Interpretation of high-throughput biological data requires a knowledge of the design principles underlying the networks that sustain cellular functions. Of particular importance is the genetic network, a set of genes that interact through directed transcriptional regulation. Genes that exert a regulatory role encode dedicated transcription factors (hereafter referred to as regulating proteins) that can bind to specific DNA control regions of regulated genes to activate or inhibit their transcription. Regulated genes may themselves act in a regulatory manner, in which case they participate in a causal pathway. Looping pathways form feedback circuits. Because a gene can have several connections, circuits and pathways may crosslink and thus represent connected components. We have created a graph of 909 genetically or biochemically established interactions among 491 yeast genes. The number of regulating proteins per regulated gene has a narrow distribution with an exponential decay. The number of regulated genes per regulating protein has a broader distribution with a decay resembling a power law. Assuming in computergenerated graphs that gene connections fulfill these distributions but are otherwise random, the local clustering of connections and the number of short feedback circuits are largely underestimated. This deviation from randomness probably reflects functional constraints that include biosynthetic cost, response delay and differentiative and homeostatic regulation.In integrating genome-wide data on transcript abundance 1 into a dynamic view of gene networks, recent studies have focused on abstracting the principles that underlie the architecture and causal interplay of these networks. At present, the yeast Saccharomyces cerevisiae is the most suitable eukaryotic organism for achieving this goal, as much information about its transcriptional regulations has been accumulated 2,3 . Of roughly 6,000 yeast genes, 124 have been shown through genetic and biochemical experiments to encode regulating proteins that can influence the expression of specific genes 2 . These data were obtained from a previous review 2 and were validated and updated, until July 2001, by manual inspection of the websites of MIPS, SwissProt, Yeast Protein Database, S. cerevisiae Promoter Database and the Saccharomyces Genome Database (see Web Note A online). The elements of the general transcription initiation machinery were excluded from this study, although some have differential roles in transcription of large subsets of genes 3 . Some of the 124 regulatory genes transcriptionally control a set of 367 non-regulatory genes ( Fig. 1) through 837 connections (see Web Table A online). Of the 124 regulatory genes, 52 interact with themselves or with other regulatory genes through 72 additional links (see Web Table A online). A transcriptional regulatory network can thus be represented as a graph where vertices are genes and directed edges denote activating or repressing effects on transcription. The graph of these 52 'interregulatory' gene...

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.

It is shown that globally coupled oscillators with pulse interaction can synchronize under broader conditions than widely believed from a theorem of Mirollo and Strogatz. This behavior is stable against frozen disorder. Beside the relevance to biology, it is argued that synchronization in relaxation oscillator models is related to self-organized criticality in stick-slip-like models.PACS numbers: 05.45.+b, 05.40.+j Large assemblies of oscillator units can spontaneously evolve to a state of large scale organization. Collective synchronization is the best known phenomenon of this kind, where after some transient regime a coherent oscillatory activity of the set of oscillators emerges. This effect has attracted much interest in biology for the study of large scale rhythms in populations of interacting elements [1]. The southeastern fireflies, where thousands of individuals gathered on trees flash in unison, is the most cited example [2]. Other examples are the rhythmic activity of cells of the heart pacemaker, of cells of the pancreas, and of neural networks [2 -4]. Most of the works on synchronization have used models in which the interaction between the oscillators is smooth and continuous in time (see, e. g., [5]). Comparatively, few analytical results are known on models where the interactions are episodic and pulselike [1,3,6,7], although they are relevant to several biological situations as fireflies and neural networks. This Letter deals with the emergence of synchronization in a very simple model of globally coupled integrate and fire (IF) oscillators; see Eq. (1) for the definition and [2]. It is shown that synchronization occurs under broad conditions on the properties of the oscillators, thus generalizing a theorem of Mirollo and Strogatz [1], the usual interpretation of which restricted the synchronization conditions in a too drastic way. Furthermore, I show that the synchronized state is stable against a frozen disorder of the oscillator properties, a subject much studied in models with continuous interaction [5]. This result is different from that of a previous study [7] on a closely related model.Besides synchronization, another form of collective organized behavior is known to occur in large assemblies of elements with pulse interaction, that is, self-organized criticality (SOC). This concept has been proposed in [8] to describe out of equilibrium systems that are generically critical, i.e. , that organize into a scale invariant critical state spontaneously, without tuning of a control parameter. Systems displaying SOC are externally driven with a drive slower than any other characteristic time. These models are made critical by the choice of a threshold dynamics that forbids them to follow adiabatically the exter-nal drive. They can be modeled as coupled map lattices and can be divided into two subclasses based on the concept of oscillators. In subclass (a) the external drive acts globally and continuously on all the lattice sites of the coupled map, until one of them reaches the threshold, in wh...

In this article we study the behavior of globally coupled assemblies of a large number of Integrate and Fire oscillators with excitatory pulse-like interactions. On some simple models we show that the additive effects of pulses on the state of Integrate and Fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synchronization occurs in two forms depending on the system: either the oscillators evolve "en bloc" at the same phase and therefore relax together or the oscillators do not remain in phase but their relaxations occur always in stable avalanches. We prove that synchronization can occur independently of the convexity or concavity of the oscillators evolution function. Furthermore the presence of disorder, up to some level, is not only compatible with synchronization, but removes some possible degeneracy of identical systems and allows new mechanisms towards this state.