This paper presents a general method for determining logic functions from gene expression. Given a gene predictor set (biological connectivity graph) and corresponding gene expression observations in the form of input/ouput gene state pairs, the goal is to determine the logic function of all the genes in the Boolean network. The problem of assigning logic to the network is the inverse problem of logic simulation, and is important to genomics and systems biology. Our method utilizes Boolean Satisfiability (SAT) techniques from logic synthesis to represent the functionality of each gene of the Boolean network, and uses gene expression observations to constrain the solution space of valid logic function assignments. The gene functions and resulting networks obtained by our SAT-based method can help infer gene regulatory networks and/or guide experimental design. Our method has been validated on synthetic and real biological networks, and results show that the solution space can be greatly constrained by increasing the number of gene expression observations.
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