Fig 1.
A: Loregic first inputs a gene regulatory network that consists of regulatory factors and their target genes; B: Next, it identifies all possible RF1-RF2-T triplets where RF1 and RF2 co-regulate the target gene T. Note that T can be also a RF; C: Loregic queries binarized gene expression data for each triplet, and D: it extracts the triplet’s binarized gene expression data; E: Loregic matches the triplet’s gene expression against all 16 possible two-input-one-output logic gates based on the binary values, and F: finds the matched logic gate if the triplet is gate-consistent, and calculates the consistency score. Then, Loregic repeats steps C-F for all triplets from Step B in the regulatory network and finds all logic-gate-consistent triplets. In Step G, the gate-consistent triplets can be further mapped onto other regulatory features such as: 1) indirectly bound TFs and 2) feed-forward loops.
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.
Fig 3.
Cooperative logics found by Loregic for yeast regulatory triples.
A—Loregic gives for each triplet a matched logic gate as shown in the table. The bar plot shows the distribution of 4126 gate-consistent TF-TF-target triplets across matched logic gates. The symmetric gate pairs are marked using diamonds on top of bars with identical superscript numbers due to randomly assigning TFs as TF1 or TF2. B—Top: an example RF pair (RF1 is YML113W, RF2 is YBR083W) with “homogenous” gate-consistent triplets—matching the same, logic gate across all targets; middle: an example RF pair (RF1 is YKL015W, RF2 is YKL032C) with “inhomogeneous” gate-consistent triplets—matching different logic gates across all targets; and bottom: an example RF pair (RF1 is YMR037C, RF2 is YOR344C) with non-gate-consistent triplets, i.e. triplets inconsistent with all logic gates across all targets.
Fig 4.
Distributions by logic gate of all gate-consistent human regulatory triples in acute myeloid leukemia.
A—TF-TF-target triplets. The symmetric gate pairs are marked using diamonds on top of bars with identical superscript numbers; B—miRNA-TF-target triplets; C—distTF-TF-triplets. The triplets from B and C have different distributions from A, including notably at symmetric gates because their RF1s are miRNA/distTF. Also, the “T = RF2” gate matches more triplets than any other gate in B and C.
Fig 5.
Distributions by logic gate of gate-consistent human regulatory triples associated with AML-related TFs.
The bar color represents-log10(hyper-geometric enrichment p-value) (Materials and Methods). A—The triplets in which RF1 is MYC, RF2 is chosen from other human TFs, and T is a common target. The two most enriched logic gates are “T = RF1” (133 triplets, hyper-geometric test p(133, 2153, 1110, 50865)< 4.3*10-27) and “T = RF1+RF2 (OR)” (211 triplets, hyper-geometric test p(211, 2153, 2505, 50865)< 1.1*10-21), which supports the finding that MYC is a universally amplifier for its target expression; B—the triplets in which RF1 is chosen from AML-related TFs, RF2 is chosen from TFs not relating to AML, and T is a common target as shown in top, and the triplets in which both RF1 and RF2 are chosen from TFs not relating to AML, and T is a common target as shown in bottom. “T = RF1” and “T = ~RF1” are the two most enriched matched logic gates when RF1 is AML-related TF, which implies that AML-related TFs dominate the regulation of their target expression.
Fig 6.
Promoter motifs for AND-consistent yeast triplets with directly and indirectly bound TFs.
We present two example yeast triplets, (RF1 is the TF YEL009C, RF2 is the TF YER040W, T is the gene YDL066W) at top and (RF1 is the TF YNL216W, RF2 is the TF YNL167C, T is the gene YHR033W) at bottom, both of which are consistent with the AND gate by Loregic. Both TFs in the top triplet have motifs in the target promoter region, but only one TF, YNL216W, in the bottom triplet has a motif in the target promoter region. The other TF, YNL167C, cooperates with YNL216W in an AND logical relation via protein-protein interaction.
Fig 7.
Depiction of two logic circuit regulatory pathways targeting PPIL2.
Two logic circuit regulatory pathways targeting the PPIL2 gene, an important cyclophilin member in immunological suppression, are found by Loregic: 1: PPIL2 is co-regulated by HDAC2 and SP1 forming the triplet of (RF1 is HDAC2, RF2 is SP1, T is PPIL2), which is consistent with the “T = ~RF1+RF2” gate (the ORN gate[22]), and SP1 is co-regulated by EGR1 and NFYA forming the triplet of (RF1 is EGR1, RF2 is NFYA, T is SP1), which is consistent with the “T = ~RF1*~RF2 (the NAND gate); 2: PPIL2 is also co-regulated by BRF1 and NFE2 forming the triplet of (RF1 is BRF1, RF2 is NFE2, T is PPIL2), which is consistent with OR gate, and NFE2 is co-regulated by TAL1 and GATA2 forming the triplet of (RF1 is TAL1, RF2 is GATA2, T is NFE2), which is also consistent with OR gate. We replace the triplets on these pathways using matched logic gates, and depict the pathways using logic circuits to summarize the regulatory logics targeting PPIL2 at the pathway level.