Constant Electric Field and Membrane Voltage in GROMACS

User discussions
1

Dear GROMACS developers and users,

I would like to ask for clarification regarding the interpretation of a constant electric field applied to a membrane system using electric-field-z in GROMACS, particularly how the corresponding transmembrane voltage should be defined.

Consider a membrane-protein system whose membrane normal is aligned with the z direction and which is simulated using periodic boundary conditions (PBC) and PME electrostatics. A constant electric field can be applied along the membrane normal using electric-field-z.

I would greatly appreciate clarification on the following points:

  1. For a membrane system simulated with PBC and PME, is the nominal applied voltage associated with electric-field-z given by

V = E × Lz

where Lz is the full simulation-box length along the direction of the applied field?

In other words, if the goal is to simulate a specified transmembrane voltage V, should the input electric field be determined as

E = V / Lz

rather than using the physical thickness of the membrane?

  1. From a physical point of view, if most of the electrostatic potential drop becomes localized within the low-dielectric membrane region after dielectric response, V / Lmem could be regarded as an estimate of the average total electric field within the membrane.

Should this quantity be distinguished from the constant applied field specified by electric-field-z?

In particular, would it be incorrect to use V / Lmem directly as the input value for electric-field-z?

  1. Is the following interpretation appropriate?

E × Lz represents the nominal/applied voltage imposed on the periodic simulation cell, whereas the actual spatial electrostatic-potential profile V(z), including the potential difference between the bulk-water regions on the two sides of the membrane, results from the response of water, ions, lipids, and proteins and should therefore be determined separately from the simulation trajectory.

In other words, should one avoid interpreting E × Lmem directly as the actual transmembrane potential?

  1. If the simulation is performed under NPT conditions, Lz fluctuates with time while the value of electric-field-z remains fixed. Does this imply that the instantaneous nominal applied voltage also fluctuates according to

V(t) = E × Lz(t)?

If a specific target membrane voltage is desired, is it generally recommended to determine E using the average equilibrated box length?

  1. The current GROMACS documentation also notes that the interpretation of constant-field simulations under Ewald electrostatic boundary conditions may become more complicated when the dielectric properties of the system change significantly during the simulation, for example when a membrane-protein pore opens or closes.

For simulations investigating voltage-induced conformational changes in membrane proteins, how should this limitation generally be considered? Is V = E × Lz still the appropriate relation for defining the nominal applied voltage in such cases?

Thank you very much for your help.

2

When applying an electric field over a system with very high dieletric (e.g. water) and low dieletric regions, de voltage drop is going to be nearly completely concentrated in the low dielectric region. That is why V = E x Lz can be used as the voltage of the membrane.

Lz will fluctuate negligibly, so in practice you can assume V is constant.

For membrane protein there will be an issue when you have a water chain that connects all the way through the protein.