Asymptotic states and topological structure of an activation-deactivation chemical network. (English) Zbl 1451.92132
Summary: The influence of the topology on the asymptotic states of a network of interacting chemical species has been studied by simulating its time evolution. Random and scale-free networks have been designed to support relevant features of activation-deactivation reactions networks (mapping signal transduction networks) and the system of ordinary differential equations associated to the dynamics has been numerically solved. We analysed stationary states of the dynamics as a function of the network’s connectivity and of the distribution of the chemical species on the network; we found important differences between the two topologies in the regime of low connectivity. In particular, only for low connected scale-free networks it is possible to find ‘zero activity patterns’ as stationary states of the dynamics which work as signal off-states. Asymptotic features of random and scale-free networks become similar as the connectivity increases.
Keywords:
protein-protein interaction networks; dynamical systems; activation-deactivation chemical reactions; stationary states; stabilityReferences:
| [1] | Aladana, M.; Cluzel, P., A natural class of robust networks, Proc. Natl. Acad. Sci., 100, 15, 8710-8714 (2003) |
| [2] | Albert, R., Scale-free networks in cell biology, J. Cell. Sci., 118, Pt21, 4947-4957 (2005) |
| [3] | Albert, R.; Barabasi, A.-L., Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47 (2002) · Zbl 1205.82086 |
| [4] | Albert, R.; Jeong, H.; Barabasi, A.-L., Error and attack tolerance of complex networks, Nature, 406, 378 (2000) |
| [5] | Aleksiejuk, A.; Holyst, J. A.; Stauffer, D., Ferromagnetic phase transition in Barabasi-Albert networks, Physica A, 310, 260 (2002) · Zbl 0995.82016 |
| [6] | Aluffi-Pentini, F.; De Fonso, V.; Parisi, V., A novel algorithm for the numerical integration of systems of ordinary differential equations arising in chemical problems, J. Math. Chem., 33, 1 (2003) · Zbl 1018.92044 |
| [7] | Arita, M., The metabolic world of Escherichia coli is not small, Proc. Natl Acad. Sci. USA, 101, 6, 1543-1547 (2004) |
| [8] | Arita, M., Scale-freeness and biological networks, J. Biochem. (Tokyo), 138, 1, 1-4 (2005) |
| [9] | Barabasi, A.-L.; Albert, R., Emergence of scaling in random networks, Science, 286, 509 (1999) · Zbl 1226.05223 |
| [10] | Bhalla, U. S.; Ram, P. T.; Iyengar, R., MAP kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network, Science, 297, 5583, 1018-1023 (2002) |
| [11] | Binder, B.; Heinrich, R., Interrelations between dynamical properties and structural characteristics of signal transduction networks, Genome Inform., 15, 13 (2004) |
| [12] | Christley, R. M.; Pinchbek, G. L.; Bowers, R. G.; Clancy, D.; French, N. P.; Bennett, R.; Turner, J., Infection in social networks: using network analysis to identify high-risk individuals, Am. J. Epidem., 162, 10, 1024-1031 (2005) |
| [13] | Cusick, M. E.; Klitgord, N.; Vidal, M.; Hill, D. E., Interactome: gateway into Systems Biology, Hum. Mol. Genet., 14, Spec.Num.2, R171 (2005) |
| [14] | Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F.F., Ising model on networks with an arbitrary distribution of connections, Phys. Rev. E, 66, 016104 (2002) |
| [15] | Eguiluz, V. M.; Chialvo, D. R.; Cecchi, D. A.; Baliki, M.; Apkarian, A. V., Scale-free brain functional networks, Phys. Rev. Lett., 94, 1, 018102 (2005) |
| [16] | Haugh, J. M.; Schneider, I. C.; Lewis, J. M., On the cross-regulation of protein tyrosine phosphatases and receptor tyrosine kinases in intracellular signaling, J. Theor. Biol., 230, 1, 119-132 (2004) · Zbl 1447.92181 |
| [17] | Hautamiemi, S.; Kharait, S.; Iwabu, A.; Wells, A.; Lauffenburger, D. A., Modelling of signal-response cascades using decision tree analysis, Bioinformatics, 21, 9, 2027-2035 (2005) |
| [18] | Hirano, K.; Derkach, D. N.; Hirano, M.; Nishimura, J.; Kanaide, H., Protein kinase network in the regulation of phosphorylation and dephosphorylation of smooth muscle myosin light chain, Mol. Cell. Biochem., 248, 1-2, 105-114 (2003) |
| [19] | Homberg, J. J.; Bruggeman, F. J.; Binder, B.; Geest, C. R.; de Vaate, A. J.; Lankeima, J.; Heinrich, R.; Westerhoff, H. V., Principles behind the multifarious control of signal transduction. ERK phosphorylation and kinase/phosphatase control, FEBS, 272, 1, 244-258 (2005) |
| [20] | Ibarra, R. U.; Edwards, J. S.; Palsson, B. O., Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth, Nature, 420, 6912, 186-189 (2002) |
| [21] | Joy, M. P.; Brock, A.; Ingber, D. E.; Huang, S., High-betweenness proteins in the yeast protein interaction network, J. Biomed. Biotechnol., 2005, 2, 96-103 (2005) |
| [22] | Kashtan, N.; Alon, U., Spontaneous evolution of modularity and network motifs, Proc. Natl Acad. Sci. USA, 102, 309, 13773-13778 (2005) |
| [23] | Kauffman, S. A., Requirements for evolvability in complex systems: orderly dynamics and frozen components, Physica D, 42, 135 (1990) |
| [24] | Klemm, K., Bornholdt, S., 2005. Topology of biological networks and reliability of information processing. Proc. Natl Acad. Sci. USA 102 (51) 18414-18419. |
| [25] | Lee, R. E.; Megeney, L. A., The yeast kinome displays scale free topology with functional hub clusters, BMC Bioinform., 6, 271 (2005) |
| [26] | Li, F.; Long, T.; Lu, Y.; Ouyang, Q.; Tang, C., The yeast cell-cycle is robustly designed, Proc. Natl Acad. Sci., 101, 14, 4781-4786 (2004) |
| [27] | Martin, H.; Flandez, M.; Nombela, C.; Molina, M., Protein phosphatases in MAPK signalling: we keep learning from yeast, Mol. Microbiol., 58, 1, 6-16 (2005) |
| [28] | Mazurie, A.; Bottani, S.; Vergassola, M., An evolutionary and functional assessment of regulatory network motifs, Genome Biol., 6, 4, R35 (2005) |
| [29] | Middendorf, M.; Ziv, E.; Adams, C.; Hom, J.; Koytcheff, R.; Levovitz, C.; Woods, G.; Chen, L.; Wiggins, C., Discriminative topological features reveal biological network mechanism, BMC Bioinform., 5, 181 (2004) |
| [30] | Newman, M. E.J., The structure and function of complex networks, SIAM Rev., 45, 167-256 (2003) · Zbl 1029.68010 |
| [31] | Rodriguez-Caso, D.; Medina, M. A.; Sole, R. V., Topology, tinkering and evolution of the human transcription factor network, FEBS, 272, 24, 6423-6434 (2005) |
| [32] | Saramaki, J.; Kaski, K., Modelling development of epidemics with dynamic small-world networks, J. Theor. Biol., 234, 3, 413-421 (2005) · Zbl 1445.92280 |
| [33] | Sauro, H. M.; Kholodenko, B. N., Quantitative analysis of signaling networks, Prog. Biophys. Mol. Biol., 148, 1-2, 5-43 (2004) |
| [34] | Segre, D.; Vitkup, D.; Church, G. M., Analysis of optimality in natural and perturbated metabolic networks, Proc. Natl Acad. Sci. USA, 99, 23, 15112 (2002) |
| [35] | Song, C.; Havlin, S.; Makse, H. A., Self-similarity of complex networks, Nature, 433, 7024, 392-395 (2005) |
| [36] | Soyer, O. S.; Salathé, M.; Bonhoeffer, S., Signal transduction networks: topology, response and biochemical processes, J. Theor. Biol., 238, 416-425 (2006) · Zbl 1445.92128 |
| [37] | Sweetlove, L. J.; Fernie, A. R., Regulation of metabolic network: understanding metabolic complexity in the systems biology era, New Phytol., 168, 1, 9-24 (2005) |
| [38] | Steffen, M.; Petti, A.; Aach, J.; D’haeseleer, P.; Church, G., Automated modelling of signal transduction network, BMC Bioinform., 3, 34 (2002) |
| [39] | Tari, L., Baral, C., Dasgupta, P., 2005. Understanding the global properties of functionally-related gene networks using the gene ontology, Pac. Symp. Biocomput. 209-220. |
| [40] | Titz, B.; Schlesner, M.; Uetz, P., What do we learn from high-throughput protein interaction data?, Expert Rev. Proteomics, 1, 1, 111-121 (2004) |
| [41] | Watts, D. J.; Strogartz, S. H., Collective dynamics of “small-world” networks, Nature, 393, 393 (1998) · Zbl 1368.05139 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
