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International audience; Delays appear in the dynamics of many systems due to non-vanishing reaction times of control systems. In biochemical systems, long sequences of repeated steps, especially in biopolymerization processes, can be modeled by delays. However, modelling systems with delays is often complicated by physical constraints, such as the requirement that solutions representing concentrations of chemical species remain positive. In this work, we consider a model for a detoxifying enzyme whose synthesis is controlled by its substrate. The model includes bindingsite clearance delays, caused by the time required for an RNA polymerase or ribosome to clear its binding site before another such machine can bind. The existence of a positive equilibrium and the positivity and boundedness of solutions of the corresponding delay-differential equations are proven. In addition, the stability of the model is studied using the "small-gain" theorem.

Factorial Gaussian graphical Models (fGGMs) have recently been proposed for inferring dynamic gene regulatory networks from genomic high-throughput data. In the search for true regulatory relationships amongst the vast space of possible networks, these models allow the imposition of certain restrictions on the dynamic nature of these relationships, such as Markov dependencies of low order – some entries of the precision matrix are a priori zeros – or equal dependency strengths across time lags – some entries of the precision matrix are assumed to be equal. The precision matrix is then estimated by l 1-penalized maximum likelihood, imposing a further constraint on the absolute value of its entries, which results in sparse networks. Selecting the optimal sparsity level is a major challenge for this type of approaches. In this paper, we evaluate the performance of a number of model selection criteria for fGGMs by means of two simulated regulatory networks from realistic biological processes. The analysis reveals a good performance of fGGMs in comparison with other methods for inferring dynamic networks and of the KLCV criterion in particular for model selection. Finally, we present an application on a high-resolution time-course microarray data from the Neisseria meningitidis bacterium, a causative agent of life-threatening infections such as meningitis. The methodology described in this paper is implemented in the R package sglasso, freely available at CRAN, http://CRAN.R-project.org/package=sglasso.