A total quasi-steady-state formulation of substrate uptake kinetics in complex networks and an example application to microbial litter decomposition

Biogeosciences

Volumn 10, Issue 12, 2013, Pages 8329-8351

  Tang, J Y ^a   Riley, W J ^a  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOGEOCHEMISTRY; BIOMASS; COMPLEXITY; CONSUMER-RESOURCE INTERACTION; DECOMPOSITION; LITTER; MICROBIAL ACTIVITY; REACTION KINETICS; SUBSTRATE;

EID: 84890448059     PISSN: 17264170     EISSN: 17264189     Source Type: Journal    
DOI: 10.5194/bg-10-8329-2013     Document Type: Article

References (115)

1. Aber, J. D., Melillo, J. M., and Mcclaugherty, C. A.: Predicting long-term patterns of mass-loss, nitrogen dynamics, and soil organic-matter formation from initial fine litter chemistry in temperate forest ecosystems, Can. J. Bot., 68, 2201-2208, 1990.
2. Abrams, P. A. and Ginzburg, L. R.: The nature of predation: prey dependent, ratio dependent or neither?, Trends Ecol. Evol., 15, 337-341, doi:10.1016/S0169-5347(00)01908-X, 2000. (Pubitemid 30484261)
3. Allison, S. D.: A trait-based approach for modelling microbial litter decomposition, Ecol. Lett., 15, 1058-1070, doi:10.1111/j.1461-0248.2012.01807.x, 2012.
4. Allison, S. D.,Wallenstein, M. D., and Bradford, M. A.: Soil-carbon response to warming dependent on microbial physiology, Nat. Geosci., 3, 336-340, doi:10.1038/Ngeo846, 2010.
5. Andren, O. and Paustian, K.: Barley straw decomposition in the field-a comparison of models, Ecology, 68, 1190-1200, doi:10.2307/1939203, 1987.
6. Arditi, R. and Ginzburg, L. R.: Coupling in predator prey dynamics-ratio-dependence, J. Theor. Biol., 139, 311-326, doi:10.1016/S0022- 5193(89)80211-5, 1989.
7. Armstrong, R. A.: Nutrient uptake rate as a function of cell size and surface transporter density: A Michaelis-like approximation to the model of Pasciak and Gavis, Deep-Sea Res Pt. I, 55, 1311-1317, doi:10.1016/J.Dsr.2008.05. 004, 2008.
8. Balser, T. C. and Wixon, D. L.: Investigating biological control over soil carbon temperature sensitivity, Glob. Change Biol., 15, 2935-2949, doi:10.1111/J.1365-2486.2009.01946.X, 2009.
9. Bauer, J., Herbst, M., Huisman, J. A., Weihermuller, L., and Vereecken, H.: Sensitivity of simulated soil heterotrophic respiration to temperature and moisture reduction functions, Geoderma, 145, 17-27, doi:10.1016/J.Geoderma.2008. 01.026, 2008.
10. Bender, C. M. and Orzag, S. A.: Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag, New York, 1999.
11. Berg, H. C. and Purcell, E. M.: Physics of Chemoreception, Biophys. J., 20, 193-219, 1977. (Pubitemid 8220672)
12. Berg, B. and Staaf, H.: Decomposition rate and chemical changes of Scots pine litter. II. Influence of chemical composition, Ecol. Bull., 32, 373-390, 1980.
13. Berg, B., Hannus, K., Popoff, T., and Theander, O.: Changes in organic-chemical components of needle litter during decomposition-long-term decomposition in a scots pine forest .1., Can. J. Bot., 60, 1310-1319, 1982. (Pubitemid 13283579)
14. Beven, K.: A manifesto for the equifinality thesis, Journal of Hydrology, 320, 18-36, doi:10.1016/J.Jhydrol.2005.07.007, 2006.
15. Bonachela, J. A., Raghib, M., and Levin, S. A.: Dynamic model of flexible phytoplankton nutrient uptake, P. Natl. Acad. Sci. USA, 108, 20633-20638, doi:10.1073/Pnas.1118012108, 2011.
16. Bonner, W. D., Gore, W. L., and Yost, D. M.: The thermal reaction between gaseous iodine monochloride and hydrogen, J. Am. Chem. Soc., 57, 2723-2724, doi:10.1021/Ja01315a502, 1935.
17. Borghans, J. A. M. and Deboer, R. J.: A minimal model for T-cell vaccination, P. Roy. Soc. B.-Biol. Sci., 259, 173-178, doi:10.1098/Rspb.1995. 0025, 1995.
18. Borghans, J. A. M., DeBoer, R. J., and Segel, L. A.: Extending the quasi-steady state approximation by changing variables, B. Math. Biol., 58, 43-63, doi:10.1007/Bf02458281, 1996. (Pubitemid 126690448)
19. Bouskill, N. J., Tang, J. Y., Riley, W. J., and Brodie, E. L.: Traitbased representation of biological nitrification: model development, testing, and predicted community composition, Front. Microbiol., 3, 364, doi:10.3389/fmicb. 2012.00364, 2012.
20. Broekhuizen, N., Rickard, G. J., Bruggeman, J., and Meister, A.: An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems, Appl. Numer. Math., 58, 319-340, doi:10.1016/J.Apnum.2006.12.002, 2008. (Pubitemid 351175688)
21. Burnett, T.: Influences of natural temperatures and controlled host densities on oviposition of an insect parasite, Physiol. Zool., 27, 239-258, 1954.
22. Campbell, A.: Conditions for existence of bacteriophage, Evolution, 15, 153-165, doi:10.2307/2406076, 1961.
23. Caperon, J.: Population growth in micro-organisms limited by food supply, Ecology, 48, 715-722, doi:10.2307/1933728, 1967.
24. Cha, S. and Cha, C. J. M.: Kinetics of cyclic enzyme systems, Mol. Pharmacol., 1, 178-189, 1965.
25. Childs, R. E. and Bardsley, W. G.: Steady-state kinetics of peroxidase with 2,2'-Azino-Di-(3-Ethylbenzthiazoline-6-Sulphonic Acid) as chromogen, Biochem. J., 145, 93-103, 1975.
26. Choy, K. K. H., Porter, J. F., and McKay, G.: Langmuir isotherm models applied to the multicomponent sorption of acid dyes from effluent onto activated carbon, J. Chem. Eng. Data, 45, 575-584, doi:10.1021/Je9902894, 2000.
27. Ciliberto, A., Capuani, F., and Tyson, J. J.: Modeling networks of coupled enzymatic reactions using the total quasisteady state approximation, Plos Comput. Biol., 3, 463-472, doi:10.1371/Journal.Pcbi.0030045, 2007. (Pubitemid 46535738)
28. Cornish-Bowden, A.: Fundamentals of Enzyme Kinetics, rev. ed., Portland Press, London, 1995.
29. Davidson, E. A. and Janssens, I. A.: Temperature sensitivity of soil carbon decomposition and feedbacks to climate change, Nature, 440, 165-173, doi:10.1038/Nature04514, 2006. (Pubitemid 43372088)
30. Davidson, E. A., Samanta, S., Caramori, S. S., and Savage, K.: The dual Arrhenius and Michaelis-Menten kinetics model for decomposition of soil organic matter at hourly to seasonal time scales, Glob. Change Biol., 18, 371-384, doi:10.1111/J.1365-2486.2011.02546.X, 2012.
31. De Boer, R. J. and Perelson, A. S.: T-cell repertoires and competitive-exclusion, J. Theor. Biol., 169, 375-390, doi:10.1006/Jtbi.1994. 1160, 1994. (Pubitemid 24294136)
32. De Boer, R. J. and Perelson, A. S.: Towards a general function describing T-cell proliferation, J. Theor. Biol., 175, 567-576, doi:10.1006/Jtbi.1995. 0165, 1995.
33. Dilly, O. and Munch, J. C.: Microbial biomass content, basal respiration and enzyme activities during the course of decomposition of leaf litter in a black alder (Alnus glutinosa (L) Gaertn) forest, Soil Biol. Biochem., 28, 1073-1081, doi:10.1016/0038-0717(96)00075-2, 1996. (Pubitemid 27079388)
34. Druhan, J. L., Steefel, C. I., Molins, S., Williams, K. H., Conrad, M. E., and DePaolo, D. J.: Timing the onset of sulfate reduction over multiple subsurface acetate amendments by measurement and modeling of sulfur isotope fractionation, Environ. Sci. Technol., 46, 8895-8902, doi:10.1021/Es302016p, 2012.
35. Dybzinski, R., Farrior, C., Wolf, A., Reich, P. B., and Pacala, S. W.: Evolutionarily stable strategy carbon allocation to foliage, wood, and fine roots in trees competing for light and nitrogen: an analytically tractable, individual-based model and quantitative comparisons to data, Am. Nat., 177, 153-166, doi:10.1086/657992, 2011.
36. Eyring, H.: The activated complex and the absolute rate of chemical reactions, Chem. Rev., 17, 65-77, doi:10.1021/Cr60056a006, 1935.
37. Eyring, H.: The activated complex in chemical reactions, J. Chem. Phys., 3, 107-115, doi:10.1063/1.1749604, 1935.
38. Felmy, A. R., Girvin, D. C., and Jenne, E. A.: MINTEQ: A computer program for calculating aqueous geochemical equilibria, EPA-600/3-84-032, Office Res. Dev., USEPA, Athens, GA, 1984.
39. Follows, M. J., Dutkiewicz, S., Grant, S., and Chisholm, S. W.: Emergent biogeography of microbial communities in a model ocean, Science, 315, 1843-1846, doi:10.1126/Science.1138544, 2007. (Pubitemid 46580143)
40. Ginzburg, L. R. and Akcakaya, H. R.: Consequences of ratiodependent predation for steady-state properties of ecosystems, Ecology, 73, 1536-1543, doi:10.2307/1940006, 1992. (Pubitemid 23396430)
41. Goldbeter, A. and Koshland, D. E.: An amplified sensitivity arising from covalent modification in biological-systems, P. Natl. Acad. Sci.-Biol., 78, 6840-6844, doi:10.1073/Pnas.78.11.6840, 1981. (Pubitemid 12216857)
42. Grant, R. F., Juma, N. G., and Mcgill, W. B.: Simulation of carbon and nitrogen transformations in soil-mineralization, Soil Biol. Biochem., 25, 1317-1329, doi:10.1016/0038-0717(93)90046-E, 1993.
43. Gu, C. H., Maggi, F., Riley, W. J., Hornberger, G. M., Xu, T., Oldenburg, C. M., Spycher, N., Miller, N. L., Venterea, R. T., and Steefel, C.: Aqueous and gaseous nitrogen losses induced by fertilizer application, J. Geophys. Res.-Biogeo., 114, G01006, doi:10.1029/2008jg000788, 2009.
44. Hall, S. R.: Stoichiometrically explicit competition between grazers: Species replacement, coexistence, and priority effects along resource supply gradients, Am. Nat., 164, 157-172, doi:10.1086/422201, 2004. (Pubitemid 39098920)
45. Herman, J., Moorhead, D., and Berg, B.: The relationship between rates of lignin and cellulose decay in aboveground forest litter, Soil Biol. Biochem., 40, 2620-2626, doi:10.1016/J.Soilbio.2008.07.003, 2008.
46. Holling, C. S.: The components of predation as revealed by a study of small-mammal predation of the european pine sawfly, Can. Entomol., 91, 293-320, doi:10.4039/Ent9129-7, 1959.
47. Jacobson, M. Z.: Studying the effects of calcium and magnesium on size-distributed nitrate and ammonium with EQUISOLV II, Atmos. Environ., 33, 3635-3649, doi:10.1016/S1352-2310(99)00105-3, 1999. (Pubitemid 29324721)
48. Jacobson, M. Z., Tabazadeh, A., and Turco, R. P.: Simulating equilibrium within aerosols and nonequilibrium between gases and aerosols, J. Geophys. Res.-Atmos., 101, 9079-9091, doi:10.1029/96jd00348, 1996.
49. Jenkinson, D. S. and Coleman, K.: The turnover of organic carbon in subsoils. Part 2. Modelling carbon turnover, Eur. J. Soil Sci., 59, 400-413, doi:10.1111/J.1365-2389.2008.01026.X, 2008. (Pubitemid 351342149)
50. Jennings, A. A., Kirkner, D. J., and Theis, T. L.: Multicomponent equilibrium chemistry in groundwater quality models, Water Resour. Res., 18, 1089-1096, doi:10.1029/Wr018i004p01089, 1982. (Pubitemid 13262363)
51. Jin, Q. and Bethke, C. M.: The thermodynamics and kinetics of microbial metabolism, Am. J. Sci., 307, 643-677, doi:10.2475/04.2007.01, 2007. (Pubitemid 47225986)
52. Karp-Boss, L., Boss, E., and Jumars, P. A.: Nutrient fluxes to planktonic osmotrophs in the presence of fluid motion, Oceanogr. Mar. Biol., 34, 71-107, 1996. (Pubitemid 27125048)
53. Keeler, B. L., Hobbie, S. E., and Kellogg, L. E.: Effects of long-term nitrogen addition on microbial enzyme activity in eight forested and grassland sites: implications for litter and soil organic matter decomposition, Ecosystems, 12, 1-15, doi:10.1007/S10021-008-9199-Z, 2009.
54. Klotzbucher, T., Kaiser, K., Guggenberger, G., Gatzek, C., and Kalbitz, K.: A new conceptual model for the fate of lignin in decomposing plant litter, Ecology, 92, 1052-1062, 2011.
55. Koen-Alonso, M.: A process-oriented approach to the multispecies functional response, in: From Energetics to Ecosystems: The Dynamics and Structure of Ecological Systems, edited by: Rooney, N., McCann, M. S., and Noakes, D. L. G., Springer, Dordrecht, The Netherlands, 1-36, 2007.
56. Kooijman, S. A. L. M.: The Synthesizing Unit as model for the stoichiometric fusion and branching of metabolic fluxes, Biophys. Chem., 73, 179-188, doi:10.1016/S0301-4622(98)00162-8, 1998. (Pubitemid 28325703)
57. Kooijman, S. A. L. M. and Troost, T. A.: Quantitative steps in the evolution of metabolic organisation as specified by the Dynamic Energy Budget theory, Biol. Rev., 82, 113-142, doi:10.1111/J.1469-185x.2006.00006.X, 2007.
58. Koven, C. D., Riley, W. J., Subin, Z. M., Tang, J. Y., Torn, M. S., Collins, W. D., Bonan, G. B., Lawrence, D. M., and Swenson, S. C.: The effect of vertically resolved soil biogeochemistry and alternate soil C and N models on C dynamics of CLM4, Biogeosciences, 10, 7109-7131, doi:10.5194/bg-10-7109-2013, 2013.
59. Kratina, P., Vos, M., Bateman, A., and Anholt, B. R.: Functional responses modified by predator density, Oecologia, 159, 425-433, doi:10.1007/S00442-008-1225-5, 2009.
60. Kumar, A. and Josic, K.: Reduced models of networks of coupled enzymatic reactions, J. Theor. Biol., 278, 87-106, doi:10.1016/J.Jtbi.2011.02.025, 2011.
61. Ladd, J. N., Amato, M., Zhou, L. K., and Schultz, J. E.: Differentialeffects of rotation, plant residue and nitrogen-fertilizer on microbial biomass and organic-matter in an Australian Alfisol, Soil Biol. Biochem., 26, 821-831, doi:10.1016/0038-0717(94)90298-4, 1994. (Pubitemid 2093671)
62. Lambers, H., Mougel, C., Jaillard, B., and Hinsinger, P.: Plantmicrobe-soil interactions in the rhizosphere: an evolutionary perspective, Plant Soil, 321, 83-115, doi:10.1007/S11104-009-0042-X, 2009.
63. Legovic, T. and Cruzado, A.: A model of phytoplankton growth on multiple nutrients based on the Michaelis-Menten-Monod uptake, Droop's growth and Liebig's law, Ecol. Model., 99, 19-31, doi:10.1016/S0304-3800(96)01919-9, 1997. (Pubitemid 27222135)
64. Li, C. S., Frolking, S., and Frolking, T. A.: A model of nitrous-oxide evolution from soil driven by rainfall events .1. model structure and sensitivity, J. Geophys. Res.-Atmos., 97, 9759-9776, 1992. (Pubitemid 23372966)
65. Lindeman, R. L.: The trophic-dynamic aspect of ecology, Ecology, 23, 399-418, doi:10.2307/1930126, 1942.
66. Litchman, E., Klausmeier, C. A., Schofield, O. M., and Falkowski, P. G.: The role of functional traits and trade-offs in structuring phytoplankton communities: scaling from cellular to ecosystem level, Ecol. Lett., 10, 1170-1181, doi:10.1111/J.1461-0248.2007.01117.X, 2007. (Pubitemid 350060404)
67. Liu, Y.: Overview of some theoretical approaches for derivation of the Monod equation, Appl. Microbiol. Biotech., 73, 1241-1250, 2007. (Pubitemid 46089495)
68. Lotka, A. J.: Contribution to quantitative parasitology, J. Wash. Acad. Sci. 13, 152-158, 1923.
69. Machinet, G. E., Bertrand, I., and Chabbert, B.: Assessment of Lignin-Related Compounds in Soils and Maize Roots by Alkaline Oxidations and Thioacidolysis, Soil Sci. Soc. Am. J., 75, 542-552, doi:10.2136/Sssaj2010.0222, 2011.
70. Maggi, F. and Riley, W. J.: Transient competitive complexation in biological kinetic isotope fractionation explains nonsteady isotopic effects: Theory and application to denitrification in soils, J. Geophys. Res.-Biogeo., 114, G04012, doi:10.1029/2008jg000878, 2009.
71. Maggi, F., Gu, C., Riley, W. J., Hornberger, G. M., Venterea, R. T., Xu, T., Spycher, N., Steefel, C., Miller, N. L., and Oldenburg, C. M.: A mechanistic treatment of the dominant soil nitrogen cycling processes: Model development, testing, and application, J. Geophys. Res.-Biogeo., 113, G02016, doi:10.1029/2007jg000578, 2008.
72. Magill, A. H. and Aber, J. D.: Long-term effects of experimental nitrogen additions on foliar litter decay and humus formation in forest ecosystems, Plant Soil, 203, 301-311, doi:10.1023/A:1004367000041, 1998. (Pubitemid 28537050)
73. Mayes, M. A., Heal, K. R., Brandt, C. C., Phillips, J. R., and Jardine, P. M.: Relation between soil order and sorption of dissolved organic carbon in temperate subsoils, Soil Sci. Soc. Am. J., 76, 1027-1037, doi:10.2136/Sssaj2011. 0340, 2012.
74. McCarty, P. L.: Thermodynamic electron equivalents model for bacterial yield prediction: Modifications and comparative evaluations, Biotechnol. Bioeng., 97, 377-388, doi:10.1002/Bit.21250, 2007. (Pubitemid 46852933)
75. McGill, B. J. and Brown, J. S.: Evolutionary game theory and adaptive dynamics of continuous traits, Annu. Rev. Ecol. Evol. S., 38, 403-435, doi:10.1146/Annurev.Ecolsys.36.091704.175517, 2007.
76. McGuire, A. D., Melillo, J. M., Kicklighter, D.W., Pan, Y. D., Xiao, X. M., Helfrich, J., Moore, B., Vorosmarty, C. J., and Schloss, A. L.: Equilibrium responses of global net primary production and carbon storage to doubled atmospheric carbon dioxide: Sensitivity to changes in vegetation nitrogen concentration, Global Biogeochem. Cy., 11, 173-189, doi:10.1029/97gb00059, 1997.
77. Melillo, J. M., Aber, J. D., and Muratore, J. F.: Nitrogen and lignin control of hardwood leaf litter decomposition dynamics, Ecology, 63, 621-626, doi:10.2307/1936780, 1982. (Pubitemid 13283591)
78. Melillo, J. M., Aber, J. D., Linkins, A. E., Ricca, A., Fry, B., and Nadelhoffer, K. J.: Carbon and nitrogen dynamics along the decay continuum-plant litter to soil organic-matter, Plant Soil, 115, 189-198, doi:10.1007/ Bf02202587, 1989.
79. Michaelis, L. and Menten, M. L.: The kenetics of the inversion effect, Biochem. Z., 49, 333-369, 1913.
80. Machinet, G. E., Bertrand, I., Barriere, Y., Chabbert, B., and Recous, S.: Impact of plant cell wall network on biodegradation in soil: Role of lignin composition and phenolic acids in roots from 16 maize genotypes, Soil Biol. Biochem., 43, 1544-1552, doi:10.1016/J.Soilbio.2011.04.002, 2011.
81. Molins, S., Trebotich, D., Steefel, C. I., and Shen, C. P.: An investigation of the effect of pore scale flow on average geochemical reaction rates using direct numerical simulation, Water Resour. Res., 48, W03527, doi:10.1029/2011wr011404, 2012.
82. Moorhead, D. L. and Sinsabaugh, R. L.: A theoretical model of litter decay and microbial interaction, Ecol. Monogr., 76, 151-174, doi:10.1890/0012-9615(2006)076[0151:Atmold]2.0.Co;2, 2006.
83. Murdoch, W. W.: Functional Response of Predators, J. Appl. Ecol., 10, 335-342, 1973.
84. Osono, T.: Ecology of ligninolytic fungi associated with leaf litter decomposition, Ecol. Res., 22, 955-974, doi:10.1007/S11284-007-0390-Z, 2007. (Pubitemid 50001764)
85. Parton, W. J., Stewart, J. W. B., and Cole, C. V.: Dynamics of C, N, P and S in grassland soils-a model, Biogeochemistry, 5, 109-131, doi:10.1007/Bf02180320, 1988.
86. Pasciak, W. J. and Gavis, J.: Transport limitation of nutrient uptake in phytoplankton, Limnol. Oceanogr., 19, 881-898, 1974.
87. Pasciak, W. J. and Gavis, J.: Transport limited nutrient uptake rates in Ditylum-Brightwellii, Limnol. Oceanogr., 20, 604-617, 1975.
88. Persson, L., Leonardsson, K., de Roos, A. M., Gyllenberg, M., and Christensen, B.: Ontogenetic scaling of foraging rates and the dynamics of a size-structured consumer-resource model, Theor. Popul. Biol., 54, 270-293, doi:10.1006/Tpbi.1998.1380, 1998. (Pubitemid 29000624)
89. Pilinis, C., Seinfeld, J. H., and Seigneur, C.: Mathematical modeling of the dynamics of multicomponent atmospheric aerosols, Atmos. Environ., 21, 943-955, doi:10.1016/0004-6981(87)90090-4, 1987. (Pubitemid 17050652)
90. Reynolds, H. L. and Pacala, S. W.: An analytical treatment of rootto-shoot ratio and plant competition for soil nutrient and light, Am. Nat., 141, 51-70, doi:10.1086/285460, 1993. (Pubitemid 23401477)
91. Riley, W. J. and Matson, P. A.: NLOSS: A mechanistic model of denitrified N2O and N-2 evolution from soil, Soil Sci., 165, 237-249, doi:10.1097/00010694- 200003000-00006, 2000. (Pubitemid 30184133)
92. Riley, W. J., Subin, Z. M., Lawrence, D. M., Swenson, S. C., Torn, M. S., Meng, L., Mahowald, N. M., and Hess, P.: Barriers to predicting changes in global terrestrial methane fluxes: analyses using CLM4Me, a methane biogeochemistry model integrated in CESM, Biogeosciences, 8, 1925-1953, doi:10.5194/bg-8-1925-2011, 2011.
93. Rodrigo, A., Recous, S., Neel, C., and Mary, B.: Modelling temperature and moisture effects on C-N transformations in soils: comparison of nine models, Ecol. Model., 102, 325-339, doi:10.1016/S0304-3800(97)00067-7, 1997. (Pubitemid 27506484)
94. Saggar, S., Parshotam, A., Sparling, G. P., Feltham, C. W., and Hart, P. B. S.: C-14-labelled ryegrass turnover and residence times in soils varying in clay content and mineralogy, Soil Biol. Biochem., 28, 1677-1686, doi:10.1016/S0038-0717(96)00250-7, 1996. (Pubitemid 27195232)
95. Schenk, D., Bersier, L. F., and Bacher, S.: An experimental test of the nature of predation: neither prey-nor ratiodependent, J. Anim. Ecol., 74, 86-91, doi:10.1111/J.1365-2656.2004.00900.X, 2005. (Pubitemid 40252741)
96. Schimel, J. P.,Wetterstedt, J. A. M., Holden, P. A., and Trumbore, S. E.: Drying/rewetting cycles mobilize old C from deep soils from a California annual grassland, Soil Biol. Biochem., 43, 1101-1103, doi:10.1016/J.Soilbio.2011.01. 008, 2011.
97. Schnell, S. and Maini, P. K.: Enzyme kinetics at high enzyme concentration, B Math. Biol., 62, 483-499, doi:10.1006/Bulm.1999.0163, 2000.
98. Schnell, S. and Mendoza, C.: Enzyme kinetics of multiple alternative substrates, J. Math. Chem., 27, 155-170, doi:10.1023/A:1019139423811, 2000.
99. Segel, L. A. and Slemrod, M.: The quasi-steady-state assumption-a case-study in perturbation, Siam. Rev., 31, 446-477, doi:10.1137/1031091, 1989.
100. Sposito, G. and Coves, J.: SOILCHEM: A computer program for the calculation of chemical spcciation in soils, Keamey Found. Soil Sci., Univ. California, Riverside, 1988.
101. Suzuki, I., Lizama, H. M., and Tackaberry, P. D.: Competitiveinhibition of ferrous iron oxidation by thiobacillus-ferrooxidans by increasing concentrations of cells, Appl. Environ. Microbiol., 55, 1117-1121, 1989. (Pubitemid 19120708)
102. Taylor, K. E.: Summarizing multiple aspects of model performance in a single diagram., J. Geophys. Res.-Atmos, 106, 7183-7192, doi:10.1029/ 2000jd900719, 2001.
103. Tang, J. Y. and Zhuang, Q. L.: Equifinality in parameterization of process-based biogeochemistry models: A significant uncertainty source to the estimation of regional carbon dynamics, J. Geophys. Res.-Biogeo., 113, G04010, doi:10.1029/2008jg000757, 2008.
104. Tang, J. Y., Tang, J., and Wang, Y.: Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations, Appl. Math. Mech.-Engl., 28, 317-325, doi:10.1007/S10483-007-0305-Z, 2007.
105. Thornton, P. E., Lamarque, J. F., Rosenbloom, N. A., and Mahowald, N. M.: Influence of carbon-nitrogen cycle coupling on land model response to CO2 fertilization and climate variability, Global Biogeochem. Cy., 21, Gb4018, doi:10.1029/2006gb002868, 2007. (Pubitemid 351386640)
106. Tilman, D.: Resource competition between planktonic algae-experimental and theoretical approach, Ecology, 58, 338-348, doi:10.2307/1935608, 1977.
107. Vayenas, D. V. and Pavlou, S.: Chaotic dynamics of a food web in a chemostat, Math. Biosci., 162, 69-84, doi:10.1016/S0025-5564(99)00044-9, 1999.
108. Volterra, V.: Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mew. Acad. Lincei., 6, 31-113, 1926.
109. Vrugt, J. A., ter Braak, C. J. F., Clark, M. P., Hyman, J. M., and Robinson, B. A.: Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44, W00b09, doi:10.1029/2007wr006720, 2008.
110. Vucetich, J. A., Peterson, R. O., and Schaefer, C. L.: The effect of prey and predator densities on wolf predation, Ecology, 83, 3003-3013, doi:10.2307/3071837, 2002. (Pubitemid 36524677)
111. Wang, G. S. and Post, W. M.:, A note on the reverse Michaelis-Menten kinetics, Soil Biol. Biochem., 57, 946-949, doi:10.1016/j.soilbio.2012.08.028, 2013.
112. Wang, G. S., Post, W. M., Mayes, M. A., Frerichs, J. T., and Sindhu, J.: Parameter estimation for models of ligninolytic and cellulolytic enzyme kinetics, Soil Biol. Biochem., 48, 28-38, doi:10.1016/J.Soilbio.2012.01.011, 2012.
113. Wang, G. S., Post, W. M., and Mayes, M. A.: Development of microbial-enzyme-mediated decomposition model parameters through steady-state and dynamic analyses, Ecol. Appl., 23, 255-272, 2013.
114. Wickings, K., Grandy, A. S., Reed, S. C., and Cleveland, C. C.: The origin of litter chemical complexity during decomposition, Ecol. Lett., 15, 1180-1188, doi:10.1111/J.1461-0248.2012.01837.X, 2012.
115. Williams, P. J.: Validity of Application of Simple Kinetic Analysis to Heterogeneous Microbial Populations, Limnol. Oceanogr., 18, 159-164, 1973.