Information flow during gene activation by signaling molecules: ethylene transduction in Arabidopsis cells as a study system

Background: We study root cells from the model plant Arabidopsis thaliana and the communication channel conformed by the ethylene signal transduction pathway. A basic equation taken from our previous work relates the probability of expression of the gene ERF1 to the concentration of ethylene. Results: The above equation is used to compute the Shannon entropy (H) or degree of uncertainty that the genetic machinery has during the decoding of the message encoded by the ethylene specific receptors embedded in the endoplasmic reticulum membrane and transmitted into the nucleus by the ethylene signaling pathway. We show that the amount of information associated with the expression of the master gene ERF1 (Ethylene Response Factor 1) can be computed. Then we examine the system response to sinusoidal input signals with varying frequencies to determine if the cell can distinguish between different regimes of information flow from the environment. Our results demonstrate that the amount of information managed by the root cell can be correlated with the frequency of the input signal. Conclusion: The ethylene signaling pathway cuts off very low and very high frequencies, allowing a window of frequency response in which the nucleus reads the incoming message as a sinusoidal input. Out of this window the nucleus reads the input message as an approximately non-varying one. From this frequency response analysis we estimate: a) the gain of the system during the synthesis of the protein ERF1 (similar to-5.6 dB); b) the rate of information transfer (0.003 bits) during the transport of each new ERF1 molecule into the nucleus and c) the time of synthesis of each new ERF1 molecule (similar to 21.3 s). Finally, we demonstrate that in the case of the system of a single master gene (ERF1) and a single slave gene (HLS1), the total Shannon entropy is completely determined by the uncertainty associated with the expression of the master gene. A second proposition shows that the Shannon entropy associated with the expression of the HLS1 gene determines the information content of the system that is related to the interaction of the antagonistic genes ARF1, 2 and HLS1.