How would you estimate the number of ATPs required to transcribe, export and translate a single eukariotic protein?
The cost of transcribing and translating a hypothetical average gene in yeast has been calculated as 551 activated phosphate bonds ~P per second (Wagner, 2005).
The median length of a yeast RNA molecule is 1,474 nucleotides, and the median cost of precursor synthesis per nucleotide (derived from the base composition of yeast-coding regions) is 49.3 ∼P. With a median mRNA abundance of R = 1.2 mRNA molecules per cell and a median mRNA decay constant of dR = 5.6 × 10−4 s−1, the mRNA synthesis costs calculates as 49.3 × 1,474 × 1.2 × (5.6 × 10−4) = 48.8 ∼P per second and cell. This is a fraction 48.8/1.34 × 107 = 3.6 × 10−6 of the total RNA synthesis cost per second. The median length of a yeast protein is 385 amino acids, with a combined biosynthesis and polymerization cost of 30.3 ∼P per amino acid. The median abundance is 2,460 protein molecules per cell. No currently available data allows a meaningful estimate of the median protein half-life, but a protein of an intermediate half-life (see below) of 10 h (decay constant dP = 1.92 × 10−5 s−1) yields an overall synthesis cost of 30.3 × 385 × 2,460 × (1.92 × 10−5) = 551 ∼P s−1.
For your question about a single gene, the cost would be 49.3 * 1474 ~P for the mRNA and 30.3 * 385 ~P for the translation, which would result in around 84 thousand ~P. This is probably a very misleading statistic as you can transcribe multiple proteins from a single mRNA.
How the cost of mRNA synthesis and translation are calculated is described in detail in the paper. A large part of the cost comes from the synthesis of the basic building blocks, the nucleotides and the amino acids.