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Dynamical analysis of cellular networks based on the Green’s function matrix. (English) Zbl 1403.92094
Summary: The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green’s function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.
MSC:
92C42 Systems biology, networks
92C37 Cell biology
Software:
SBML-SAT; sbtoolbox
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[1] Aldridge, B.B.; Haller, G.; Sorger, P.K.; Lauffenburger, D.A., Direct Lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour, Syst. biol. (stevenage), 153, 425-432, (2006)
[2] Arfken, G.B.; Weber, H.-J., Mathematical methods for physicists, (2005), Elsevier Boston · Zbl 1066.00001
[3] Auffray, C.; Imbeaud, S.; Roux-Rouquie, M.; Hood, L., From functional genomics to systems biology: concepts and practices, C. R. biol., 326, 879-892, (2003)
[4] Barkai, N.; Leibler, S., Robustness in simple biochemical networks, Nature, 387, 913-917, (1997)
[5] Batt, G.G.; Yordanov, B.; Weiss, R.; Belta, C., Robustness analysis and tuning of synthetic gene networks, Bioinformatics, 23, 2415-2422, (2007)
[6] Bhalla, U.S.; Iyengar, R., Robustness of the bistable behavior of a biological signaling feedback loop., Chaos, 11, 221-226, (2001) · Zbl 0992.92033
[7] Borisy, A.A.; Elliott, P.J.; Hurst, N.W.; Lee, M.S.; Lehar, J.; Price, E.R.; Serbedzija, G.; Zimmermann, G.R.; Foley, M.A.; Stockwell, B.R.; Keith, C.T., Systematic discovery of multicomponent therapeutics, Proc. natl. acad. sci. USA, 100, 7977-7982, (2003)
[8] Breckenridge, D.G.; Nguyen, M.; Kuppig, S.; Reth, M.; Shore, G.C., The procaspase-8 isoform, procaspase-8L, recruited to the BAP31 complex at the endoplasmic reticulum, Proc. natl. acad. sci. USA, 99, 4331-4336, (2002)
[9] Carlson, J.M.; Doyle, J., Complexity and robustness, Proc. natl. acad. sci. USA, 99, Suppl. 1, 2538-2545, (2002)
[10] Chaves, M.; Sontag, E.D.; Albert, R., Methods of robustness analysis for Boolean models of gene control networks, Syst. biol. (stevenage), 153, 154-167, (2006)
[11] Chen, B.-S.; Wang, Y.-C.; Wu, W.-S.; Li, W.-H., A new measure of the robustness of biochemical networks, Bioinformatics, 21, 2698-2705, (2005)
[12] Chen, C.-T., Linear system theory and design, (1999), Oxford University Press New York
[13] Chu, Y.; Jayaraman, A.; Hahn, J., Parameter sensitivity analysis of IL-6 signalling pathways, IET syst. biol., 1, 342-352, (2007)
[14] Eissing, T.; Allgower, F.; Bullinger, E., Robustness properties of apoptosis models with respect to parameter variations and intrinsic noise, Syst. biol. (stevenage), 152, 221-228, (2005)
[15] Fesik, S.W., Promoting apoptosis as a strategy for cancer drug discovery, Nat. rev. cancer, 5, 876-885, (2005)
[16] Gunawan, R.; Doyle, F.J., Isochron-based phase response analysis of Circadian rhythms, Biophys. J., 91, 2131-2141, (2006)
[17] Gunawan, R.; Doyle, F.J., Phase sensitivity analysis of Circadian rhythm entrainment, J. biol. rhythms, 22, 180-194, (2007)
[18] Gunawan, R.; Cao, Y.; Petzold, L.; Doyle, F.J., Sensitivity analysis of discrete stochastic systems, Biophys. J., 88, 2530-2540, (2005)
[19] Hartwell, L.H.; Hopfield, J.J.; Leibler, S.; Murray, A.W., From molecular to modular cell biology, Nature, 402, C47-C52, (1999)
[20] Hoare, A.; Regan, D.G.; Wilson, D.P., Sampling and sensitivity analyses tools (sasat) for computational modelling, Theor. biol. med. model, 5, 4, (2008)
[21] Hu, D.; Yuan, J.M., Time-dependent sensitivity analysis of biological networks: coupled MAPK and PI3K signal transduction pathways, J. phys. chem. A, 110, 5361-5370, (2006)
[22] Hua, F.; Hautaniemi, S.; Yokoo, R.; Lauffenburger, D.A., Integrated mechanistic and data-driven modelling for multivariate analysis of signalling pathways, J. R. soc. interface, 3, 515-526, (2006)
[23] Hua, F.; Cornejo, M.G.; Cardone, M.H.; Stokes, C.L.; Lauffenburger, D.A., Effects of bcl-2 levels on fas signaling-induced caspase-3 activation: molecular genetic tests of computational model predictions, J. immunol., 175, 985-995, (2005)
[24] Ideker, T.; Lauffenburger, D., Building with a scaffold: emerging strategies for high- to low-level cellular modeling, Trends biotechnol., 21, 255-262, (2003)
[25] Ihekwaba, A.E.; Broomhead, D.S.; Grimley, R.L.; Benson, N.; Kell, D.B., Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kappab pathway: the roles of IKK and ikappabalpha, Syst. biol. (stevenage), 1, 93-103, (2004)
[26] Ihekwaba, A.E.; Broomhead, D.S.; Grimley, R.; Benson, N.; White, M.R.; Kell, D.B., Synergistic control of oscillations in the NF-kappab signalling pathway, Syst. biol. (stevenage), 152, 153-160, (2005)
[27] Ingalls, B., Sensitivity analysis: from model parameters to system behaviour, Essays biochem., 45, 177-193, (2008)
[28] Ingalls, B.P., Autonomously oscillating biochemical systems: parametric sensitivity of extrema and period, Syst. biol. (stevenage), 1, 62-70, (2004)
[29] Iwamoto, K.; Tashima, Y.; Hamada, H.; Eguchi, Y.; Okamoto, M., Mathematical modeling and sensitivity analysis of G1/S phase in the cell cycle including the DNA-damage signal transduction pathway, Biosystems, 94, 109-117, (2008)
[30] Kim, J.; Bates, D.G.; Postlethwaite, I.; Ma, L.; Iglesias, P.A., Robustness analysis of biochemical network models, Syst. biol. (stevenage), 153, 96-104, (2006)
[31] Kim, P.-J.; Lee, D.-Y.; Kim, T.Y.; Lee, K.H.; Jeong, H.; Lee, S.Y.; Park, S., Metabolite essentiality elucidates robustness of Escherichia coli metabolism, Proc. natl. acad. sci. USA, 104, 13638-13642, (2007)
[32] Kitano, H., Cancer robustness: tumour tactics, Nature, 426, 125, (2003)
[33] Kitano, H., Biological robustness, Nat. rev. genet., 5, 826-837, (2004)
[34] Kitano, H., A robustness-based approach to systems-oriented drug design, Nat. rev. drug discovery, 6, 202-210, (2007)
[35] Kremling, A.; Fischer, S.; Gadkar, K.; Doyle, F.J.; Sauter, T.; Bullinger, E.; Allgower, F.; Gilles, E.D., A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions, Genome res., 14, 1773-1785, (2004)
[36] Larder, B.A.; Kemp, S.D.; Harrigan, P.R., Potential mechanism for sustained antiretroviral efficacy of AZT-3TC combination therapy, Science, 269, 696-699, (1995)
[37] Morohashi, M.; Winn, A.E.; Borisuk, M.T.; Bolouri, H.; Doyle, J.; Kitano, H., Robustness as a measure of plausibility in models of biochemical networks, J. theor. biol., 216, 19-30, (2002)
[38] Nelson, H.S., Advair: combination treatment with fluticasone propionate/salmeterol in the treatment of asthma, J allergy clin. immunol., 107, 398-416, (2001)
[39] Nishimura, S.; Adachi, M.; Ishida, T.; Matsunaga, T.; Uchida, H.; Hamada, H.; Imai, K., Adenovirus-mediated transfection of caspase-8 augments anoikis and inhibits peritoneal dissemination of human gastric carcinoma cells, Cancer res., 61, 7009-7014, (2001)
[40] Okazaki, N.; Asano, R.; Kinoshita, T.; Chuman, H., Simple computational models of type I/type II cells in fas signaling-induced apoptosis, J theor. biol., 250, 621-633, (2008) · Zbl 1397.92170
[41] Pollack, I.F.; Erff, M.; Ashkenazi, A., Direct stimulation of apoptotic signaling by soluble apo2l/tumor necrosis factor-related apoptosis-inducing ligand leads to selective Killing of glioma cells, Clin. cancer res., 7, 1362-1369, (2001)
[42] Qi, Y.; Ge, H., Modularity and dynamics of cellular networks, Plos comput. biol., 2, e174, (2006)
[43] Rand, D.A., Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law, J. R. soc. interface, 5, S59-S69, (2008)
[44] Reed, J.C.; Doctor, K.S.; Godzik, A., The domains of apoptosis: a genomics perspective, Sci. STKE, re9, (2004)
[45] Scaffidi, C.; Fulda, S.; Srinivasan, A.; Friesen, C.; Li, F.; Tomaselli, K.J.; Debatin, K.M.; Krammer, P.H.; Peter, M.E., Two CD95 (APO-1/fas) signaling pathways, Embo j., 17, 1675-1687, (1998)
[46] Schmidt, H.; Jirstrand, M., Systems biology toolbox for MATLAB: a computational platform for research in systems biology, Bioinformatics, 22, 514-515, (2006)
[47] Stelling, J.R.; Gilles, E.D.; Doyle, F.J., Robustness properties of Circadian clock architectures, Proc. natl. acad. sci. USA, 101, 13210-13215, (2004)
[48] Stelling, J.R.; Sauer, U.; Szallasi, Z.; Doyle, F.J.; Doyle, J., Robustness of cellular functions, Cell, 118, 675-685, (2004)
[49] Stephanopoulos, G., Challenges in engineering microbes for biofuels production, Science, 315, 801-804, (2007)
[50] Turányi, T., Sensitivity analysis of complex kinetic systems. tools and applications, J. math. chem., 5, 203-248, (1990)
[51] Tyson, J.J.; Chen, K.C.; Novak, B., Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell, Curr. opin. cell biol., 15, 221-231, (2003)
[52] Varma, A.; Morbidelli, M.; Wu, H., Parametirc sensitivity in chemical systems, (1999), Cambridge University Press Cambridge, UK
[53] Wagner, A., Robustness, evolvability, and neutrality, FEBS lett., 579, 1772-1778, (2005)
[54] Westerhoff, H.V.; Chen, Y.D., How do enzyme activities control metabolite concentrations? an additional theorem in the theory of metabolic control, Eur. J. biochem., 142, 425-430, (1984)
[55] Yamada, S.; Shiono, S.; Joo, A.; Yoshimura, A., Control mechanism of JAK/STAT signal transduction pathway, FEBS lett., 534, 190-196, (2003)
[56] Yue, H.; Brown, M.; Knowles, J.; Wang, H.; Broomhead, D.S.; Kell, D.B., Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kappab signalling pathway, Mol. biosyst., 2, 640-649, (2006)
[57] Zi, Z.; Zheng, Y.; Rundell, A.E.; Klipp, E., SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool, BMC bioinf., 9, 342, (2008)
[58] Zi, Z.; Cho, K.H.; Sung, M.H.; Xia, X.; Zheng, J.; Sun, Z., In silico identification of the key components and steps in IFN-gamma induced JAK-STAT signaling pathway, FEBS lett., 579, 1101-1108, (2005)
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