There are thousands of examples, here I list just a few.
- macrophageMacrophage 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
- the lac operon
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
- phosphorylationPhosphorylation 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
- neurotransmitterNeurotransmitter 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.