Signal propagation in small-world biological networks with weak noise

Journal of Theoretical Biology

Volumn 262, Issue 2, 2010, Pages 370-380

  Hong, Dawei ^a   Man, Shushuang ^b  

^a RUTGERS UNIVERSITY   (United States)

^b SOUTHWEST MINNESOTA STATE UNIVERSITY   (United States)

Author keywords

Measure concentration; Signal propagation; Small world network; Stochastic differential equation; Weak internal noise

Indexed keywords

COMPUTER SIMULATION; EQUATION; MODELING; NOISE; SIGNAL PROCESSING; STOCHASTICITY;

ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; CONCENTRATION PROCESS; MATHEMATICAL ANALYSIS; NONHUMAN; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; QUORUM SENSING; SACCHAROMYCES CEREVISIAE; SIGNAL NOISE RATIO; SIGNAL TRANSDUCTION; STRUCTURE ANALYSIS; SYSTEMS BIOLOGY; TRANSCRIPTION REGULATION;

MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; SIGNAL TRANSDUCTION;

SACCHAROMYCES CEREVISIAE;

EID: 70450227414     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.10.019     Document Type: Article

References (29)

1. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (1974) 716-723
2. Albert R. Scale-free networks in cell biology. Journal of Cell Science 118 (2005) 4947-4957
3. Alon U. An Introduction to Systems Biology: Design Principles of Biological Circuits (2006), CRC Press, Boca Raton
4. Barkai N., and Shilo B.-Z. Variability and robustness in biomolecular systems. Molecular Cell 28 (2007) 755-759
5. Bassett D.S., Meyer-Lindenberg A., Achard S., Duke T., and Bullmore E. Adaptive reconfiguration of fractal small-world human brain functional networks. Proceedings of the National Academy of Sciences of the United States of America 103 (2006) 19518-19523
6. Chen K.-C., Wang T.-Y., Tseng H.-H., Huang C.-Y.F., and Kao C.-Y. A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae. Bioinformatics 21 (2005) 2883-2890
7. Chen L., Wang R.-S., and Zhang X.-S. Biomolecular Networks: Methods and Applications in Systems Biology (2009), Wiley, New York
8. Chung K.L., and Williams R.J. Introduction to Stochastic Integration. second ed. (1990), Birkhäuser, Basel
9. El Karoui N., Peng S., and Quenez M.C. Backward stochastic differential equations in finance. Mathematical Finance 7 (1997) 1-71
10. Galán R.F., Fourcaud-Trocmé N., Ermentrout G.B., and Urban N.N. Correlation-induced synchronization of oscillations in olfactory bulb neurons. Journal of Neuronscience 26 (2006) 3646-3655
11. Hagmann P., Cammoun L., Gigandet X., Meuli R., Honey C.J., Wedeen V.J., and Sporns O. Mapping the structural core of human cerebral cortex. PLoS Biology 6 (2008) e159
12. Hoeffding W. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 (1963) 13-30
13. Hong D. Analysis of noise-induced phase synchronization in nervous systems: from algorithmic perspective. Information Processing Letters 105 (2007) 35-39
14. Hong D., Saidel W.M., Man S., and Martin J.V. Extracellular noise-induced stochastic synchronization in heterogeneous quorum sensing network. Journal of Theoretical Biology 245 (2007) 726-736
15. Kleinberg, J., 2000. The small-world phenomenon: an algorithmic perspective. In: Proceedings of 32nd ACM Symposium on Theory of Computing, pp. 163-170.
16. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations (1999), Springer, Berlin
17. Ledoux M., and Talagrand M. Probability in Banach Spaces (1991), Springer, Brlin
18. Ma J., Protter P., San Martin J., and Torres S. Numerical method for backward stochastic differential equations. Annals of Applied Probability 12 (2002) 302-316
19. Nakao H., Arai K.-S., Nagai K., Tsubo Y., and Kuramoto Y. Synchrony of limit-cycle oscillators induced by random impulses. Physical Review E 72 (2005) 026220
20. Øksendal B. Stochastic Differential Equations: An Introduction with Applications. sixth ed. (2007), Springer, Berlin
21. Palsson B. Ø. Systems Biology: Properties of Reconstructed Networks (2006), Cambridge University Press, Cambridge
22. Pardoux E., and Peng S. Adapted solution of a backward stochastic differential equation. Systems & Control Letters 14 (1990) 55-61
23. Potapov A.P., Voss N., Sasse N., and Wingender E. Topology of mammalian transcription networks. Genome Informatics 16 2 (2005) 270-278
24. Schröder I., Harlfinger P., Huth T., and Hansen U.P. A subsequent fit of time series and amplitude histogram of patch-clamp records reveals rate constants up to 1 per microsecond. The Journal of Membrane Biology 203 (2005) 83-99
25. Talagrand M. Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l'Institut des Hautes Etudes Scientifiques 81 (1995) 73-205
26. Teramae J.-N., and Tanaka D. Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Physical Review Letters 93 (2004) 204103
27. Van Kampen N.G. Stochastic Processes in Physics and Chemistry. third ed. (2007), North-Holland, Amsterdam
28. Watts D.J., and Strogatz S.H. Collective dynamics of small-world networks. Nature 393 (1998) 440-442
29. Zhou T.S., Chen L.N., and Aihara K. Molecular communication through stochastic synchronization induced by extracellular fluctuations. Physical Review Letters 95 (2005) 178103