Accurate Kinetic Modeling of Alkaline Phosphatase in the Escherichia coli Periplasm: Implications for Enzyme Properties and Substrate Diffusion†

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Abstract
Alkaline phosphatase in the periplasm of Escherichia coli presents many of the complex factors that may influence enzymes in vivo. These include an environment that contains a high enzyme concentration, is densely populated with other macromolecules, and is separated from other compartments by a partial diffusion barrier. A previous study provided a partial description of this situation and developed a model that utilized kinetic behavior to estimate the permeability of the outer membrane [Martinez, M. B., et al., (1992) Biochemistry 31, 11500]. This study extends that description to provide a complete model for the enzyme at all substrate levels. Some of the parameters needed for complete modeling include the following: outer membrane permeability to the substrate and product, catalytic efficiency of the enzyme, number of enzymes per cell, and effects of the reaction product (an inhibitor) on the enzyme. The theoretical model fit the data quite well over a wide range of values for each of these parameters. The best fit of theory with experimental data required that the rate constant for product escape from the periplasm was 4-fold greater than that for substrate entry. This correlated with the relative sizes of the substrate and product. The excellent fit of theory and results suggested that alkaline phosphatase and its substrate were unaffected by the solution conditions in the periplasm. That is, the catalytic parameters (kcat and KM), determined for the enzyme in dilute solution, appeared to be unchanged by the conditions in the periplasm. The major factor that altered the kinetic behavior was the combined effect of the permeability barrier and the dense population of enzyme molecules in the periplasm. Given the large impact of these parameters on reaction properties, the excellent fit of theory and results was striking. Overall, this study demonstrated that enzyme action in the complex biological environment can be accurately modeled, if all factors that influence enzyme behavior are known.

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