In their paper released today, Jafari et al make major strides in answering this question. First, they systematically knocked down 611 transcription factors in Drosophila (~80% of the total) in four representative classes of olfactory sensory neurons. They identified seven whose loss led to a strong decrease in odorant receptor expression.
Next, they showed that knocking down at least one of these seven transcription factors in almost all of the known olfactory sensory neuron classes (32/34) caused that class to stop expressing its olfactory receptor.
In their discussion, the authors mention that the seven transcription factors they found is likely to be an underestimate. This makes sense because the library wasn’t available to screen every transcription factor, and RNAi is stochastic. Regardless, their data set and paradigm should open up many avenues for studying combinatorial transcriptional coding.
Jafari S, Alkhori L, Schleiffer A, Brochtrup A, Hummel T, et al. (2012) Combinatorial Activation and Repression by Seven Transcription Factors Specify Drosophila Odorant Receptor Expression. PLoS Biol 10(3): e1001280. doi:10.1371/journal.pbio.1001280