NAD is essential for ketosis because it powers beta-oxidation, the process that breaks fat into ketones, and then helps convert those ketones into usable energy in the Krebs cycle. Without enough NAD, your body can't efficiently burn fat or maintain ketosis.
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What does NAD do for ketosis? Ketones are produced when fat is metabolized. And when fat is metabolized, that requires energy, because the process of beta oxidation of fats, that's how fats are removed in adipocytes in the fat cells. It's an energetic process when insulin isn't present. And that process requires energy in order to process the processing of fats, in order to degrade them. So when you are ketotic, because you're breaking down fats, you need energy to facilitate that process. So NAD can help with breaking down fat, so you can be in ketosis. The other thing to keep in mind is that NAD is very important in the Krebs cycle. There are two molecules of NAD which enter into the Krebs cycle, and the Krebs cycle is using ketones and incorporating them. So it is a very central part of intermediary metabolism. So, yes, you do need to have good NAD levels when you're ketotic.