Introduction

1. Life Cycle of an Electropore: A Molecular Dynamics Investigation of the Electroporation of Heterogeneous Lipid Bilayers (PC:PS) in the Presence of Calcium Ions Zachary A. Levine1,2, Matthew J. Ziegler1,3, and P. Thomas Vernier1,4 1 MOSIS, Information Sciences Institute, Viterbi School of Engineering (VSoE), University of Southern California (USC), Marina del Rey, USA 2 Department of Physics and Astronomy, College of Letters, Arts, and Sciences, USC, Los Angeles, USA 3 Mork Family Department of Chemical Engineering and Materials Science, VSoE, USC, Los Angeles, USA 4 Ming Hsieh Department of Electrical Engineering, VSoE, USC, Los Angeles, USA, Introduction Pore Annihilation — Another View Internal Electric Field Dependence To aid in understanding electric field-driven pore formation in lipid bilayers, we propose a scheme for characterizing the life cycle of a transient membrane electropore, from the formation of the initial defect to the restoration of the intact bilayer. We apply this analysis to heterogeneous phospholipid bilayers (phosphatidylcholine:phosphatidylserine, PC:PS) in the presence of calcium ions. Previous reports of molecular dynamics (MD) simulations of PC:PS systems containing Ca2+ [1,2] are consistent with experimental observations [3]. We report here the effects of PS and Ca2+ on pore creation and annihilation time. Systems containing either Ca2+ or PS are more difficult to electroporate and have shorter pore lifetimes at low porating electric fields. At higher fields PS and Ca2+ have little effect on pore creation and annihilation times. We also report the binding isotherm for Ca2+ and PC:PS bilayers, a metric for the validity of phospholipid bilayer simulations containing calcium. There is an exponential relationship between the pore creation time and the bilayer internal electric field. Each point is averaged over three trials. PS and Ca2+ do not significantly modify the magnitude of the internal electric field (data not shown). Methods All simulations were performed using the GROMACS 3.3.3 software package. Bilayers consisted of 128 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) lipids and 9006 water molecules. Mixed bilayers were obtained by replacing 20 phosphatidylcholine (PC) molecules on one leaflet with 20 phosphatidylserine (PS) molecules and then equilibrating until the total area per lipid was constant. Pore life cycles were determined using custom Perl scripts which follow the criteria described below. For pore creation in the presence of calcium we used the GROMACS function ‘genion’ to replace bulk water molecules with calcium ions, after which the system was equilibrated for 150 ns. For calcium effects on pore annihilation the calcium was inserted at the same time that the external electric field was removed. Stages of pore annihilation are demarcated by the number of cathode phosphorus atoms which are 1.2 nm away from an anode phosphorus atom, and by the number of waters present in the bilayer interior (0.1 nm from the midplane). Note in this plot from a typical simulation the period of destabilization before the pore begins to degrade. Pore Creation Time at Higher Fields Life Cycle of an Electropore 400 MV/m 600 MV/m At high electric fields the effects of PS and Ca2+ on pore creation are much less pronounced in absolute terms. Simulations with greater time resolution are required to establish whether the effects are still operative at higher fields. The electropore life cycle has two broad divisions. Pore creation is the period from the application of an external electric field to the appearance of a mature pore (a pore which contains at least 10 cathode phosphorus atoms at a distance of no more than 1.2 nm from anode phosphorus atoms [4]). Pore annihilation begins with the removal of the electric field and ends with the permanent separation of water groups (determined by density profiles across the membrane interior). Pore creation and annihilation are divided into substages based on the connections of water and phosphorus groups. PS and Ca2+ — Pore Creation Pore Annihilation from Another View Values averaged over three simulations with Eexternal = 400 MV/m. Pore Creation Calcium Binding Isotherm Calcium binding to the bilayer interface in our simulations resembles the 1:2 Langmuir binding isotherm established by experiment [3]. Values are calculated after the system has equilibrated for 150 ns. This observation shows the operational validity of the calcium ion model in Gromacs. PS and Ca2+ — Pore Annihilation Initiation Construction Maturation Values averaged over four simulations with a pore-initiating Eexternal = 400 MV/m. H2O Group Merger P Connections  10 P Group Merger E = Eporating Annihilation Conclusions Identification of the stages in the life cycle of an electropore provides a scheme for characterizing the mechanisms of pore creation and annihilation. Calcium and PS increase pore creation time and decrease pore annihilation time at low porating electric fields. At higher fields, these effects are minimal. Pore creation times appear to depend exponentially on the bilayer internal electric field. MD simulations containing calcium show binding isotherms similar to those observed in experiment. 1. Böckmann, R. A., and H. Grubmüller. 2004. Multistep binding of divalent cations to phospholipid bilayers: A molecular dynamics study. Angewandte Chemie-International Edition 43:1021-1024. 2. Vernier, P. T., M. J. Ziegler, and R. Dimova. 2009. Calcium binding and head group dipole angle in phosphatidylserine-phosphatidylcholine bilayers. Langmuir 25:1020-1027. 3. Sinn, C. G., M. Antonietti, and R. Dimova. 2006. Binding of calcium to phosphatidylcholine-phosphatidylserine membranes. Colloids and Surfaces A -Physicochemical and Engineering Aspects 282:410-419. 4. Sengupta, D., H. Leontiadou, A. E. Mark, and S. J. Marrink. 2008. Toroidal pores formed by antimicrobial peptides show significant disorder. Biochimica et Biophysica Acta-Biomembranes 1778:2308-2317. Computation for this work was supported by the University of Southern California Center for High-Performance Computing and Communications (www.usc.edu/hpcc). Special thanks to MOSIS for providing additional resources and funding for this project. Stabilization Degradation Deconstruction Dissolution H2O Separation P Separation ≥ 10 P Connections P Connections  1 E = 0