Variations in weight change for a given Calorie change - An Engineer's Perspective.

Another techie post, inspired by Insulin Doesn't Regulate Fat Mass. Consider the inverting amplifier using an Op-Amp, below:-

From HERE

As the amplifier is inverting (i.e. a ↑ input on V_in results in a ↓ output on V_out), the feedback from V_out via R₂ opposes V_in via R₁ at the - terminal of the Op-Amp.

If R1 = R2 and V_in changes from 0V to 1V, the change in V_- (the voltage on the - terminal of the Op-Amp) varies with A (the magnitude of the Op-Amp gain) as follows*:-

A_____________Change in V_-(V)
∞_____________0
1,000,000_____~0.000001
1,000_________~0.001
100___________~0.01
10____________~0.08
8_____________0.1
5_____________~0.14
3_____________0.2
2_____________0.25
1_____________~0.33
0_____________0.5

As the body operates on biochemical principles, slopes of input/output transfer functions aren't steep at their steepest points. E.g.

From http://bja.oxfordjournals.org/content/85/1/69.long

Therefore, the gains in the various parts of the Leptin "adipostat" NFB loop are not very high. Therefore, there will be a significant variation in weight change vs Calorie change, and there will be significant variations in the variation due to loop gain variations from person to person.

Insulin Resistance makes the slopes of  the above input/output transfer functions shallower, reducing the gain in the system. This increases the variation in weight change vs Calorie change. For ways to reduce Insulin Resistance, see Insulin Resistance: Solutions to problems.

*In case anyone thinks that I've made the numbers up, here's the maths:-
Current in/out of the - terminal of the Op-Amp = 0.
∴ I_R1 = I_R2
I set R1 = R2 to keep the maths simple. By Ohm's Law, V = I * R.
∴ V_R1 = V_R2
With a 0V input:-
All currents & voltages = 0.

With a 1V input:-
V_R1 = 1 - V_-
V_R2 = V_- - V_out.  As V_out is negative, - V_out is positive.
- V_out = A * V_-
∴ V_R2 = V_- + (A * V_-)
∴ 1 - V_- = V_- + (A * V_-)
Rearranging:-
1 = (2 * V_-) + (A * V_-)
Dividing both sides by V_-:-
(1/V_-) = 2 + A
∴ V_- = 1/(2 + A)

Resistance is useless!

...said the Vogon guard. If that means nothing to you, watch this...


You probably know all about Insulin Resistance (IR) if you've read my blog for some time, as I may have mentioned it once or twice ;-) There's also Leptin Resistance (LR) in the brain, which reduces the amount of appetite suppression that leptin is supposed to produce. Robb Wolf's just written about Adrenaline Resistance (AR?) and chronically-high serum cortisol seems to induce Cortisol Resistance (CR?) in the hippocampus, resulting in poor short-term memory.

When the level of "X" in the blood is low most of the time, "X" receptors in the body up-regulate, so when the level of "X" in the blood goes high, it has an effect. When the level of "X" in the blood is high all of the time, "X" receptors in the body down-regulate, so when the level of "X" in the blood goes higher, it has a reduced effect.

The above suggests that regularly "grazing" on food is not a good idea, as this results in a fairly constant slightly elevated serum insulin level. Eating a meal, not eating for a few hours then eating another meal results in high serum insulin while the meal is being absorbed and low serum insulin for the rest of the time.