If you have a long, wide, thin beam floating in space, it has a low first natural frequency (mode 7) as it bends along its length, which could be around 1 Hz. Modes 1-6 are zero for bodies floating in space. Adding a fixed support to the long wide side of the beam is the same as preventing any motion on all the nodes on that face. The remaining nodes through the thickness now have extremely high stiffness relative to the fixed nodes. The first natural frequency (mode 1) of the body with a fixed support could be around 100,000 Hz.

If the cell is floating in water and the water is wetting the surface of a glass slide, then the cell is not really fixed to the slide. Floating in a water is a bit like floating in space, but it is not the same. The modes are lower due to the mass of water that has to move.