Hi,

check my paper (Antibiotic uptake across gram-negative outer membranes: better predictions towards better antibiotics). It was done for antibiotics, but the technique was initially applied for water molecules crossing channels or membranes.

Dear Budheswar Dehury

Usually you can calculate the permeability via the inhomogeneous-solubility diffusion model, which requires the free energy profile and the diffusion coefficient along the reaction coordinate of choice. In your case this will probably be the transbilayer axis which is also the axis of the acquaporin.

There are different ways to calculate both the diffusion coefficient and the potential of the mean force. Via equilibrium MD you can use umbrella sampling with WHAM or the average force acting on the COM of the permeant to calculate the free energy profile and then methods based on the autocorrelation of position, velocities or forces to calculate the diffusion coefficient.

A good review to get started on diffusion is [Awoonor-Williams E., Rowley C.N.][2016] Molecular Simulation of Nonfacilitated Membrane Permeation.

For the inhomogeneou solubility diffusion model and the calculation of free energy and diffusion profiles look at pioneering work from Marrink and Berendsen

[Marrink S.J., Berendsen H.J.C.][1996] Permeation Process of Small Molecules Across Lipid Membranes Studied by Molecular Dynamics Simulation

[Marrink S.J., Berendsen H.J.C.][1994] Simulation of Water Transport Through a Lipid Membrane

[Berendsen H. J. C. et al.][1993] Molecular dynamics of water transport through membranes - Water from solvent to solute

for the diffusion coefficient from autocorrelation of position or velocities look at

[Gaalswyk K., Awoonor-Williams E., Rowley C.N.][2016] Generalized Langevin Methods for Calculating Transmembrane Diffusivity

which also offer the tool to compute the relevant quantities.

If you want to use non equilibrium MD, like SMD, then for sure there is the forward reverse method

[Kosztin I., Barz B., Janosi L.][2005] Calculating Potentials of Mean force Diffusion Coefficients from Nonequilibrium Processes Without Jarzynski's Equality

which can also be extended via the Chen correction

[Chen L.Y.][2008] Nonequilibrium Fluctuation-Dissipation Theorem of Brownian Dynamics

to obtain a weighted forward-reverse method as implemented for example in

[Lundborg M. et al.][2018] Predicting Drug Permeability Through Skin Using Molecular Dynamics Simulation

There are other non equilibrium methods, albeit the Jarzynski equality equality is delicate and needs the sampling of rare states (as explained in the latter paper from Kosztin), so I personally prefer to use both forward and reverse trajectories (recently US + WHAM has also been compared to Jarzisnki and overall it seems better to not use steered MD with just one trajectory, see [Noh S.Y. et al.][2020] Comparison of Umbrella Sampling and Steered Molecular Dynamics Methods for Computing Free Energy Profiles of Aromatic Substrates through Phospholipid Bilayers).

There are other methods, like Bayesian ones to calculate the diffusion, but they are quite hard to implement with respect to other approaches that are naturally built in MD softwares like GROMACS. I think a very common way to proceed for channels is dividing the system in windows and go with WHAM for the free energy profile and then couple an autocorrelation method (forces, position or velocities) to calculate the diffusion. Probably forces and position are the more natural given that the force and the position of the COM of the permeant are the standard input for WHAM prediction, therefore you can derive both free energy profile and diffusion from the same set of data.

Hope this helps,

Nicola

Hi again,

in July 10 (or August 7 for the eBook) a detailed step-by-step methodology for calculating permeabilities (for GROMACS) will be published, with all the advantages, drawbacks and expected caveats.

You can check here on this link:

https://www.springer.com/gp/book/9781071614679

Ricardo J Ferreira thank you so much for your kind inputs and suggestion. I am having trouble in gmx select and defining the index group to compute the water that passes through pore of each monomer. Could you please help me?

Nicola Piasentin thank you so much for detailed inputs . I am not interested to calculate the PMF or Free energy profile ..Just I am interested to compute the osmotic water permeability (Pf), I need the statistics or exact value by computing the permeation events in the MD trajectory..

If you have suggestion regarding scripts in python please let me know..

With regards

Budheswar

Dear Budheswar Dehury

Not really sure about the permeation events since I think that they can be usually very uncommon on the time scales of typical MD simulations.

Take a look at

Article Water Transport in Aquaporins: Osmotic Permeability Matrix A...

Article Osmotic Water Permeation through a Carbon Nanotube

Article Osmotic water permeability of aquaporin-1 under radial tensi...

If you are having permeation through the acquaporin and you want to count the events than you should probably use dynamical selection of water molecules, that is you define geometrically the region corresponding to your channel and let gromacs select dynamically the water molecules entering in this region along the whole trajectory. Take a look at gmx select (https://manual.gromacs.org/documentation/current/onlinehelp/gmx-select.html)