Epinasty refers to the way leaves and stems turn downward when their tops grow faster than their bottoms.
While we all know that many plants move to follow the path of the sun each day (phototropism), sometimes plant movements are more random. These are called nastic movements. Epinasty is a nastic movement. Hyponasty is the opposite of epinasty.
The weight of a heavy flower or fruit is an example of mechanical epinasty. Over time, the upper portion of a stem grows longer and faster as the weight of the fruit or flower pulls downward.
The most common cause of epinasty is ethylene. Ethylene is a gaseous plant hormone that helps fruits ripen. It is also a major survival tactic in cases of flooding, either temporary or permanent. Let me explain. When roots experience flooding, they generate an amino acid that I cannot pronounce, but botanists call it ACC. ACC is the precursor to ethylene. ACC moves up the xylem where it is turned into ethylene gas. This ethylene stimulates roots to create hollow tubes that connect to adventitious roots. These tiny roots and tubes are used to draw oxygen into the plant. Other signs of ethylene exposure include chlorosis, thickening stems, petal loss, and deformed or aborted flowers. Epinasty from ethylene gas is common among plants grown in greenhouses with poorly maintained propane or natural gas heaters.
If your tomato plants are exhibiting downward curling leaves, it may be that the soil needs more time to dry out between waterings.
I hope this information inspires you to grow more of your own food. You can ask your garden questions on my Home page.