Molecular Simulations Reveal the Free Energy Landscape and Transition State of Membrane Electroporation

The formation of pores over lipid membranes by the application of electric fields, termed membrane electroporation, is widely used in biotechnology and medicine to deliver drugs, vaccines, or genes into living cells. Continuum models for describing the free energy landscape of membrane electroporation were proposed decades ago, but they have never been tested against spatially detailed atomistic models. Using molecular dynamics (MD) simulations with a recently proposed reaction coordinate, we computed potentials of mean force of pore nucleation and pore expansion in lipid membranes at various transmembrane potentials. Whereas the free energies of pore expansion are compatible with previous continuum models, the experimentally important free energy barrier of pore nucleation is at variance with established models. The discrepancy originates from different geometries of the transition state; previous continuum models assumed the presence of a membrane-spanning defect throughout the process, whereas, according to the MD simulations, the transition state of pore nucleation is typically passed before a transmembrane defect has formed. A modified continuum model is presented that qualitatively agrees with the MD simulations. Using kinetics of pore opening together with transition state theory, our free energies of pore nucleation are in excellent agreement with previous experimental data.

Figure 1

(a)–(c) Simulation snapshots of pore nucleation and (c)–(e) pore expansion. Lipid headgroups are shown as green spheres, tails in gray, water within the membrane as red and white spheres, and other water as red and white sticks. The respective positions along the reaction coordinate ${\xi }_p$ and pore radius $R$ are shown in the panels. (f),(g) Potentials of mean force (PMFs) for pore nucleation and pore expansion across a DPPC membrane at transmembrane voltages between 0 and 500 mV [for color code see panel (f)]. Lower and upper abscissas show the reaction coordinate and the pore radius, respectively. The dashed box in panel (f) indicates the region highlighted in panel (g).

Figure 2

(a) PMFs of pore nucleation at transmembrane voltages $U$ between 0 and 1900 mV (see legend) as a function of the chain coordinate ${\xi }_{\mathrm{ch}}$, which quantifies the connectivity of the transmembrane defect. (b) Free energy barrier for pore nucleation as taken from the maxima of the PMFs in panel (a). (c) Position of ${\xi }_{\mathrm{ch}}$ at the transition state. Dashed lines in panels (b) and (c) are linear fits to guide the eye. (d)–(f) MD snapshots of the transition state for voltages of 0 mV, 600 mV, or 1900 mV [panel (a), black circles], characterized by discontinuous partial defects for $U\ge 600\mathrm{mV}$.

Figure 3

Energetics of pore nucleation by the three-cylinder continuum model. (a) Gradual formation of a transmembrane defect modeled by three cylindrical capacitors in series. (b) Free energy profiles of pore nucleation for transmembrane voltages between 0 and 4500 mV (for color code, see legend); (c) free energy barrier and (d) position of the transition state [colored dots in panel (b)].

Figure 4

(a) PMFs of pore nucleation in a DPhPC membrane at voltages between 0 mV and 1200 mV (see legend). (b) Mean time of pore opening derived from MD simulations based on transition state theory and using the pore free energies (or free energy barriers, if present) in panel (a) (colored dots). Black dots: Experimental data by Melikov et al. [8].