Question

What is the ratio of [isocitrate] to [citrate] under cellular conditions at 37°C?

Short answer

Answer

The ratio of isocitrate to citrate at cellular level at the given temperature is found to be 0.14.

Step-by-step solution

Conversion of citrate to isocitrate

Aconitase is an enzyme that catalyzes the citrate to isocitrate conversion.

The reaction can be summarized as shown below:

The standard free energy change for aconitase obtained from the table of citric acid cycle reactions is found to be $\mathit{\Delta }{\mathit{G}}^{\mathbf{o}\mathbf{\text{'}}}\mathbf{=}\mathbf{5}\mathbf{}{\mathbf{\text{kJ mol}}}^{\mathbf{-}\mathbf{1}}$.

Ratio of fumarate to succinate calculation

The ratio of isocitrate to citrate is calculated using the following equation:

$\mathit{\Delta }\mathit{G}\mathbf{=}\mathit{\Delta }{\mathit{G}}^{\mathbf{0}}\mathbf{+}\mathit{R}\mathit{T}\mathit{l}\mathit{n}\mathit{K}$

Substituting the values in the equation,

$$\begin{gathered} 0=5000Jmo{l}^{-1}+8.314J{K}^{-1}mo{l}^{-1}\times 310K\times \ln \left(\frac{c\left(isocitrate\right)}{c\left(citrate\right)}\right) \\ -\ln \left(\frac{c\left(isocitrate\right)}{c\left(citrate\right)}\right)=\frac{5000J/mol}{2577.34J/mol} \end{gathered}$$

Taking ln to the right-hand side,

$$\begin{gathered} \left(\frac{c\left(isocitrate\right)}{c\left(citrate\right)}\right)=e^{-1.94} \\ =0.14 \end{gathered}$$

The ratio of isocitrate to citrate is 0.14.