Before I even start, I want to clarify that the focus is on losing fat, not losing weight. Basically, we are all composed of fat, muscle, water, and everything else. We can think of "everything else" as a constant. Yes, bone density can change, organ size can change, but those are outside of the scope of this topic. Water weight can be lost and gained quickly by drinking water, eating, going to the bathroom, letting yourself get dehydrated, eating carbs. It can fluctuate by 5 or more pounds in a given day. We need a minimum level of hydration. We need to compensate for those changes. That leaves fat and muscle.
In general, more muscle = good, more fat = bad, all within limits of course. So when we talk about losing weight, the focus needs to be on fat. You don't want to lose muscle, and water weight is not relevant.
So the equation, expressed in Excelese is
DeltaBF = MIN ( MAX ( deltaE, -31.5 * lbs. body fat), k + f (Max(0, carbs in - 50)))
deltaE is simply calories in - calories out (be careful, it's not quite that simple though).
lbs. body fat is weight * % body fat.
f (carbs in-50) is the slope of the upper limit on fat deposition related to the biochemical need of spent carbs in your system to store fat in your fat cells after allowing for 50 grams to fuel the brain.
k is some amount of body fat that can be deposited even on a zero carb diet through alternate biochemical pathways.
Lower Limit on Delta(FatDeposition)
A recent paper called "A limit on the energy transfer rate from the human fat store in hypophagia" helps us begin to understand how much fat we can take off in a given day. This estimates the amount of energy that can be removed from fat to fuel your body. The answer is (290+/-25) kJ/kgd.
Converting 290 *(239 calories/kJ)*(1Calorie/1000calories)*(1kg/2.2lb)= 31.5 Cal/lb fat +/-2.7
This effectively sets a limit on the maximum amount of fat you can burn each day with moderate activity and no steroids. It may be possible to lose more fat with activity because of the hormones excreted by that activity, but it seems like a reasonable way to think about it.
Note: As you lose body fat, the amount of fat you can lose in a day will decrease. Consider a 200 lb guy with 20% body fat. He is carrying 40 lbs of fat. So if he cuts his food intake by 1240 calories per day below basal metabolic rate, he can lose that much fat per day without eating into his muscle (lean body mass or LBM). Once he loses 10 lbs. of body fat, for example, he must limit his intake cut to 930 calories. Other metabolic changes are likely happening, for example, with cut in intake metabolism slows down, so that adjustment needs to be considered as well.
Upper Limit on Delta(FatDeposition)
The other day, I saw something on a blog. The author said something like, "If you're low carbin', calories aren't important. If you're low fattin', calories count."
For the low carb-ingestion cases, you can gain weight by eating lots of calories, but your body adapts to the high calories by upping your metabolism and giving you a sense of high energy. Even though ingesting low-carb, you will put on fat through some alternative metabolic pathways. It's just not as fast.
As you increase the amount of carbs that you eat. You open up a more efficient pathway for fat conversion. Your body uses the spent carbs to create triglyceride molecules. This is the primary storage form of fat. The slope of the line is a ratio of fat to carbs in a triglyceride molecule. I don't have that number.
The Ratchet Effect
The delta E Trap
What you lose is equal to what you eat minus what you burn. Burn more than you eat you lose weight; eat more than you burn you gain weight.
DeltaE is a common way of thinking about weight loss. It is a true relationship, but there is complexity in the relationship between the composition of what you eat and delta E. In fact, there is reason to believe that what you eat, more than simply being an independent variable is actually a driver of deltaE. I think the basic energy equation should be written as
E(out) = E(in) - deltaE. In fact, it is perhaps better to think of it as a giant feedback loop, because the calories you eat actually alter your metabolism as well over time.
We as a society often see obese people and think that they have no willpower. They must be either pigs (gluttons) or lazy (sloths). But they are no different than any of us. When they feel hunger they eat, when they have energy they play. Let's think about this. People eat because a. they feel hungry or b. social pressures or pleasure. Hunger is not a character defect. We all know obese people who do not eat much, but stay obese anyway. What is the driver there? Something is altering the energy balance away from the balance that leaner people have.
In general, if you don't feel hungry, you should not eat. Your body's cells do not need anything in that moment. If is likely that sustenance will be stored as fat. The key is to eat right so you don't feel hungry before you need the sustenance.
When you eat carbohydrates, especially simple carbs like sugar, white rice, or white flour, your blood sugar increases. This causes your body to put out insulin to regulate blood sugar. It does this by pushing that sugar into your cells, where it can be used for fuel. At the end the spent glucose then allows for deposition of fat into fat cells.
Now because the insulin has swept your blood clean of sugar, you begin to feel hungry. If you respond by eating carbs, the cycle starts again. The fundamental issue is that your body really wants to store carbs for later.
Repeat this, as we tend to with a Standard American Diet (SAD), and your muscles become resistant to the effects of insulin. You need more and more sugar to fuel yourself. Your body has trouble using its fat stores for fuel. This drives deltaE up and therefore E(Out) down. You gain weight.
You do not need carbohydrates to survive, your body will convert protein to sugar and use fat for fuel, but you want to ingest some carbohydrates to prevent the conversion of muscle into sugar (gluconeogenesis), as well as to prevent the feeling of foggy headedness that some people get when they eat low-carb. Lyle McDonald estimates a minimum of 50 - 100 g of carbs per day is good, more if you're doing resistance training.
At the end of the day, if you are paying attention to your weight, you can, in theory, lose weight by simple willpower. Those who have hormonal and enzyme issues, such as insulin resistance will have a more difficult time of it unless they eat right. For most of us though, we do not obsess over every calorie or gram that we eat. So we need a more automatic method. For me, limiting carbs has been a pretty reasonable automatic method. I have felt stronger than I have before when limiting calories and so far have lost almost 40 pounds.
But even with low carbs you have to eat mindfully. Eat only when you're hungry. Limit sweets. Pass up the cake at the company function. It's too easy to fall back into bad habits.
The following link is to a tool that can help you measure your progress on the road to better health.