Showcasing research from the group of Dr Hideya Nakamura,
Department of Chemical Engineering,Osaka Metropolitan University, JapanAs featured in:Volume 25
Number 47
21 December 2023
Pages 32275–32730

Enhancement of cell membrane permeability by using
charged nanoparticles and a weak external electric field

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Physical Chemistry Chemical Physics
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This study investigated cell-membrane crossing of dextran
with Mw of 3000–5000 using charged nanoparticles
and a weak external electric field. Even when the applied
electric field was below the critical strength for membrane
breakdown, dextran was able to cross the membranewithout causing membrane breakdown. These results
indicate that adding nanomaterials under a weak electricfield can enhance the translocation of delivery compounds
across the membrane with less damage, suggesting a new
strategy for intracellular delivery systems.

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PAPER
Gaige Zheng et al.
Weyl semimetal mediated epsilon-near-zero hybrid
polaritons and the induced nonreciprocal radiation

See Hideya Nakamura et al.,Phys. Chem. Chem. Phys.,2023, 25, 32356.

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Enhancement of cell membrane permeability byusing charged nanoparticles and a weak external
electric field†
Hideya Nakamura, *a Takumi Okamura,a Masaya Tajima,a Ryuji Kawano,
Misa Yamaji,b Shuji Ohsakia and Satoru Watanoab

Because the cell membrane is the main barrier of intracellular delivery, it is important to facilitate andcontrol the translocation of extracellular compounds across it. Our earlier molecular dynamics
simulations suggested that charged nanoparticles under a weak external electric field can enhance thepermeability of the cell membrane without disrupting it. However, this membrane permeabilization
approach has not been tested experimentally. This study investigated the membrane crossing of amodel compound (dextran with a Mw of 3000–5000) using charged nanoparticles and a weak external
electric field. A model bilayer lipid membrane was prepared by using a droplet contact method. The perReceived 12th July 2023,
Accepted 26th October 2023

meability of the membrane was evaluated using the electrophysiological technique. Even when the

DOI: 10.1039/d3cp03281g

the membrane without causing membrane breakdown. These results indicate that adding nanomaterials

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under a weak electric field may enhance the translocation of delivery compounds across the cell
membrane with less damage, suggesting a new strategy for intracellular delivery systems.

applied electric field was below the critical strength for membrane breakdown, dextran was able to cross

Introduction
Intracellular delivery is a key technology in biological researchand biomedical/therapeutic applications. For instance, thedelivery of DNA, RNA, and proteins is vital for gene editing
and gene therapy.1–4 Engineered nanoparticles (NPs) have been
extensively studied for carrying extracellular compounds, drugdelivery, intracellular imaging, etc.5,6 A variety of NPs were
designed and synthesized to achieve high delivery efficacy
and multiple functionalities.5,6 Despite a large body ofresearch, however, the development of efficient intracellulardelivery systems remains a major challenge.
The cell membrane is the main barrier of intracellulardelivery. To facilitate and control the translocation of extracellular compounds, researchers frequently enhance the permeability of the cell membrane by subjecting cells to external
force fields.2,7 Electroporation is a common physical method8that applies an external electric field (high-intensity electricpulse) to the cell. This electric field can cause transienta

Department of Chemical Engineering, Osaka Metropolitan University, 1-1 Gakuencho, Naka-ku, Sakai, Osaka 599-8531, Japan. E-mail: hideyanakamura@omu.ac.jpbDepartment of Biotechnology and Life Science, Tokyo University of Agriculture andTechnology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan† Electronic supplementary information (ESI) available. See DOI: https://doi.org/
10.1039/d3cp03281g

32356 | Phys. Chem. Chem. Phys., 2023, 25, 32356–32363

membrane disruption and thus facilitate subsequent translocation of extracellular compounds across the membrane. Unfortunately, electroporation also exposes cells to excessive stressand thus increases their mortality.
Previously, we used molecular dynamics (MD) simulation toinvestigate the translocation of charged NPs across a phospholipid bilayer (a model for the cell membrane) under an external
electric field.9–11 Under the applied electric field, charged NPs candirectly translocate across the bilayer without the membrane
wrapping around them. There was no membrane disruption after
the translocation of NPs. Remarkably, the NPs could cross themembrane under a weak electric field below the critical strength
for membrane disruption. In other words, there is no need todisrupt the cell membrane prior to NP crossing, which is different
from the conventional electroporation approach. It is also noteworthy that after the NPs passed through, the membrane showed
self-resealing, suggesting less damage. Our studies further
revealed that this membrane crossing can be driven by a locallyenhanced electric potential across the membrane that is inducedby superimposing the potential of charged NPs and the externallyapplied electric potential.10 These findings suggest that combining charged NPs with a weak electric field can enhance cell
membrane permeability without causing membrane disruption.
Nevertheless, no experimental studies have used this membrane
permeabilization approach for the translocation of delivery compounds across the cell membrane.

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Paper
Artificial phospholipid bilayer membranes are an ideal
model system for the experimental exploration of physicochemical interactions between NPs and cell membrane.12,13 Suchbilayer membranes can be prepared as either threedimensional liposomes and vesicles or two-dimensional supported and free-standing bilayers. Planar bilayer lipid membranes (BLMs) were used to experimentally investigate the cell
membrane-crossing of ions and compounds under an electricfield with the electrophysiological technique.12,13 Numerous
studies on membrane proteins such as ion channels wereconducted on BLMs with the electrophysiology technique.14
Recently, BLMs with the electrophysiological technique werealso used to investigate the interaction between nanomaterials
and phospholipid bilayer membrane.15–21 Several studies foundthat NPs could alter membrane permeability, sometimes leading to pore formation and membrane breakdown.22–27 However, there has been no attempt to utilize NPs and an external
electric field to facilitate the translocation of compounds acrossthe BLM while minimizing membrane damage.
This study tested the aforementioned cell membrane permeabilization strategy suggested by MD simulations. The lipid
membrane-crossing of a model delivery compound without
membrane breakdown was experimentally investigated under
the combined eﬀects of charged NPs and a weak external
electric field. The BLM was prepared by the droplet contact
method.28 The critical applied voltage for membrane breakdown was measured. Then, eﬀects of NPs on electrical properties of the BLM (such as membrane capacitance) were evaluatedusing an electrophysiological technique to identify experimental conditions that influence membrane permeability.
Finally, charged NPs and the model delivery compound wereadded together to the BLM system, and experiments wereconducted to examine whether the NPs under the weak electricfield could induce the model delivery compound to cross theBLM without membrane breakdown.

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Table 1

Physical properties of charged NPs used in this study

Nanoparticle (NP)Median diametera [nm]Amine-PSL
Carboxy-PSL

42.5
52.1

Surface potentiala [mV]
36.2
27.0

a

Measured in 50 mM KCl (aq.), which was used in the BLM
experiments.

charged. These NPs have sufficiently high surface potentials
even when dispersed in 50 mM KCl solution (the electrolyte
used for BLM in this study). Their measured mean diameters
were the same as the nominal value of 50 nm, indicating gooddispersibility of the NPs.
Setup and procedure
Planar BLMs were prepared by the droplet contact method(DCM)28,30,31 as shown in Fig. 1a. First, two aqueous droplets
covered with lipid monolayers were prepared in a lipid/oil
solution. When the two droplets contacted each other, a BLM
was spontaneously formed at the contact interface. A doublewell device (Fig. 1b and c) was employed to prepare a BLM by
the DCM, and details of the device were described in theliterature.28,30,31 Briefly, the device consisted of two wells(4.0 mm in diameter and 5.0 mm in depth), a separator with asingle through-hole (100 mm in diameter), and an Ag/AgCl electrode at the bottom of each well. The two droplets contacted eachother at the through-hole to form the BLM there. The Ag/AgClelectrodes allow the application of a transmembrane external
electric field and the measurement of transmembrane current.
Fig. 2a shows the experimental setup, which was composedof the double-well device, recording electrodes, patch-clamp
amplifier, function generator, and personal computer for controlling and data recording. To monitor transmembrane current through the BLM, the double-well device was connected toMaterials and methods
Reagents and chemicals
The following reagents were used in this study: 1,2-diphytanoylsn-glycero-3-phosphocholine (DPhPC, Avanti Polar Lipids,
850356), n-decane (040-21602, FUJIFILM Wako Pure Chemical),and KCl (169-03542, FUJIFILM Wako Pure Chemical). Fluorescein isothiocyanate-labeled dextran (FITC–dextran, SigmaAldrich, FD4) was used as the model delivery compound,because its molecular weight (3000–5000) is similar to typicaldelivery compounds such as SiRNA.29 Two types of NPs wereused: amine-modified polystyrene nanoparticles (amine-PSLNPs, Sigma-Aldrich, L0780) and carboxylate-modified polystyrene nanoparticles (carboxy-PSL-NPs, Micromod, 01-02-501).
Their preliminary characterization results are shown in
Table 1. The mean diameter and surface potential were measured using a surface potential and particle size analyzer(Zetasizer Nano ZS, Malvern). The amine-PSL-NPs were positively charged, while the carboxy-PSL-NPs were negatively

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Fig. 1 (a) Planar bilayer lipid membrane (BLM) prepared by the droplet
contact method (DCM). (b) Top view and (c) side view of the double-welldevice used in this study.

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Fig. 2 (a) Experimental setup. (b) Double-well devices connected to thesolderless breadboard and recording electrode.

the multi-channel patch-clamp amplifier (Flex, Tecella). The
patch-clamp amplifier was also connected to the function generator (FG110, Yokogawa Electric) for applying transmembrane
voltage to the BLM. Ag/AgCl electrodes at the bottom of well wereattached to a solderless breadboard, which was connected to arecording electrode to the patch-clamp amplifier (Fig. 2b). In the
study, multiple double-well devices were connected to therecording electrode, and the BLM experiments were performedin parallel. To minimize noise, the double-well devices andpatch-clamp amplifier were placed in a Faraday cage.
The experimental procedures were as follows. First, 1.2 mL oflipid/oil solution (10 mg mL 1 of DPhPC/n-decane) was dropped
into each well. Second, 20 mL of KCl solution (50 mM) without
NPs or FITC–dextran was dropped into each well. Within a few
minutes of adding KCl solution, the two droplets contacted eachother at the single through-hole in the separator to form a BLM.
To ensure proper BLM formation, the membrane resistance Rm
and capacitance Cm were measured in situ using a discharge
pulse method.32 A suitable BLM was considered to have Rm Z
1 GO and Cm Z 0.4 mF cm 2. After the BLM passed the quality
check, 2.0 mL of KCl solution (50 mM) containing NPs and FITC–
dextran was then injected into one of the aqueous droplets bypipetting under predetermined conditions. Finally, an external
voltage was applied to the BLM, and the transmembrane current
was detected using a 0.25 kHz low-pass filter at a sampling
frequency of 1.0 kHz.

Fig. 3 Typical current response of a BLM under linearly rising membrane
voltage. Dcappl,C denotes the critical applied voltage for membrane breakdown. The mean value of Dcappl,C is indicated on the figure.

Dcappl,C was 372  70 mV (mean  S.D.). This value is very
similar to those reported in previous studies,33,34 confirming
the validity of Dcappl,C measurement here.
Eﬀects of NPs on the electrical properties of BLM

Critical applied voltage for membrane breakdown

To identify the experimental conditions that aﬀect membrane
permeability, the BLM properties were measured in the presence
and absence of NPs. After forming the BLM, a specific amount of
NPs with positive or negative surface charge was injected into theaqueous droplets. A pulsed voltage smaller than Dcappl,C (100 mV
for 20 ms and 0 mV for 40 ms) was then continuously applied, andthe membrane stability and membrane capacitance were measured at diﬀerent exposure times.
Fig. 4 shows the probability of membrane breakdown (basedon 5 experimental runs) at diﬀerent concentrations of aminePSL-NPs and exposure times. The membrane breakdown was
defined as when the current reached the maximum measurable
current during the experiment. The amine-PSL-NPs were added
to the well connected to the positive voltage side (inset in Fig. 4).
The NP concentration corresponds to the NP number concentration based on the final aqueous droplet in the well.
Membrane breakdown was more likely at higher NP concentrations, particularly above 1.0  106 particles per mL. The probably

Before investigating the proposed cell membrane permeabilization, it is necessary to ascertain the critical applied voltage formembrane breakdown (Dcappl,C). We measured Dcappl,C in a
voltage-controlled experiment,32 by applying a linearly risingtransmembrane voltage (slope: 20 mV s 1) to the BLM andmonitoring the transmembrane current. Fig. 3 shows the
typical current response. The current noise observed in thisstudy was approximately 5 pA, thus, the current noise was notappreciable in Fig. 3. Under the linearly rising applied voltage(black solid line), the transmembrane current (red solid line)
initially remained very low and then suddenly increased toreach the maximum measurable current of the amplifier (bluedashed line). The voltage at which the current increased rapidly
was defined as Dcappl,C (black dashed line). We measured
Dcappl,C in 26 independent experiments, and the 10% trimmed
mean was calculated. As indicated on Fig. 3, the determined

Fig. 4 Fraction of membrane breakdown (n = 5) at diﬀerent NP concentrations and exposure times. The amine-PSL-NPs were added to the wellconnected to positive voltage side (inset).

Results and discussion

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Paperof membrane breakdown also became higher at longer exposure times, indicating that destabilization of BLM by NPs is atime-dependent phenomenon. However, the probability ofmembrane breakdown was the same at 10 and 30 min, suggesting that BLM destabilization did not progress significantly after
10 min.
We also recorded the capacitance of the surviving BLMs andcalculated its increase (DCm = Cm(t) Cm0, where Cm(t) is themembrane capacitance at exposure time t and Cm0 is the initialmembrane capacitance before adding NPs). Fig. 5 shows DCm
as a function of exposure time at diﬀerent concentrations ofamine-PSL-NPs. There was no significant change in DCm at NP
concentrations below 1.0  109 particles per mL, whereas at
1.0  1010 particles per mL DCm exhibited a considerable
increase. This increase in membrane capacitance may be
attributed to the thinning of BLM and a higher charge on its
surface, which can be caused by the closer association ofconcentrated charged NPs with the BLM.
To further investigate the impact of NPs on the BLM,
we varied the direction of the Coulomb force exerted on theNPs. Specifically, we measured the temporal change in DCm in
two scenarios depicted in Fig. 6a. Positively charged amine-PSLNPs were added to either the well connected to the positive
voltage side (top) or the other well connected to the ground(bottom). Similar experiments were performed with negatively
charged carboxy-PSL-NPs (Fig. 6b). The schematics in Fig. 6 also
depict the direction of the electric field across the BLM (E). For
amine-PSL-NPs, an increase in DCm was observed when the NPs
were added to the well connected to the positive voltage side
but not that connected to the ground. The opposite trend wasobserved for carboxy-PSL-NPs, namely that DCm increased
when the NPs were added to the well connected to the groundrather than the positive voltage side. Thus, DCm increased when
the Coulomb force exerted on the NPs was oriented toward
the BLM, whether the NPs carried positive or negative
surface charge. These results indicate that the increase in
DCm was caused by the approach and accumulation of charged
NPs on the membrane, which were mainly driven byelectrophoresis.

Fig. 5 Temporal change in the increase in membrane capacitance (DCm)at diﬀerent concentrations of amine-PSL-NPs.

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Fig. 6 Temporal change in DCm after adding NPs to the well connected
to either the positive voltage side or the ground. (a) Amine-PSL-NPs
with positive surface charge and (b) carboxy-PSL-NPs with negative surface charge.

Membrane crossing of FITC–dextran assisted by charged NPs
and a weak electric field
Next, we examined whether the charged NPs facilitate themembrane crossing of delivery compounds (represented hereby FITC–dextran) under a weak electric field without inducing
membrane breakdown. First, a BLM was formed from aqueous
droplets free of NPs and FITC–dextran. Subsequently, theamine-PSL-NPs and FITC–dextran were injected into the droplet connected to the positive voltage side, as depicted inFig. 7a. The FITC–dextran concentration in the aqueous droplet
was adjusted to 1.0 mg mL 1. The NP concentration was set at
106 particles per mL or higher based on the results in Fig. 4.
A pulsed voltage (100 mV for 20 ms and 0 mV for 40 ms) was
then applied for several tens of seconds to measure the initialmembrane capacitance and resistance. Subsequently, a constant positive voltage smaller than Dcappl,C was applied for
3 min to facilitate the membrane crossing of FITC–dextran, andthe transmembrane current was monitored at the same time.
After removing the applied voltage, the membrane capacitanceand resistance were measured again. Finally, the aqueous dropletsin both wells were sampled by pipetting, and their absorbance at
494 nm was measured using a microvolume spectrophotometer(Nano Drop, Thermo Fisher Scientific) to quantify the FITC–
dextran concentration in each droplet. Because the amin-PSLNPs exhibit negligible absorbance at wavelengths above 400 nm,
the measured absorbance at 494 nm should be solely due to
FITC–dextran.
If FITC–dextran translocates across the BLM in the experimental system, the transmembrane current should be significantly higher than that without translocation. Thus, we firstmeasured the transmembrane current. Fig. 7b shows theoccurrence rate for transmembrane current signal higher or

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Fig. 7 (a) Schematic of experiments with charged NPs and FITC–dextran.
Both amine-PSL-NPs and FITC–dextran were injected into the droplet
connected to the positive voltage side. The applied voltage was 0.8
Dcappl,C, which was select based on our MD simulation results.9–11 (b)Occurrence rate for transmembrane current signal higher or lower than 10
pA as a function of NP concentration (n = 4 experiments). (c) Translocation
ratio of FITC–dextran across the BLM defined as APV/(APV + AG) [%], where
APV and AG are the absorbances of FITC–dextran in the droplets connectedto the positive voltage side and ground, respectively.

lower than 10 pA. The threshold value of 10 pA is significantly
higher than the average transmembrane currents when neither
NPs nor FITC–dextran is present. In the absence of NPs, a hightransmembrane current was not observed, whereas adding NPs
to the system resulted in a significantly higher transmembranecurrent, suggesting that the NPs enhanced membrane permeability. The occurrence rate of high transmembrane current
became higher at higher NP concentrations. Fig. 7c shows thetranslocation ratio of FITC–dextran across the BLM. Only
negligible translocation was observed without NPs, whereas asignificant translocation ratio (12–20%) was detected in thepresence of NPs. This confirmed that the NPs facilitated thetranslocation of FITC–dextran across the BLM.
Fig. 8a shows the typical transmembrane current signals
during the application of constant voltage at diﬀerent NP concentrations. Persistent current signals were observed at all NP concentrations, suggesting the existence of transmembrane pores
during this whole process. We estimated the diameter of thesepores from the current signals. For simplicity, we assumed that
there was only a single pore filled with electrolyte in themembrane, although membrane defects may occur at multiple
locations. The diameter of this single pore was estimated using
Hille’s equation:35 V/I = 4rL/pD2 + r/D. V is the applied voltage, I is
the measured current, r = 1.43 O m is the resistivity of theelectrolyte solution (determined using the surface potential analyzer), L = 5.1 nm36 is the length of the pore, and D is the estimatedpore diameter. Fig. 8b shows the distribution of estimated D values
at each NP concentration. D ranges from 7 to 23 nm, significantly
smaller than the diameter of amine-PSL-NPs (ca. 50 nm, Table 1).
Considering the limitation of the single-pore assumption, the sizeof actual pores should be smaller than the estimated D values.
Consequently, we suppose that only FITC–dextran translocatedacross the BLM, not the NPs. Moreover, the estimated hydrodynamic diameter of folded dextran with a molecular weight of 5000

32360 | Phys. Chem. Chem. Phys., 2023, 25, 32356–32363

Fig. 8 (a) Transmembrane current signals and (b) distribution of transmembrane pore diameter during the application of a constant voltage of
0.8 Dcappl,C at diﬀerent NP concentrations. The pore diameter was
estimated using Hille’s equation.35(4.2 nm)37,38 is smaller than the aforementioned pore diameters,
supporting the membrane crossing of FITC–dextran in this study.
Fig. 8b also shows that the estimated pore diameter is smaller athigher NP concentrations. This is probably because a larger
number of NPs adhering to the BLM inhibit the formation oflarger transmembrane pores. Details of the dependence of poresize on the NP concentration are still unknown and should befurther investigated.
We compared the estimated transmembrane pore diameterto those reported in the literature. Table 2 shows the estimateddiameters of transmembrane pores resulting from the interaction with NPs or peptides.22,23,26,27,30,31 The pore diameter
observed in this study was much larger than those fromprevious studies, suggesting the uniqueness of membrane
permeability enhancement in the present case.
We investigated changes in BLM properties under an external voltage in the context of membrane integrity. Table 3

Table 2 Previously reported transmembrane pore diameters resulting
from the interaction with NPs or peptides

BLM permeability enhancer

Pore diameter [nm]Ref.

Quantum dots NPs
Quantum dots NPs
Gold NPs
Polystyrene NPs
Antimicrobial peptide
Insecticidal protein

0.33–0.92
1.9
0.20–0.40
0.58–2.72
0.90–1.30
0.80–1.40

22
23
26
27
30
31

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Table 3

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Membrane resistance and capacitance before and after applying an external voltage of 0.8 DCappl,c at each NP concentration

Membrane resistance before/after
applying external voltage [GO]Membrane capacitance before/after
applying external voltage [pF]

NP concentration [mL ]BeforeAfter

BeforeAfter

Without
NP
6
108
109
10

0.8
0.4
1.2
1.8

0.9
0.4
1.2
1.7

68
67
62
71

69
67
63
71

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1

presents the membrane resistance and capacitance before andafter application of the constant voltage. Both the membrane
resistance and capacitance remained unchanged after applying a
constant voltage of 0.8 Dcappl,C, at which point the membranecrossing of FITC–dextran was confirmed to occur (see Fig. 7c).
This suggests that membrane integrity was retained despite theapplication of this constant voltage and the membrane crossingof FITC–dextran. In other words, the model delivery compound
successfully crossed the membrane aided by the charged NPs
and weak electric field without causing membrane breakdown.
Finally, we discussed the NP concentrations used in thisstudy (106 to 109 particles per mL) in detail. First, surface coverageof NP on the membrane surface at 106 to 109 particles per mL wasestimated. The surface coverage was estimated to check whether
all the NPs were adhered to the inner surface of the aqueous
droplet in the well. The surface coverage was also estimated byassuming that the inner surface of the aqueous droplet was coverwith NPs in a close-packed single layer. The results suggest thatthe surface coverage can be 0.502% to 502% at 106 to 109
particles per mL. Details can be seen in the ESI† (Table S1). Thisestimation implies that membrane crossing of FITC–dextran canoccur even at less than 100% surface coverage of NPs. Second, we
compared the NP concentrations used in this study to the safe
dose to real biological cells. Safe dose data were extracted fromliterature reports39–41 using the same amine-PSL-NPs (Sigma
Aldrich, L0780) as in this study. Details can be seen in the ESI†
(Table S2). The results indicated that the NP concentrations of
106 to 109 particles per mL can fall within a range of no adverse
effects on mammalian cell lines39 and bacteria.40,41

Conclusions
This study investigated membrane crossing of a model delivery
compound (FITC–dextran with Mw of 3000–5000) under theassistance of charged NPs (amine-modified polystyrene nanoparticles with 50 nm in diameter) and a weak external electricfield. The cell membrane was modeled by a BLM prepared by
DCM. The BLM was broken down at a critical applied voltage ofDcappl,C = 372 mV, very similar to the previously reported values.
We found that membrane breakdown was likely to occur at higher
NP concentrations and longer exposure times (up to 10 min
before saturation). The capacitance of surviving BLMs increased
significantly at a higher NP concentration of 1.0  1010 particles
per mL, which was attributed to membrane thinning and a higher
surface charge on the BLM that could be caused by closer
association of charged NPs with the BLM. Our results alsoThis journal is © the Owner Societies 2023

suggested that the increase in membrane capacitance was mainly
due to electrophoresis of charged NPs. Finally, we demonstrated
that adding charged NPs under a weak external electric field could
allow the model delivery compound to cross the membranewithout membrane breakdown. We verified that FITC–dextran
translocated across the BLM even at an applied voltage below
Dcappl,C. Moreover, the membrane resistance and capacitanceremained unchanged before and after constant voltage application. The diameter of transmembrane pore formed in our experiments was estimated to be 7 to 23 nm, considerably smaller thanthe NP diameter (50 nm) but larger than the hydrodynamic
diameter of folded dextran (4.2 nm). These estimated sizes
support the translocation of FITC–dextran across the BLM.
The results here provide proof of concept for the proposedcell membrane-crossing strategy using charged NPs and a weakelectric field, which can lead to a new strategy for intracellulardelivery systems.
Nevertheless, it is clear that there is a gap between the BLM
system and real cell membrane. Even from the viewpoint of themembrane deformability, BLM is not perfect mimic of the realcell membrane. Thus, the eﬀect of NP concentration on thepore size found in this study may change in real cell membranes and needs to be further investigated in in vitro tests.

Author contributions
Hideya Nakamura: conceptualization, formal analysis, funding
acquisition, methodology, project administration, resources,
supervision, visualization, writing – original draft, writing –review & editing. Takumi Okamura: data curation, investigation, visualization, writing – original draft. Masaya Tajima: data
curation, investigation. Ryuji Kawano: methodology, resources.
Misa Yamaji: methodology, resources. Shuji Ohsaki: resources,
validation, writing – review & editing. Satoru Watano: resources,
validation, writing – review & editing.

Conflicts of interest
There are no conflicts of interest to declare.

Acknowledgements
This work was mainly supported by the Japan Society for the
Promotion of Science, KAKENHI Grant Numbers 18H03536,
19K22976, and 19KK0129.

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