# Integration of several environmental signals

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.

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).

• 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] Sep 9 '14 at 8:47
• [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. Sep 9 '14 at 8:49
• @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. Sep 9 '14 at 18:14
• 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 Sep 11 '14 at 7:39
• 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. Sep 11 '14 at 13:38

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"