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An Algorithm for the Determination of All Significant Pathways in Chemical Reaction Systems

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Abstract

When the output of a complex chemical model is analysed, a typical topic isthe determination of pathways, i.e., reaction sequences, that produce ordestroy a chemical species of interest.A representative example is the investigation of catalytic ozone destruction cycles in the stratosphere.An algorithm for the automatic determination of pathways in any given reactionsystem is presented. Under the assumption that reaction rates are known, it finds all significant pathways, i.e., all pathways with a rate above a prescribed threshold.The algorithm forms pathways step by step, starting from single reactions.The chemical species in the system are consecutively considered as `branching points'.For every branching-point species, each pathway producing it is connected witheach pathway consuming it.Rates proportional to `branching probabilities' are calculated.Pathways with a rate that is smaller than a prescribed threshold arediscarded.If a newly formed pathway contains sub-pathways, e.g., null cycles, it is split into these simpler pathways.In order to demonstrate the performance of the algorithm, it has been applied to the determination of catalytic ozone destruction cycles and methaneoxidation pathways in the stratosphere.

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References

  • Anderson, J. G., Brune, W. H., Lloyd, S. A., Toohey, D. W., Sander, S. P., Starr, W. L., Loewenstein, M., and Podolske, J. R., 1989: Kinetics of O3 destruction by ClO and BrO within the Antarctic vortex. An analysis based on in situ ER-2 data, J. Geophys. Res. 94, 11480-11520.

    Google Scholar 

  • Andronova, N. G. and Schlesinger, M. E., 1991: The application of cause-and-effect analysis to mathematical models of geophysical phenomena, 1. Formulation and sensitivity analysis, J. Geophys. Res. 96, 941-946.

    Google Scholar 

  • Brasseur, G. P., Tie, X. X., Rasch, P. J., and Lefèvre, F., 1997: A three-dimensional simulation of the Antarctic ozone hole: Impact of anthropogenic chlorine on the lower stratosphere and upper troposphere, J. Geophys. Res. 102, 8909-8930.

    Google Scholar 

  • Carslaw, K. S., Luo, B., and Peter, T., 1995: An analytic expression for the composition of aqueous HNO3-H2SO4 stratospheric aerosols including gas phase removal of HNO3, Geophys. Res. Lett. 22, 1877-1880.

    Google Scholar 

  • Chapman, S., 1930: A theory of upper atmospheric ozone, Quart. J. Roy. Meteorol. Soc. 3, 103-125.

    Google Scholar 

  • Cicerone, R. J., 1987: Changes in stratospheric ozone, Science 237, 35-42.

    Google Scholar 

  • Clarke, B. L., 1988: Stoichiometric network analysis, Cell Biophys. 12, 237-253.

    Google Scholar 

  • Happel, J. and Sellers, P. H., 1982: Multiple reaction mechanisms in catalysis, Ind. Eng. Chem. Fundam. 21, 67-76.

    Google Scholar 

  • Heise, D. R., 1975: Causal Analysis, Wiley and Sons, New York.

    Google Scholar 

  • Johnson, B. G. and Corio, P. L., 1993: Computer construction of reaction mechnisms, J. Phys. Chem. 97, 12100-12105.

    Google Scholar 

  • Johnston, H. and Kinnison, D., 1998: Methane photooxidation in the atmosphere: Contrast between two methods of analysis, J. Geophys. Res. 103, 21967-21984.

    Google Scholar 

  • Johnston, H. S. and Podolske, J., 1978: Interpretation of stratospheric photochemistry, Rev. Geophys. Space Phys. 16, 491-519.

    Google Scholar 

  • Jucks, K. W., Johnson, D. G., Chance, K. V., Traub, W. A., Salawitch, R. J., and Stachnik, R. A., 1996: Ozone production and loss rate measurements in the middle stratosphere, J. Geophys. Res. 101, 28785-28792.

    Google Scholar 

  • Kinnison, D. E., Grant, K. E., Connell, P. S., Rotman, D. A., and Wuebbles, D. J., 1994: The chemical and radiative effects of the Mount Pinatubo eruption, J. Geophys. Res. 99, 25705-25731.

    Google Scholar 

  • Lary, D. J., 1997: Catalytic destruction of atmospheric ozone, J. Geophys. Res. 102, 21515-21526.

    Google Scholar 

  • Lehmann, R., 2002: Determination of dominant pathways in chemical reaction systems: An algorithm and its application to stratospheric chemistry, J. Atmos. Chem. 41, 297-314.

    Google Scholar 

  • Mavrovouniotis, M. L., 1992: Synthesis of reaction mechanisms consisting of reversible and irreversible steps. 2. Formalization and analysis of the synthesis algorithm, Ind. Eng. Chem. Res. 31, 1637-1653.

    Google Scholar 

  • Mavrovouniotis, M. L., Stephanopoulos, G., and Stephanopoulos, G., 1990: Computer-aided synthesis of biochemical pathways, Biotechnol. Bioeng. 36, 1119-1132.

    Google Scholar 

  • Milner, P. C., 1964: The possible mechanisms of complex reactions involving consecutive steps, J. Electrochem. Soc. 111, 228-232.

    Google Scholar 

  • Molina, L. T. and Molina, M. J., 1987: Production of Cl2O2 from the self-reaction of the ClO radical, J. Phys. Chem. 91, 433-436.

    Google Scholar 

  • Nevison, C. D., Solomon, S., and Gao, R. S., 1999: Buffering interactions in the modeled response of stratospheric O3 to increased NOx and HOx, J. Geophys. Res. 104, 3741-3754.

    Google Scholar 

  • Noži$#x010D;ka, F., Guddat, J., Hollatz, H., and Bank, B., 1974: Theorie der linearen parametrischen Optimierung, Akademie-Verlag, Berlin.

    Google Scholar 

  • Rabitz, H., Kramer, M., and Dacol, D., 1983: Sensitivity analysis in chemical kinetics, Ann. Rev. Phys. Chem. 34, 419-461.

    Google Scholar 

  • Ross, M. N., Ballenthin, J. O., Gosselin, R. B., Meads, R. F., Zittel, P. F., Benbrook, J. R., and Sheldon, W. R., 1997a: In-situ measurements of Cl2 and O3 in a stratospheric solid rocket motor exhaust plume, Geophys. Res. Lett. 24, 1755-1758.

    Google Scholar 

  • Ross, M. N., Benbrook, J. R., Sheldon, W. R., Zittel, P. F., and Mc Kenzie, D. L., 1997b: Observations of stratospheric ozone depletion in rocket exhaust plumes, Nature 390, 62-64.

    Google Scholar 

  • Saltelli, A., 1999: Sensitivity analysis: Could better methods be used?, J. Geophys. Res. 104, 3789-3793.

    Google Scholar 

  • Salawitch, R. J., Wofsy, S. C., Gottlieb, E. W., Lait, L. R., Newman, P. A., Schoeberl, M. R., Loewenstein, M., Podolske, J. R., Strahan, S. E., Proffitt, M. H., Webster, C. R., May, R. D., Fahey, D.W., Baumgardner, D., Dye, J. E., Wilson, J. C., Kelly, K. K., Elkins, J.W., Chan, K. R., and Anderson, J. G., 1993: Chemical loss of ozone in the Arctic polar vortex in the winter of 1991-1992, Science 261, 1146-1149.

    Google Scholar 

  • Schilling, C. H., Schuster, S., Palsson, B. O., and Heinrich, R., 1999: Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era, Biotechnol. Prog. 15, 296-303.

    Google Scholar 

  • Schilling, C. H., Letscher, D., and Palsson, B.Ø., 2000: Theory for the systematic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective, J. Theor. Biol. 203, 229-248.

    Google Scholar 

  • Schuster, R. and Schuster, S., 1993: Refined algorithm and computer program for calculating all nonnegative fluxes admissible in steady states of biochemical reaction systems with or without some flux rates fixed, Comp. Appl. Biosci. 9, 79-85.

    Google Scholar 

  • Schuster, S. and Hilgetag, C., 1994: On elementary flux modes in biochemical reaction systems at steady state, J. Biol. Syst. 2, 165-182.

    Google Scholar 

  • Schuster, S., Danekar, T., and Fell, D. A., 1999: Detection of elementary flux modes in biochemical networks: A promising tool for pathway analysis and metabolic engineering, Trends Biotechnol. 17, 53-60.

    Google Scholar 

  • Schuster, S., Hilgetag, C., Woods, J. H., and Fell, D. A., 2002: Reaction routes in biochemical reaction systems: Algebraic properties, validated calculation procedure and example from nucleotide metabolism, J. Math. Biol. 45, 153-181.

    Google Scholar 

  • Seressiotis, A. and Bailey, J. E., 1988: MPS: An artificially intelligent software system for the analysis and synthesis of metabolic pathways, Biotechnol. Bioeng. 31, 587-602.

    Google Scholar 

  • Shimazaki, T., 1984: The photochemical time constants of minor constituents and their families in the middle atmosphere, J. Atmos. Terr. Phys. 46, 173-191.

    Google Scholar 

  • Turányi, T., 1990: Sensitivity analysis of complex kinetic systems. Tools and applications, J. Math. Chem. 5, 203-248.

    Google Scholar 

  • Von Hohenbalken, B., Clarke, B. L., and Lewis, J. E., 1987: Least distance methods for the frame of homogeneous equation systems, J. Comp. Appl. Math. 19, 231-241.

    Google Scholar 

  • Wennberg, P. O., Cohen, R. C., Stimpfle, R. M., Koplow, J. P., Anderson, J. G., Salawitch, R. J., Fahey, D. W., Woodbridge, E. L., Keim, E. R., Gao, R. S., Webster, C. R., May, R. D., Toohey, D.W., Avallone, L.M., Proffitt, M. H., Loewenstein, M., Podolske, J. R., Chan, K. R., and Wofsy, S. C., 1994: Removal of stratospheric O3 by radicals: in situ measurements of OH, HO2, NO, NO2, ClO, and BrO, Science 266, 398-404.

    Google Scholar 

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Lehmann, R. An Algorithm for the Determination of All Significant Pathways in Chemical Reaction Systems. Journal of Atmospheric Chemistry 47, 45–78 (2004). https://doi.org/10.1023/B:JOCH.0000012284.28801.b1

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  • DOI: https://doi.org/10.1023/B:JOCH.0000012284.28801.b1

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