3-\(\alpha \)-HSD Kinetic Model

\(\begin{array}{l}\frac{{d\left[ {3 - \alpha - d} \right]}}{{dt}} = \frac{{d{{\left[ {3 - \alpha - d} \right]}_{forward}}}}{{dt}} + \frac{{d{{\left[ {3 - \alpha - d} \right]}_{backward}}}}{{dt}} = \\ = \left[ {3 - \alpha - HSD} \right] \cdot \left( {{K_{ca{t_1}}} \cdot \frac{{\left[ {DHT} \right]}}{{{K_{{m_1}}} + \left[ {DHT} \right]}} - {K_{ca{t_2}}} \cdot \frac{{\left[ {3 - \alpha - d} \right]}}{{{K_{{m_2}}} + \left[ {3 - \alpha - d} \right]}}} \right)\end{array}\)

Background

3-\(\alpha \)-HSD is a name of a group of enzymes which convert certain hormones (like DHT) to another hormone (like 3-α-diol) and vice versa by means of oxidation and reduction. There are several strands of this enzyme, with different level of potency. In humans, the enzyme is encoded by the AKR1C4 gene, while in rat it is encoded by the AKR1C9 gene. We chose the rat version of the enzyme because it is more efficient in breaking down DHT ^{[need article]}.

All AKRs catalyze an ordered bi-bi reaction in which the cofactor binds first, followed by the binding of the steroid substrate. The steroid product is the first to leave, and the cofactor is the last. In this mechanism, \({K_{cat}}\) represents the slowest step in the kinetic sequence ^[2].