René Thomas

Bio: René Thomas is an academic researcher from Université libre de Bruxelles. The author has contributed to research in topics: Lysogenic cycle & Jacobian matrix and determinant. The author has an hindex of 32, co-authored 79 publications receiving 5341 citations.

On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations

Abstract: Simple feedback loops behave in two essentially different ways depending on whether they contain an odd number of inhibitory elements (“negative” loops) or an even number of inhibitory elements (“positive” loops); for proper values of parameters or delays, the former generate sustained oscillations, the latter, multiple steady states. For more complex systems, as far as one can tell, the presence of at least one negative loop in the logical structure appears as a necessary (but not sufficient) condition for a permanent periodic behaviour, and the presence of at least one positive loop as a necessary (but not sufficient) condition for multiple steady states.

Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior.

Abstract: A biological introduction serves to remind us that differentiation is an epigenetic process, that multistationarity can account for epigenetic differences, including those involved in cell differentiation, and that positive feedback circuits are a necessary condition for multistationarity and, by inference, for differentiation. The core of the paper is comprised of a formal description of feedback circuits and unions of disjoint circuits. We introduce the concepts of full-circuit (a circuit or union of disjoint circuits which involves all the variables of the system), and of ambiguous circuit (a circuit whose sign depends on the location in phase space). We describe the partition of phase space (a) according to the signs of the ambiguous circuits, and (b) according to the signs of the eigenvalues or their real part. We introduce a normalization of the system versus one of the circuits; in two variables, this permits an entirely general description in terms of a common diagram in the “circuit space.” The paper ends with general statements concerning the requirements for multistationarity, stable periodicity, and deterministic chaos.

Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits

Abstract: Circuits and their involvement in complex dynamics are described in differential terms in Part I of this work. Here, we first explain why it may be appropriate to use a logical description, either by itself or in symbiosis with the differential description. The major problem of a logical description is to find an adequate way to involve time. The procedure we adopted differs radically from the classical one by its fully asynchronous character. In Sec. II we describe our “naive” logical approach, and use it to illustrate the major laws of circuitry (namely, the involvement of positive circuits in multistationarity and of negative circuits in periodicity) and in a biological example. Already in the naive description, the major steps of the logical description are to: (i) describe a model as a set of logical equations, (ii) derive the state table from the equations, (iii) derive the graph of the sequences of states from the state table, and (iv) determine which of the possible pathways will be actually followed in terms of time delays. In the following sections we consider multivalued variables where required, the introduction of logical parameters and of logical values ascribed to the thresholds, and the concept of characteristic state of a circuit. This generalized logical description provides an image whose qualitative fit with the differential description is quite remarkable. A major interest of the generalized logical description is that it implies a limited and often quite small number of possible combinations of values of the logical parameters. The space of the logical parameters is thus cut into a limited number of boxes, each of which is characterized by a defined qualitative behavior of the system. Our analysis tells which constraints on the logical parameters must be fulfilled in order for any circuit (or combination of circuits) to be functional. Functionality of a circuit will result in multistationarity (in the case of a positive circuit) or in a cycle (in the case of a negative circuit). The last sections deal with “more about time delays” and “reverse logic,” an approach that aims to proceed rationally from facts to models.

Construction of a genetic toggle switch in Escherichia coli

Abstract: It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy.

Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays.

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.

Modeling and simulation of genetic regulatory systems: a literature review.

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.

Structure and function of the feed-forward loop network motif

Abstract: Engineered systems are often built of recurring circuit modules that carry out key functions. Transcription networks that regulate the responses of living cells were recently found to obey similar principles: they contain several biochemical wiring patterns, termed network motifs, which recur throughout the network. One of these motifs is the feed-forward loop (FFL). The FFL, a three-gene pattern, is composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene. The FFL has eight possible structural types, because each of the three interactions in the FFL can be activating or repressing. Here, we theoretically analyze the functions of these eight structural types. We find that four of the FFL types, termed incoherent FFLs, act as sign-sensitive accelerators: they speed up the response time of the target gene expression following stimulus steps in one direction (e.g., off to on) but not in the other direction (on to off). The other four types, coherent FFLs, act as sign-sensitive delays. We find that some FFL types appear in transcription network databases much more frequently than others. In some cases, the rare FFL types have reduced functionality (responding to only one of their two input stimuli), which may partially explain why they are selected against. Additional features, such as pulse generation and cooperativity, are discussed. This study defines the function of one of the most significant recurring circuit elements in transcription networks.