Specialist cells (Statocytes) in plants are able to sense gravity. Thus shooting tips grow upwards contrary to the Earth's gravitational field, while roots grow downwards.
Statoliths are dense amyloplasts, organelles that synthesize and store starch involved in the perception of gravity by the plant (gravitropism), that collect in specialized cells called statocytes. Statocytes are located in the starch parenchyma cells near vascular tissues in the shoots and in the columella in the caps of the roots.
“How amyloplast sedimentation is sensed within the root statocytes remains unsolved, however. It is possible that sedimenting statoliths might contact receptors embedded in sensitive membranes on the side of the statocyte, thereby triggering gravity signalling within the cell (Braun, 2002).”
There is also evidence (primarily from experiments in zero-gravity) that so called 'non-professional' cells can also somehow sense gravitational fields. As yet this is unexplained. The same seems to be true of many other types of cells in fungi, and even animals.
“Sensing gravity by ‘non-specialized’ cells is still puzzling. We don’t know where or by which mechanism such cells sense gravity. These questions in ‘gravisensing’ are not much different from questions in general mechanobiology. Numerous studies have been reported in this field in the last couple of decades. What are the mechanical properties of a cell? Are there differences in mechanical properties between cell types and if so why?”
Source; Mechanomics and Physicomics in Gravisensing in Microgravity Sci. Technol (2009) 21:159–167