The cost and capacity of signaling in the Escherichia coli protein reaction network

In systems biology new ways are required to analyze the large amount of existing data on regulation of cellular processes. Recent work can be roughly classified into either dynamical models of well-described subsystems, or coarse-grained descriptions of the topology of the molecular networks at the scale of the whole organism. In order to bridge these two disparate approaches one needs to develop simplified descriptions of dynamics and topological measures which address the propagation of signals in molecular networks. Transmission of a signal across a reaction node depends on the presence of other reactants. It will typically be more demanding to transmit a signal across a reaction node with more input links. Sending signals along a path with several subsequent reaction nodes also increases the constraints on the presence of other proteins in the overall network. Therefore counting in and out links along reactions of a potential pathway can give insight into the signaling properties of a particular molecular network. Here, we consider the directed network of protein regulation in E. coli, characterizing its modularity in terms of its potential to transmit signals. We demonstrate that the simplest measure based on identifying subnetworks of strong components, within which each node could send a signal to every other node, does indeed partition the network into functional modules. We suggest that the total number of reactants needed to send a signal between two nodes in the network can be considered as the cost associated with transmitting this signal. Similarly we define spread as the number of reaction products that could be influenced by transmission of a successful signal. Our considerations open for a new class of network measures that implicitly utilize the constrained repertoire of chemical modifications of any biological molecule. The counting of cost and spread connects the topology of networks to the specificity of signaling across the network. Thereby, we address the signaling specificity within and between modules, and show that in the regulation of E. coli there is a systematic reduction of the cost and spread for signals traveling over more than two intermediate reactions.

[1]  K. Sneppen,et al.  Time delay as a key to apoptosis induction in the p53 network , 2002, cond-mat/0207236.

[2]  Kim Sneppen,et al.  Quantifying the benefits of translation regulation in the unfolded protein response , 2004, Physical biology.

[3]  Kiyoko F. Aoki-Kinoshita,et al.  From genomics to chemical genomics: new developments in KEGG , 2005, Nucleic Acids Res..

[4]  K. Sneppen,et al.  Minimal model of spiky oscillations in NF-κB signaling , 2006 .

[5]  J. Hopfield,et al.  From molecular to modular cell biology , 1999, Nature.

[6]  S. V. Aksenov,et al.  Dynamics of the inducing signal for the SOS regulatory system in Escherichia coli after ultraviolet irradiation. , 1999, Mathematical biosciences.

[7]  An-Ping Zeng,et al.  Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach , 2004, BMC Bioinformatics.

[8]  D. Bray,et al.  Computer simulation of the phosphorylation cascade controlling bacterial chemotaxis. , 1993, Molecular biology of the cell.

[9]  A. Barabasi,et al.  The topology of the transcription regulatory network in the yeast , 2002, cond-mat/0205181.

[10]  Kim Sneppen,et al.  Minimal model of spiky oscillations in NF-kappaB signaling. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[11]  K. Sneppen,et al.  Theoretical Analysis of Epigenetic Cell Memory by Nucleosome Modification , 2007, Cell.

[12]  Andrew Wuensche,et al.  A model of transcriptional regulatory networks based on biases in the observed regulation rules , 2002, Complex..

[13]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[14]  U. Alon,et al.  Robustness in bacterial chemotaxis , 2022 .

[15]  Kim Sneppen,et al.  Structure and function of negative feedback loops at the interface of genetic and metabolic networks , 2006, Nucleic acids research.

[16]  Peter D. Karp,et al.  The comprehensive updated regulatory network of Escherichia coli K-12 , 2006, BMC Bioinformatics.

[17]  Sergei Maslov,et al.  UV-Induced Mutagenesis in Escherichia coli SOS Response: A Quantitative Model , 2007, PLoS Computational Biology.

[18]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[19]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Mukund Thattai,et al.  Metabolic switching in the sugar phosphotransferase system of Escherichia coli. , 2003, Biophysical journal.

[21]  Sergei Maslov,et al.  Spreading out of perturbations in reversible reaction networks , 2007, New journal of physics.

[22]  A. Hoffmann,et al.  The I (cid:1) B –NF-(cid:1) B Signaling Module: Temporal Control and Selective Gene Activation , 2022 .

[23]  B. Palsson,et al.  The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[24]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[25]  K Sneppen,et al.  Thermodynamics of heat-shock response. , 1999, Physical review letters.

[26]  R. Tsien,et al.  Specificity and Stability in Topology of Protein Networks , 2022 .

[27]  Peter D. Karp,et al.  The EcoCyc Database , 2002, Nucleic Acids Res..

[28]  B. Palsson,et al.  Regulation of gene expression in flux balance models of metabolism. , 2001, Journal of theoretical biology.