# Enthalpy-Entropy contributions for PMF in an umbrella sampling

GROMACS version: 2018.7
GROMACS modification: No

Dear Gmx users,
I performed the umbrella sampling simulations of a peptide on the membrane. I extracted PMF as discussed in prof. Justin’s tutorial. I would like to analyze deeply, if you do not mind please suggest some possible analyses?

I also want to know about the Enthalpy-Entropy contributions, separately. Is there any analysis tool in gromacs?

Best regards,

Mijiddorj

No, but you can compute ΔH and ΔS from the van’t Hoff relation by running umbrella sampling at multiple temperatures.

Ideally, I would use NPT ensemble to calculate temperature dependence of Gibbs free energy ΔG = ΔH - TΔS,
whereas NVT ensemble directly calculates the Helmholtz free energy ΔF = ΔU - TΔS = ΔH - VΔP - TΔS.
The assumption here is that the ΔS is temperature independent.

Dear Justin,
I run the umbrella sampling at three temperatures: 300K, 310K, and 320K.
I used the PMF at 300 and 320K to obtain the entropy at 310K, how can I estimate the uncertainty for my calculation of entropy?
Best regards,

Using error propagation. All values that go into your calculation have uncertainties.

Dear professor David,
when using error propagation, the error in entropy estimation will be amplified largely.

When using g_WHAM to derive the PMF profiles, I used Bayesian bootstrap with 200 bootstraps.
Is it reasonable if I used bootstrap sampling again to calculate the difference between 200 PMF profiles at 320K and 200 PMF profiles at 300K? this give me a much smaller error.

Best regards,

Typically we report unrealistically small errors based on any MD calculation since we ignore important error sources. Your task is to provide a realistic error estimate, not a small error estimate. It would be helpful if you provide the Delta G you get at both T with uncertainty estimate.

Another method that you can use is to use the potential energy at 310 as a proxy for the enthalpy. But the potential energy typically converges slower, also leading to large error bars.

Here are a couple of papers where we used that:

Carl Caleman, Jochen S. Hub, Paul J. van Maaren and David van der Spoel: Atomistic Simulation of Ion Solvation in Water Explain Surface Preference of Halides Proc. Natl. Acad. Sci. U.S.A. 108 pp. 6838-6842 ( 2011 )

Jochen S. Hub, Carl Caleman and David van der Spoel: Organic molecules on the surface of water droplets - An energetic perspective Phys. Chem. Chem. Phys. 14 pp. 9537-9545 ( 2012 )

Haiyang Zhang, Tianwei Tan, Csaba Hetényi and David van der Spoel: Quantification of solvent contribution to the stability of non-covalent complexes J. Chem. Theor. Comput. 9 pp. 4542-4551 ( 2013 )

Dear professor David,
In the attachment is dG together with standard deviation. Please have a look

bs_res_320K.xvg (16.1 KB) bs_res_300K.xvg (16.2 KB)

Best regards,

What numbers do you get when you integrate from the minimum to infinity taking error bars into account?

sorry, I didn’t get your point. could you clarify it?

What do you want to get out of your calculation? I had interpreted this as if you would like to compute Gibbs energy of association between the peptide and the membrane, right?

So what is the energy of association? If those plots you sent are energies and not forces you can just read it off the curves, the energies are tiny though, less than kT.

However, if I were to referee a paper about this I would ask how the rotational and conformational degrees of freedom are taken into account.

Dear Professor David,