Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics of the system. We prove that, in a random regulatory network, initial conditions converge almost surely to a periodic attractor. We study the subnetworks, which we call modules, where the periodic asymptotic oscillations are concentrated. We proof that those modules are dynamically equivalent to independent regulatory networks.Comment: 23 pages, 3 figure

Organismal benefits of transcription speed control at gene boundaries

RNA polymerase II (RNAPII) transcription is crucial for gene expression. RNAPII density peaks at gene boundaries, associating these key regions for gene expression control with limited RNAPII movement. The connections between RNAPII transcription speed and gene regulation in multicellular organisms are poorly understood. Here, we directly modulate RNAPII transcription speed by point mutations in the second largest subunit of RNAPII in Arabidopsis thaliana. A RNAPII mutation predicted to decelerate transcription is inviable, while accelerating RNAPII transcription confers phenotypes resembling auto‐immunity. Nascent transcription profiling revealed that RNAPII complexes with accelerated transcription clear stalling sites at both gene ends, resulting in read‐through transcription. The accelerated transcription mutant NRPB2‐Y732F exhibits increased association with 5′ splice site (5′SS) intermediates and enhanced splicing efficiency. Our findings highlight potential advantages of RNAPII stalling through local reduction in transcription speed to optimize gene expression for the development of multicellular organisms.SynopsisRNAPII mutations that accelerate transcription cause auto‐immunity‐like phenotypes, read‐through transcription at RNAPII stalling sites and enhanced splicing in Arabidopsis, indicating that controlled transcription speed is required for optimal gene expression and plant development.A point mutation in RNAPII that increases the speed of RNAPII transcription triggers auto‐immunity‐like phenotypes.plaNET‐seq reveals reduced RNAPII stalling at gene boundaries in fast transcription mutants.Increasing the speed of transcription reduces the efficiency of transcriptional termination, resulting in read‐through transcription that blurs the spatial separation of genes.Accelerating RNAPII transcription enhances splicing efficiency in the multi‐cellular context.RNAPII mutations that accelerate transcription cause auto‐immunity‐like phenotypes, read‐through transcription at RNAPII stalling sites and enhanced splicing in Arabidopsis, indicating that controlled transcription speed is required for optimal gene expression and plant development.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154978/1/embr201949315-sup-0001-EVFigs.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154978/2/embr201949315.reviewer_comments.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154978/3/embr201949315.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154978/4/embr201949315_am.pd

Genetic noise control via protein oligomerization

Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling. While there have been numerous studies correlating the architecture of cellular reaction networks with noise tolerance, only a limited effort has been made to understand the dynamic role of protein-protein interactions. Here we have developed a fully stochastic model for the positive feedback control of a single gene, as well as a pair of genes (toggle switch), integrating quantitative results from previous in vivo and in vitro studies. We find that the overall noise-level is reduced and the frequency content of the noise is dramatically shifted to the physiologically irrelevant high-frequency regime in the presence of protein dimerization. This is independent of the choice of monomer or dimer as transcription factor and persists throughout the multiple model topologies considered. For the toggle switch, we additionally find that the presence of a protein dimer, either homodimer or heterodimer, may significantly reduce its random switching rate. Hence, the dimer promotes the robust function of bistable switches by preventing the uninduced (induced) state from randomly being induced (uninduced). The specific binding between regulatory proteins provides a buffer that may prevent the propagation of fluctuations in genetic activity. The capacity of the buffer is a non-monotonic function of association-dissociation rates. Since the protein oligomerization per se does not require extra protein components to be expressed, it provides a basis for the rapid control of intrinsic or extrinsic noise

Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the critical value $K_c =2$ in the limit of large system size $N$. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.Comment: 4 pages RevTeX, 4 figures PostScript, revised versio

RSAT 2011: regulatory sequence analysis tools

RSAT (Regulatory Sequence Analysis Tools) comprises a wide collection of modular tools for the detection of cis-regulatory elements in genome sequences. Thirteen new programs have been added to the 30 described in the 2008 NAR Web Software Issue, including an automated sequence retrieval from EnsEMBL (retrieve-ensembl-seq), two novel motif discovery algorithms (oligo-diff and info-gibbs), a 100-times faster version of matrix-scan enabling the scanning of genome-scale sequence sets, and a series of facilities for random model generation and statistical evaluation (random-genome-fragments, random-motifs, random-sites, implant-sites, sequence-probability, permute-matrix). Our most recent work also focused on motif comparison (compare-matrices) and evaluation of motif quality (matrix-quality) by combining theoretical and empirical measures to assess the predictive capability of position-specific scoring matrices. To process large collections of peak sequences obtained from ChIP-seq or related technologies, RSAT provides a new program (peak-motifs) that combines several efficient motif discovery algorithms to predict transcription factor binding motifs, match them against motif databases and predict their binding sites. Availability (web site, stand-alone programs and SOAP/WSDL (Simple Object Access Protocol/Web Services Description Language) web services): http://rsat.ulb.ac.be/rsat/

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Characterization of Reachable Attractors Using Petri Net Unfoldings

International audienceAttractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. In this paper, we present a new algorithm that exploits the concurrency between transitions of parallel acting components in order to reduce the search space. The algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being %so far more generic since it applies to any safe Petri net

Delay-Induced Transient Increase and Heterogeneity in Gene Expression in Negatively Auto-Regulated Gene Circuits

A generic feature in all intracellular biochemical processes is the time required to complete the whole sequence of reactions to yield any observable quantity-from gene expression to circadian rhythms. This widespread phenomenon points towards the importance of time delay in biological functions. Theoretically time delay is known to be the source of instability, and has been attributed to lead to oscillations or transient dynamics in several biological functions. Negative feedback loops, common in biochemical pathways, have been shown to provide stability and withstand considerable variations and random perturbations of biochemical parameters. The interaction of these two opposing factors-of instability and homeostasis-are features that are widespread in intracellular processes. To test the effect of these divergent forces in the dynamics of gene expression, we have designed and constructed simple negatively auto-regulated gene circuits consisting of a basic regulator and transcriptional repressor module, and compared it with one, which has delayed repression. We show, both theoretically and experimentally, that delayed repression induces transient increase and heterogeneity in gene expression before the gain of stability effected by the negative feedback. This design, therefore, seems to be suitable for conferring both stability and variability in cells required for adaptive response to a noisy environment

Computing paths and cycles in biological interaction graphs

<p>Abstract</p> <p>Background</p> <p>Interaction graphs (signed directed graphs) provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops) and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments.</p> <p>Results</p> <p>We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible) this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops.</p> <p>Conclusion</p> <p>The calculation of shortest positive/negative paths and cycles in interaction graphs is an important method for network analysis in Systems Biology. This contribution draws the attention of the community to this important computational problem and provides a number of new algorithms, partially specifically tailored for biological interaction graphs. All algorithms have been implemented in the <it>CellNetAnalyzer </it>framework which can be downloaded for academic use at <url>http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html</url>.</p