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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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UNIFAC is a computational method for the estimation of Rault's law activity coefficients. Being a group contribution method, it can calculate activity coefficients in systems for which there is no experimental data by assessing the individual contribution of each chemical group which makes up the system. Use of this method requires three types of parameters for each group in the system: the group's surface area, the volume of the group, and empirically determined parameters which reflect the free energy of interaction between a given group and every other group in the system, (a) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: New York, 1977. (b) Steen, S.-J.; Bärbel, K.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714. (c) Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Process Des. Dev. 1982. 21, 118. (d) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 678. (e) Teigs, D.: Gmehling, J.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 159. (f) Hansen, H. K.; Rasmussen, P.; Schiller, M.; Gmehling, J. Ind. Eng. Chem. Res. 1991, 30, 2355.
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Such cross-linked crystals of various enzymes have been employed as robust catalysts in synthetic transformations: (a) St. Clair, N. L.; Navia, M. A. J. Am. Chem. Soc. 1992, 114, 7314. (b) Sobolov, S. B.; Bartoszko-Malik, A.; Oeschger, T. R.; Monlelbano, M. M. Tetrahedron Lett. 1994, 35, 7751. (c) Persichetti, R. A.; St. Clair, N. L.; Griffith, J. P.; Navia, M. A.; Margolin, A. L. J. Am. Chem. Soc. 1995, 117, 2732. (d) Lalonde, J. J.; Govardhan, C.; Khalaf, N.; Martinez, A. G.; Visuri, K.; Margolin, A. L. J. Am. Chem. Soc. 1995, 117, 6845. (e) Sobolov, S. B.; Leonida, M. D.; Bartoszko-Malik, A.; Veivodov, K. I.; McKinney, F.; Kim, J.; Fry, A. J. J. Org. Chem. 1996, 61, 2125. (f) Schmitke, J. L.; Wescott, C. R.: Klibanov, A. M. J. Am. Chem. Soc. 1996, 118, 3360.
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10 then it also should be the same in other organic solvents because the differences in physicochemical properties among them are less than those between water and hexane. Furthermore, cross-linking followed by placement in acetonitrile does not affect the structure of two other serine proteases, subtilisin Carlsberg (Fitzpatrick, P. A.; Steinmetz, A. C. U.; Ringe, D.; Klibanov, A. M. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 8653. Fitzpatrick, P. A.; Ringe, D.; Klibanov, A. M. Biochem. Biophys. Res. Commun. 1994, 198, 675) and porcine pancreatic elastase (Allen, K. N.; Bellamacina, C. R.; Ding, X.; Jeffery, C. J.; Mattos, C.; Petsko, G. A.; Ringe, D. J. Phys. Chem. 1996, 100, 2605).
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note
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This work was financially supported by NIH grant GM39794. H.N. gratefully acknowledges a fellowship from the Tokyo Metropolitan Government.
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