A Model for the Self-Organization of Microtubules Driven by Molecular Motors

We propose a two-dimensional model for the organization of stabilized microtubules driven by molecular motors in an unconfined geometry. In this model two kinds of dynamics are competing. The first one is purely diffusive, with an interaction between the rotational degrees of freedom, the second one is a local drive, dependent on microtubule polarity. As a result, there is a configuration dependent driving field. Applying a molecular field approximation, we are able to derive continuum equations. A study on the solutions shows nonequilibrium steady states. The presence and stability of such self-organized states are investigated in terms of entropy production. Numerical simulations confirm analytical results.Comment: 23 pages, 10 figures, LaTeX, ep

Random Networks Tossing Biased Coins

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to generate an ensemble of random directed graphs with, asymptotically, scale-free outdegree and compact indegree. Entries in each row of the adjacency matrix are set to be zero or one according to the toss of a biased coin, with a chosen probability distribution for the biases. This defines a quick and simple algorithm, which yields good results already for graphs of size n ~ 100. Perhaps more importantly, many of the relevant observables are accessible analytically, improving upon previous estimates for similar graphs

Hierarchy and Feedback in the Evolution of the E. coli Transcription Network

The E.coli transcription network has an essentially feedforward structure, with, however, abundant feedback at the level of self-regulations. Here, we investigate how these properties emerged during evolution. An assessment of the role of gene duplication based on protein domain architecture shows that (i) transcriptional autoregulators have mostly arisen through duplication, while (ii) the expected feedback loops stemming from their initial cross-regulation are strongly selected against. This requires a divergent coevolution of the transcription factor DNA-binding sites and their respective DNA cis-regulatory regions. Moreover, we find that the network tends to grow by expansion of the existing hierarchical layers of computation, rather than by addition of new layers. We also argue that rewiring of regulatory links due to mutation/selection of novel transcription factor/DNA binding interactions appears not to significantly affect the network global hierarchy, and that horizontally transferred genes are mainly added at the bottom, as new target nodes. These findings highlight the important evolutionary roles of both duplication and selective deletion of crosstalks between autoregulators in the emergence of the hierarchical transcription network of E.coli.Comment: to appear in PNA

Computational core and fixed-point organisation in Boolean networks

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby the computational core of the network. Second we apply the cavity method to analyse number and organisation of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter one being characterised by the existence of an exponential number of macroscopically separated fixed-point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied to analysis and in silico experiments on the gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the segment-polarity genes of the fruit-fly drosophila melanogaster.Comment: 29 pages, 18 figures, version accepted for publication in JSTA