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 https://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)

Hyperinsulinaemia and Insulin Resistance - An Engineer's Perspective.

Another techie post!

There's been some arguing discussion over whether Hyperinsulinaemia (HI) causes Insulin Resistance (IR). My answer is...Yes and No.

HI increases IR, long-term. See Downregulation and upregulation: The Insulin Receptor and Insulin oscillation.

HI doesn't increase IR, short-term. How can I claim this? Consider a Negative Feedback (NFB) control system, which is how Blood Glucose is regulated.

"Input" represents Glucose from digested sugars and starches. The arrow pointing at AOL represents Blood Glucose (BG). The triangle containing AOL represents pancreatic beta cells. "Output" represents Insulin Secretion (ISec). More BG = More ISec.

The box containing ß represents three things that work in parallel to reduce Blood Glucose.
1) The Liver. More ISec = Hepatic Glucose Production rate decreased.
2) Muscle mass. More ISec = Glucose intake to Muscle mass rate increased, via Glu-T4.
3) Fat mass. More ISec = Glucose intake to Fat mass rate increased, via Glu-T4.
The three things aren't of equal strength, but they provide overall negative feedback.

If overall negative feedback is halved due to doubling of overall IR in the above three paths, ISec doubles. If you don't believe me, see Idealised Negative Feedback Inverting Amplifier using an idealised op amp on WolframAlpha. Double the value of resistance 2 (the negative feedback resistor R2). and the output voltage on the inverting amplifier doubles from -10V to -20V.

The idealised Negative Feedback Inverting Amplifier using an idealised op amp on WolframAlpha is interesting in that an idealised op amp (the triangle with + and - inputs) has infinity gain and ±infinity voltage on its power supplies. As a result, there is zero volts (output voltage divided by infinity) between the idealised op amp's + terminal and its - terminal. If the idealised op amp's + terminal is connected to 0V (a.k.a. "Earth"), its - terminal is at 0V (a.k.a. "Virtual Earth") and has zero variation, whatever the input voltage. An actual op amp has a voltage gain of ~140dB (~10,000,000), so an output voltage of -10V can be achieved with a voltage of 1uV (one millionth of a Volt) on its - terminal.

If pancreatic beta cells had a zero threshold and infinity gain like an idealised op amp, BG would be zero and have zero variation with varying Glucose input. Pancreatic beta cells actually have a positive threshold and low gain, so BG is positive and varies slightly with varying Glucose input.

If ISec becomes zero (as in type 1 diabetes), there is zero negative feedback and BG increases. The same thing happens to the voltage on the idealised op amp's - terminal if its power supplies are 0V instead of ±infinity.

If ISec becomes insufficient (as in type 2 diabetes), there is insufficient negative feedback and BG increases. The same thing happens to the voltage on the idealised op amp's - terminal if its power supplies are limited to ±5V.

Having established that ISec is proportional to overall IR, what would happen if overall IR was proportional to ISec? If ISec doubled, overall IR would double, which would double ISec, which would double overall IR, ad infinitum. ISec would increase to maximum instantly. THIS DOESN'T HAPPEN. Therefore, IR doesn't increase in proportion to ISec, short term.

Long-term, increased ISec increases IR for a variety of reasons, one of them being that increased ISec increases the rate at which cells fill with glycogen. Once full of glycogen, cells must down-regulate their intake by down-regulating Glu-T4 and Glu-T2 (fat and liver cells also up-regulate their output of stuff) or burst.

Reduce your IR by addressing all of the factors in Insulin Resistance: Solutions to problems.

Chris Highcock emailed me a link to Muscular strength and markers of insulin resistance in European adolescents: the HELENA Study.