Equivalence of charge imbalance and external electric fields during free energy calculations of membrane electroporation

Abstract

Electric fields across lipid membranes play important roles in physiology, medicine, and biotechnology, rationalizing the wide interest in modeling transmembrane potentials in molecular dynamics simulations. Transmembrane potentials have been implemented with external electric fields or by imposing charge imbalance between the two water compartments of a stacked double-membrane system. We compare the two methods in the context of membrane electroporation, which involves a large change of membrane structure and capacitance. We show that, given that Ewald electrostatics are defined with tinfoil boundary conditions, the two methods lead to (i) identical potentials of means force (PMFs) of pore formation and expansion at various potentials, demonstrating that the two methods impose equivalent driving forces for large-scale transitions at membranes and (ii) to identical polarization of water within thin water wires or open pores, suggesting that the two methods furthermore impose equivalent local electric fields. Without tinfoil boundary conditions, effects from external fields on pore formation are spuriously suppressed or even removed. Together, our study shows that both methods, external fields and charge imbalance, are well suitable for studying large-scale transitions of lipid membranes that involve changes of membrane capacitance. However, using charge imbalance is technically more challenging for maintaining a constant transmembrane potential since it requires updating of the charges as the capacitance of the membrane changes.

Dynamic Second Harmonic Imaging of Proton Translocation Through Water Needles in Lipid Membranes

“…ξ ch is a coordinate that quantifies the degree of connectivity of defects across the bilayer for 0.1 < ξ ch ≲ 0.8 or the size of the defect for ξ ch ≳ 0.8. ξ ch = 0.1 and ξ ch = 1 correspond to an unperturbed membrane and to a completely open pore, respectively. 55,57 PMF calculations along ξ ch have previously been used to quantify the effects of membrane-active peptides 66 or polymers, 67 small molecules, 68 or electric fields 69 on pore formation. The MD snapshot of Figure 3A shows a transient aqueous defect (water needle) obtained at ξ ch = 0.74.…”

Efficient Simulations of Solvent Asymmetry Across Lipid Membranes Using Flat-Bottom Restraints

“…On some occasions, the limitations with modeling the lipid asymmetry can be surmounted by including the membrane potential via an applied external electric field instead of explicitly modeled ion imbalance. While these two approaches have similar effects on the bilayer properties 24 as well as on the energetics of membrane pore formation, 25 this is not always sufficient. If ions or other charged molecules play a role beyond inducing the potential, such as in the case of specific protein−ion interactions, 26,27 the electric field approach is clearly inadequate.…”

Efficient Simulations of Membrane and Solvent Asymmetry With Flat-Bottom Restraints

“…On some occasions, the limitations with modeling the lipid asymmetry can be surmounted by including the membrane potential via an applied external electric field instead of explicitly modeled ion imbalance. While these two approaches have similar effects on the bilayer properties 22 as well as on the energetics of membrane pore formation, 23 this is not always sufficient. If the role of ions or other charged molecules is not only to induce the potential, such as in the case of specific protein-ion interactions, 24,25 the electric field approach is clearly inadequate.…”