An analytical solution to the evolution of presteady state substrate and product concentration profiles in spherical enzyme supports
✍ Scribed by Reiner Kühnau; Jürgen Lasch
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 499 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0022-5193
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✦ Synopsis
The time evolution of substrate and product profiles in spherical particles grafted with Michaelian enzymes has been investigated theoretically. Assuming that only internal diffusion interferes with the enzyme reaction, an analytical solution to the partial differential equation governing the presteady state of the immobilized enzyme system has been found.
Employing parameters (Ds, I~, k,,,, R) encountered in practical situations, numerical examples are given and the results graphed as evolving reactant profiles and substrate waves arriving at the center of the spheres. An approximation formula for the computation of half accumulation times of substrate at the center of the spheres, tl/2 ~ R/(2xlkDs), has been derived and compared with the exact solution. Half accumulation times never exceed 12 s in real systems. The arrival of the substrate wave at the center of the sphere is profoundly modified by the kinetic parameters of the enzyme.