On the Interplay between Entropy and Robustness of Gene Regulatory Networks

Assessing RNA-Seq Workflow Methodologies Using Shannon Entropy

RNA-seq faces persistent challenges due to the ongoing, expanding array of data processing workflows, none of which have yet achieved standardization to date. It is imperative to determine which method most effectively preserves biological facts. Here, we used Shannon entropy as a tool for depicting the biological status of a system. Thus, we assessed the measurement of Shannon entropy by several RNA-seq workflow approaches, such as DESeq2 and edgeR, but also by combining nine normalization methods with log2 fold change on paired samples of TCGA RNA-seq representing datasets of 515 patients and spanning 12 different cancer types with 5-year overall survival rates ranging from 20% to 98%. Our analysis revealed that TPM, RLE, and TMM normalization, coupled with a threshold of log2 fold change ≥1, for identifying differentially expressed genes, yielded the best results. We propose that Shannon entropy can serve as an objective metric for refining the optimization of RNA-seq workflows and mRNA sequencing technologies.

Common factors among three types of cells aged in mice

The greatest risk factor for the formation of numerous significant chronic disorders is aging. Understanding the core molecular underpinnings of aging can help to slow down the inevitable process. Systematic study of gene expression or DNA methylation data is possible at the transcriptomics and epigenetics levels. DNA methylation and gene expression are both affected by aging. Gene expression is an important element in the aging of Homo sapiens. In this work, we evaluated the expression of differentially expressed genes (DEGs), proteins, and transcription factors (TFs) in three different types of cells in mice: antibody-secreting cells, cardiac mesenchymal stromal cells, and skeletal muscle cells. The goal of this article is to uncover a common cause during aging among these cells in order to increase understanding about establishing complete techniques for preventing aging and improving people's quality of life. We conducted a comprehensive network-based investigation to establish which genes and proteins are shared by the three different types of aged cells. Our findings clearly indicated that aging induces gene dysregulation in immune, pharmacological, and apoptotic pathways. Furthermore, our research developed a list of hub genes with differential expression in aging responses that should be investigated further to discover viable anti-aging treatments.

An Approximate Method of System Entropy in Discrete-Time Nonlinear Biological Networks

This study discusses the calculation of entropy of discrete-time stochastic biological systems. First, measurement methods of the system entropy of discrete-time linear stochastic networks are introduced. The system entropy is found to be characterized by system matrices of the discrete-time biological systems. Secondly, the system entropy of nonlinear discrete-time stochastic biological systems is discussed and is calculated based on a global linearization method. The approximation of the values of system entropy of nonlinear stochastic systems needs to solve an optimization problem that is constrained by a kind of linear matrix inequality (LMI). Finally, a practical biochemical system is provided to verify the effectiveness of the proposed calculation method.

The contribution of microRNA-mediated regulation to short- and long-term gene expression predictability

MicroRNAs are a class of short, noncoding RNAs which are essential for the coordination and timing of cell differentiation and embryonic development. However, despite their guiding role in development, microRNAs are dysregulated in many pathologies, including nearly all cases of cancer. While both development and oncogenesis can be thought of as extremes of phenotypic plasticity, they characteristically manifest on much different time scales: one taking place over a matter of weeks, the other typically requiring decades. Because microRNAs are believed to support this plasticity, a critically important question is how microRNAs affect phenotypic stability on different time scales, and what dynamical characteristics shift the balance between these two roles. To address this question, we extend a well-established mathematical model of transcriptional gene regulation to include translational regulation by microRNAs, and examine their effects on both short- and long-term gene expression predictability. Our findings show that microRNAs greatly improve short-term predictability for earlier, developmental phenotypes while causing a small decrease in long-term predictability, and that these effects are difficult to separate. In addition to providing a theoretical explanation for this seemingly duplicitous behavior, we describe some of the properties which determine the cost-benefit balance between short-term stabilization and long-term destabilization.

Uncertainty Evaluation in Multistage Assembly Process Based on Enhanced OOPN

This study investigated the uncertainty of the multistage assembly process from the viewpoint of a stream of defects in the product assembly process. The vulnerable spots were analyzed and the fluctuations were controlled during this process. An uncertainty evaluation model was developed for the assembly process on the basis of an object-oriented Petri net (OOPN) by replacing its transition function with a fitted defect changing function. The definition of entropy in physics was applied to characterize the uncertainty of the model in evaluating the assembly process. The uncertainty was then measured as the entropy of the semi-Markov chain, which could be used to calculate the uncertainty of a specific subset of places, as well as the entire process. The OOPN model could correspond to the Markov process because its reachable token can be directly mapped to the Markov process. Using the steady-state probability combined with the uncertainty evaluation, the vulnerable spots in the assembly process were identified and a scanning test program was proposed to improve the quality of the assembly process. Finally, this work analyzed the assembly process on the basis of the uncertainty of the assembly structure and the variables of the assembly process. Finally, the case of a certain product assembly process was analyzed to test the advantages of this method.

Investigating the specific core genetic-and-epigenetic networks of cellular mechanisms involved in human aging in peripheral blood mononuclear cells

Aging is an inevitable part of life for humans, and slowing down the aging process has become a main focus of human endeavor. Here, we applied a systems biology approach to construct protein-protein interaction networks, gene regulatory networks, and epigenetic networks, i.e. genetic and epigenetic networks (GENs), of elderly individuals and young controls. We then compared these GENs to extract aging mechanisms using microarray data in peripheral blood mononuclear cells, microRNA (miRNA) data, and database mining. The core GENs of elderly individuals and young controls were obtained by applying principal network projection to GENs based on Principal Component Analysis. By comparing the core networks, we identified that to overcome the accumulated mutation of genes in the aging process the transcription factor JUN can be activated by stress signals, including the MAPK signaling, T-cell receptor signaling, and neurotrophin signaling pathways through DNA methylation of BTG3, G0S2, and AP2B1 and the regulations of mir-223 let-7d, and mir-130a. We also address the aging mechanisms in old men and women. Furthermore, we proposed that drugs designed to target these DNA methylated genes or miRNAs may delay aging. A multiple drug combination comprising phenylalanine, cholesterol, and palbociclib was finally designed for delaying the aging process.

Investigating core genetic-and-epigenetic cell cycle networks for stemness and carcinogenic mechanisms, and cancer drug design using big database mining and genome-wide next-generation sequencing data

Recent studies have demonstrated that cell cycle plays a central role in development and carcinogenesis. Thus, the use of big databases and genome-wide high-throughput data to unravel the genetic and epigenetic mechanisms underlying cell cycle progression in stem cells and cancer cells is a matter of considerable interest.

Real genetic-and-epigenetic cell cycle networks (GECNs) of embryonic stem cells (ESCs) and HeLa cancer cells were constructed by applying system modeling, system identification, and big database mining to genome-wide next-generation sequencing data. Real GECNs were then reduced to core GECNs of HeLa cells and ESCs by applying principal genome-wide network projection. In this study, we investigated potential carcinogenic and stemness mechanisms for systems cancer drug design by identifying common core and specific GECNs between HeLa cells and ESCs. Integrating drug database information with the specific GECNs of HeLa cells could lead to identification of multiple drugs for cervical cancer treatment with minimal side-effects on the genes in the common core. We found that dysregulation of miR-29C, miR-34A, miR-98, and miR-215; and methylation of ANKRD1, ARID5B, CDCA2, PIF1, STAMBPL1, TROAP, ZNF165, and HIST1H2AJ in HeLa cells could result in cell proliferation and anti-apoptosis through NFκB, TGF-β, and PI3K pathways. We also identified 3 drugs, methotrexate, quercetin, and mimosine, which repressed the activated cell cycle genes, ARID5B, STK17B, and CCL2, in HeLa cells with minimal side-effects.

Network Biomarkers of Bladder Cancer Based on a Genome-Wide Genetic and Epigenetic Network Derived from Next-Generation Sequencing Data

Epigenetic and microRNA (miRNA) regulation are associated with carcinogenesis and the development of cancer. By using the available omics data, including those from next-generation sequencing (NGS), genome-wide methylation profiling, candidate integrated genetic and epigenetic network (IGEN) analysis, and drug response genome-wide microarray analysis, we constructed an IGEN system based on three coupling regression models that characterize protein-protein interaction networks (PPINs), gene regulatory networks (GRNs), miRNA regulatory networks (MRNs), and epigenetic regulatory networks (ERNs). By applying system identification method and principal genome-wide network projection (PGNP) to IGEN analysis, we identified the core network biomarkers to investigate bladder carcinogenic mechanisms and design multiple drug combinations for treating bladder cancer with minimal side-effects. The progression of DNA repair and cell proliferation in stage 1 bladder cancer ultimately results not only in the derepression of miR-200a and miR-200b but also in the regulation of the TNF pathway to metastasis-related genes or proteins, cell proliferation, and DNA repair in stage 4 bladder cancer. We designed a multiple drug combination comprising gefitinib, estradiol, yohimbine, and fulvestrant for treating stage 1 bladder cancer with minimal side-effects, and another multiple drug combination comprising gefitinib, estradiol, chlorpromazine, and LY294002 for treating stage 4 bladder cancer with minimal side-effects.

Constructing an integrated genetic and epigenetic cellular network for whole cellular mechanism using high-throughput next-generation sequencing data

Background

Epigenetics has been investigated in cancer initiation, and development, especially, since the appearance of epigenomics. Epigenetics may be defined as the mechanisms that lead to heritable changes in gene function and without affecting the sequence of genome. These mechanisms explain how individuals with the same genotype produce phenotypic differences in response to environmental stimuli. Recently, with the accumulation of high-throughput next-generation sequencing (NGS) data, a key goal of systems biology is to construct networks for different cellular levels to explore whole cellular mechanisms. At present, there is no satisfactory method to construct an integrated genetic and epigenetic cellular network (IGECN), which combines NGS omics data with gene regulatory networks (GRNs), microRNAs (miRNAs) regulatory networks, protein-protein interaction networks (PPINs), and epigenetic regulatory networks of methylation using high-throughput NGS data.

Results

We investigated different kinds of NGS omics data to develop a systems biology method to construct an integrated cellular network based on three coupling models that describe genetic regulatory networks, protein–protein interaction networks, microRNA (miRNA) regulatory networks, and methylation regulation. The proposed method was applied to construct IGECNs of gastric cancer and the human immune response to human immunodeficiency virus (HIV) infection, to elucidate human defense response mechanisms. We successfully constructed an IGECN and validated it by using evidence from literature search. The integration of NGS omics data related to transcription regulation, protein-protein interactions, and miRNA and methylation regulation has more predictive power than independent datasets. We found that dysregulation of MIR7 contributes to the initiation and progression of inflammation-induced gastric cancer; dysregulation of MIR9 contributes to HIV-1 infection to hijack CD4+ T cells through dysfunction of the immune and hormone pathways; dysregulation of MIR139-5p, MIRLET7i, and MIR10a contributes to the HIV-1 integration/replication stage; dysregulation of MIR101, MIR141, and MIR152 contributes to the HIV-1 virus assembly and budding mechanisms; dysregulation of MIR302a contributes to not only microvesicle-mediated transfer of miRNAs but also dysfunction of NF-κB signaling pathway in hepatocarcinogenesis.

Conclusion

The coupling dynamic systems of the whole IGECN can allow us to investigate genetic and epigenetic cellular mechanisms via omics data and big database mining, and are useful for further experiments in the field of systems and synthetic biology.

EntropyExplorer: an R package for computing and comparing differential Shannon entropy, differential coefficient of variation and differential expression

Background

Differential Shannon entropy (DSE) and differential coefficient of variation (DCV) are effective metrics for the study of gene expression data. They can serve to augment differential expression (DE), and be applied in numerous settings whenever one seeks to measure differences in variability rather than mere differences in magnitude. A general purpose, easily accessible tool for DSE and DCV would help make these two metrics available to data scientists. Automated p value computations would additionally be useful, and are often easier to interpret than raw test statistic values alone.

Results

EntropyExplorer is an R package for calculating DSE, DCV and DE. It also computes corresponding p values for each metric. All features are available through a single R function call. Based on extensive investigations in the literature, the Fligner-Killeen test was chosen to compute DCV p values. No standard method was found to be appropriate for DSE, and so permutation testing is used to calculate DSE p values.

Conclusions

EntropyExplorer provides a convenient resource for calculating DSE, DCV, DE and associated p values. The package, along with its source code and reference manual, are freely available from the CRAN public repository at http://cran.r-project.org/web/packages/EntropyExplorer/index.html.

Electronic supplementary material

The online version of this article (doi:10.1186/s13104-015-1786-4) contains supplementary material, which is available to authorized users.

Information theory in systems biology. Part II: protein-protein interaction and signaling networks

By the development of information theory in 1948 by Claude Shannon to address the problems in the field of data storage and data communication over (noisy) communication channel, it has been successfully applied in many other research areas such as bioinformatics and systems biology. In this manuscript, we attempt to review some of the existing literatures in systems biology, which are using the information theory measures in their calculations. As we have reviewed most of the existing information-theoretic methods in gene regulatory and metabolic networks in the first part of the review, so in the second part of our study, the application of information theory in other types of biological networks including protein-protein interaction and signaling networks will be surveyed.

Meta-analysis of prostate cancer gene expression data identifies a novel discriminatory signature enriched for glycosylating enzymes

BACKGROUND

Tumorigenesis is characterised by changes in transcriptional control. Extensive transcript expression data have been acquired over the last decade and used to classify prostate cancers. Prostate cancer is, however, a heterogeneous multifocal cancer and this poses challenges in identifying robust transcript biomarkers.

METHODS

In this study, we have undertaken a meta-analysis of publicly available transcriptomic data spanning datasets and technologies from the last decade and encompassing laser capture microdissected and macrodissected sample sets.

RESULTS

We identified a 33 gene signature that can discriminate between benign tissue controls and localised prostate cancers irrespective of detection platform or dissection status. These genes were significantly overexpressed in localised prostate cancer versus benign tissue in at least three datasets within the Oncomine Compendium of Expression Array Data. In addition, they were also overexpressed in a recent exon-array dataset as well a prostate cancer RNA-seq dataset generated as part of the The Cancer Genomics Atlas (TCGA) initiative. Biologically, glycosylation was the single enriched process associated with this 33 gene signature, encompassing four glycosylating enzymes. We went on to evaluate the performance of this signature against three individual markers of prostate cancer, v-ets avian erythroblastosis virus E26 oncogene homolog (ERG) expression, prostate specific antigen (PSA) expression and androgen receptor (AR) expression in an additional independent dataset. Our signature had greater discriminatory power than these markers both for localised cancer and metastatic disease relative to benign tissue, or in the case of metastasis, also localised prostate cancer.

CONCLUSION

In conclusion, robust transcript biomarkers are present within datasets assembled over many years and cohorts and our study provides both examples and a strategy for refining and comparing datasets to obtain additional markers as more data are generated.

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-offs on Phenotype Robustness in Biological Networks. Part III: Synthetic Gene Networks in Synthetic Biology

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental disturbances, is also proposed, together with a simulation example.

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Trade-off on Phenotype Robustness in Biological Networks Part I: Gene Regulatory Networks in Systems and Evolutionary Biology

Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view.

A Unifying Mathematical Framework for Genetic Robustness, Environmental Robustness, Network Robustness and their Tradeoff on Phenotype Robustness in Biological Networks Part II: Ecological Networks

In ecological networks, network robustness should be large enough to confer intrinsic robustness for tolerating intrinsic parameter fluctuations, as well as environmental robustness for resisting environmental disturbances, so that the phenotype stability of ecological networks can be maintained, thus guaranteeing phenotype robustness. However, it is difficult to analyze the network robustness of ecological systems because they are complex nonlinear partial differential stochastic systems. This paper develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance sensitivity in ecological networks. We found that the phenotype robustness criterion for ecological networks is that if intrinsic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations and environmental disturbances. These results in robust ecological networks are similar to that in robust gene regulatory networks and evolutionary networks even they have different spatial-time scales.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Synthetic biology: mapping the scientific landscape

This article uses data from Thomson Reuters Web of Science to map and analyse the scientific landscape for synthetic biology. The article draws on recent advances in data visualisation and analytics with the aim of informing upcoming international policy debates on the governance of synthetic biology by the Subsidiary Body on Scientific, Technical and Technological Advice (SBSTTA) of the United Nations Convention on Biological Diversity. We use mapping techniques to identify how synthetic biology can best be understood and the range of institutions, researchers and funding agencies involved. Debates under the Convention are likely to focus on a possible moratorium on the field release of synthetic organisms, cells or genomes. Based on the empirical evidence we propose that guidance could be provided to funding agencies to respect the letter and spirit of the Convention on Biological Diversity in making research investments. Building on the recommendations of the United States Presidential Commission for the Study of Bioethical Issues we demonstrate that it is possible to promote independent and transparent monitoring of developments in synthetic biology using modern information tools. In particular, public and policy understanding and engagement with synthetic biology can be enhanced through the use of online interactive tools. As a step forward in this process we make existing data on the scientific literature on synthetic biology available in an online interactive workbook so that researchers, policy makers and civil society can explore the data and draw conclusions for themselves.

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network's evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective.

Information theory and the ethylene genetic network

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.

Information flow in plant signaling pathways

Systems biology and mathematical approaches are required for understanding how genetic regulatory networks process information from the environment. A typical genetic communication channel is conformed by: 1) an encoder, which is a specific membrane receptor that perceives the environmental information in the form of a concentration of a specific phytohormone. In the particular case of the ethylene signaling pathway, the encoder is the ETR1,2 specific receptor to ethylene; 2) a transmitting pathway, which is a signaling pathway. In the case, the ethylene signaling pathway; 3) a decoder, which is the molecular transcriptional machinery associated with the ERF1 and downstream genes and 4) an effector, which is the molecular translational machinery associated to the ethylene genetic network. Every communication channel is subject to noise, i.e., any physicochemical process that can alter the message carried from the encoder to the decoder and effector. Noise introduces a certain amount of uncertainty in any message spread through the communication channel. The amount of uncertainty in the content of a message is measured with the Shannon's entropy function H and, consequently, the amount of information actually carried by the message can be measured with the information function I = Hmax-H. Genetic networks are composed of a relative low and fluctuating amount of molecules and this characteristic, together with the effect of noise, produces a genetic response at time t with a probability p(t) of being correct with respect to the input message, and a probability 1-p(t) of been incorrect. From these probability values, H and I functions can be evaluated and, for the first time, it is possible to assign a measure of information content to each message associated to a given concentration of phytohormone. This type of analysis can be applied to any other plant genetic regulatory network.