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. Author manuscript; available in PMC: 2012 Jun 26.
Published in final edited form as: Biotechnol J. 2012 Jan 10;7(3):374–386. doi: 10.1002/biot.201100222

Figure 1. Constrained Fuzzy Logic.

Figure 1

A: Constrained fuzzy logic describes interactions between biological species with logic gates. The logic gates are evaluated based on the output of the transfer function (f) that quantitatively relates the input and output species. In this example, AND gates are evaluated with the PRODUCT operator and OR gates are evaluated with the SUM operator. Evaluation of the AND and OR gates with the MIN and MAX operators, respectively, is also supported by Q2LM. Note that the SUM operator is not identical to arithmetic sum, but rather, the logical sum of two possible values is equal to the first plus the second minus the product of the two (i.e. V1 + V2 − V1V2, where V1 is the value of one possible output and V2 is the value of the other).

B: The quantitative relationship between any two species is specified with a transfer function. In this paper, we use a normalized Hill function multiplied by a gain as the transfer function, although other functional forms can easily be imagined.