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)

How a B.Sc.(Hons) in Electronic Engineering is relevant to Diet & Nutrition.

The human body regulates various processes using negative feedback loops. Here's blood glucose regulation.

From http://www.studyblue.com/notes/note/n/ch-47-chemical-signals-in-animals/deck/3085387

Here's a generic Hypothalamus-Pituitary-X Axis loop, where X may be thyroid, adrenal, gonadal etc.

From http://www.studyblue.com/notes/note/n/ch-47-chemical-signals-in-animals/deck/3085387

Electronic Engineers understand how negative feedback systems work, such as phase-locked loops & amplifiers.

Negative feedback control systems can overshoot, especially if there's a delay in the feedback path that's longer than the rise time of the input step.

An example of this is the first-phase insulin response. Loss of the first-phase insulin response occurs in over-fat people who are hyperinsulinaemic. Without the first-phase insulin response, there's a delay between an increase in blood glucose and an increase in insulin secretion. A rapid upwards step in blood glucose (say, from eating a high-GL meal) causes a massive overshoot in insulin secretion, resulting in postprandial sleepiness, also down-regulation of insulin receptor activity in the appetite centres of the brain, causing ravenous hunger when the insulin level falls to normal.

See also Blood Glucose, Insulin & Diabetes.

People shouldn't be too quick to write-off the knowledge of an Electronic Engineer who's delving into the mysteries of the human body.