# [AMBER] Query on thermodynamic integration of complexes involving metal ions

From: Muthukumaran Rajagopalan <kumaran.bicpu.edu.in>
Date: Wed, 31 Jan 2018 18:46:02 +0530

Dear AMBER users,

I am performing thermodynamic integration for the disappearing of few ions in protein complex.
I am using Sander to convert an ion (initial state) to a dummy atom (final state).
Initially, I create a lib file for the initial state. Then change the atom name of the ion to DN (Dummy atom) and charge to 0 in the .lib file to use as final state. I also load an .frcmod file to define the DN atom type with 0 non-bonded parameters.
I am modifying both the charge and vdw parameters at the same time to make the ion disappear.

I am following the tutorial in the below link as a starting point.
http://www.rosswalker.co.uk/tutorials/psc_workshop/Tutorial_seven/

Since an ion disappears in the perturbed state, I am also using klambda=4.
I have tried with 3 clambda points as well as 9 points using the lambda and weight values given in amber tutorial.
As an example, I have shown the dv/dl averages for both 3 point and 9 point simulations.

charge+vdw; 3-point integral

deltaG of ligand in water
(154.3493*0.27777)+(92.5205*0.44444)+(28.6495*0.27777)
91.951387696

deltaG of complex in water
(162.1025*0.27777)+(115.3253*0.44444)+(46.1965*0.27777)
109.114389562

17.163001866

charge + vdW perturbation 9 point integral

deltaG of ligand in water
(173.5368*0.04064)+(162.0287*0.09032)+(143.6997*0.13031)+(119.1542*0.15617)+(92.7112*0.16512)+(64.9622*0.15617)+(40.2767*0.13031)+(22.7675*0.09032)+(0.3334*0.04064)
91.792773928

deltaG of complex in water
(177.4860*0.04064)+(179.4916*0.09032)+(157.9280*0.13031)+(138.5222*0.15617)+(113.0255*0.16512)+(80.1116*0.15617)+(60.2231*0.13031)+(38.9880*0.09032)+(-6.7603*0.04064)
107.905450867

16.112676939/

deltaG of ligand in water (klambda 4)
(621.0709*0.04064)+(391.0648*0.09032)+(165.8701*0.13031)+(45.9019*0.15617)+(8.6732*0.16512)+(-0.5524*0.15617)+(-2.3720*0.13031)+(-2.0549*0.09032)+(-1.0472*0.04064)
90.152924946

deltaG of complex in water (klambda 4) with restraints
(626.9129*0.04064)+(488.8959*0.09032)+(266.8167*0.13031)+(117.8476*0.15617)+(37.3120*0.16512)+(9.5520*0.15617)+(1.9104*0.13031)+(0.1281*0.09032)+(0.0008*0.04064)
130.721201821

40.568276875

The use of klambda=4 makes a huge difference in the obtained deltadeltaG.
When I check the elec and vdw energies, the elec energies contribute almost entirely to the dv/dl (ex. dv/dl=470.0083; elec=488.4165; vdw=-18.4082).
This is understandable because, the ion-protein interaction is majorly electrostatic.

Also, even with a restraint weight of 10, the ions move from their initial positions and so the energies may not be reliable.

How do I decide the number of clambdas required for my system. My system is relatively small (~700 atoms) and highly charged (~-20).
How do I handle the ion movement. Position restraints doesnt seem to work.

Any suggestions and pointers regarding this would be very helpful.