Boolean formalization of genetic control circuits
TL;DR: This paper is an attempt to formalize in Boolean terms genetic situations, from simple concepts like recessitivity and cis-dominance, to models describing complex control circuits, to describe in compact and unambiguous way, systems which become more and more difficult to describe as their complexity is being unravelled.
About: This article is published in Journal of Theoretical Biology.The article was published on 1973-12-01. It has received 986 citations till now. The article focuses on the topics: Expression (mathematics) & Binary function.
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TL;DR: In this paper, a two-way clustering algorithm was applied to both the genes and the tissues, revealing broad coherent patterns that suggest a high degree of organization underlying gene expression in these tissues.
Abstract: Oligonucleotide arrays can provide a broad picture of the state of the cell, by monitoring the expression level of thousands of genes at the same time. It is of interest to develop techniques for extracting useful information from the resulting data sets. Here we report the application of a two-way clustering method for analyzing a data set consisting of the expression patterns of different cell types. Gene expres- sion in 40 tumor and 22 normal colon tissue samples was analyzed with an Affymetrix oligonucleotide array comple- mentary to more than 6,500 human genes. An efficient two- way clustering algorithm was applied to both the genes and the tissues, revealing broad coherent patterns that suggest a high degree of organization underlying gene expression in these tissues. Coregulated families of genes clustered together, as demonstrated for the ribosomal proteins. Clustering also separated cancerous from noncancerous tissue and cell lines from in vivo tissues on the basis of subtle distributed patterns of genes even when expression of individual genes varied only slightly between the tissues. Two-way clustering thus may be of use both in classifying genes into functional groups and in classifying tissues based on gene expression.
4,131 citations
TL;DR: This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equation, stochastic equations, and so on.
Abstract: The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.
2,739 citations
TL;DR: Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction, and by understanding the dynamics of these networks the authors can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated.
Abstract: Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.
1,128 citations
TL;DR: A Boolean model of the segment polarity gene network is proposed which is able to reproduce the wild-type gene expression patterns, as well as the ectopic expression patterns observed in overexpression experiments and various mutants, and gives important insights into the functioning of the network.
900 citations
Additional excerpts
...This type of network modeling is rooted in the pioneering work of Kauffman (1969, 1993) on random Boolean networks and of Thomas (1973, Thomas & D’Ari 1990) on Boolean models describing generic gene networks....
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...This type of network modeling is rooted in the pioneering work of Kauffman (1969, 1993) on random Boolean networks and of Thomas (Thomas, 1973; Thomas and D’Ari, 1990) on Boolean models describing generic gene networks....
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TL;DR: In this article, a Boolean model of the Drosophila segment polarity gene network is proposed, which is based on a binary ON/OFF representation of transcription and protein levels, and in which the interactions are formulated as logical functions.
Abstract: Expression of the Drosophila segment polarity genes is initiated by a prepattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyze a Boolean model of this network which is based on a binary ON/OFF representation of transcription and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild type gene expression patterns, as well as the ectopic expression patterns observed in over-expression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the prepattern.
853 citations
References
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TL;DR: The synthesis of enzymes in bacteria follows a double genetic control, which appears to operate directly at the level of the synthesis by the gene of a shortlived intermediate, or messenger, which becomes associated with the ribosomes where protein synthesis takes place.
5,588 citations
TL;DR: The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”.
4,250 citations
TL;DR: The Novick-Weiner effect and the one to be analyzed here prove to be aspects of the same situation and a heterogeneity with respect to the induced synthesis of ,B-galactosidase simulating genetic differences could be provoked within a growing population of otherwise identical cells.
Abstract: The observation has been made repeatedly that the induced synthesis of many different enzymes can be inhibited by a wide variety of carbohydrates (Benzer, 1953; Cohn, 1957, 1958; Epps and Gale, 1942; Gale, 1943; Happold and Hoyle, 1936; Herzenberg, 1958; Monod, 1941, 1947, 1956; Monod and Cohn, 1952; Neidhardt and Magasanik, 1956). One of the most characteristic and potent of these carbohydrate inhibitors is glucose. As a result the general phenomenon has been called the glucose effect (Cohn, 1956; Cohn and Monod, 1953). During an investigation of the glucose effect, it was observed that under certain conditions a remarkable situation arose: two bacterial populations of identical genotype growing under identical conditions could be maintained indefinitely with different phenotypes; one population produced f3-galactosidase whereas the other did not (maintenance). Furthermore, a heterogeneity with respect to the induced synthesis of ,B-galactosidase simulating genetic differences could be provoked within a growing population of otherwise identical cells. An investigation of maintenance as well as of heterogeneity in the ",B-galactoside-enzyme system" under conditions of low inducer concentration has been described by Novick and Weiner (1957). The Novick-Weiner effect and the one to be analyzed here prove to be aspects of the same situation. Our studies will be described in three papers.
165 citations
TL;DR: The kinetics of induction of the galactozymase of certain yeasts and the permease-3-galactosidase system of Escherichia coli can, under certain conditions, be described as autocatalytic.
Abstract: The kinetics of induction of the galactozymase of certain yeasts (Spiegelman, 1951) and the permease-3-galactosidase system of Escherichia coli (Monod, 1956) can, under certain conditions, be described as autocatalytic. Essentially two hypotheses have been proposed to account for such findings: (a) that the enzyme-forming system itself is autocatalytically activated (Campbell and Spiegelman, 1956) or self-reproducing (Spiegelman, 1946), or (b) that in some way the enzyme being induced intervenes in its own induction (Monod and Cohn, 1952). To evaluate these hypotheses, it should be recalled that the kinetics of formation of an enzyme by a population of cells describes events at the cellular level only if the response of each individual cell is simultaneous and equal (Benzer, 1953; Monod and Cohn, 1952). Such a response we term homogeneity. The first experimental analysis of this problem we owe to Benzer (1953) who defined the experimental conditions under which the induction of f-galactosidase would proceed in a homogeneous fashion in an E. coli (lac+) population. These were (a) conditions of gratuity, i. e., neither the presence of the enzyme itself nor its inducer influences general cellular metabolism, and (b) a saturating concentration of inducer. Benzer (1953) also showed that heterogeneity is generated under conditions of nongratuity. The question remained however as to what the response would be at nonsaturating concentrations of inducer.
116 citations
TL;DR: The theory presented by the author in his previous paper in this journal, which concerned the use of logical circuits or symbolic logic, is revised and extended and the idea of a molecular automaton is introduced.
98 citations