A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails
Tài liệu tham khảo
Henri, 1903
Brown, 1902, Enzyme action, J. Chem. Society Trans., 81, 373, 10.1039/CT9028100373
Michaelis, 1913, Die kinetik der invertinwirkung, Biochem. Z., 49, 333
Cornish-Bowden, 2015, One hundred years of Michaelis-Menten kinetics, Perspect. Sci., 4, 3, 10.1016/j.pisc.2014.12.002
Pedersen, 2008, Quasi steady-state approximations in complex intracellular signal transduction networks - a word of caution, J. Math. Chem., 43, 1318, 10.1007/s10910-007-9248-4
Pedersen, 2008, The total quasi-steady-state approximation for complex enzyme reactions, Math. Comput. Simulat., 79, 1010, 10.1016/j.matcom.2008.02.009
Pedersen, 2007, The total quasi-steady-state approximation for fully competitive enzyme reactions, B. Math. Biol., 69, 433, 10.1007/s11538-006-9136-2
Ciliberto, 2007, Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation, PLOS Comput. Biol., 3, 463, 10.1371/journal.pcbi.0030045
Eilertsen, 2018, Phase-plane geometries in coupled enzyme assays, Math. Biosci., 306, 126, 10.1016/j.mbs.2018.09.008
Bartholomay, 1962, A stochastic approach to statistical kinetics with application to enzyme kinetics, Biochemistry, 1, 223, 10.1021/bi00908a005
Qian, 2002, Single-molecule enzymology: stochastic Michaelis - Menten kinetics, Biophys. Chem., 101, 565, 10.1016/S0301-4622(02)00145-X
Herath, 2018, Reduced linear noise approximation for biochemical reaction networks with time-scale separation: the stochastic tQSSA+, J. Chem. Phys., 148, 094108, 10.1063/1.5012752
Barik, 2008, Stochastic simulation of enzyme-catalyzed reactions with disparate timescales, Biophys. J., 95, 3563, 10.1529/biophysj.108.129155
Kim, 2015, The relationship between stochastic and deterministic quasi-steady state approximations, BMC Syst. Biol., 9, 87, 10.1186/s12918-015-0218-3
Choi, 2017, Beyond the Michaelis-Menten equation: accurate and efficient estimation of enzyme kinetic parameters, Sci. Rep.-UK, 7, 17018, 10.1038/s41598-017-17072-z
Cornish-Bowden, 2014
Cárdenas, 2013, Michaelis and Menten and the long road to the discovery of cooperativity, FEBS Lett., 587, 2767, 10.1016/j.febslet.2013.07.014
Chen, 2010, Classic and contemporary approaches to modeling biochemical reactions, Gene Dev., 24, 1861, 10.1101/gad.1945410
Deichmann, 2014, Commemorating the 1913 Michaelis-Menten paper die kinetik der invertinwirkung: three perspectives, FEBS J., 281, 435, 10.1111/febs.12598
Schnell, 2003, A century of enzyme kinetics. Should we believe in the Km and Vmax estimates?, Comments Theor. Biol., 8, 169
Schnell, 2014, Validity of the Michaelis - Menten equation, steady-state or reactant stationary assumption: that is the question, FEBS J., 281, 464, 10.1111/febs.12564
Bersani, 2015, New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis - Menten paper, Continuum. Mech. Therm., 27, 659, 10.1007/s00161-014-0367-4
Briggs, 1925, A note on the kinetics of enzyme action, Biochem. J., 19, 338, 10.1042/bj0190338
Lineweaver, 1934, The determination of enzyme dissociation constants, J. Am. Chem. Soc., 56, 658, 10.1021/ja01318a036
Eisenthal, 1974, The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters, Biochem. J., 139, 715, 10.1042/bj1390715
Atkins, 1975, A comparison of seven methods for fitting the Michaelis-Menten equation, Biochem. J., 149, 775, 10.1042/bj1490775
Ainsworth, 1977
Atkins, 1980, Current trends in the estimation of Michaelis-Menten parameters, Anal. Biochem., 104, 1, 10.1016/0003-2697(80)90268-7
Bisswanger, 2014, Enzyme assays, Perspect. Sci., 1, 41, 10.1016/j.pisc.2014.02.005
Stroberg, 2016, On the estimation errors of Km and V from time-course experiments using the Michaelis-Menten equation, Biophys. Chem., 219, 17, 10.1016/j.bpc.2016.09.004
Fan, 2018, In vivo guiding nitrogen-doped carbon nanozyme for tumor catalytic therapy, Nat. Commun., 9, 1440, 10.1038/s41467-018-03903-8
Dindas, 2018, AUX1-mediated root hair auxin influx governs SCFTIR1/AFB-type Ca2+ signaling, Nat. Commun., 9, 1174, 10.1038/s41467-018-03582-5
Fry, 2018, Predicting retinal tissue oxygenation using an image-based theoretical model, Math. Biosci., 305, 1, 10.1016/j.mbs.2018.08.005
la Cecilia, 2018, Glyphosate dispersion, degradation, and aquifer contamination in vineyards and wheat fields in the Po Valley, Italy, Water Res., 146, 37, 10.1016/j.watres.2018.09.008
Gwanpua, 2018, Modelling ethylene regulated changes in Hass avocado quality, Postharvest Biol. Technol., 136, 12, 10.1016/j.postharvbio.2017.10.002
Tagliafico, 2018, Optimizing heterotrophic feeding rates of three commercially important scleractinian corals, Aquaculture, 483, 96, 10.1016/j.aquaculture.2017.10.013
Gonzalez-Gil, 2018, Why are organic micropollutants not fully biotransformed? A mechanistic modelling approach to anaerobic systems, Water Res., 142, 115, 10.1016/j.watres.2018.05.032
Busch, 2018, LC–MS/MS method for the simultaneous quantification of intestinal CYP and UGT activity, J. Pharmaceut. Biomed., 155, 194, 10.1016/j.jpba.2018.04.003
Liang, 2018, Gibbs free-energy gradient along the path of glucose transport through human glucose transporter 3, ACS Chem. Neurosci., 9, 2815, 10.1021/acschemneuro.8b00223
Straus, 1943, Zone behavior of enzymes illustrated by the effect of dissociation constant and dilution on the system cholinesterase-physostigmine, J. Gen. Physiol., 26, 559, 10.1085/jgp.26.6.559
Hommes, 1962, Analog computer studies of the carboxypeptidase A-catalyzed hydrolysis of chloroacetyl-l-phenylalanine, Arch. Biochem. Biophys., 96, 37, 10.1016/0003-9861(62)90446-0
Wong, 1965, On the steady-state method of enzyme kinetics, J. Am. Chem. Soc., 87, 1788, 10.1021/ja01086a032
Srere, 1967, Enzyme concentrations in tissues, Science, 158, 936, 10.1126/science.158.3803.936
Cha, 1970, Kinetic behavior at high enzyme concentrations magnitude of errors of Michaelis-Menten and other approximations, J. Biol. Chem., 245, 4814, 10.1016/S0021-9258(18)62865-0
Laidler, 1955, Theory of the transient phase in kinetics, with special reference to enzyme kinetics, Can. J. Chem., 33, 1614, 10.1139/v55-195
Seshadri, 1980, Analytical solutions of a simple enzyme kinetic problem by a perturbative procedure, Biophys. Struct. Mech., 6, 111, 10.1007/BF00535748
Segel, 1988, On the validity of steady state assumption of enzyme kinetics, B. Math. Biol., 50, 579, 10.1007/BF02460092
Segel, 1989, The quasi-steady-state assumption: a case study in perturbation, SIAM Rev., 31, 446, 10.1137/1031091
Heineken, 1967, On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics, Math. Biosci., 1, 95, 10.1016/0025-5564(67)90029-6
Schauer, 1979, Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction, J. Theor. Biol., 79, 425, 10.1016/0022-5193(79)90235-2
Palsson, 1984, Mathematical modelling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics, J. Theor. Biol., 111, 273, 10.1016/S0022-5193(84)80211-8
Schnell, 2000, Enzyme kinetics at high enzyme concentration, B. Math. Biol., 62, 483, 10.1006/bulm.1999.0163
Borghans, 1996, Extending the quasi-steady state approximation by changing variables, B. Math. Biol., 58, 43, 10.1007/BF02458281
Schnell, 2002, Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations, Math. Comput. Model., 35, 137, 10.1016/S0895-7177(01)00156-X
Tzafriri, 2003, Michaelis-Menten kinetics at high enzyme concentrations, J. Math. Biol., 65, 1111, 10.1016/S0092-8240(03)00059-4
Dingee, 2008, A new perturbation solution to the Michaelis-Menten problem, AICHE J., 54, 1344, 10.1002/aic.11461
Murugan, 2018, Theory on the rate equation of Michaelis - Menten type single-substrate enzyme catalyzed reactions, J. Math. Chem., 56, 508, 10.1007/s10910-017-0791-3
Fenichel, 1979, Geometric singular perturbation theory for ordinary differential equations, J. Diff. Eqs., 31, 53, 10.1016/0022-0396(79)90152-9
Kaper, 1999, An introduction to geometric methods and dynamical systems theory for singular perturbation problems, 85
Verhulst, 2005, vol. 50
Kuehn, 2015, vol. 191
Hek, 2010, Geometric singular perturbation theory in biological practice, J. Math. Biol., 60, 347, 10.1007/s00285-009-0266-7
Lam, 1989, Understanding complex chemical kinetics with computational singular perturbation, Proc. Comb. Inst., 22, 931, 10.1016/S0082-0784(89)80102-X
Lam, 1993, Using CSP to understand complex chemical kinetics, Combust. Sci. Technol., 89, 375, 10.1080/00102209308924120
Hadjinicolaou, 1998, Asymptotic solution of stiff PDEs with the CSP method: the reaction diffusion equation, SIAM J. Sci. Comp., 20, 781, 10.1137/S1064827596303995
Maas, 1992, Simplifying chemical kinetics - intristic low dimensional manifolds in composition space, Comb. Flame, 88, 239, 10.1016/0010-2180(92)90034-M
Zagaris, 2004, Analysis of the computational singular perturbation reduction method for chemical kinetics, J. Nonlinear Sci., 14, 59, 10.1007/s00332-003-0582-9
Goussis, 2012, Quasi steady state and partial equilibrium approximations: their relation and their validity, Combust. Theor. Model., 16, 869, 10.1080/13647830.2012.680502
Goussis, 2015, Model reduction: when singular perturbation analysis simplifies to partial equilibrium approximation, Combust. Flame, 162, 1009, 10.1016/j.combustflame.2014.09.022
Zagaris, 2004, Fast and slow dynamics for the computational singular perturbation method, Multiscale Model. Sim., 2, 613, 10.1137/040603577
Kaper, 2015, Geometry of the computational singular perturbation method, Math. Model. Nat. Phenom., 10, 16, 10.1051/mmnp/201510303
Valorani, 2001, Explicit time-scale splitting algorithms for stiff problems: auto-ignition of gaseous mixtures behind a steady shock, J. Comp. Phys., 169, 44, 10.1006/jcph.2001.6709
Goussis, 2006, Model reduction and physical understanding of slowly oscillating processes: the circadian cycle, Multiscale Model. Sim., 5, 1297, 10.1137/060649768
Kourdis, 2013, Algorithmic asymptotic analysis of the NF-κB signaling system, Comput. Math. Appl., 65, 1516, 10.1016/j.camwa.2012.11.004
Patsatzis, 2016, Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches, B. Math. Biol., 78, 1121, 10.1007/s11538-016-0176-y
Maris, 2015, The hidden dynamics of the Rössler attractor, Physica D, 295, 66, 10.1016/j.physd.2014.12.010
Goussis, 1992, A study of homogeneous methanol oxidation kinetic using CSP, Proc. Comb. Inst., 24, 113, 10.1016/S0082-0784(06)80018-4
Valorani, 2003, CSP analysis of a transient flame-vortex interaction: time scales and manifolds, Comb. Flame, 134, 35, 10.1016/S0010-2180(03)00067-1
Michalaki, 2018, Asymptotic analysis of a tmdd model: when a reaction contributes to the destruction of its product, J. Math. Biol., 77, 821, 10.1007/s00285-018-1234-x
Sols, 1970, Concentrations of metabolites and binding sites. Implications in metabolic regulation, Curr. Top. Cell. Reg., 2, 227, 10.1016/B978-0-12-152802-7.50013-X
Albe, 1990, Cellular concentrations of enzymes and their substrates, J. Theor. Biol., 143, 163, 10.1016/S0022-5193(05)80266-8
Schnell, 2002, Enzyme kinetics far from the standard quasi-steady state and equilibrium approximations, Math. Comput. Model., 35, 137, 10.1016/S0895-7177(01)00156-X
Flach, 2006, Use and abuse of the quasi-steady-state approximation, IEEE Syst. Biol., 153, 187, 10.1049/ip-syb:20050104
Gunawardena, 2014, Time-scale separation - Michaelis and Menten’s old idea, still bearing fruit, FEBS J., 281, 473, 10.1111/febs.12532
Hanson, 2008, Reactant stationary approximation in enzyme kinetics, J. Phys. Chem. A, 112, 8654, 10.1021/jp8026226