the open state and curved inwards (concave)in the closed state, with an elastic buckling instability during the transition.

The authors used a combination of mirrors and UV-fluorescent dots to track the shape change of the leaf over time (Fig. 1b). This allowed them to quantify the local curvature over the surface of the leaf at each time step (Fig. 1c). From this, they constructed a graph of the average (i.e. arithmetic) mean curvature (Fig. 1d) and the spatially average Gaussian (i.e. geometric mean) curvature (Fig. 1e) over time. This shows how the transition seems to occur in three steps: two slow stages with a fast change in the middle.

To study the stess over the surface of the leaves, the researchers cut strip either parallel (y) or perpendicular (x) to the stem axis and observed the resulting deformation (Fig. 2). The cuts remove the coupling between the stretching and bending modes of deformation. This allows the natural curvature along each axis to be determined (i.e. <math>\kappa_{xn}</math> and <math>\kappa_{yn}</math>).

By combining all this information, the authors created a "phase diagram" from the system by plotting the mean curvature as a function of the natural x-curvature. For certain combinations of leaf length, curvature, and thickness, the system passes through a state of instability (blue line in Fig. 3).

## Soft Matter Aspects

As Prof. Howard Stone often advocates for fluid mechanics problems, the best way to approach this situation is to identify the relevant parameters can create a dimensionless parameter. In this case,

<math>\alpha = L^4 \kappa^2 / h^2</math>,

where L is the length of the leaf, <math>\kappa</math> is the observed Gaussian curvature of the open lead, and h is the leaf thickness. A larger value of <math>\alpha</math> corresponds to more difficulty in stretching the midplane by changing the curvature of the leaf. As shown in Fig. 3, by varying this parameter, the leaves can smoothly transition from open to closed or they can undergo a sudden deformation. This is somewhat analogous to dewetting of a surface, in which a liquid can either gradually decrease in thickness or transition to areas with no surface coverage.

*written by: Naveen N. Sinha*