Adapting Particle Swarm Optimizationto Dynamic Environments

Abstract

Escherichia coli dihydrofolate reductase was shown to follow slow transient kinetics (hysteresis). Nonlinear reaction velocities were detected during the enzyme assay and required 10-15 min to reach a steady-state rate. The degree of hysteresis was influenced by the enzyme concentration and the order of substrate addition. Incubation of the enzyme with NADPH before addition of dihydrofolate resulted in slow initial velocities that increased up to 2-fold during the course of the assay. Increasing the enzyme concentration from 0.2 to 1 nM resulted in diminished hysteresis. NADPH-initiated reactions were linear at all enzyme concentrations tested. Certain drugs had profound effects on hysteresis. Pyrimethamine practically eliminated the hysteresis of dihydrofolate-started reactions, whereas trimethoprime augmented the non-linearities in the sense that hysteresis was detected in both enzyme- and NADPH-started reactions. The shape of these reaction tracings makes trimethoprim is not a slow-binding inhibitor when assayed under conditions that eliminate hysteresis. Contrary to this, sulfamethoxazole did not affect hysteresis or augment inhibition of the enzyme by trimethoprim. Sulfamethoxazole alone (at 6 mM) did not inhibit the hysteresis and allow reliable determinations of Ki values of both weak and tight binding inhibitors. For example, Ki values for pyrimethamine, trimethoprim, and methotrexate were found to be 214 nM, 1.3 nM, and 0.021 nM, respectively.