# Determine enthalpy and entropy from measurements of Kd at different temperatures?

In biochemical experiments, it is very common to measure IC50 (half inhibitory concentration) eg by adding different amounts of an inhibitor to an enzyme+substrate and measuring the reaction rate or amount of products. From this, Kd can be calculated (with some assumptions).

Is possible to calculate dH (change in enthalpy) and dS (change in entropy) from running this experiment several times at different temperatures?

The idea is that dG (Gibbs free energy) can be calculated from Kd (or IC50) as dG = - RT ln Kd. Also dG = dH - TdS, so most of the variation of dG with temperature in the second equation would come from the TdS term which enables dH and dS to be fitted from dG at several temperatures. Can dH be assumed to be relatively flat with temperature? How about dS? (this is over a relatively narrow range where bio experiments can be carried out, let's say 5C to 40C)

• Yes, $\Delta H$ and $\Delta S$ can likely be considered approximately constant over this small temperature range. For example, the van't Hoff equation usually fits data pretty well despite assuming $\Delta H^\circ$ and $\Delta S^\circ$ are constant. Dec 29, 2022 at 13:09