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Glucokinase (GK), an enzyme critical to glucose metabolism, exhibits thermal instability, which can affect its enzymatic activity under physiological and pathological conditions. This study aims to mathematically model the thermal denaturation kinetics of GK and empirically validate the model using experimental data. To establish a mathematical model on thermal denaturation of glucokinase (E.C.2.7.1.2) and its experimental validation, the enzyme glucokinase was investigated in a 0.075M Tris HCl buffer with pH 9.0 at 30^∘C and 0.6M MgCl₂. A first-order kinetic model was developed to describe the enzyme’s denaturation, incorporating temperature-dependent reaction rates based on the Arrehenius equation. Empirical data were collected through Spectrophotometer across a temperature range of 20^∘–60^∘C. Experimental validation revealed that GK undergoes irreversible denaturation above 60^∘ with a significant reduction as temperature increases. Moreover, the thermal denaturation of GK in the presence of osmolyte Urea is a critical process affecting enzyme stability and function. This study also aims to mathematically model and empirically validate the impact of Urea on GK’s thermal denaturation behavior. Results demonstrated that Urea significantly reduces the thermal stability of GK, lowering its denaturation temperature. The results are simulated graphically using the Wolfram MATHEMATICA software. The mathematical predictions closely matched experimental data, confirming the model’s accuracy.

We have previously hypothesized that density-dependent natural selection is responsible for a genetic polymorphism in crowded cultures of Drosophila. This genetic polymorphism entails two alternative phenotypes for dealing with crowded Drosophila larval cultures. The first phenotype is associated with rapid development, fast larval feeding rates but reduced absolute viability, especially in the presence of nitrogenous wastes like ammonia. The second phenotype has associated with it the opposite set of traits, slow development, slow feeding rates and higher viability. We suggested that these traits are associated due to genetic correlations and that an important selective agent in crowded larval cultures was high levels of ammonia. To test this hypothesis we have examined viability and larval feeding rates in populations kept at low larval densities but selected directly for (i) rapid egg-to-adult development, (ii) tolerance of ammonia in the larval environment and (iii) tolerance of urea in the larval environment. Consistent with our hypothesis we found that (i) larvae selected for rapid development exhibited increased feeding rates, and decreased viability in food laced with ammonia or urea relative to controls, and (ii) larvae selected to tolerate either ammonia or urea in their larval environment show reduced feeding rates but elevated survival in toxin-laced food relative to controls. It would appear that development time and larval feeding rate are important characters for larvae adapting to crowded cultures. The correlated fitness effects of these characters provide important insights into the nature of density-dependent natural selection.