I assume that I am referring to the correct part of a tomato plant.

I'm wondering if anyone has seen any study on the amount of, or quality of, lignen in various types of tomatoes. The reason that I ask is that I have this one heart-shaped variety (Heartthrob) that I grow nearly every year. No other variety, in my trials, comes close to basically wanting to grow sideways, then downward, and finally upward, rather than just upward. The thin, top of the header almost always droops downward, until it thickens and then straightens up (but, at that point, it is no longer the top of the header).

Could this be due to some sort of lignen deficiency?

I have not seen/looked for any lignen papers, but considering its role in plant structure, ait certainly could indicate a deficiency

I know what you're talking about... and it's definitely genetic. Some varieties are way more 'viney' than others.. The long bits want to droop and run along the ground. Others can be way more sturdy and self supporting, in the same conditions.

http://www.centrumdp.sk/wr/201606/08.pdf
This gives a table of average values for lignin and alpha cellulose in different plant materials - tomato stems would be on average around 17% lignin.

Here's something about tomato lignin genetics:
https://www.plantbreedbio.org/journal/v ... &&vmd=Full
https://academic.oup.com/plphys/article ... ogin=false

I wonder if wispy leaf also reflects differences in lignin metabolism?