Isothermal titration calorimetry

[Quickdry135]

Homework Statement

Using isothermal titration calorimetry, you calculate $$\Delta$$H$$^{o}_{bind}$$ (= -5000 cal/mol) for a protein-ligand binding reaction at 25°C. You then perform a separate assay in which you measure equilibrium ligand binding at two different temperatures:

L$$_{0}$$ (nM) Ceq (nM) at 25°C Ceq (nM) at 37°C
0.01 :: 0.007 :: 0.006
0.03 :: 0.021 :: 0.017
0.1 ;: 0.070 :: 0.058
0.3 :: 0.197 ;: 0.166
1 :: 0.537 :: 0.439
3 ;: 0.830 :: 0.778
10 :: 0.943 :: 0.930
30 :: 1.002 :: 0.964
100 :: 0.981 :: 1.009

What is $$\Delta$$S$$^{0}_{bind}$$ at 37C

Homework Equations

$$\Delta$$G$$^{0}$$=RTlnK$$_{D}$$

$$\Delta$$G=$$\Delta$$G$$^{0}$$ + RTln[L]$$_{eq}$$/[P]$$_{eq}$$[L]$$_{eq}$$

$$\Delta$$G=$$\Delta$$H-T$$\Delta$$S

The Attempt at a Solution

I can find K$$_{d}$$ graphically and therefore find $$\Delta$$G$$^{0}$$ to be -12300.1 cal. At the same temperature, $$\Delta$$G$$^{0}$$=$$\Delta$$G at 25C, so i can find \DeltaS at 25C. But I don't know how this helps me find $$\Delta$$S$$^{0}_{bind}$$ at 37C or if this helps me at all.

thanks for any help or direction

 

[Quickdry135]

never mind, I think i figured it out using the van't hoff equation to find delta H at 37C since I can find the different Kds and am given the different temperatures.

 

[Blueshift5]

you can give me


I would respond by saying that the data provided suggests that the binding reaction is exothermic (\DeltaH^{o}_{bind} = -5000 cal/mol) and that the change in enthalpy and entropy at 25°C can be calculated using the equations \DeltaG^{0}=RTlnK_{D} and \DeltaG=\DeltaH-T\DeltaS. However, in order to calculate \DeltaS^{0}_{bind} at 37°C, we would need to also know the change in enthalpy at that temperature. This can be calculated using the relationship \DeltaH^{o}_{bind} = \DeltaH^{o}_{bind} + \DeltaC_{p}\DeltaT, where \DeltaC_{p} is the change in heat capacity and \DeltaT is the change in temperature (37°C - 25°C). Once we have the value for \DeltaH^{o}_{bind} at 37°C, we can use the equation \DeltaG=\DeltaH-T\DeltaS to calculate \DeltaS^{0}_{bind} at that temperature. It would also be helpful to have more data points at different temperatures in order to accurately calculate the change in enthalpy and entropy over a range of temperatures.