Satiety is mediated by cholecystokinin released in reaction to the presence of fatty acids and certain amino acids (partially digested fats and proteins) in the duodenum, or first part of the small intestines. That hormone stimulates the release of bile and pancreatic enzymes (necessary for the further digestion of fats and proteins) and also parts of your limbic system, which is the part of your brain that regulates satiety. In particular, it affects the ventromedial hypothalamus.

In other words, fats and proteins satisfy your hunger. You can eat really dense carbohydrates until your stomach bursts (it won't but it might feel like it's going to -- it's the stretch receptors signalling your limbic system to stop or it's going to tell you to vomit) and you still won't feel satisfied. Slather a bit of (protein-rich high-fat) peanut butter on your celery sticks and you'll be fine.

The best advice is balance.