Ind. Eng. Chem. Res. 1991, 30, 2358-2359
2358 100,
A\
=\ t
6
I
I
-I-
I
I
I
I
1
Colussi, A. J.; Amorebieta, V. T. Heterogeneous Decomposition of Trichlorofluoromethane on Carbonaceous Surfaces. J. Chem. SOC.,Faraday Trans. 1 1987,83, 3055-3059. Hudgens, J. W. In Situ Studies of Infrared Multiple Photon Laserinduced Decomposition of CF& and CFC13. J. Chem. Phys. 1978, 68, 777-778. Imamura, S.; Ando, M. Oxidation of Tristearin on Manganese/Cerium Composite Oxide. Znd. Eng. Chem. Res. 1989,28,1452-1456. Imamura, S.; Ikeda, T.; Ishida, S. Multiple-step Catalytic Combustion of 1,2-Dichloroethane. Nippon Kagaku Kaishi 1989a, 139-144. Imamura, S.; Tarumoto, H.; Ishida, S. Decomposition of 1,2-Dichloroethane on TiOz/SiOz. Ind. Eng. Chem. Res. 198913, 28, 1449-1452. Imamura, S.; Shiomi, T.; Ishida, S.; Utani, K.; Jindai, H. Decomposition of Dichlorodifluoromethane on Ti02/SiOz. Znd. Erg. Chem. Res. 1990,29, 1758-1761. Imamura, S.; Imakubo, K.; Fujimura, Y.Catalytic Decomposition of Dichlorodifluoromethane-A Study on the Catalysts Durable Against Fluorine. Nippon Kagaku Kaishi 1991,645-647. Okazaki, S.; Kurosaki, A. Decomposition of Chlorofluorocarbons by the Reaction with Water Vapor Catalyzed by Iron Oxide Supported on Activated Carbon. Chem. Lett. 1989,1901-1904. Oku, A.; Kimura, K.; Sato, M. Chemical Decomposition of Chlorofluorocarbons by Reductive Dehalogenation Using Sodium Naphthalenide. Chem. Lett. 1988, 1789-1792. Oku, A.; Kimura, K.; Sato, M. Complete Destruction of Chlorofluorocarbons by Reductive Dehalogenation Using Sodium Nephthalenide. Znd. Eng. Chem. Res. 1989,28, 1055-1059. Ozaki, A. Ed. Shokubai Chosei Kagaku; Kodansha: Tokyo, 1980, pp 254-258. Utsumi, S.; Ito, S.; Isozaki, A. Determination of a Trace Amount of Boron by Extraction-Spectrophotometric Method. Nippon Kagaku Kaishi 1965,86,921-925. Witt, S. D.; Wu, E. C.; Loh, K. L.; Tang, Y. N. Heterogeneous Hydrogenolysis of Some Fluorocarbons. J. Catal. 1981,71,270-277. Zitter, R. N.; Koster, D. F.; Choudhury, T. K.; Cantoni, A. Kinetics and Mechanisms of the CO, Laser Induced Decompositions of CFC1, and CFzCl2. J. Phys. Chem. 1990,94, 2374-2377.
Seiichiro Imamura,* Ken-ichiro Imakubo Setsuo Furuyoshi Department of Chemistry Kyoto Institute of Technology Matsugasaki, Sakyo-ku, Kyoto 606, J a p a n
Hitoshi Jindai Nippon Fine Gas Co. Ltd. 1 - 4 Takasago, Takaishi, Osaka 592, J a p a n
Literature Cited Aida, T.; Higuchi, R.; Niiyama, H. Decomposition of Freon-12 and Methyl Chloride over Supported Gold Catalysts. Chem. Lett. 1990, 2247-2250.
Received for review April 15, 1991 Revised manuscript received July 2, 1991 Accepted July 26, 1991
CORRESPONDENCE A Note on Differing Characterization of the Mechanisms for Glucose to Pyruvate Conversion Sir: In our recent paper in this Journal (Happel et al., 1990), our final example was the conversion of glucose to
pyruvate, as presented by Seressiotis and Bailey (1988). In this correspondence we wish to state that what we described as a “discrepancy”between the two papers involves no error or inconsistency. The matter has been resolved after further discussion with the authors and we believe that the conclusions may be of interest to readers con0888-5885/91/2630-2358$02.50/0
cerned with this type of problem. Both papers had as their object the complete listing of all minimal or (as we say) direct mechanisms for the conversion of glucose to pyruvate. In Happel et al, (1990) this conversion was assumed to be a combination of two linearly independent reactions advancing a t independent rates. In contrast, Seressiotis and Bailey (1988) view the conversion as having alternative forms that could be de@ 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30,No. 10,1991 2359 scribed by distinct chemical reactions such as G = 2P,G = P 3C,3G = 5P + 3C,using the letter abbreviations G, glucose; P, pyruvate; and C, COz. Each of these equations has only one rate associated with it. Happel et al. (1990)and Seressiotis and Bailey (1988) both proceed to list all the minimal or direct mechanisms that produce the conversion of glucose to pyruvate. All the mechanisms listed by Happel et al. (1990)assume a given two parameter reaction system described by G = 2P and 3G = 5P 3C,although any other choice of two independent reactions would be suitable. In Table XI11 we exhibited the combined mechanisms. We noted that there were five different ways that the reaction 3G + 5P + 3C could occur, (ml, m5,m6,m7,and m8).However, two of these mechanisms require the simultaneous occurrence of G = 2P (m,and m6). On the other hand, the mechanisms listed by Seressiotis and Bailey (1988)include five mechanisms for G = 2P, three mechanisms for 3G = 5P + 3C,and two mechanisms for G = P + 3C. Thus it is in effect assumed that, if the reaction 3G = 5P + 3C occurs, no other reaction such as G = 2P will occur simultaneously in the system. Mathematically, these two ways of describing the conversion of glucose to pyruvate are analogous to describing a square as a single two-dimensional object or in terms of its four one-dimensional sides. The relationship between
+
+
these two approaches has been explained in geometrical terms by Sellers (1983).Every mechanism can be seen as a point in a polyhedron which can be described by its vertices, its edges, its faces, etc. Which description is most satisfactory depends on the context. A complete description of the polyhedron would require a list of all ita faces in each dimension. Literature Cited Happel, J.; Sellers, P. H.; Otarod, M. Mechanistic Study of Chemical Reaction Systems. Znd. Eng. Chem. Res. 1990,29, 1057-1064. Sellers, P.H. The Classification of Chemical Systems from a Geometric Viewpoint. Chemical Applications of Topology and Graph Theory; King, R. B., Ed.; Elsevier: New York, 1983; pp 420-429. Seressiotis, A.; Bailey, J. E. MPS: An Artificially Intelligent Software System for the Analysis and Synthesis of Metabolic Pathways. Biotechnol. Bioeng. 1988,31, 587-602.
Peter H.Sellers The Rockefeller University 1230 York Ave., New York, New York 10021
John Happel* Department of Chemical Engineering and Applied Chemistry Columbia University New York,New York 10027
-
