A method of ‘speed coefficients’ for biochemical model reduction applied to the NF-\(\kappa\)B system. (English) Zbl 1306.92022
The authors propose an algorithm for the reduction of biochemical reaction systems, which does not rely on a intuition-based extraction of key regulatory components. This new approach is based on fast-slow asymptotics and uses the ranking on the approach of system variables at their momentary steady-state. First, the perturbation theory for fast-slow systems is presented. It is followed by a description of the parametric embedding used for the identification of small parameters. Next, a heuristic method for the identification of speed coefficients is described; the section concludes with a full description of the model reduction algorithm. The authors present the results of this approach on several examples including the minimal model of the NF-kB system, in response to continuous or pulsed \(\mathrm{TNF}\alpha\), and an application for the Krishna model.
Reviewer: Irina Ioana Mohorianu (Norwich)
Keywords:
model reduction; characteristic timescales; signaling networks; nuclear factor kappa B; perturbation theory; fast-slow systems; parameter embedding; Krishna modelReferences:
| [1] | Anosov DV (1960) Limit cycles of systems of differential equations with small parameters in the highest derivatives. Mat Sb (NS) 50(92)(3):299-334 · Zbl 0476.34034 |
| [2] | Ashall L, Horton CA, Nelson DE, Paszek P, Harper CV, Sillitoe K, Ryan S, Spiller DG, Unitt JF, Broomhead DS, Kell DB, Rand DA, See V, White MR (2009) Pulsatile stimulation determines timing and specificity of nf-kappab-dependent transcription. Science 324(5924):242-246 · doi:10.1126/science.1164860 |
| [3] | Biktashev VN, Suckley R (2004) Non-tikhonov asymptotic properties of cardiac excitability. Phys Rev Lett 93(168):103 |
| [4] | Biktasheva IV, Simitev RD, Suckley R, Biktashev VN (2006) Asymptotic properties of mathematical models of excitability. Philos Trans R Soc Lond A Math Phys Eng Sci 364(1842):1283-1298 · Zbl 1152.37348 · doi:10.1098/rsta.2006.1770 |
| [5] | Briggs GE, Haldane JBS (1925) A note on the kinetics of enzyme action. Biochem J 19:338-339 |
| [6] | Danø S, Madsen MF, Schmidt H, Cedersund G (2006) Reduction of a biochemical model with preservation of its basic dynamic properties. FEBS J 273(21):4862-4877 · doi:10.1111/j.1742-4658.2006.05485.x |
| [7] | Doedel E, Paffenroth R, Champneys A, Fairgrieve T, Kuznetsov Y, Sandstede B, Wang X (2000) Auto 2000: continuation and bifurcation software for ordinary differential equations (with homcont). Technical report, California Institute of Technology |
| [8] | Ermentrout B (2002) Simulating, analysing, and animating dymaical systems: a guide to XPPAUT for researchers and students. Software, Environments, and Tools, vol 14. SIAM, Philadelphia · Zbl 1003.68738 |
| [9] | Fenichel N (1979) Geometric singular perturbation theory for ordinary differential equations. J Differ Equ 31:53-98 · Zbl 0476.34034 · doi:10.1016/0022-0396(79)90152-9 |
| [10] | Gorban AN, Karlin IV (2003) Method of invariant manifold for chemical kinetics. Chem Eng Sci 58:4751-4768 · doi:10.1016/j.ces.2002.12.001 |
| [11] | Hayden MS, Ghosh S (2008) Shared principles in nf-kappab signaling. Cell 132(3):344-362 · doi:10.1016/j.cell.2008.01.020 |
| [12] | Hoffmann A, Baltimore D (2006) Circuitry of nuclear factor kappab signaling. Immunol Rev 210:171-186 · doi:10.1111/j.0105-2896.2006.00375.x |
| [13] | Hoffmann A, Levchenko A, Scott ML, Baltimore D (2002) The ikappab-nf-kappab signaling module: temporal control and selective gene activation. Science 298(5596):1241-1245 · doi:10.1126/science.1071914 |
| [14] | Ihekwaba AE, Broomhead DS, Grimley RL, Benson N, Kell DB (2004) Sensitivity analysis of parameters controlling oscillatory signalling in the nf-kappab pathway: the roles of ikk and ikappabalpha. Syst Biol (Stevenage) 1(1):93-103 · doi:10.1049/sb:20045009 |
| [15] | Ihekwaba AE, Broomhead DS, Grimley R, Benson N, White MR, Kell DB (2005) Synergistic control of oscillations in the nf-kappab signalling pathway. Syst Biol (Stevenage) 152(3):153-160 · doi:10.1049/ip-syb:20050050 |
| [16] | Jacobsen EW, Cedersund G (2008) Structural robustness of biochemical network models-with application to the oscillatory metabolism of activated neutrophils. IET Syst Biol 2(1):39-47. doi:10.1049/iet-syb:20070008 · doi:10.1049/iet-syb:20070008 |
| [17] | Kitano H (2002) Computational systems biology. Nature 420(6912):206-210 · doi:10.1038/nature01254 |
| [18] | Klonowski W (1983) Simplifying principles for chemical and enzyme reaction-kinetics. Biophys Chem 18(2):73-87 · doi:10.1016/0301-4622(83)85001-7 |
| [19] | Kourdis PD, Palasantza AG, Goussis DA (2013) Algorithmic asymptotic analysis of the NF-\[ \kappa\] κB signaling system. Comput Math Appl 65(10):1516-1534 · Zbl 1339.92027 · doi:10.1016/j.camwa.2012.11.004 |
| [20] | Krishna S, Jensen MH, Sneppen K (2006) Minimal model of spiky oscillations in nf-kappab signaling. Proc Natl Acad Sci USA 103(29):10840-10845 |
| [21] | Kutumova E, Zinovyev A, Sharipov R, Kolpakov F (2013) Model composition through model reduction: a combined model of CD95 and NF-\[ \kappa\] κB signaling pathways. BMC Syst Biol 7(1):13. doi: 10.1186/1752-0509-7-13 · doi:10.1186/1752-0509-7-13 |
| [22] | Lam SH, Goussis DA (1994) The CSP method for simplifying kinetics. Int J Chem Kinetics 26(4):461-486 · doi:10.1002/kin.550260408 |
| [23] | Lipniacki T, Paszek P, Brasier AR, Luxon B, Kimmel M (2004) Mathematical model of nf-kappab regulatory module. J Theor Biol 228(2):195-215 · Zbl 1439.92076 · doi:10.1016/j.jtbi.2004.01.001 |
| [24] | Maas U, Pope SB (1992) Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space. Combust Flame 88:239-264 · doi:10.1016/0010-2180(92)90034-M |
| [25] | Maeda Y, Pakdaman K, Nomura T, Doi S, Sato S (1998) Reduction of a model for an onchidium pacemaker neuron. Biol Cybern 78(4):265-276 · Zbl 0909.92009 · doi:10.1007/s004220050432 |
| [26] | Mengel B, Krishna S, Jensen MH, Trusina A (2012) Nested feedback loops in gene regulation. Phys Stat Mech Appl 391(1-2):100-106 · Zbl 1188.92009 |
| [27] | Nelson DE, Ihekwaba AE, Elliott M, Johnson JR, Gibney CA, Foreman BE, Nelson G, See V, Horton CA, Spiller DG, Edwards SW, McDowell HP, Unitt JF, Sullivan E, Grimley R, Benson N, Broomhead D, Kell DB, White MR (2004) Oscillations in nf-kappab signaling control the dynamics of gene expression. Science 306(5696):704-708 · doi:10.1126/science.1099962 |
| [28] | Novak B, Tyson JJ (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9(12):981-991 · doi:10.1038/nrm2530 |
| [29] | Paszek P, Jackson DA, White MR (2010) Oscillatory control of signalling molecules. Curr Opin Genet Dev 20(6):670-676 · doi:10.1016/j.gde.2010.08.004 |
| [30] | Radulescu O, Gorban AN, Zinovyev A, Lilienbaum A (2008) Robust simplifications of multiscale biochemical networks. BMC Syst Biol 2:86. doi:10.1186/1752-0509-2-86 · doi:10.1186/1752-0509-2-86 |
| [31] | Rand DA (2008) Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law. J R Soc Interface 5(Suppl 1):S59-S69 · doi:10.1098/rsif.2008.0084.focus |
| [32] | Saez-Rodriguez J, Kremling A, Conzelmann H, Bettenbrock K, Gilles ED (2004) Modular analysis of signal transduction networks. IEEE Control Syst Mag 24(4):35-52 · Zbl 1395.93108 · doi:10.1109/MCS.2004.1316652 |
| [33] | Schneider KR, Wilhelm T (2000) Model reduction by extended quasi-steady-state approximation. J Math Biol 40(5):443-450 · Zbl 0970.92028 · doi:10.1007/s002850000026 |
| [34] | Segel LA, Slemrod M (1989) The quasi-steady-state assumption: a case study in perturbation. SIAM Rev 31:446-477 · Zbl 0679.34066 · doi:10.1137/1031091 |
| [35] | Suckley R, Biktashev V (2003) Comparison of asymptotics of heart and nerve excitability. Phys Rev E 68(011):902 |
| [36] | Sung MH, Salvatore L, De Lorenzi R, Indrawan A, Pasparakis M, Hager GL, Bianchi ME, Agresti A (2009) Sustained oscillations of nf-kappab produce distinct genome scanning and gene expression profiles. PLoS ONE 4(9):e7163 · doi:10.1371/journal.pone.0007163 |
| [37] | Tay S, Hughey JJ, Lee TK, Lipniacki T, Quake SR, Covert MW (2010) Single-cell nf-kappab dynamics reveal digital activation and analogue information processing. Nature 466(7303):267-271 · doi:10.1038/nature09145 |
| [38] | Tikhonov AN (1952) Systems of differential equations with small parameters at the derivatives. USSR Math Sbornik 31(3):575-586 · Zbl 0048.07101 |
| [39] | Turányi T, Tomlin AS, Pilling MJ (1993) On the error of the quasi-steady-state approximation. J Phys Chem 97:163-172 · doi:10.1021/j100103a028 |
| [40] | Turner DA, Paszek P, Woodcock DJ, Nelson DE, Horton CA, Wang Y, Spiller DG, Rand D, White MR, Harper CV (2010) Physiological levels of tnfalpha stimulation induces stochastic dynamics of nf-kappab respose in single living cells. J Cell Sci |
| [41] | Vasil’eva AB (1952) On differential equations containing small parameters. Mat Sb (NS) 31(73)(3):587-644 · Zbl 0048.07102 |
| [42] | Volpert AI, Hudjaev SI (1985) Analysis in classes of discontinuous functions and the equations of mathematical physics. Nijhoff, Dordrecht · Zbl 0564.46025 |
| [43] | Wang Y, Paszek P, Horton CA, Yue H, White MR, Kell DB, Muldoon MR, Broomhead DS (2012) A systematic survey of the response of a model nf-\[ \kappa\] κb signalling pathway to tnf \[\alpha\] α stimulation. J Theor Biol 297:137-147 · Zbl 1336.92029 · doi:10.1016/j.jtbi.2011.12.014 |
| [44] | Whiteley JP (2010) Model reduction using a posteriori analysis. Math Biosci 225(1):44-52 · Zbl 1188.92009 · doi:10.1016/j.mbs.2010.01.008 |
| [45] | Yablonskii GS, Bykov VI, Gorban AN, Elokhin VI (1991) Kinetic models of catalytic reactions, comprehensive chemical kinetics, vol 32. Elsevier, Amsterdam |
| [46] | Zagaris A, Kaper HG, Kaper TJ (2004) Fast and slow dynamics for the computational singular perturbation method. Multiscale Model Simul 2(4):613-638 · Zbl 1065.34049 · doi:10.1137/040603577 |
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.
