Loregic: A Method to Characterize the Cooperative Logic of Regulatory Factors
Fig 2
Procedures for mapping logic gates and calculating consistency scores.
In this mock example we have binarized expression values for an RF1-RF2-T triplet across a dataset of 20 samples; i.e., m = 20 binary vectors. There are 5 vectors with RF1 = 0 and RF2 = 0, all of which have output of T = 0 (red), so (RF1 = 0, RF2 = 0, T = 0) is chosen as the most suitable triplet-logic gate match, and its succession probability s1 = (5+1)/(5+2) = 6/7 with n1 = 5 and m1 = 5 by Laplace’s rule of succession. Next, there are 5 vectors with RF1 = 0 and RF2 = 1, four of which have output of T = 0 (green), and one of which has output of T = 1. We choose (RF1 = 0, RF2 = 1, T = 0) as the most common triplet with its succession probability s2 = (4+1)/(5+2) = 5/7 with n2 = 4 and m2 = 5, because for the given input the majority of cases have zero as the output value. Similarly, when RF1 = 1 and RF2 = 0, T = 0 is chosen (magenta) because it appears more than T = 1, and its succession probability s3 = (5+1)/(5+2) = 6/7 with n3 = 5 and m3 = 5. Finally, when RF1 = 1 and RF2 = 1, T = 1 is chosen (orange) because it appears four times while T = 0 appears only once, and its succession probability s4 = (4+1)/(5+2) = 5/7 with n4 = 5 and m4 = 5. Combining the outputs chosen for four different input combinations of RF1 and RF2, we obtain the triplet’s truth table, and find that it best matches the AND logic gate. As such we consider this triplet to be consistent with the AND gate, and calculate its consistency score to be CAND = s1 *s2 *s3 *s4 = 0.37.