What chemicals and structures control the *direction* of plant growth in leaves, stems and roots?
PART 1 : Phototropism

The movement of plant shoot towards light is called phototropism. This process is mainly stimulated by the blue light. The photoreceptor involved is called Phot1 (Phototropin 1) or JK244. 

Auxins such as IAA (indole acetic acid) are plant hormones, expressed highly in meristem, which cause shoot growth. On illumination this phototropin, through currently unknown messengers, causes inhibition of polar Auxin transport in the illuminated side. This causes the non-illuminated side to grow more and thus bending the plant towards light. 



The image represents an older model which proposed lateral movement of auxin. The mechanism mentioned in last paragraph is the currently accepted model. The below figure illustrates 'polar auxin transport'



For details refer to this nice review on phototropism.

PART 2 : Geotropism and Hydrotropism 

Geotropism or gravitropism is movement of roots towards earth (gravity) and hydrotropism is movement of roots towards water. Both phenomena interact with each other and share some common pathways. But hydrotropsim can inhibit geotropism and it is evident in conditions when root goes towards an adjacent water source.

Ethylene and Auxin signaling is involved in root growth both in geotropism and hydrotropism. In geotropism the auxin is stimulated by statoliths (clustered and membrane bound grains of starch) in the amyloplasts- the organelles which store starch. The model suggests that amyloplst sediments under the influence of gravity and thereby affect auxin polar transport (the second figure co-incidentally illustrates polar auxin transport in geotropism). 

The exact moisture sensor is unknown but Abscissic acid (ABA), which is well known for its involvement in drought tolerance, is known to affect hydrotropism. 

MIZ1/2 are some proteins uniquely involved in hyrdotropism. 

Both pathways are dependent on Calcium as a secondary messenger.
To conclude, these pathways are not as clear as those of phototropism. 

Reference:


http://www.academicjournals.org/ajar/pdf/Pdf2006/Nov/Dexian%20and%20South.pdf
http://www.sciencedirect.com/science/article/pii/S1360138504002717
http://www.plantphysiol.org/content/133/4/1677.full