First, lets talk about fat and fat cells. In the science world, they are called adipose cells or when there is a collection, it is called adipose tissue. When we eat and the body does not use all of the energy we ingested, it is stored. It can be stored as glycogen (stored energy in our muscles) or as fat. It is only stored as fat when our glycogen stores are full and the food has no other place to go. Carbohydrates and protein can be stored as fat too; it all gets broken down into the same type of compounds and stored.
Surprisingly, we cannot burn off fat cells; they do not just go away. Fat cells will grow in size as more unused energy is stored, and when it is burned, the cells shrink in size. We do not kill or burn away the cells. That is why it is easier to gain weight back after you lose a good amount because the cells are already there. And, we can add new fat cells as well.
I have heard from many people that they are trying a low fat diet in hopes that they will burn off their excess weight. Our primary energy source is carbohydrates. They help us when we need that sudden burst of energy to sprint as well as a long distance run. When the body uses up its stores of carbohydrates, it turns to fat. As your sitting here reading this and I am sitting here typing this, our bodies are using fat as its energy source. When you're walking on the treadmill at about 3.5 miles per hour with a decent incline at a heart rate of about 120 bpm, you're primarily burning fat. When you take fat out of your diet, and you burn all of your carbohydrate stores, the only thing left for the body to turn to is stored protein, which is muscle. If you cut out fat, and all you have left stored is protein then your body will break down it's muscles to feed itself.
We, as future dietitians, learn in school that 20-35% of our daily caloric intake needs to come from polyunsaturated fat or monounsaturated fat. These fats are known as the "healthy fats". Saturated fat is what can clog arteries and raise cholesterol levels, while poly and monounsaturated fats reduce cholesterol and prevent clogged arteries. Based on a 2000 calorie a day diet, at the most 16g of fat or 144 calories should be coming from saturated fat.
So don't be scared of fat, you need it, our bodies need it, and it does have a purpose for us.
