How does an organism extract relevant information from transcription factor concentrations?

How does an organism regulate its genes? The involved regulation typically occurs in terms of a signal processing chain: an externally applied stimulus or a maternally supplied transcription factor leads to the expression of some downstream genes, which, in turn, are transcription factors for further genes. Especially during development, these transcription factors are frequently expressed in amounts where noise is still important; yet, the signals that they provide must not be lost in the noise. Thus, the organism needs to extract exactly relevant information in the signal. New experimental approaches involving single-molecule measurements at high temporal precision as well as increased precision in manipulations directly on the genome are allowing us to tackle this question anew. These new experimental advances mean that also from the theoretical side, theoretical advances should be possible. In this review, I will describe, specifically on the example of fly embryo gene regulation, how theoretical approaches, especially from inference and information theory, can help in understanding gene regulation. To do so, I will first review some more traditional theoretical models for gene regulation, followed by a brief discussion of information-theoretical approaches and when they can be applied. I will then introduce early fly development as an exemplary system where such information-theoretical approaches have traditionally been applied and can be applied; I will specifically focus on how one such method, namely the information bottleneck approach, has recently been used to infer structural features of enhancer architecture.