Although insulin promotes storage of fat in adipose tissue, this occurs in the context of multiple layers of regulation where energy balance is the final determinant of how much fat we store. In a caloric deficit, the low energy status of muscle and heart will lead them to take up fat rather than adipose tissue, even in the presence of insulin. Insulin combined with low energy status will promote the uptake of glucose in skeletal muscle over adipose tissue and will promote the oxidation of glucose rather than its incorporation into fat. Some advocates of the carbohydrate hypothesis of obesity have argued that glucose is needed to form the glycerol backbone of triglycerides within adipose tissue. Although glucose can serve this role, it isn’t necessary because adipose glyceroneogenesis and hepatic gluconeogenesis can both provide the needed glycerol phosphate. Further, low energy status promotes the use of glycerol as fuel and high energy status is needed to promote the formation of glycerol from glucose. Finally, fatty acids are needed to store fat in adipose tissue and they overwhelmingly come from dietary fat in almost any circumstance. Insulin can only promote de novo lipogenesis, the synthesis of fatty acids from other precursors such as carbohydrate, in the context of excess energy, and this pathway is minor in conditions of caloric deficit, caloric balance, or moderate caloric excess. Thus, although insulin does promote storage of fat in adipose tissue, it doesn’t directly affect energy balance, and energy balance is the determinant of how much fat you store overall.
What the primary thing that shuts down fat burning? It’s carbs, right? Insulin? Nope. The primary thing that shuts down fat burning is having too much energy. The following video covers the regulation of beta-oxidation. The primary regulation of beta-oxidation occurs at the mitochondrial membrane, where fatty acids are transported into the mitochondrion. Acetyl CoA carboxylase governs both the formation of fatty acids from non-carbohydrate precursors and the transport of fatty acids into the mitochondrion. Its product, malonyl CoA, is a substrate for fatty acid synthesis in the cytosol but a regulator of fatty acid transport in the mitochondrion. Thus, there are two isoforms of acetyl CoA carboxylase that are regulated similarly. The cytosolic isoform plays a direct role in fatty acid synthesis and the mitochondrial isoform regulates beta-oxidation. This ensures that the two processes are regulated reciprocally, so that one is shut down to the extent the other is activated, thereby preventing wasteful futile cycling. The primary regulator of acetyl CoA carboxylase activity is, as you might expect by this point, energy status. When a cell needs more energy, it lets fatty acids into the mitochondrion. When it has too much, it shuts down fat-burning.