What cell organelle causes a plant to wlit and droop

This is just what happens either when the plant gets too little amounts of water or too much sometimes. I don't think an organelle can control that. 
Hope this helps :)

tap water will cause a plant to droop because of the addititve such as flouride, rain water is best for plants
If the plant is being underwatered it may also droop. Peace Lily's for example, will droop when they need to be watered.

Is there any pictures in the question? i can’t answer the question without seeing the model.