What is membrane-partitioning free energy? Can it be simulated?
In the biological context, membrane-partitioning is usually referring to the stage in which the transmembrane-destined region of a protein moves from interacting with the water, to interact with the interface of the membrane. 

In the diagram below showing a four step thermodynamic cycle, the partitioning free energy can be referred to as-is ΔGwiu in terms of free energy where w is water, i is the interface, and u is unfolded. The image comes from the same paper that introduced the famous Wimley and White octanol-interface scale from 1999.



Note that in a more recent 2015 article, they comment that the partitioning phase ΔGwiu is generally the only experimentally accessible step. With that in mind, simulating ΔGwif where f is the folded helix becomes necessary. This 2014 Nature Comms paper use folding-partitioning molecular dynamics simulations to estimate the free energies that are experimentally inaccessible. They used Gomacs 4.5. In fact, a study using a simulation from 2005 suggests that folding isn't necessarily required for insertion of the helices. 



Note that all the information here is behind a paywall. Feel free to ask me for clarification or expansion in the comments.