Enzyme electrodes based on complexing a water-soluble copolymer of acrylamide and vinylimidazole with [Os(dmebpy)2C1]+/2+ (dmebpy = 4,4'-dimethyl-2,2'-bipyridine) and cross-linking with oxidases by water-soluble cross-linkers are described. The potential of the polyacrylamide-based redox polymer is +55 mV (SCE), a typical electron diffusion coefficient (De) in the redox hydrogel that results from its cross-linking is (1.3 +/- 0.1) x 10(-9) cm2/s. The properties of the enzyme electrodes formed when this redox hydrogel "wired" horseradish peroxidase (HRP), lactate oxidase (LOx) or glucose oxidase (GOx) depended on the thickness of the hydrogel film, the chemistry of their cross-linking, and their enzyme content. At the wired HRP electrodes, H2O2 was electrocatalytically reduced to water at 0.0 V (SCE). Lactate and glucose were electrocatalytically oxidized at 0.16 V (SCE). The GOx electrodes, when made with 140 micrograms/cm2 thick polymer films, were selective for glucose in the presence of physiological concentrations of urate and ascorbate.

Under what circumstances can finite difference approximations serve as substitutes for analytical derivatives in unconstrained optimization? Are such techniques as good as using derivative-free methods? We investigated these two questions via both theoretical analysis and the solution of 15 test problems on the computer. It was discovered as expected that the error in the derivative substitutes influences algorithm performance only near termination, and that simple difference formulas are more efficient than more complex ones if the step size is selected properly. Among all the algorithms tested, the Davidon algorithm was the best both for the class using analytical derivatives and for the class with finite difference substitutes. Derivative-free algorithms were not as efficient.