I am planning on doing some ligand relative binding free energy calculations using pmx that involve charged mutations. The recommended protocol seems ‘one box two systems’. If I apply this to my problem, I would build two boxes in total:
box1: Mutating Protein-Ligand 1 → Protein- Ligand 2 and Ligand 2 → Ligand 1
box2: Mutating Protein-Ligand 2 → Protein- Ligand 1 and Ligand 1 → Ligand 2
If my understanding is correct, for one fast transition in box1 you basically sum the work for Protein-Ligand 1 → Protein- Ligand 2 and Ligand 2 → Ligand 1. This allows you to calculate the free energy difference by only two simulations, essentially calculating ΔGPL1,PL2 + ΔGL2,L1 instead of ΔGPL1,PL2 - ΔGL1,L2.
To keep the ligand in water system seperate from the protein-ligand system, positional restraints are applied on one central atom. This way translational entropy is impacted, but not the rotational entropy. In literature it is then explained:
The contribution of such position restraints to the translational partition function will be the same in both legs of the thermodynamic cycle and will cancel from the ΔΔG estimate.
Based on this, I have the following questions:
1 ) Am I correct in understanding that the contibution of the positional restraints cancel out because the free energy difference of restraining Ligand 1 is almost the same as the free energy difference of restraining Ligand 2? I have provided a pdf as attachment with the thermodynamic cycle and some equations to clarify this question. Is the analysis in the pdf correct?
2) If my understanding is correct, then I assume that “one box two systems” is only valid for small transformations. Is this correct?
3) If my understanding is not correct, how exactly does the effect of restraining translation cancel out?
doc17-11-2023_0_22.214.171.1243.pdf (585.9 KB)