Genotype-to-phenotype maps and the related fitness landscapes that include
epistatic interactions are difficult to measure because of their high
dimensional structure. Here we construct such a map using the recently
collected corpora of high-throughput sequence data from the 75 base pairs long
mutagenized E. coli lac promoter region, where each sequence is associated with
its phenotype, the induced transcriptional activity measured by a fluorescent
reporter. We find that the additive (non-epistatic) contributions of individual
mutations account for about two-thirds of the explainable phenotype variance,
while pairwise epistasis explains about 7% of the variance for the full
mutagenized sequence and about 15% for the subsequence associated with protein
binding sites. Surprisingly, there is no evidence for third order epistatic
contributions, and our inferred fitness landscape is essentially single peaked,
with a small amount of antagonistic epistasis. There is a significant selective
pressure on the wild type, which we deduce to be multi-objective optimal for
gene expression in environments with different nutrient sources. We identify
transcription factor (CRP) and RNA polymerase binding sites in the promotor
region and their interactions without difficult optimization steps. In
particular, we observe evidence for previously unexplored genetic regulatory
mechanisms, possibly kinetic in nature. We conclude with a cautionary note that
inferred properties of fitness landscapes may be severely influenced by biases
in the sequence data