0

5

10

15

20

25

1000 1500 2000

Po

re C

rea

tio

n T

ime

(n

s)

Membrane Einternal (MV/m)

Pore Creation Time Versus Einternal

POPC (0 PS:0 Ca)POPC (0 PS:100 Ca)POPC (20 PS:0 Ca)POPC (20 PS:100 Ca)

Electropore Life Cycles in HeterogeneousPhospholipid Bilayers in the Presence of Calcium

Zachary A. Levine1,2 and P. Thomas Vernier1,3

1 MOSIS, Information Sciences Institute, Viterbi School of Engineering (VSoE), University of Southern California (USC), Marina del Rey, CA, USA2 Department of Physics and Astronomy, College of Letters, Arts, and Sciences, USC, Los Angeles, USA

3 Ming Hsieh Department of Electrical Engineering, VSoE, USC, Los Angeles, USA,

Introduction

MethodsAll simulations were performed using the GROMACS set of programs version 3.3.3. Bilayers consisted of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) lipids. Each system contained a total of 128 lipids and at least 4480 water molecules. Mixed bilayers (a) were obtained by replacing 20 neutral phosphatidylcholine (PC) molecules on one leaflet with 20 negatively charged phosphatidylserine (PS) molecules and then equilibrating until the total area per lipid was constant.

Pore life cycles were determined using custom Perl scripts. Pore creation (b) 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 [1] from anode phosphorus atoms). Pore annihilation begins with the removal of the electric field and ends with the permanent separation of water groups, as indicated from density profiles across the membrane interior. Pore creation and annihilation are divided into stages based on the connections of water and phosphorus groups. For pore creation in the presence of calcium we used the GROMACS function ‘genion’ to place calcium ions in bulk water, 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.

Molecular dynamics simulations of electroporation of homogeneous phospholipid bilayers show that the pore creation time is strongly dependent on the magnitude of the difference between the electric field in the membrane interior and the field in the bulk medium. Here we investigate whether heterogeneous bilayers containing phospholipids with zwitterionic and anionic headgroups and different internal electric field profiles exhibit a similar dependence. To facilitate this analysis we divide the life cycle of an electropore into several stages marking the sequence of steps from pore creation through pore annihilation (re-sealing after the removal of the electric field). We also report simulations of calcium binding isotherms and the effects of calcium ions on the electroporation of heterogeneous lipid bilayers.

Ele

ctr

ic F

ield

MOSISMOSIS

Computation for this work was supported by the University of Southern California Center for High-Performance Computing and Communications (http://www.usc.edu/hpcc). Special thanks to MOSIS for providing additional resources and funding for this project.

0.40.4

0.40.9

0.1 0.1 0.10.2

0.2 0.2 0.1

0.3

0.7 0.7 0.7

1.3

0

1

2

0 PS:0 Ca 0 PS:100 Ca 20 PS:0 Ca 20 PS:100 Ca

Tim

e (

ns

)

Initiation

Construction

Maturation

Creation

10.3

8.63.8 3.84.4 5.0

3.4 4.0

27.4

35.4

10.4 11.1

1.5 0.8 1.8 1.3

43.6

49.8

19.420.2

0

10

20

30

40

50

60

70

0 PS:0 Ca 0 PS:10 Ca 20 PS:0 Ca 20 PS:10 Ca

Tim

e A

fter

Eex

tis

Rem

ove

d (

ns)

DestabilizationDegradationDeconstructionDissolutionAnnihilation

14.7

4.21.6 2.9

1.9 3.7 2.7 3.1

19.713.8

12.3

4.01.7 1.2 0.7 1.3

38.1

22.8

17.311.3

0

10

20

30

40

50

60

70

0 PS:0 Ca 0 PS:10 Ca 20 PS:0 Ca 20 PS:10 Ca

Tim

e A

fter

Eex

tis

Rem

ove

d (

ns)

DestabilizationDegradationDeconstructionDissolutionAnnihilation

4.78.2

3.5 3.84.3 5.92.0 2.1

27.6

17.2

10.2 7.9

0.7 1.13.0

0.9

37.232.3

18.814.8

0

10

20

30

40

50

60

70

0 PS:0 Ca 0 PS:10 Ca 20 PS:0 Ca 20 PS:10 Ca

Tim

e A

fter

Eex

tis

Rem

ove

d (

ns)

Destabilization

Degradation

Deconstruction

Dissolution

Annihilation

PS and Ca2+ — Pore CreationValues averaged over three simulations

300

MV

/m40

0 M

V/m

500

MV

/m60

0 M

V/m

PS and Ca2+ — Pore AnnihilationValues averaged over five simulations

320

MV

/m40

0 M

V/m

600

MV

/m

ConclusionsIdentification of the stages in the life cycle of an electropore provides an objective scheme for characterizing the mechanisms of pore creation and annihilation.

Calcium and PS increase pore creation time. PS decreases pore annihilation time.

Pore creation time is an inverse function of the bilayer internal electric field.

MD simulations of calcium binding are consistent with experimental data.

Pore creation time depends on the externally applied electric field as expected [2], but we observe longer pore creation times for mixed PC:PS bilayers than for pure PC systems. Calcium also extends the pore creation time, but at higher electric fields the effects of PS and calcium are less evident.

Calcium Binding Isotherm

Internal Electric Field Dependence

(a) (b)

Cyan – PC Lipids Orange – CalciumMagenta – PS Lipids Green – ChlorideBlue – Nitrogen Red/White – WaterGold – Phosphorus

Pore creation time is inversely dependent on the bilayer internal electric field for all systems reported here. This functional relation may facilitate reconciliation of molecular and continuum models and experiments. Each data point in the plot to the left is averaged over three trials. PS and Ca2+ do not significantly modify the magnitude of the internal electric field (data not shown).

1. 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 1778:2308-2317.2. Ziegler, M.J., Vernier, P.T. 2008. Interface Water Dynamics and Porating Electric Fields for Phospholipid Bilayers. Journal of Physical Chemistry B 112:13588-135963. 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.

Pore annihilation appears to be independent of the pore-initiating electric field and depends instead on the structure and composition of the pore. In these simulations calcium does not have a large effect on pore annihilation. Mixed PC:PS bilayers have shorter pore annihilation times than pure PC bilayers for all electric fields observed.

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.

A binding constant of K = 2.65 M-1 was determined by fitting the data obtained in simulations [shown to the right].

)1)][4

11(

][4

11(

2

1

][

][ 2 tottottot

bound

CaKCaKLipid

Ca

2.0

5.0

3.1

7.0

0.2 0.2 0.2 0.10.8 0.4 0.4 0.8

2.9

5.6

3.7

7.8

0

2

4

6

8

10

0 PS:0 Ca 0 PS:100 Ca 20 PS:0 Ca 20 PS:100 Ca

Tim

e (

ns

)

Initiation

Construction

Maturation

Creation

9.5

> 50.0

15.2

> 50.0

0.3 0.10.6 N/A 0.6 N/A

10.4

> 50.0

15.9

>50.0

0

10

20

30

40

50

0 PS:0 Ca 0 PS:100 Ca 20 PS:0 Ca 20 PS:100 Ca

Tim

e (

ns

)

Initiation

Construction

Maturation

Creation

0.6 0.80.9

1.7

0.2 0.1 0.1 0.1

0.8

0.30.4

0.4

1.6

1.1

1.42.2

0

1

2

3

4

0 PS:0 Ca 0 PS:100 Ca 20 PS:0 Ca 20 PS:100 Ca

Tim

e (

ns

)

Initiation

Construction

Maturation

Creation