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If product A inhibits the expression of product B, and product B inhibits the expression of product A, is this a positive feedback loop?

My thinking was to consider the scenario that A starts off high, and so B is naturally low. Then, a large amount of B is added to the system. This inhibits the production of A, so the level of A falls, and that in turn enables the production of more B, which further decreases the production of A and in turn further increases the production of B, in a never-ending cycle. This runaway amplification is characteristic of positive feedback loops, whereas negative feedback loops cause a return to equilibrium.

Yet the Wikipedia page says that, for it to be a positive feedback loop, it must be set up so an increase in A causes an increase in B.

So what is it?

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  • $\begingroup$ This is probably not a biology question. The phenomenon you describe is a positive feedback IMHO. $\endgroup$ – Memming Apr 25 '16 at 21:13
  • $\begingroup$ In essence yes, because the more A, the less B, the more A. In practice it would be a pretty unstable system so you'd end up with either all A, or all B. $\endgroup$ – Kelvin Apr 25 '16 at 21:59
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The situation that you presented in which an entity A inhibits the production of another entity B which in turn inhibits A, is a positive feedback.

In a network path or a loop the overall sign of the loop/path is the product of the signs of individual edges (interactions). In this case it is negative times negative which gives a positive sign to the loop.

In simple words, a positive feedback should lead to an entity promoting its own production, directly or indirectly; it can auto-activate itself, activate an activator or inhibit an inhibitor. In this case A inhibits its inhibitor. Sometimes you can have large loops like this:

                                                            

This is still a positive feedback.

Moreover, your case would exhibit (with the right parameters) the dynamic properties of positive feedbacks (such as bistability and hysteresis).

Sometimes people also refer to this type of positive feedback as double-negative feedback (which I personally do not like because it is misleading).

Positive and negative feedback loops may consist of a single component that activates and represses directly its own activity, respectively (Fig. 1B,C); or they may include several components and involve indirect interactions (Fig. 1D–G). The overall sign of a complex feedback loop (i.e. positive or negative) depends on the constituting elementary interactions (Fig. 1D–G).(1) For example, two mutually repressing components form a positive feedback loop (PFL, also termed “double-negative feedback loop”).


Mitrophanov & Groisman, 2008

However, not all positive feedbacks lead to runaway amplification. That is a property of an unstable system. The degradation of the molecules (or death) ensures a finite (and stable) steady state. Sometimes (with certain parameter combinations, as previously mentioned) positive feedbacks can have two stable steady states. Depending on the initial condition, the system can settle to either of the states. In your example the two states can be — High-A Low-B and Low-A High-B.


Further reading:
Mitrophanov, Alexander Y., and Eduardo A. Groisman. "Positive feedback in cellular control systems." Bioessays 30.6 (2008): 542-555.

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Although the situation you describe involves amplification rather than homeostasis it is not a positive feedback loop under the standard definition of the latter:

In a a positive feedback loop:

  1. An increase in A leads (directly or indirectly) to an increase in B.

  2. The increase in B leads (directly or indirectly) to an increase in A.

  3. This repeats step 1., leading to a further increase in B.

The second step is feedback, as it is affecting the initial propagator of the action, and positive, as it causes an increase in that propagator, A as well as target B.

Your model differs from this in two ways. First, only B is amplified — A is suppressed. Second, when A falls to zero B will reach a maximum, whereas in a positive feedback loop things theoretically keep on running out of control. (Yes they generally stop, but that is because of the intervention of something outside the simple A/B system.)

Some biological examples illustrate this difference (please, I am not concerned whether they are true or not).

An example of a positive feedback loop might be atmospheric warming (A) causing production of more water vapour (B) which has a greenhouse effect and increases atmospheric temperature (A), which...

An example of your model might be the territorial encroachment of smart and aggressive Homo sapiens (A) causes a decline in the population of H. neanderthalensis (B) which is then less able to resist Homo sapiens, leading to a further decline and eventual extinction of H. neanderthalensis.

At the end of the day, we are arguing about semantics. Your point of view would seem to be that the current definition of positive feedback should be extended to include your model. My point of view is that scientific terminology allows us to distinguish between similar but different things. So, (not meant as a serious proposal) one might include both effects under a broader description as ‘augmentative cycles’, including both the standard ‘positive feedback loop’ and your model, which could be called a ‘positive–negative feedback loop’ or a ‘terminal-positive feedback loop’ or whatever takes your fancy.

Postscript

There is a paper in Current Opinions in Cell Biology which discusses the type of motif you describe under the subheading ‘Positive Feedback Loops’, although also refering to them in the text and in the title of a table as ‘double-negative feedback loops’. As @WYSWYG mentions, the review he originaly quoted only uses the latter term, and has a diagram of two-component regulatory motifs, which I reproduce below, distinguishing this from positive feedback. This bears out what I wrote — not that your point of view is necessarily wrong — but that this is a question of semantics, and scientists find it useful to use different terms to distinguish different but related things. In any case, the authors of the review have done the reader a service in defining their terminology.

Classification of two-component regulatory motifs

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  • $\begingroup$ I disagree. If you consider that increasing the presence of A increases the absence of B which increases the presence of A, then it fits your definition of a positive feedback loop. In other words, the absence of B corresponds to an increase in the signal of its absence. And what really matters is that more A leads to more A. So it acts like a positive feedback loop because it is unstable. Whereas a negative feedback loop would reach a stable equilibrium where more A leads to less A and vice versa. $\endgroup$ – Kelvin Apr 25 '16 at 23:14
  • $\begingroup$ @Kelvin -- I don't think there's much room to disagree. In the context of Biology a Positive Feedback Loop has a distinct definition; an increase in A leads to an increase in B, whose product or byproduct leads to an increase in A in an (IIRC) exponential fashion until a limiting factor is involved. $\endgroup$ – MCM Apr 26 '16 at 0:17
  • $\begingroup$ I concur with Kelvin. A inhibiting B and B inhibiting A is a positive feedback. @MCM there is a room to disagree because this answer is not correct. In a positive feedback, an increase in A should directly or indirectly lead to increase in its own levels. It can auto-activate itself, activate an activator or inhibit an inhibitor. $\endgroup$ – WYSIWYG Apr 26 '16 at 8:01
  • $\begingroup$ I think it's a matter of perspective: If you're more focused on the detail and technical definitions you see only the individual steps; but if you're more focused on the big picture, you look at the system as a whole. And since biology itself focuses on big picture systems and outcomes (via evolution), it's probably more useful to think in the same way than get bogged down in largely irrelevant technical details and definitions. $\endgroup$ – Kelvin Apr 26 '16 at 8:35
  • $\begingroup$ @Kelvin Apologies to you and the questioner that my original answer did not address the question adequately. Late at night, but that's not an excuse. I have not changed my opinion over yes or no, but I have argued and discussed it in a manner that pays more respect to the questioner's arguments. $\endgroup$ – David Apr 26 '16 at 8:36

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