Emergence of switch-like behavior in a large family of simple biochemical networks

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the most elementary biochemical processes). We find that there exist reaction rate constants leading to bistability in ~90% of these GRN models, including several circuits that do not contain any of the TF cooperativity commonly associated with bistable systems, and the majority of which could only be identified as bistable through an original subnetwork-based analysis. A topological sorting of the two-gene family of networks based on the presence or absence of biochemical reactions reveals eleven minimal bistable networks (i.e., bistable networks that do not contain within them a smaller bistable subnetwork). The large number of previously unknown bistable network topologies suggests that the capacity for switch-like behavior in GRNs arises with relative ease and is not easily lost through network evolution. To highlight the relevance of the systematic application of CRNT to bistable network identification in real biological systems, we integrated publicly available protein-protein interaction, protein-DNA interaction, and gene expression data from Saccharomyces cerevisiae, and identified several GRNs predicted to behave in a bistable fashion.Comment: accepted to PLoS Computational Biolog

Compositionality, stochasticity and cooperativity in dynamic models of gene regulation

We present an approach for constructing dynamic models for the simulation of gene regulatory networks from simple computational elements. Each element is called a ``gene gate'' and defines an input/output-relationship corresponding to the binding and production of transcription factors. The proposed reaction kinetics of the gene gates can be mapped onto stochastic processes and the standard ode-description. While the ode-approach requires fixing the system's topology before its correct implementation, expressing them in stochastic pi-calculus leads to a fully compositional scheme: network elements become autonomous and only the input/output relationships fix their wiring. The modularity of our approach allows to pass easily from a basic first-level description to refined models which capture more details of the biological system. As an illustrative application we present the stochastic repressilator, an artificial cellular clock, which oscillates readily without any cooperative effects.Comment: 15 pages, 8 figures. Accepted by the HFSP journal (13/09/07

Adaptive evolution of transcription factor binding sites

The regulation of a gene depends on the binding of transcription factors to specific sites located in the regulatory region of the gene. The generation of these binding sites and of cooperativity between them are essential building blocks in the evolution of complex regulatory networks. We study a theoretical model for the sequence evolution of binding sites by point mutations. The approach is based on biophysical models for the binding of transcription factors to DNA. Hence we derive empirically grounded fitness landscapes, which enter a population genetics model including mutations, genetic drift, and selection. We show that the selection for factor binding generically leads to specific correlations between nucleotide frequencies at different positions of a binding site. We demonstrate the possibility of rapid adaptive evolution generating a new binding site for a given transcription factor by point mutations. The evolutionary time required is estimated in terms of the neutral (background) mutation rate, the selection coefficient, and the effective population size. The efficiency of binding site formation is seen to depend on two joint conditions: the binding site motif must be short enough and the promoter region must be long enough. These constraints on promoter architecture are indeed seen in eukaryotic systems. Furthermore, we analyse the adaptive evolution of genetic switches and of signal integration through binding cooperativity between different sites. Experimental tests of this picture involving the statistics of polymorphisms and phylogenies of sites are discussed.Comment: published versio

Epigenetic Chromatin Silencing: Bistability and Front Propagation

The role of post-translational modification of histones in eukaryotic gene regulation is well recognized. Epigenetic silencing of genes via heritable chromatin modifications plays a major role in cell fate specification in higher organisms. We formulate a coarse-grained model of chromatin silencing in yeast and study the conditions under which the system becomes bistable, allowing for different epigenetic states. We also study the dynamics of the boundary between the two locally stable states of chromatin: silenced and unsilenced. The model could be of use in guiding the discussion on chromatin silencing in general. In the context of silencing in budding yeast, it helps us understand the phenotype of various mutants, some of which may be non-trivial to see without the help of a mathematical model. One such example is a mutation that reduces the rate of background acetylation of particular histone side-chains that competes with the deacetylation by Sir2p. The resulting negative feedback due to a Sir protein depletion effect gives rise to interesting counter-intuitive consequences. Our mathematical analysis brings forth the different dynamical behaviors possible within the same molecular model and guides the formulation of more refined hypotheses that could be addressed experimentally.Comment: 19 pages, 5 figure

Stochastic Gene Expression in a Lentiviral Positive Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity

Stochastic gene expression has been implicated in a variety of cellular processes, including cell differentiation and disease. In this issue of Cell, Weinberger et al. (2005) take an integrated computational-experimental approach to study the Tat transactivation feedback loop in HIV-1 and show that fluctuations in a key regulator, Tat, can result in a phenotypic bifurcation. This phenomenon is observed in an isogenic population where individual cells display two distinct expression states corresponding to latent and productive infection by HIV-1. These findings demonstrate the importance of stochastic gene expression in molecular "decision-making."Comment: Supplemental data available as q-bio.MN/060800

RNA packaging motor: From structure to quantum mechanical modelling and sequential-stochastic mechanism

The bacteriophages of the Cystoviridae family package their single stranded RNA genomic precursors into empty capsid (procapsids) using a hexameric packaging ATPase motor (P4). This molecular motor shares sequence and structural similarity with RecA-like hexameric helicases. A concerted structural, mutational and kinetic analysis helped to define the mechanical reaction coordinate, i.e. the conformational changes associated with RNA translocation. The results also allowed us to propose a possible scheme of coupling between ATP hydrolysis and translocation which requires the cooperative action of three consecutive subunits. Here, we first test this model by preparing hexamers with defined proportions of wild type and mutant subunits and measuring their activity. Then, we develop a stochastic kinetic model which accounts for the catalytic cooperativity of the P4 hexamer. Finally, we use the available structural information to construct a quantum-chemical model of the chemical reaction coordinate and obtain a detailed description of the electron density changes during ATP hydrolysis. The model explains the results of the mutational analyses and yields new insights into the role of several conserved residues within the ATP binding pocket. These hypotheses will guide future experimental work

The bacterial antitoxin HipB establishes a ternary complex with operator DNA and phosphorylated toxin HipA to regulate bacterial persistence

Nearly all bacteria exhibit a type of phenotypic growth described as persistence that is thought to underlie antibiotic tolerance and recalcitrant chronic infections. The chromosomally encoded high-persistence (Hip) toxin-antitoxin proteins HipA(SO) and HipB(SO) from Shewanella oneidensis, a proteobacterium with unusual respiratory capacities, constitute a type II toxin-antitoxin protein module. Here we show that phosphorylated HipA(SO) can engage in an unexpected ternary complex with HipB(SO) and double-stranded operator DNA that is distinct from the prototypical counterpart complex from Escherichia coli. The structure of HipB(SO) in complex with operator DNA reveals a flexible C-terminus that is sequestered by HipA(SO) in the ternary complex, indicative of its role in binding HipA(SO) to abolish its function in persistence. The structure of HipA(SO) in complex with a non-hydrolyzable ATP analogue shows that HipA(SO) autophosphorylation is coupled to an unusual conformational change of its phosphorylation loop. However, HipA(SO) is unable to phosphorylate the translation factor Elongation factor Tu, contrary to previous reports, but in agreement with more recent findings. Our studies suggest that the phosphorylation state of HipA is an important factor in persistence and that the structural and mechanistic diversity of HipAB modules as regulatory factors in bacterial persistence is broader than previously thought

Phenotypic Heterogeneity in Mycobacterial Stringent Response

A common survival strategy of microorganisms subjected to stress involves the generation of phenotypic heterogeneity in the isogenic microbial population enabling a subset of the population to survive under stress. In a recent study, a mycobacterial population of M. smegmatis was shown to develop phenotypic heterogeneity under nutrient depletion. The observed heterogeneity is in the form of a bimodal distribution of the expression levels of the Green Fluorescent Protein (GFP) as reporter with the gfp fused to the promoter of the rel gene. The stringent response pathway is initiated in the subpopulation with high rel activity.In the present study, we characterize quantitatively the single cell promoter activity of the three key genes, namely, mprA, sigE and rel, in the stringent response pathway with gfp as the reporter. The origin of bimodality in the GFP distribution lies in two stable expression states, i.e., bistability. We develop a theoretical model to study the dynamics of the stringent response pathway. The model incorporates a recently proposed mechanism of bistability based on positive feedback and cell growth retardation due to protein synthesis. Based on flow cytometry data, we establish that the distribution of GFP levels in the mycobacterial population at any point of time is a linear superposition of two invariant distributions, one Gaussian and the other lognormal, with only the coefficients in the linear combination depending on time. This allows us to use a binning algorithm and determine the time variation of the mean protein level, the fraction of cells in a subpopulation and also the coefficient of variation, a measure of gene expression noise.The results of the theoretical model along with a comprehensive analysis of the flow cytometry data provide definitive evidence for the coexistence of two subpopulations with overlapping protein distributions.Comment: 24 pages,8 figures, supplementary information and 5 supplementary figure