22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Monte Carlo poration model of cell membrane permeabilization for plasma
gene transfection
A. Zerrouki1, 2, M. Yousfi1, A. Rhallabi3, H. Motomura2 and M. Jinno2
1
2
University of Toulouse, LAPLACE, CNRS, 118 Route de Narbonne, Toulouse, France
Ehime University, Department of Electrical and Electronic Engineering, Matsuyama, Ehime 79-8577, Japan
3
University of Nantes, IMN, 2 Rue de la Houssinière, Nantes, France
Abstract: A specific Monte Carlo method is developed to simulate pore formation through
multilayer cell membranes during the interactions with plasma species (electron, ions and
radicals). Membrane layers are assumed as a succession of contiguous super-sites in which
occur macro-processes (recombination, reflection, site activation, opening, etc.) when
collided by incident plasma super-particles. It is shown interesting and promising results
for plasma gene transfection.
Keywords: Monte Carlo poration code, cell membrane permeabilization, plasma gene
transfection
1. Introduction
Gene transfection is a technique of deliberately
introducing nucleic acids (DNA) into cells through
membrane in order to give them specific characteristics.
In practice, this can be achieved following three different
ways: chemical method (as e.g., phosphate DNA carriers),
physical method (electroporation) and viral method [1].
All these reliable methods are limited to a few
experimental systems and can have specific drawbacks
(small payload or chemical toxicity or viral risk).
Furthermore, due to the costly equipment that is required,
these methods cannot usually applicable for the routine
transfection of cultured cells. Therefore, the development
of a new safe and damage-free technique is in demand.
A technique using low temperature atmospheric
pressure plasma was invented by the group involving
Satoh in 2002 [2] and was reported by Ogawa et al. in
2005 [3]. The plasma irradiation can lead to a transient
permeabilization of the cell membrane allowing processes
of gene transfection in which DNA and cells are both
exposed to fluxes of active plasma species (electrons, ions
and neutral radicals) and also to plasma-induced electric
The mechanisms leading to membrane
field.
permeabilization during plasma species/cell interactions
are partly evoked in the literature [4] as twofold
mechanisms: cell charging and lipid peroxidation.
Obviously, the well-known membrane electroporation
could be the third mechanism provided high enough
plasma-induced electric field is present. In fact, physical
cell charging is assumed to generate Coulomb forces at
the membrane surface thus in turn can lead to temporary
cell membrane disruption while chemical lipid
peroxidation can be initiated by plasma radical species
such as OH reacting with lipid bilayer and ultimately is
also able to create transient pores.
However, as already stated in the literature (see e.g.,
[5]), the mechanisms of more particularly membrane
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poration are far to be clear and controlled. Therefore
fundamental understanding on plasma-induced membrane
permeabilization is required for further progress in the
field of plasma gene transfection. It is worth noting that
some studies are devoted to reactive molecular dynamics
for the description of the plasma species/cell interactions
(see e.g., [6] or [7]). However, they cannot for the
moment help us to better understand the plasma-poration
of membranes since these works give, at the atomic scale
during a very short time, interesting information on the
breaking of some molecular bounds by several plasma
species but without any relevant link with transient pore
creation.
In order to contribute to a better understanding of the
pore formation through cell membranes by interactions of
some plasma species (electrons, ions and radicals) with a
multilayer membrane, we developed a Monte Carlo
poration model. The latter has been inspired from works
on plasma deep silicon etching applied to nano-electronic
devices (see e.g., [8]). As cell membranes are generally
formed by a complex structure mainly involving lipids
and proteins, it has been assumed for this preliminary
work a model membrane formed with 3 layers (2 protein
layers enveloping an internal wide lipid layer).
Section 2 following present introduction is devoted to
the description of the Monte Carlo method for simulation
of pore formation while input data on reaction processes
and preliminary results are discussed in section 3.
2. Description of Monte Carlo poration method
As previously emphasized, the present model inspired
from plasma deep silicon etching [8]) is aimed to
statistically simulate the pore formation during plasma
interactions with membrane. Thus, the displacement of
the active plasma species through the membrane and the
interactions processes taken into account are governed by
stochastic formalism and random numbers. Before
1
describing Monte Carlo algorithm, it is useful to give
information on the considered reaction processes and also
the membrane structure.
2.1. Reaction processes and membrane structure
First, the proportion of the plasma species (electrons or
ions or radicals) arriving to the membrane are estimated
from their fluxes calculated with the help of kinetics
model not described in this work. Each species is
considered as a macro-species (or super-particles)
representing a large number of particles.
Second, the membrane is assumed having a multilayer
structure composed for instance by two phospholipid-like
layer surrounded by a protein-like external layer. Fig. 1
displays such structure with blue external layers (layers 1
and 4) which are assumed composed by proteins and
green internal layers (layers 2 and 3) which are wider and
composed by lipids. Each layer is assumed as a
homogeneous medium of “macro-molecules” of lipids or
proteins. This multilayer structure is then divided or
discretized into small grids or meshes for the numerical
calculations. Each mesh represents a large number of
macro-molecules proportional to the density of the real
number of molecules of lipids or proteins. In the
framework of this ‘’coarse grained’’ approximation, the
interactions are assumed to occur between plasma superparticles and macro-molecules of the different layer
meshes. This macroscopic concept does not require a
definition at the molecular or atomic scale of the
membrane. Therefore, the successive interactions with
membrane layers is assumed as global or macro-processes
involving the incident plasma super-particles (electrons,
ions and radicals) arriving to the membrane surface.
Fig. 1. Multilayer membrane and discretisation domain.
We assumed the following macro-processes during the
interactions of plasma particles with membrane layers: (1)
Layer mesh opening; (2) Layer mesh activation leading
to activated site (3) layer mesh opening of activated site;
(3) Particle recombination or neutralization with layer
mesh; (4) Particle reflection on the internal walls of the
pore. Obviously the probability of occurrence of these
processes depends on the considered particle (electrons or
ions or radicals) and also on the nature of the layer nature
(lipid for layers 2 and 3 or protein for layers 1 and 4). In
the case of reflection, the particle is generally subjected to
2
new displacements until to reach a no-void (or full) site
inside the membrane layer.
Last, a given probability of occurrence of each macro
processes is assigned to each super-particle based on a
parametric study of such processes.
2.2. Domain of discretisation
Fig. 1 displays the 2D simulation domain represented
by a superposition of 4 layers (two external protein layers
with thicknesses LY1 and LY4 and two internal lipid
layers with thicknesses LY2 and LY3). The sum of the
4 layer thicknesses is chosen coherent with usual
membrane thickness (for instance LY1 + LY2 + LY3 +
LY4 ≈ 10 nm). The simulation domain is discretised into
small meshes called super-sites with step sizes ∆x and ∆y
along x and y axis. The step sizes can be chosen regular
or not.
At the beginning of the simulation, a given plasma
particle interacts first with the surface of layer 1. This is
why the surface of layer 1 is initialized by an initial
distribution of activated sites that are the starting point of
the pore formation. The mechanisms of the formation of
such initial activated sites are note described in this study.
The fraction of the activated sites uniformly distributed
over the surface of layer 1 can be chosen for instance
from experimental observations of the membrane surface
morphology at the nanoscale using for instance Atomic
Force Microscopy. These initial activated sites when
impacted by incident plasma particle can be transformed
into void site thus starting membrane opening.
It is worth noting that each super-site (or mesh) is
numerically defined by a matrix of numbers associated to
the state of the mesh before or after the interactions with
plasma species. The different possible state of a given
super-site inside a given layer can be for instance virgin
(or full) site or activated site or void site or recombined
site, etc.
2.3. Monte Carlo algorithm
Fig. 2 displays a simplified flowchart of the developed
Monte Carlo poration method that describes the
successive simulation steps from the interactions with the
surface of layer 1 up to the pore formation crossing the 4
considered layers following the previously evocated
different reaction processes. For each super-particle
(electrons or ions or radicals), a given number of initial
particles is chosen proportional to the corresponding
particle flux. The particle interacting with the layer
surface is selected from uniform random number
compared to the fraction of particle flux over total flux.
The position (x p,s , y p,s ) of the super-particle p along x
axis inside the super-site s and the angular distribution of
the incident angle θ p,s are also determined from random
numbers. x p,s varies between 0 and surface length LX in
the simulation domain and y p,s was assumed constant and
equal to a fraction of the mesh step size (y p,s =∆y 1 /10) in
the beginning of the simulation at the domain entrance
(surface layer 1)
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activation or recombination or opening, etc.), a new
particle is therefore selected. The Monte Carlo simulation
is stopped when the entire considered numbers of each
kind of super-particle is treated.
During Monte Carlo simulation, each selected superparticle is displaced until to interact with the first supersite of the surface or with a no-void (or full) super-site
corresponding to the walls or to the bottom of a given
pore. The elementary particle displacement dl for an
elementary variation along x and y axis is written as:
dl=(∆x2 + ∆y2)1/2
The new position x p,s+1 of the current super-particle p
is determined from its initial coordinates x p,s , y p,s, the
incidence angle θ p and a factor f modulating the
displacement:
x p,s+1 = x p,s + f x dl x cos(θ p )
y p,s+1 = y p,s + f x dl x sin (θ p )
3. Input parameters, first results and discussions
Fig. 2. Simplified flowchart of Monte Carlo method for
pore formation.
The plasma parameters are chosen close to the low
temperature capillary plasma generated at atmospheric
pressure and used for the experimental study of gene
transfection at Ehime University [1, 9]. Therefore, the
temperature of radicals and ions is considered close to
background gas temperature with a Maxwell distribution
for the particle energy and an isotropic angular
distribution while the electron mean energy can reach
several eV and can have a strongly anisotropic angular
distribution in the forward direction.
The interactions between super-particles and super-sites
are treated using predefined reaction probabilities for the
different macro-processes. Before and after each process
occurring in a super-site, the entire super-particle
neighbours need to be identified (as shown in Fig. 3) and
the new matrix numbers are stored in order to take into
account the change occurring inside the considered supersite (or mesh).
3.1. Simulation conditions
Present stochastic poration method is aimed to simulate
the pore formation under specific parameters of plasma
particles impinging the membrane surface.
The
simulation parameters are summarized in Table 1.
Table.1. Parameters used for simulation.
Particle number
and Plasma
fluxes
Total number of initial particles N p
to3.5x106 (electrons, ions and radicals)
Sizes of
membrane
layers
Discretization
1010-2
Radical flux/Electron flux
3
Ion flux/Electron flux
Length LX
Membrane thickness LY
Layer 1 thickness LY1
Layer 2 thickness LY2
Layer 3 thickness LY3
Layer 3 thickness LY3
Step size ∆x=∆y
Mesh number
7x105 up
100
10
2
3
3
2
[nm]
[nm]
[nm]
[nm]
[nm]
[nm]
0.25
16000
[nm]
Fraction of activated sites on layer1 surface
10-2
The chosen number of initial total super-particles is
varied from Np = 7x105 to 3.5x106 while the information
on the flux fractions of ions F ion and radicals F rad relative
to electron flux is chosen coherent with the considered
low temperature plasma, i.e.,
F ion = Ion flux/electron flux = 10-2
F rad = Radical flux/electron flux = 10-3
Fig. 3. Super-site scheme and the 4 neighbouring
particles.
When the considered super-particle interacts with a novoid site and undergoes a specific end-process (as site
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Concerning the domain geometry, the membrane length
LX was taken equal to 100 nm with thickness LY equal to
10 nm. The last is divided into 2 external protein layers
with thicknesses LY1 = LY4 = 2 nm, and two internal
lipid layers with thicknesses LY2 = LY3 = 3 nm. The
simulation domain is discretised into 16000 small regular
3
meshes (super-sites) with step sizes ∆x = ∆y = 0.25 nm.
Last, the fraction of the initial activated sites which are
the starting points of the pore formation on the first upper
layer (layer 1) is chosen equal to 10-2. This corresponds in
our simulation to 5 activated sites uniformly distributed
over the surface of layer 1.
3.2. Reaction probabilities and preliminary results
It is important to give information on the considered
occurrence probabilities of each macro-process already
emphasized in section 2 in the cases of each super-particle
(electrons, ions and radicals). The following notations are
used for these reaction probabilities.
In the case of electrons, probability P eAct corresponds to
site activation, P eOp-V-s to direct opening of virgin site, and
P eOp-Act-s to opening of activated site. As electron energy
is relatively high, the electron probability reflection P eRefl
is assumed negligible for the present preliminary
simulations.
In the case of radical/super-site and ion/super-site
interactions, the predefined reaction probabilities are
chosen for these preliminary calculations similar since in
our low temperature plasmas the energy of ion and neutral
species is quite close to the background gas energy. The
reaction probabilities are P radOp and P ionOp (index rad for
radicals and ion for ions) for opening of virgin site,
P radOp-Act and P ionOp-Act for opening of activated site, P radRec
and P ionRec for particle recombination or neutralization
inside layer mesh and P radRefl and P ionRefl for particle
reflection on the internal walls of the current pore. For the
deviation angle distribution, the reflection processes are
assumed specular (incidence angle =reflection angle).
Furthermore, only electrons are assumed playing a role
on the site activation due to their high energy. In fact, a
given super-site once activated by an electron impact is
ready to be opened by an impact of either another electron
or also by ion or radical. It is noteworthy that any superparticle can also have the possibility to directly open any
site but for the moment such probability is neglected.
Figs. 4a,b display the pore formation without (Fig. 4a)
and with (Fig. 4b) the effect of electron site opening.
When only opening of activated sites by impacts of ions
and radicals is considered (Fig 4a), it is necessary to use
larger particle number Np to have significant membrane
poration but without reaching the deeper layers. As soon
as the electron opening of activated sites is allowed, pores
become deeper even if lower Np is taken into account.
Fig. 4c displaying the pore formation without the effect of
the particle reflection clearly emphasizes the role of the
reflection to widen the pore diameter.
Figs. 5a and 5b display the pore formation for two
initial numbers of total particle Np under the same
probabilities conditions as in Fig. 4b (i.e., involving
reflection and additional action of electron to open
activated sites). We can see that the increase of Np
maintains the same number of pores (5 in the present
case) but pores become wider and a little bite deeper.
Therefore, we can directly correlate the number of initial
4
particles Np to the exposition time of the cell membrane
to the plasma. Under the present simulation conditions,
the pore wideness (or diameter) is close to 10 nm which is
coherent with standard diameters expected for gene
transfection (see e.g. [10]).
Fig. 4. Pore formation through multilayer membrane:
(a) N p = 3.5x106, P eOp-V-s = P eRefl = P eOp-Act-s = 0, P eAct =
1, and P radOp-V-s = P ionOp-V-s = 0, P radOp-Act-s = P ionOp-Act-s =
0.2, P radRec = P ionRec = 1 and P radRefl = P ionRefl = 0.3;
(b) N p = 7x105, P eOp-V-s = 0, P eAct = 0.99 on layer 1 and
0.95 elsewhere, P eOp-Act-s = P eRefl = 0.01 on layer 1 and
0.05 elsewhere, P radOp-V-s = P ionOp-V-s = 0, P radOp-Act-s =
P ionOp-Act- = 0.2, P radRec = P ionRec = 1 and P radRefl = P ionRefl
= 0.3;
(c) N p = 7x105, ’’same probabilities as those of fig. 4b’’
except for P radRefl = P ionRefl = 0.
Fig. 5. Pore formation through multilayer membrane with
the same predefined probabilities as those of fig. 4b. (a)
Np = 6.5x105, (b) Np = 1.2x106.
Next steps will be devoted to a wider parametric study
involving the different reaction processes between superparticles and layer-meshes to better emphasize processes
playing a main role in membrane poration. We will also
perform an experimental validation step using
comparisons with atomic force microscopy of cells
permeabilized by low temperature plasmas.
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