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I have read here that "signals from two different pathways may be needed to activate a response, which is like a logical "AND." Alternatively, either of two pathways may trigger the same response, which is like a logical "OR." But no example is mentioned. I want to know some specific examples in which cell signalling uses logical OR and Logical AND. Any references will be appreciated.

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There are thousands of examples, here I list just a few.

1) Macrophage activation. This is a complex case with many proteins acting as AND/OR. The following paper depicts a nice scheme that helps to understand the circuit.

https://bmcsystbiol.biomedcentral.com/articles/10.1186/1752-0509-2-36

2) The Lac operon that follows the logic:

if low_glucose AND lactose:
    express(lac_genes)

if (high_glucose OR low_glucose) AND no_lacotse:
    inhibit(lac_genes)

if high_glucose AND lacotse:
    express_at_low_level(lac_genes)

https://en.wikipedia.org/wiki/Lac_operon

https://en.wikipedia.org/wiki/Synthetic_biological_circuit

3) Phosphorylation and ubiquitination pathways. For example,

... proteins primed through phosphorylation by one protein kinase are often phosphorylated processively on the N-terminal side of the priming phosphate by GSK3 at a series of Ser/Thr spaced by three residues, with the cluster of phosphates regulating protein activity (e.g., glycogen synthase, β-catenin). If the two sites are phosphorylated by different protein kinases, then this can in principle provide a logical AND gate in a downstream response.

http://www.sciencedirect.com/science/article/pii/S1097276507007988

4) Neurotransmitter signaling pathways. Figure 2 of the following paper

http://www.sciencedirect.com/science/article/pii/S0022519306003675

describes the boolean logic underlining the signaling pathway

Tyrosine hydroxylase activates itself in this model. There is an “AND NOT” gate between tyrosine hydroxylase and COMT to activate dopamine as tyrosine hydroxylase and not COMT activates dopamine...

...adenylate cyclase is activated by dopamine receptor 1 and not by dopamine receptor 2, which has been represented by the “AND NOT” gate between the input nodes.

...

DARPP32, is activated by protein kinase A, and not by calcineurin, therefore protein kinase A “AND NOT” calcineurin activates DARPP32.

DARPP32 inhibits protein phosphatase1, which is represented by the “NOT” gate from DARPP32 for protein phosphatase1. ... The activation of glutamate receptor, needs the presence of both protein kinase A and the ligand, glutamate therefore, a “AND” gate between protein kinase A and glutamate, “AND NOT” protein phosphatase 1. ...

Here the link to a database of natural and artificial biological logic gates and here the article presenting the database

To conclude, I would like to highlight this work on the engineering of a biological transistor.

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  • $\begingroup$ In the paper linkI find this statement TSC2 can be directly phosphorylated by both ERK and ERK-activated ribosomal protein S6 kinase (RSK) on S664 and S1798, respectively, as well as by AKT (on S939 and T1362. in figure 4. Can you please advise if this is an example of OR where TSC2 can be phosphorylated either by RSK and ERK or by AKT. In case if it is not do you know any such logical signalling in cancer metabolism. $\endgroup$ – Userhanu Aug 17 '17 at 12:45
  • $\begingroup$ If you consider phosphorylation in general, it is an OR. But since you get different residues phosphorylated by different enzymes then I would rather consider them separately. What is the output you are looking for in this case? $\endgroup$ – alec_djinn Aug 18 '17 at 10:20
  • $\begingroup$ If my 1 at output means to phosphorylate and 0 means not to phosphorylate then can it be considered as an OR Boolean logic? $\endgroup$ – Userhanu Aug 22 '17 at 6:10
  • $\begingroup$ Yes, if you consider "just phosphorylation" then yes, it's an OR. Indeed you will have 1 as output as long at least one among ERK, RSK and AKT, are active. $\endgroup$ – alec_djinn Aug 22 '17 at 8:34

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