High selectivity of frequency induced transcriptional responses

Cells continuously interact with their environment, detect its changes and generate responses accordingly. This requires interpreting the variations and, in many occasions, producing changes in gene expression. In this paper we use information theory and a simple transcription model to analyze the extent to which the resulting gene expression is able to identify and assess the intensity of extracellular stimuli when they are encoded in the amplitude, duration or frequency of a transcription factors nuclear concentration. We find that the maximal information transmission is, for the three codifications, ~ 1.5 - 1.8 bits, i.e., approximately 3 ranges of input strengths can be distinguished in all cases. The types of promoters that yield maximum transmission for the three modes are all similarly fast and have a high activation threshold. The three input modulation modes differ, however, in the sensitivity to changes in the parameters that characterize the promoters, with frequency modulation being the most sensitive and duration modulation, the least. This turns out to be key for signal identification. Namely, we show that, because of this sensitivity difference, it is possible to find promoter parameters that yield an information transmission within 90% of its maximum value for duration or amplitude modulation and less than 1 bit for frequency modulation. The reverse situation cannot be found within the framework of a single promoter transcription model. This means that pulses of transcription factors in the nucleus can selectively activate the promoter that is tuned to respond to frequency modulations while prolonged nuclear accumulation would activate several promoters at the same time. Thus, frequency modulation is better suited than the other encoding modes to allow the identification of external stimuli without requiring other mediators of the transduction.