Calculate diffusion coefficients for umbrella sampling

GROMACS version: 2021
GROMACS modification: No

I have performed an umbrella sampling protocol pulling a small molecule through a lipid membrane. I have 44 windows simulated for 20ns to reach convergence. I would like to calculate the permeability of this small molecule through the membrane but for this I require the diffusivity at each point along the US trajectory. How would I go about calculating these diffusivity values?

At first I assumed I could use gmx msd on each window and plot these points in line with their PMF values however I have nearly 5 fold more PMF values then I do diffusivity.
Could one fit a line to these values corresponding to their z positions and then calculate a value for diffusion for each PMF point from this fitted line?

Some feedback on best practice would be brilliant, if there is a more succinct way around this without fitting a line that would be ideal as it is a technique I haven’t much experience in.

The umbrellas, which by definition need to be tight, will destroy any kinetic information.

A fruitful method is using AWH instead of umbrella sampling. AWH will give you both the PMF and the diffusion constant as a function of the reaction coordinate.

Are the any good tutorials for applying Umbrella Sampling or AWH to small molecule permeability of a membrane?

I don’t know of tutorials. Here is a paper using AWH to compute permeabilities: