Abstract
The following problems arise in the analysis of biological networks: We have a boolean function of n variables, each of which has some default value. An experiment fixes the values of any subset of the variables, the remaining variables assume their default values, and the function value is the result of the experiment. How many experiments are needed to determine (reconstruct) the function? How many experiments that involve fixing at most q values are needed? What are the answers to these questions when an unknown subset of the variables are actually involved in the function? In the biological context, the variables are genes and the values are gene expression intensities. An experiment measures the gene levels under conditions that perturb the values of a subset of the genes. The goal is to reconstruct the particular logic (regulation function) by which a subset of the genes together regulate one target gene, using few experiments that involve minor perturbations. We study these questions under the assumption that all functions belong to a biologically motivated set of so‐called chain functions. We give optimal reconstruction schemes for several scenarios and show their application in reconstructing the regulation of galactose utilization in yeast.
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