Transcriptional delay stabilizes bistable gene networks

Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner

Failed "nonaccelerating" models of prokaryote gene regulatory networks

Much current network analysis is predicated on the assumption that important biological networks will either possess scale free or exponential statistics which are independent of network size allowing unconstrained network growth over time. In this paper, we demonstrate that such network growth models are unable to explain recent comparative genomics results on the growth of prokaryote regulatory gene networks as a function of gene number. This failure largely results as prokaryote regulatory gene networks are "accelerating" and have total link numbers growing faster than linearly with network size and so can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. In the limit, these networks can undergo transitions so marked as to constrain network sizes to be below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are indeed characterized by an accelerating quadratic growth with gene count and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. We develop two "nonaccelerating" network models of prokaryote regulatory gene networks in an endeavor to match observation and demonstrate that these approaches fail to reproduce observed statistics.Comment: Corrected error in biological input parameter: 13 pages, 9 figure

Designer Gene Networks: Towards Fundamental Cellular Control

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics.Comment: 35 pages, 8 figure

Stochastic models and numerical algorithms for a class of regulatory gene networks

Regulatory gene networks contain generic modules like those involving feedback loops, which are essential for the regulation of many biological functions. We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady state distributions of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in synthetic biology and in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loop

A Fast Reconstruction Algorithm for Gene Networks

This paper deals with gene networks whose dynamics is assumed to be generated by a continuous-time, linear, time invariant, finite dimensional system (LTI) at steady state. In particular, we deal with the problem of network reconstruction in the typical practical situation in which the number of available data is largely insufficient to uniquely determine the network. In order to try to remove this ambiguity, we will exploit the biologically a priori assumption of network sparseness, and propose a new algorithm for network reconstruction having a very low computational complexity (linear in the number of genes) so to be able to deal also with very large networks (say, thousands of genes). Its performances are also tested both on artificial data (generated with linear models) and on real data obtained by Gardner et al. from the SOS pathway in Escherichia coli.Comment: 12 pages, 3 figure

Spectral analysis of gene expression profiles using gene networks

Microarrays have become extremely useful for analysing genetic phenomena, but establishing a relation between microarray analysis results (typically a list of genes) and their biological significance is often difficult. Currently, the standard approach is to map a posteriori the results onto gene networks to elucidate the functions perturbed at the level of pathways. However, integrating a priori knowledge of the gene networks could help in the statistical analysis of gene expression data and in their biological interpretation. Here we propose a method to integrate a priori the knowledge of a gene network in the analysis of gene expression data. The approach is based on the spectral decomposition of gene expression profiles with respect to the eigenfunctions of the graph, resulting in an attenuation of the high-frequency components of the expression profiles with respect to the topology of the graph. We show how to derive unsupervised and supervised classification algorithms of expression profiles, resulting in classifiers with biological relevance. We applied the method to the analysis of a set of expression profiles from irradiated and non-irradiated yeast strains. It performed at least as well as the usual classification but provides much more biologically relevant results and allows a direct biological interpretation

Inference algorithms for gene networks: a statistical mechanics analysis

The inference of gene regulatory networks from high throughput gene expression data is one of the major challenges in systems biology. This paper aims at analysing and comparing two different algorithmic approaches. The first approach uses pairwise correlations between regulated and regulating genes; the second one uses message-passing techniques for inferring activating and inhibiting regulatory interactions. The performance of these two algorithms can be analysed theoretically on well-defined test sets, using tools from the statistical physics of disordered systems like the replica method. We find that the second algorithm outperforms the first one since it takes into account collective effects of multiple regulators