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A Calculus-Based Viewpoint for Negative Feedback

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A Calculus-Based Viewpoint for Negative Feedback

Postby majik1213 » Fri Jun 30, 2006 3:59 pm

At first I was confused about negative feedback, but if this viewpoint is correct, then I think I will understand negative feedback fully.

Basically my viewpoint rests upon calculus applied to homeostatic disturbances. We know from physics/calculus that the derivative of concentration is the rate of change in concentration. For example, if the concentration of compound A in the human body is [A], then deriving this concentration with respect to time would yield d[A]/dt, (leads to the rate law in general chemistry) .. yadda yadda, right?
Now the way the human body works is in a restorational fashion. That is, if the conditions that create a homeostatic balance for compound A are disrupted, the human body will act to restore the concentration of compound A back to the homeostatic level.
So let's see how the terms positive feedback and negative feedback apply through an example:

Here is a quesiton from a text that I want to dissect because I think the question, as presented, hides fundamental ideas that would make the question more enlightening:
"If ADH holds water in the body decreasing urine output and increasing blood pressure, does a person with high blood pressure (holding water) have a high ADH blood level or a low ADH blood level?" the answer is a low ADH blood level.
Now, the question is hiding a key idea that allows anyone to jump to the answer. In fact, without this key idea no one should really be able to know the answer without having seen it first, so is my humble opinion. Now the missing key idea in the question, I feel, is the mentioning that the side effects do NOT depend on ADH concentration at any given instant, but rather they depend exclusively on the rate of change in the concentration of ADH. Specifically, if d[ADH]/dt < 0, then a person will have excessive ADH concentration, and thus the body will attempt to rid itself of excess ADH in an effort to restore homeostasis, thereby making the rate of change in concentration of ADH negative. In addition, if d[ADH]/dt > 0, as it must be here, then the body is responding to low ADH concentrations by producing a positive rate of change in ADH concentration. As a result, the person experiences the side effects of a positive rate of change in ADH concentration, which much be high blood pressure and decreasing urine output.

Here's why I feel the missing key idea undermines the enlightening quality of the question itself: I think that the side effects, the decreasing urine output and increasing blood pressure, are a result of the RATE of change in ADH, NOT a result of the concentration of ADH. Why? Because, when ADH levels are low, as is the answer to the question, then the body is acting to restore ADH levels to their previous levels; therefore, the RATE of POSITIVE ADH production is >0.

In summary, negative feedback corresponds to a rate of change in the concentration of a substrate whose magnitude is > 0; positive feedback also corresponds to the same situation. The discernment between positive and negative, however, when viewed in the light of calculus, is clear. Positive feedback is dependent upon the concentration of a substrate relative to the homeostatic concentration and upon the side effects caused by the concentration. Negative feedback, in contrast, is dependent upon the rate of change in the concentration of a substrate, regardless of the homeostatic level of concentration, and on the side effects that the magnitude and direction of the rate of change cause. Coincidentally, the rate of change in the concentration of a substrate is proportional to the homeostatic level of concentration (almost by definition).

Now if i'm right, then I would expect, for an initially low ADH blood level, high blood pressure, then low blood pressure (because the body will have to eventually decrease the rate of change in ADH concentration back to 0), then normal blood pressure. Is this what I should expect? Heck, am I even right with the missing key idea? Let me know.

I'd like to thank Dr. Stein, as he (unknowingly) has helped me to develop this idea. His post, and my source, are at, viewtopic.php?t=2004&highlight=negative+feedback
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Postby majik1213 » Sat Jul 15, 2006 3:58 pm

Well, after giving the idea more thought, I am inclined to change my viewpoint. Lets say hormone A increased blood pressure. And let's say that [A] is sufficient concentration under normal conditions for a particular human being to have normal blood pressure. Now, what makes me change my viewpoint is the consideration of what changes blood pressure. Certainly, any deviation in [A] will affect blood pressure, but I didn't realize that other events could, regardless of [A], change the blood pressure. So let's say such an event, unrelated to the effect of hormone A, occurs where this particular human's blood pressure drops. To compensate, the body will then increase [A] to x*[A] (x>1). And there you have it: negative feedback caused by an event unrelated to the hormone, but an event whose effect ultimately triggers stimulation of the production of A, increasing [A] to x*[A]. The simpler view is usually the better view.

This is not to say that I think what I wrote in the previous post is entirely invalid. Just under-sighted. In the event that the blood pressure drops as a direct consequence of a change in [A], then my description written in my initial post, I hope, would be an accurate reflection of the only way to call subsequent events "negative feedback."
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Postby majik1213 » Wed Jun 06, 2007 4:31 pm

I don't know what I was thinking, but I recommend to ignore my previous posting (although I won't erase it .. it was a fine idea). Bionegative feedback works like a thermostat. When the temperature in the room is cold, the sensor on the thermostat causes the heater to turn on to restore what is a deviation from where we'd like the temperature to be. Similarly, in the cell, when an event causes a disturbance in dynamic homeostasis, the sensor triggers the release of a restoring factor to re-establish equilibrium. Of course, if equilibrium is actually achieved, you die; the cell depends on its dynamic disequilibrium for survival.
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Re: A Calculus-Based Viewpoint for Negative Feedback

Postby majik1213 » Sun Apr 12, 2009 3:39 am

dear past self,
interesting thoughts .. the rate of change being an important determinant fits a mathematical model that, unfortunately, does not reveal what is going on .. ADH causes aquaporin 2 proteins to be inserted into the distal nephron (DCT) .. these aquaporins selectively allow water to be resorbed into the body to increase water levels and, with it, blood pressure. So you see, past self, it isn't the rate of ADH at all that matters; rather, how much there is. Low volume will cause the paraventricular nuclei to release more AVP. So with low BP you get high [ADH]
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