Invalidation of the structure of genetic network dynamics: a geometric approach

Abstract

International audienceThis work concerns the identification of the structure of a genetic network model from measurements of gene product concentrations and synthesis rates. In earlier work, we developed a data preprocessing algorithm that is able to reject many hypotheses on the network structure by testing certain monotonicity properties for a wide family of network models. Here, we develop a geometric interpretation of the method. Then, for a relevant subclass of genetic network models, we extend our approach to the combined testing of monotonicity and convexity-like properties associated with the network structures. The theoretical aspects and practical performance of the enhanced methods are illustrated by way of numerical results

Learning the structure of genetic network dynamics: A geometric approach

“…The idea is to robustify all inconsistency conditions by taking the bounded uncertainty into account. While this is trivial for conditions on data g k , robustification is easily achieved also for all tests involving data x k (Porreca et al, 2011). As an example, condition x * ∨ ∈ L max,∨ (D , p ∨ ) for p ∨ = (1, 1) is robustified by considering the worstcase inner approximation of L max,∨ (D , p ∨ ), i.e.…”

“…Theoretical and experimental results are discussed in Section 6 by way of illustrative simulations. Mathematical proofs can be found in Porreca et al (2011).…”