# Molecular Simulation/Membrane permeability

The flux of a solute across a membrane is calculated from its permeability coefficient, *P*, and the concentration gradient across the bilayer (ΔC)

*P* can be calculated using molecular simulation using the solubility-diffusion model,^{[1]}^{[2]}

*w(z)* is the potential of mean force of the solute along the transmembrane axes, *z*. D(z) is the diffusion coefficient profile. The interval [L,-L] spans the membrane.

## Derivation edit

The solubility diffusion model can be derived from the Nernst-Planck equation,

In this equation, J(z) is the flux of the solute through the membrane at the depth z . C(z) is the concentration of the solute. w(z) and D(z) are the potential of mean force and diffusivity, respectively.

## References edit

- ↑ Marrink, Siewert-Jan; Berendsen, Herman J. C. (1994). "Simulation of water transport through a lipid membrane".
*The Journal of Physical Chemistry*.**98**(15): 4155–68. doi:10.1021/j100066a040. - ↑ Awoonor-Williams, Ernest; Rowley, Christopher N. (2016). "Molecular simulation of nonfacilitated membrane permeation".
*Biochimica et Biophysica Acta (BBA) - Biomembranes*.**1858**(7): 1672–87. doi:10.1016/j.bbamem.2015.12.014.