[icecreamxl]

Anybody can help for calculation of the heat of the following reaction?

Some background:
Ligand X bind to protein M, the product is MX. Binding affinity of X to M is K = [MX]/([M]*[X]).
[MX], [M], [X] are the concentrations of each stuff after the reaction finished.
The ratio of MX to total M is θ = [MX]/([M]+[MX]).
ΔH is the molar heat of M, V is the volume of reaction.
Mt and Xt is the concentration of total M and X at the beginning of the reaction.
So, for this reaction the heat Q = θ*Mt*ΔH*V

My Question is:
The beginning products: Xt= 50 uM, Mt=400 uM, also some [MX] = 4 um, ( Mt is the total concentration of M, including the M in MX),
V=200 ul, K= 100000 M-1, and ΔH =-4000
How to calculate the heat Q for above reaction?

Tons of thanks!!

[icecreamxl]

I guess it is hard to calculate θ, just leave it in the final answer

[billnotgatez]

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[Plontaj]

The main problem is how to calculate the conversion θ of M.

You have to develop one equation (equilibrium constant) to get one variable in it. I propose it as Z (concentration change of M).

For the start of the raction we get:
[M] = Mt, [X] = Xt, [MX] = MXt
Caused by reaction the molar change is:
-Z for [M], -Z for [X], +Z for [MX]
so in equilibrium their concentrations are:
[M] = Mt - Z, [X] = Xt - Z, [MX] = MXt + Z

Combining above expressions with constant we get:
K = [MX]/([M]*[X]) = (MXt + Z)/((Xt - Z)*(Mt - Z))
what is the quadratic equation - two solutions.

Now you should calculate the initial conversion θint of M, because it wasn't equal 0 at the beginning of the reaction. At last you have to calculate the final conversion θfin of M.

In heat equation you should put the difference between final and initial conversion (θfin - θint).

This is only an example of solution. There are many others possibilities.