Suicide substrate reaction-diffusion equations: Varying the source |
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Authors: | BURKE, MEGHAN A. MAINI, P. K. MURRAY, J. D. |
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Affiliation: | Centre for Mathematical Biology, Mathematical Institute 2429 St Giles', Oxford 0X1 3LB, UK Applied Mathematics Department FS-20, University of Washington Seattle, Washington 98195, USA |
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Abstract: | The suicide substrate reaction is a model for certain enzyme-inhibitingdrugs. This reaction system is examined assuming that the substratediffuses freely while the enzyme remains fixed. Two sets ofinitial and boundary conditions are examined: one modellingan instantaneous point source, akin to an injection of substrate,the other, a continuous point source, akin to a continuing influx,or intravenous drip, of substrate. The quasi-steady-state assumptionis applied to obtain analytical solutions for a limited parameterspace. Finally, further applications of numerical and analyticalexperimentation on pharmaceutical mechanisms are described. |
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Keywords: | suicide substrate reaction-diffusion equations analytical solution quasi-steady-state assumption instantaneous point source continuous point source |
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