[gmx-users] seeming paradox with gmx wham

[Alex]

Hi all,

I am looking at what appears to be a paradox. Consider the following 
situation: we have a graphene membrane with a single pore of a 
particular type. The pore is located at (x0, y0, h/2), where h is the 
box height. The membrane is position-restrained along its perimeter and 
immersed in a solution of NaCl. The pore is designed to trap anions -- 
and it does, if you artificially bring an anion close enough to the 
mouth of the pore and run the simulation at, say, room temp.

However, the ions do not bind by themselves. 100s of nanoseconds of 
simulations with high salt concentrations -- nothing. So, I expect a 
high barrier associated with ion dehydration when entering the pore. 
Following Justin's tutorial and generating a total of 30 1A-spaced 
configs (15 below h/2, 15 above h/2) along (x0,y0), gmx wham yields a 
6.5 kJ/mol barrier, which isn't high at all! Just from the pullf data 
when generating the configs (pull along Z with x and y restrained), the 
naive integral of the pulling force prior to overcoming the hydration 
barrier yields 4 kJ/mol -- consistent with the WHAM result. But in 
reality, ions (which aren't restrained around (x0,y0) are not observed 
to bind, which brings us to my question...

It looks like when an ion approaches the pore parallel to the membrane 
normal, the barrier is indeed low, while approach at an angle yields 
higher barriers. It appears that WHAM produces the free energy curve 
resulting from frequent sampling approach directions that have the 
lowest possible barrier. Is it possible to modify this calculation to 
give equal weight to all approach directions?

Thank you,

Alex