Explain the binding constant (Kb) and fractional saturation (Y bar) equations.

$$K_b = \frac{[ES]}{[E][S]} \quad \text{(Equation 2)}$$

Here:

• $[ES]$ is the concentration of the enzyme-substrate complex.
• $[E]$ is the concentration of free enzyme.
• $[S]$ is the concentration of free substrate.

$$[ES] = K_b [E][S] \quad \text{(Equation 3)}$$

This equation shows that the concentration of the enzyme-substrate complex is directly proportional to the binding constant, the free enzyme concentration, and the free substrate concentration.

Fractional Saturation ($\bar{Y}$)

Fractional saturation ($\bar{Y}$) represents the fraction of the total enzyme that is bound to the substrate at any given time. It indicates how much of the enzyme's active sites are occupied.

$$\bar{Y} = \frac{\text{[Complex formed]}}{\text{[Total enzyme]}}$$

In terms of enzyme kinetics:

$$\bar{Y} = \frac{[ES]}{[E_0]} \quad \text{(Equation 4)}$$

Here, $[E_0]$ (or $[E_T]$) represents the total enzyme concentration.

In the simple binding reaction $E + S \rightleftharpoons ES$, the total enzyme is either free enzyme ($[E]$) or enzyme bound in the complex ($[ES]$).

$$[E_0] = [E] + [ES] \quad \text{(Equation 5)}$$

$$\bar{Y} = \frac{[ES]}{[E] + [ES]} \quad \text{(Equation 6)}$$

This equation shows the fraction of enzyme active sites that are occupied by substrate.