Papers by El Mehdi Snoussi
Fariñas del Cerro/Logical Modeling of Biological Systems, 2014
Logic and its counterpart in computer science, namely formal methods, offer both a solid, flexibl... more Logic and its counterpart in computer science, namely formal methods, offer both a solid, flexible ground for modelling in biology, and a methodological backbone for accompanying experimental strategy within a multidisciplinary research process. We thus consider a partial knowledge setting in which we cannot take the risk to study a single model that may become a bad model when the biological knowledge increases. We manage at each step of the process the set of all the possible models according to the current knowledge. This is precisely the reason why logic is a suitable tool: it describes sets of models by their properties and it is able to manipulate them. Among those maniputations, the formal validation activity is particularly appreciated by researchers in biology: it suggest new biological experiments in a computer aided manner in such a way that some kind of completeness can be reached. The methodology proposed in this chapter is independant both of the biological object and of the underlying logic, but we illustrate its main phases in the context of discrete modelling of gene networks using a particular temporal logic.
Positive Loops and Differentiation
Journal of Biological Systems, 1995
This paper focuses on the relation between the presence of positive feedback loops and the occurr... more This paper focuses on the relation between the presence of positive feedback loops and the occurrence of multiple states of gene expression. After a short recall on single feedback loops and their properties, we discuss more extensively the properties of positive loops. This discussion includes a theorem (demonstrated elsewhere) which states that the presence of positive loop(s) is a necessary condition for multistationarity. We also discuss some general principles for pattern formation, in terms of involvement of different types of positive feedback loops. Finally, we briefly mention recent experimental results involving positive loops in crucial differentiative processes.
Bulletin of Mathematical Biology, 2013
It has been proved, for several classes of continuous and discrete dynamical systems, that the pr... more It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable 1 states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates". Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.
Bulletin of Mathematical Biology, 1993
Biological regulatory systems can be described in terms of non-linear differential equations or i... more Biological regulatory systems can be described in terms of non-linear differential equations or in logical terms (using an "infinitely non-linear" approximation). Until recently, only part of the steady states of a system could be identified on logical grounds. The reason was that steady states frequently have one or more variable located on a threshold (see below); those steady states were not detected because so far no logical status was assigned to threshold values. This is why we introduced logical scales with values 0, 10, 1, 20, 2,..., in which 10, 20,... are the logical values assigned to the successive thresholds of the scale. We thus have, in addition to the regular logical states, singular states in which one or more variables is located on a threshold. This permits identifying all the steady states on logical grounds. It was noticed that each feedback loop (or reunion of disjointed loops) can be characterized by a logical state located at the thresholds at which the variables of the loop operate. This led to the concept of loop-characteristic state, which, as we will see, enormously simplifies the analysis. The core of this paper is a formal demonstration that among the singular states of a system, only loop-characteristic states can be steady. Reciprocally, given a loop-characteristic state, there are parameter values for which this state is steady; in this case, the loop is effective (i.e. it generates multistationarity if it is a positive loop, homeostasis if it is a negative loop). This not only results in the above-mentioned radical simplification of the identification of the steady states, but in an entirely new view of the relation between feedback loops and steady states.
Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach
Dynamics and Stability of Systems, 1989
... and Kauffman, 1972; Jacob and Monod, 1961; Kauffman et al., 1985; Monod et al., 1965; Thomas ... more ... and Kauffman, 1972; Jacob and Monod, 1961; Kauffman et al., 1985; Monod et al., 1965; Thomas 1979) have argued that there is a strong similarity between the dynamical behaviour of the boolean map and the system of differential equations with Heaviside on-off functions. ...
Necessary Conditions for Multistationarity and Stable Periodicity
Journal of Biological Systems, 1998
We show in this paper that, for a differential system defined by a quasi-monotonous function f (w... more We show in this paper that, for a differential system defined by a quasi-monotonous function f (with constant sign partial derivatives) the existence of a positive loop in the interaction graph associated to the Jacobian matrix of f is a necessary condition for multistationarity, and the existence of a negative loop comprising at least two elements is a necessary condition for stable periodicity. This gives a formal proof of R.Thomas's conjectures.
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Papers by El Mehdi Snoussi