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I am looking for examples of different functions that are good fit to how signals are computed in order to respond to the environment. Let's make my question more copmrehensible with an example...

One example

I have been told (I haven't found an article yet) that in plants, in order to know if it is overshadowed by a big tree, the plant computes that ratio of two signals (UV intensity over Infrared intensity or something similar) so that it can decide whether or not it should grow bigger leaves or other attributes.

This plant radiation example would be an example of a species that computes the function $\frac{S_1}{S_2}$ (where $S_1$ and $S_2$ are two types of signals) in order to take decisions about their response to the environment.

Question

Can you please give me examples (examples with a diversity different functions, with different numbers of different signals) of organism using environmental signals to adaptively respond to their environment?

For example, can you give me examples of the adaptive response to the environment is giving by the following functions of 2 signals:

Continuous traits:

  • $f(S_1, S_2)= S_1 + S_2$
    • Produce a trait value at $K_1 + K_2\cdot \left(S_1 + S_2\right)$
  • $f(S_1, S_2)= \frac{S_1}{S_2}$
    • Produce a trait value at $K_1 + K_2\cdot \frac{S_1}{S_2}$
  • $f(S_1, S_2)= S_1^2 \cdot S_2$
    • Produce a trait value at $K_1 + K_2\cdot \left(S_1^2 \cdot S_2\right)$
  • $f(S_1, S_2)= funA(S_1, S_2)$
    • Produce a trait value at $K_1 + K_2\cdot S_1$ iff $S_1$ is detected.
  • $f(S_1, S_2)= funB(S_1, S_2)$
    • Produce a trait value at $K_1 + K_2\cdot S_1$ iff $S_1 < S_2$.

Boolean traits:

  • $f(S_1, S_2)= OR(S_1, S_2)$
    • Iff signal 1 or signal 2 is detected, produce the trait
  • $f(S_1, S_2)= AND(S_1, S_2)$
    • Iff signal 1 and signal 2 are detected, produce the trait
  • $f(S_1, S_2)= FunA(S_1, S_2)$
    • Iff $S_1$ < $S_2$, produce the trait

, where iff means if and only if and $K_1$ and $K_2$ are constant values.

What I am NOT asking

I am NOT interested in the accurate description of the signal transduction (Description of the kinase cascade and names of the genes and transcriptions factors). I am interested in having examples of mathematical functions that are computed by the cell in order to take decision about which phenotype to produce (plasticity).

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  • $\begingroup$ To me, it is unclear if you are asking for cases where we have mechanistic reason/understanding for assuming a particular function (i.e. basic understanding of how the information is integrated and weighted), or just cases where a particular function shows a good phenomenological fit to data (or both). In the example you give (leaf growth), without knowing anything about this particular case, both could seem plausible to me. My point is that any statistical model that relates environmental drivers to a response can be seen as an example of an integrating function...[cnd] $\endgroup$ – fileunderwater Sep 9 '14 at 8:47
  • $\begingroup$ [cnd:] ..., but in those cases we don't necessarily know how the integration is executed, or even if it takes place in the focal organism. Some factors could just as well be mediated through interacting species. $\endgroup$ – fileunderwater Sep 9 '14 at 8:49
  • $\begingroup$ @fileunderwater You make a good point indeed. I haven't thought about that. I'll go for the statistical fit to the data. I rewrote my question to make this point clear. Thanks. Let me know if anything is still unclear. I welcome you to edit my question if you think can improve it according to my needs. $\endgroup$ – Remi.b Sep 9 '14 at 18:14
  • $\begingroup$ In that case I find the Q extremely broad, since basically any statistically fitted model relating a response (physiological, reproductive etc) to one or many environmental factors will do as an answer. Sifting through the litterature you will find supported examples of almost anything, from single regressions, multiple regressions, quadratic relationships, non-linear responses, custom functions and a mixture of all of the above. It is certainly possible to answer the Q with examples, but I dont know what would constitute a good answer, except maybe giving a taxonomy of functions incl examples $\endgroup$ – fileunderwater Sep 11 '14 at 7:39
  • $\begingroup$ I think I understand what you mean and see what the depressant side of my question. I don't think it is easy to find an example where the function is complicated (something like $\frac{S_1+S_2}{S_3^2}$ or even something like $\frac{S_1}{S_2}$). The perfect answer would contain many referenced examples where different functions fit the way the environmental signals predict the environment. $\endgroup$ – Remi.b Sep 11 '14 at 13:38
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What you are looking for sounds like the mechanism for a fold-change detector. I would recommend looking at these two papers:

The incoherent feedforward loop can provide fold-change detection in gene regulation

As an example of this working in a real system, I recommend looking at the NFkB pathway, as recently detailed by Suzanne Gaudet:

Fold Change of Nuclear NF-κB Determines TNF-Induced Transcription in Single Cells

Here are a few others that I found just by searching for "Fold change detection"

Comparing Apples and Oranges: Fold-Change Detection of Multiple Simultaneous Inputs

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0057455

Efficient fold-change detection based on protein-protein interactions

I'm sure by looking at the referenced papers in the above you can find more examples as well.

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  • $\begingroup$ Thank you! Seems very interesting, I wasn't aware of this kind of signal. I think your answer partially answers my question. Fold-change detector might be considered as one type of function I am interested in. As fileunderwater complained about my question, it is possible that indeed this post is hard to answer because it is poorly defined. I welcome questions and comments to help me improving my question. $\endgroup$ – Remi.b Sep 13 '14 at 22:26
  • $\begingroup$ I don't think that any other kind of function, which was not classified as a fold change detector would satisfy your requirements. In fact, the example you gave (of plant radiation) is exactly this. $\endgroup$ – Danny W. Sep 14 '14 at 0:46
  • $\begingroup$ oh really? Ok, I probably misunderstood the concept of fold-change detector then. I thought that a fold-change detector is the kind of detector that does not only sense the absolute value of a signal but sense a change in the signal intensity. So that the concept of fold-change detection would have no relationship with how several signals are computed to determine the phenotype to adopt as in the examples in my post. So, did I missunderstood the concept of fold-change detector? $\endgroup$ – Remi.b Sep 16 '14 at 1:54
  • $\begingroup$ I see - I am not sure if the question is clear to me, but with your recent addition, it is. Given what you now have, I would recommend looking at Uri Alon's book - he certainly has examples of the logical operations (OR, AND, etc.) that you discuss. I doubt the more complicated mathematical functions you give exist. $\endgroup$ – Danny W. Sep 16 '14 at 17:54
  • $\begingroup$ Sorry about that. If you feel you can clarify things in my question, please feel free to edit it or to give suggestions on how to improve it. $\endgroup$ – Remi.b Sep 16 '14 at 17:56

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