Information theory and the ethylene genetic network

Abstract

The original aim of the Information Theory (IT) was to solve a purely technical problem: to increase the performance of communication systems, which are constantly affected by interferences that diminish the quality of the transmitted information. That is, the theory deals only with the problem of transmitting with the maximal precision the symbols constituting a message. In Shannon's theory messages are characterized only by their probabilities, regardless of their value or meaning. As for its present day status, it is generally acknowledged that Information Theory has solid mathematical foundations and has fruitful strong links with Physics in both theoretical and experimental areas. However, many applications of Information Theory to Biology are limited to using it as a technical tool to analyze biopolymers, such as DNA, RNA or protein sequences. The main point of discussion about the applicability of IT to explain the information flow in biological systems is that in a classic communication channel, the symbols that conform the coded message are transmitted one by one in an independent form through a noisy communication channel, and noise can alter each of the symbols, distorting the message; in contrast, in a genetic communication channel the coded messages are not transmitted in the form of symbols but signaling cascades transmit them. Consequently, the information flow from the emitter to the effector is due to a series of coupled physicochemical processes that must ensure the accurate transmission of the message. In this review we discussed a novel proposal to overcome this difficulty, which consists of the modeling of gene expression with a stochastic approach that allows Shannon entropy (H) to be directly used to measure the amount of uncertainty that the genetic machinery has in relation to the correct decoding of a message transmitted into the nucleus by a signaling pathway. From the value of H we can define a function I that measures the amount of information content in the input message that the cell's genetic machinery is processing during a given time interval. Furthermore, combining Information Theory with the frequency response analysis of dynamical systems we can examine the cell's genetic response to input signals with varying frequencies, amplitude and form, in order to determine if the cell can distinguish between different regimes of information flow from the environment. In the particular case of the ethylene signaling pathway, the amount of information managed by the root cell of Arabidopsis can be correlated with the frequency of the input signal. 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 varying input. Outside of this window the nucleus reads the input message as an approximately non-varying one. This frequency response analysis is also useful to estimate the rate of information transfer during the transport of each new ERF1 molecule into the nucleus. Additionally, application of Information Theory to analysis of the flow of information in the ethylene signaling pathway provides a deeper insight in the form in which the transition between auxin and ethylene hormonal activity occurs during a circadian cycle. An ambitious goal for the future would be to use Information Theory as a theoretical foundation for a suitable model of the information flow that runs at each level and through all levels of biological organization.

Figure 1

Block diagram of a communication channel.

Figure 2

Basic structure of the gene and the transcription process.

Figure 3

Molecular structure of the ethylene communication channel. Two mutually exclusive modules compose the ethylene signaling system. The MAPK module (left side of the figure) is switched on when ethylene is not bounded to its specific receptor, which is in its activated state. This module promotes the expression of the auxin dependent phenotype of the root by the activation of the CTR1 kinase, the subsequent expression of the POLARIS gene, among others, and the inactivation of the EIN2 molecule. The ethylene module (bottom of the figure) is switched on when ethylene binds to its specific receptor and inactivates it, inactivating the MAPK module as consequence. The inactivation of CTR1 turns on EIN2, giving rise to the expression of the ethylene dependent phenotype. In the figure, the ethylene communication channel is formed of: (1) the encoder, which is the ethylene receptor; (2) the transmitter, constituted of EIN2, and the early transcription factor EIN3; (3) the receiver of the signal, which is the promoter site of the ERF1 gene; (4) the decoder, which consists of the transcription machinery of ERF1; (5) the effector, composed by the translation machinery of ERF1. ERF1 has as a target a set of downstream genes that have a GCC box in their promoter site. The sign (+) in the figure represents an activation process, and the sign (−) an inactivation process.

Figure 4

Structure of the ERF1 gene according to the data presented in The Arabidopsis Information Resource (TAIR) and in reference .

Figure 5

Plots of the functions H and I as a function of $p_{ERF1}^{on}$. As expected, H decreases when $p_{ERF1}^{on}$ approaches to 0 or 1 and reaches its maximum value when $p_{ERF1}^{on}$ is about 0.5. H and I are measured in mers.

Figure 6

$p_{ERF1}^{on}$ exhibits very small fluctuations around its steady value (A) in response to very fast random variations of ethylene concentration (B). As consequence H exhibits small fluctuations around a steady value (C). Random changes in ethylene concentration, between 0 and 1 µM, are produced every 4 sec.

Figure 7

$p_{ERF1}^{on}$ exhibits large fluctuations around its steady value (A) in response to relative slow random variations of ethylene concentration (B). As a consequence H also exhibits large fluctuations around a steady value (C). Random changes in ethylene concentration, between 0 and 1 µM, are produced every 360 sec.

Figure 8

(A) Fluctuations in mRNA concentration in response to a random ethylene input, ranging from 0 to 1 µM; (B) Fluctuations in mRNA concentration in response to a random ethylene input ranging from 0 to 0.1 µM. The random changes in ethylene concentration are produced every 360 sec.

Figure 9

Distribution of the probabilities of expression of the master gene ERF1 and the downstream genes PDF1 and ARF2. (A) A relative low amount of ethylene produces a distribution of probabilities in which the probability of expression of the gene ARF2 is higher with respect to the distribution (B), in which a elevated amount of ethylene almost completely counteracts the expression of this gene.