I'm having a go at calculating the free energy of solvation of two small proteins, as separate systems. I am using the Bennett Acceptance Ratio approach by coupling the coloumbic and van der Waals terms to the parameter lambda (usual approach), simulated in Gromacs.
The first system will be relatively easy to set up and get running, there is no charge.
Unfortunately, the second system has two positively charged side chains. That's fine when I am performing a 'regular' simulation, but using soft potentials during the adjustment to the lambda parameter will put my system into a none net-neutral (fractional) charge.
I thought about including the counterions as part of lambda, but my free energy value would include the contribution of two calcium ions being solvated. I then thought of modeling the alchemical transition of calcium ions in water, but again, I would need counterions for that particular setup.
Any thoughts on how I could solve this problem?
What about using a B-state topology for the charged side chains and defining them to zero. But, I am not sure it would be same or equivalent to the counter ion transformation approach.
Hi Bipin,
Could you explain the idea of your approach? If by "B-state topology" you are describing dual topology, then I have done this before using PMX for single point mutations of amino side chains in a protein. I am not sure how this could be applied in a free energy of hydration/solvation calculation.
Thanks
Hi Anthony,
My idea is, that at the starting of the simulation i.e. at lambda=0, all the atoms will have their usual partial charges (A-state), as we proceed to lambda=1, the partial charges of the charged side chains are set to zero (by defining them as B-state) to make the overall system neutral at the end of simulation.
You can find an example at the section "5.7.4 Topologies for free energy calculations" of Gromacs-5.0.1 manual.
Hi Bipin,
Thanks for the suggestion. As I had said earlier, this is a simple hydration/solvation idea, so essentially at lambda=0 the protein is fully solvated and at lambda=1 all interactions are off as it has essentially moved into a gas phase out of the solvent box, although this can also be performed the other way around. Check out, http://www.gromacs.org/@api/deki/files/177/=fe_tutorial.pdf section on "Free Energy of Solvation". Therefore, there is no B-state of the charged amino acid side chain. The problem lies with the two counter ions that are in the solvent to have neutralised the charge at lambda=0, are always creating a fractional charge as the protein is driven along lambda, until lambda=1 and the protein is essentially no longer there, leaving the system in a -2 ve state.
Hi Anthony,
I understand what you are trying to do. I am suggesting that rather than keeping all the partial charges "on" at lambda=0, it might be possible to switch off the partial charges of charged side chains to zero in order to represent a neutral system. Or the other way round.
Oh right! That makes perfect sense. Thanks.
Yes, in essence, that would work. I'm now left with the question of whether that is a biologically feasible system to then model. At pH 7, the charge on arginine and lysine will be +1.
If there are some lysine or arginine residues sticking out into the bulk water, setting the net charges (not the partial charges) of two of them to zero should be a reasonable approach.
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I have charge models of neutral arginine and lysine (same topology as charged residues, but different partial charges) compatible with AMBER94 force field . . .
Hi Martin,
So to reiterate just to make sure I am understanding what you said, rather than remove the partial charge altogether, simply turn my charged arginine (and charged lysine) into their non-charged equivalent selves?
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