I'm trying to make cheddar sticks from scratch
Sodium Citrate is the most common emulsifier for cheese, it keeps it soft and flexible when cold, and like a smooth sauce when hot. Being an emulsifier it stops it separating too

See http://modernistcuisine.com/recipes/sodium-citrate-creates-silky-smooth-macaroni-and-cheese/

You can make Sodium Citrate at home, heat a tbs of lemon juice, add 1/2+ tsp of baking soda and stir. Add this to a cup of melted cheese (all very rough measurements). Experiment to get the best results for your cheese of choice!