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Several examples of two-step sequential reactions exist where, because of the poor equilibrium conversion by the first reaction, it is desirable to conduct the two reactions simultaneously. In such a scheme, the product of the first reaction is continuously removed by the second reaction, thus not allowing the first reaction to approach chemical equilibrium. Therefore, the first reaction is allowed to proceed in the desired direction at an appreciable rate. However, in many biochemical applications where enzyme catalysts are involved, the enzyme's activities are strong functions of pH. Where the pH optima of the first and second reaction differ by three to four units, the above reaction scheme would be difficult to implement. In these cases, the two reactions can be separated by a thin permeable membrane across which the desired pH gradient is maintained. In this article, it was shown, both by theory and experiment, that a thin, flat membrane of immobilized urease can accomplish this goal when one face of the membrane is exposed to the acidic bulk solution (pH(b) = 4.5) containing a small quantity of urea (0.01 M). In this particular case, the ammonia that was produced in the membrane consumed the incoming hydrogen ions and thus maintained the desired pH gradient. Experimental results indicate that with sufficient urease loading, the face of the membrane opposite to the bulk solution could be maintained at a pH that would allow many enzymes to realize their maximum activities ( approximately 7.5). It was also found that this pH gradient could be maintained even in the presence of a buffer, which greatly enhances the transport of protons into the membrane.

A transient one-dimensional mathematical model is presented to help visualize the qualitative and quantitative effects on inter-capillary tissue undergoing photodynamic therapy (PDT). The model is solved by a Crank-Nicholson finite difference formulation to provide time-dependent concentrations of the Type II mechanism's photo-oxidation species in the tissue surrounding a capillary. The time-dependent solution allows educated decisions to be made as to the optimum timing of light fractionation (on/off) cycles. Qualitative and quantitative optimization of the PDT process is considered along with a case study of data in the literature, the main goal being to provide optimized light therapy regimens for eventual clinical use.

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