The plasma membrane of a cell is a complex assembly of hundreds of different types of lipids and membrane proteins, which tightly regulate transmembrane trafficking and participate in cell signalling (Krapf, 2018; van Meer et al., 2008). The molecular organization of the plasma membrane and its integrity are essential for the life of the cell. However, when the cell is exposed to external forces, the membrane integrity can become transiently disrupted by formation of transmembrane pores. Such disruption can be useful in many clinical applications, for example when nucleic acids need to be delivered across the plasma membrane into the cell interior, where they can carry out their tasks (Gary and Weiner, 2020; Glass et al., 2018). Various physical methods can induce transmembrane pores, including ultrasound, light, electric field, and mechanical deformation (stretching/squeezing) (Gurtovenko et al., 2010; Ding et al., 2017; Yang et al., 2020; Schneckenburger, 2019). In terms of clinical applications, poration by the application of electric fields or electroporation is the most widely used method. It is approved for treatment of solid tumours, and it is being tested in clinical trials for gene therapy, vaccination against cancer and infectious diseases, and for cardiac ablation (Campana et al., 2019; Geboers et al., 2020; Algazi et al., 2020; McBride et al., 2021).

One of the bottlenecks of electroporation is that its protocol, especially the parameters of the applied electric pulses (amplitude, duration, number, repetition rate), needs to be optimized for each specific application and also for each specific cell/tissue type (Cemazar et al., 2009; Rols and Teissié, 1998; Hunter et al., 2021). When using electroporation for intracellular delivery of nucleic acids, the cells need to survive the treatment to be able to express the transgene. On the contrary, when using electroporation as an ablation modality, the cells need to die. Any electroporation-based treatment thus needs to be designed to either avoid or reach the point of no return leading to cell death. At present, the understanding of this point of no return is very limited (Batista Napotnik et al., 2021). One of the main reasons for this is our insufficient understanding of the molecular mechanisms that govern the increased cell membrane permeability induced by the applied electric field (Kotnik et al., 2019). If we can identify the molecular alterations of the cell membrane, we can begin to connect them to the biological response of the cells to pulsed electric fields.

The most accepted models, that describe electroporation on the whole-cell level, consider that pores can form only in the lipid domains of the plasma membrane and that all pores exhibit a similar kinetic behaviour (Krassowska and Filev, 2007; Li and Lin, 2011; Gowrishankar et al., 2013). However, accumulating evidence from experiments and simulations on model systems speaks against these assumptions. Poration kinetics in pure lipid bilayers has been shown to depend on the type of lipids and their phase state (Perrier et al., 2017; Sengel and Wallace, 2016). Since the lipids in the plasma membrane organize in domains (Lu and Fairn, 2018; Levental et al., 2020), there must exist locations which are more and less prone to poration. Moreover, our research suggests that pores can nucleate within some membrane proteins, causing protein denaturation and lipid rearrangement (Rems et al., 2020). Such lipid/protein pores can be more stable than pure lipid pores and are more likely to explain the persistent increase in plasma membrane permeability following exposure to electric pulses. Studies have further shown that pore formation and/or expansion is affected by the actin cytoskeleton, either via actin’s influence on lipid organization or the mechanical properties of the membrane (Muralidharan et al., 2021; Perrier et al., 2019). The current challenge is to gather this ensemble of findings into a coherent and predictive mathematical model describing electroporation of the living cell’s plasma membrane. In a living cell’s plasma membrane, pores cannot form anywhere: as soon as a sufficient number of pores are formed, the transmembrane voltage drops, preventing formation of new pores (DeBruin and Krassowska, 1999; Smith et al., 2014). In other words, pores will form preferentially in specific sites with the highest poration propensity. However, it remains to be elucidated which are the properties of these sites.

The challenge of studying pores in the plasma membrane experimentally is that pores are nanometre-sized and open only transiently, whereby most of them appear to rapidly close (ns–μs range) after turning off the electric field (Melikov et al., 2001; Bennett et al., 2014; Sözer et al., 2020). Pores have been imaged in giant unilamellar vesicles (Riske and Dimova, 2005; Lira et al., 2021); however, these pores have reached sizes on the order of 1 μm, which have not been observed in cell plasma membranes, likely because the actin cytoskeleton limits pore expansion (Perrier et al., 2019). Pores have also been imaged in real time in droplet interface bilayers with TIRF (total internal reflection fluorescence) microscopy (Sengel and Wallace, 2016); however, the membranes were exposed to seconds-long electric pulses, which are much longer than pulses used in electroporation applications (ns−ms range), and which would likely not be tolerated by living cells. A few attempts have been made to visualize pores in cells using electron microscopy (Chang and Reese, 1990; Lee et al., 2012); however, the observed pores were suggested to be artefacts of sample preparation (Teissie et al., 2005). Overall, the current state of experimental methods does not appear to be at a stage where it would provide the spatiotemporal resolution required to understand the molecular mechanisms of plasma membrane electroporation in its entirety.

In this study, we thus resort to molecular modelling methods to investigate plasma membrane electroporation. In particular, we use coarse-grained molecular dynamics simulations, building on their success in studying membrane lateral organization and dynamic behaviour (Duncan et al., 2017; Marrink et al., 2019; Khalid and Rouse, 2020). By running electroporation simulations on lipid membranes mimicking the realistic composition of plasma membranes, we confirm that pores do not form homogeneously across the membrane, but colocalize with domains that have specific features, particularly high content of polyunsaturated (PU) lipids. By training machine learning algorithms, we further demonstrate that knowing the local lipid distribution is sufficient to predict with ~80–90% accuracy the locations, which are most likely to be porated. Additionally, by analysing poration kinetics with Bayesian survival analysis we show that poration does not depend solely on local lipid arrangement, but also on membrane mechanical properties and the polarity of the electric field. Finally, we discuss how atomistic and coarse-grained molecular dynamics simulations, machine learning methods, and Bayesian survival analysis combined can help us develop more accurate cell-level models, which are required to foster new and better electroporation-based applications.

To study plasma membrane electroporation we have used coarse-grained membranes consisting of >60 different lipid types parametrized with the Martini force field (Marrink et al., 2007; de Jong et al., 2013). The membranes mimic the composition of either an idealized average mammalian plasma membrane (APM) or a human brain plasma membrane (BPM) and have been developed and equilibrated in earlier work (Ingólfsson et al., 2014; Ingólfsson et al., 2017). The lipid composition of both APM and BPM is asymmetric, the lipids in the outer leaflet being different from those of the inner leaflet. Both compositions contain similar lipid types but differ in their fractions (Figure 1, Figure 1—figure supplement 1, Tables 1 and 2).

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The following subsections present the results and analysis as follows. First, we present the results from electroporation simulations and demonstrate that all membranes exhibit preferential poration sites. Then we determine local membrane properties and examine which of them increases/decreases the poration propensity. We further investigate the importance of local membrane properties by training machine learning algorithms and predicting the sites, which are most likely to be porated. Finally, we apply Bayesian survival analysis to investigate how membrane properties influence the poration kinetics and to develop an underlying kinetic model.

Membranes exhibit preferential poration sites

The original APM and BPM membranes from Ingolfsson et al. (Ingólfsson et al., 2014; Ingólfsson et al., 2017) were cut into four pieces each (Figure 1) to increase sampling, since the analysis was focused on the first poration event. After a short re-equilibration, each of the eight membranes was subject to electroporation simulations, 60 simulations under hyperpolarizing field and 60 simulations under depolarizing electric field. Both polarities of the electric field were considered, since during exposure of a cell to an electric field, the plasma membrane becomes hyperpolarized on the side facing the positive electrode and depolarized on the side facing the negative electrode. The electric field was set to ±127.7 mV/nm, which was high enough to induce a pore within ~15 ns. Being able to observe poration over short time scales was important to minimize lateral lipid diffusion and provide a reliable mapping of local membrane features before electric field application to the likelihood of a poration event. Note that the value of the electric field strength imposed in simulations is not directly comparable to the electric field strengths reported in experimental studies (see section Molecular dynamics simulations for further explanation). After identifying when and where the pores formed in each simulation, we observed that pore locations do not distribute homogeneously along the membrane surface but often cluster together (Figure 2). An individual membrane exhibits one or more of such clusters. The location of pores is similar albeit not completely identical under depolarizing and hyperpolarizing electric field.

Figure 2

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Poration sites colocalize with domains with specific features, in particular with a high density of PU lipids

We hypothesized that pores preferably form in nanodomains with specific features. We used the recently developed tool MemSurfer (Bhatia et al., 2019) to extract from each membrane the local area per lipid (APL), membrane thickness, mean curvature, cosine of the dipole angle (cos θ_dip), charge, and lipid tail order parameter (Figure 3—figure supplement 1). We also determined the local density of individual groups of lipids, grouping the lipids either according to their head architecture or their tail saturation. These membrane features were extracted from 101 frames of a 10-ns long trajectory before electric field application, from each leaflet separately and in points corresponding to locations where a pore has or has not formed in any of the electroporation simulations. The first and second group of points are labelled as ‘porated’ and ‘non-porated’ locations, respectively (Figure 3A, left). We estimated the distribution of the values of the various features in non-porated and porated locations by constructing histograms (Supplementary file 1) and quantified the difference between probability density estimates by means of the Kullback–Leibler divergence (Figure 3B). By far the most significant feature to distinguish the locations where pore formed from locations where they did not was the presence of PU lipids, in both the APM and BPM membranes. This finding is corroborated by visualizing the colocalization of pore clusters with nanodomains enriched with PU lipids (Figure 3A). However, the analysis further showed that both the lipid head and tail architecture influence poration, with pores being favoured in regions with higher density of phosphatidylcholine (PC) lipids and lower densities of cholesterol (CHOL), gangliosides (GM), and fully saturated (FS) lipids. In BPM, the pores are also favoured in regions with higher content of phosphatidylethanolamine (PE) lipids, where most PE lipids in BPM are polyunsaturated (Figure 1—figure supplement 1). In addition, the analysis showed that pores in all membranes are favoured in regions with greater area per lipid and lower lipid order. None of the analysed features appeared markedly dependent on the electric field polarity, even when we contrasted them with 10-ns-long trajectories obtained under non-porating electric field (Figure 3—figure supplement 2).

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Knowing the lipid distribution is sufficient for machine learning models to reliably predict poration sites

The local poration propensity in both APM and BPM and under both electric field polarities is governed by similar features, for example, high density of PU lipids, as suggested by Kullback–Leibler divergence (Figure 3B). To corroborate this finding further, we trained three machine learning models, namely random forest, support vector machine (SVM), and multilayer perceptron neural network (Fleetwood et al., 2020), on selected subsets of data, that is, using features from APM or BPM and/or features obtained under hyperpolarization or depolarization. The accuracy of predicting poration in another/different subset of data typically surpassed 80% in all three models tested, with random forest exhibiting slightly superior performance (Table 3). Similar accuracy was obtained regardless of whether we trained and tested the models on (1) datasets from different membrane pairs of the same composition and the same electric field polarity (rows 1–6 in Table 3); (2) membranes of the same composition but different electric field polarity (rows 7–8 in Table 3); or (3) membranes of different composition (rows 9–11 in Table 3). Visual inspection of the prediction showed that locations corresponding to pore clusters are reliably predicted, whereas those that are scattered away from the clusters tend not to be predicted as accurately (Figure 4A).

Table 3

#	Training dataset	Test dataset	Random forest all features		SVM all features		Neural network all features		Random forestfour features
			Train	Test	Train	Test	Train	Test	Train	Test
	Same membrane composition, same E-field polarity; train on dataset from two out of four membranes
1	APM-dep, mem 1 and 2	APM-dep, mem 3 and 4	100%	83%	97%	83%	97%	81%	100%	82%
2	APM-dep, mem 1 and 3	APM-dep, mem 2 and 4	100%	80%	96%	80%	94%	77%	100%	76%
3	APM-dep, mem 1 and 4	APM-dep, mem 2 and 3	100%	85%	96%	85%	91%	81%	100%	82%
4	BPM-dep, mem 1 and 2	BPM-dep, mem 3 and 4	100%	87%	97%	86%	94%	86%	100%	84%
5	BPM-dep, mem 1 and 3	BPM-dep, mem 2 and 4	100%	82%	97%	84%	97%	79%	100%	85%
6	BPM-dep, mem 1 and 4	BPM-dep, mem 2 and 3	100%	75%	97%	83%	96%	77%	100%	82%
	Different membrane composition, same E-field polarity
7	APM-dep	BPM-dep	100%	83%	94%	82%	93%	83%	100%	83%
8	APM-hyp	BPM-hyp	100%	83%	94%	82%	95%	83%	100%	83%
	Same membrane composition, different E-field polarity
9	APM-dep	APM-hyp	100%	86%	95%	83%	94%	81%	100%	84%
10	BPM-dep	BPM-hyp	100%	90%	95%	86%	95%	84%	100%	88%
11	APM and BPM-dep	APM and BPM-hyp	100%	88%	94%	84%	93%	82%	100%	86%
	Same membrane composition, same E-field polarity; train on 60% dataset from all four membranes
12	APM-dep (60%)	APM-dep (40%)	100%	99%	94%	91%	91%	91%	100%	92%
13	APM-hyp (60%)	APM-hyp (40%)	100%	99%	94%	90%	92%	92%	100%	91%
14	BPM-dep (60%)	BPM-dep (40%)	100%	99%	95%	93%	94%	94%	100%	93%
15	BPM-hyp (60%)	BPM-hyp (40%)	100%	99%	94%	91%	95%	94%	100%	93%
16	APM and BPM-dep (60%)	APM and BPM-dep (40%)	100%	99%	94%	92%	92%	92%	100%	92%
17	APM and BPM-hyp (60%)	APM and BPM-hyp (40%)	100%	99%	92%	92%	91%	91%	100%	92%

Figure 4

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The prediction accuracy became considerably improved when a single dataset was randomly split into 60% training/40% test dataset (rows 12–17 in Table 3). In such case, random forest reached the highest accuracy of 99%. The improvement in accuracy suggests that there is something unique about poration of each membrane, even when membranes have practically identical overall composition, which the machine learning models can capture. However, this high accuracy could be partially biased by oversampling, which was performed to balance the starting number of porated locations (~60) and the number of non-porated locations (300), see Machine learning methods. When randomly choosing 60% of a given dataset for training, the values of features from all (not just 60%) actual porated locations are effectively taken into account. Therefore, we made additional tests, where we trained random forest on the first 32 porated and 150 non-porated locations for each of the APM membrane under depolarization. The accuracy of the prediction for the rest of the porated and non-porated locations was 92%, 97%, 94%, 95% for membranes 1–4, respectively. The accuracy was lower than 99%, but still considerably higher than when training/testing on pairs of different APM membranes (rows 1–3 in Table 3). Consequently, this exercise suggests that prediction accuracy might be improved by finetuning machine learning models on data from more different membranes or by adding additional features to the analysis in future studies.

From the datasets for both APM and BPM, we determined the feature importance score, which confirmed that the density of PU lipids is the most important for poration, followed by density of GM, CHOL, and FS lipids (Figure 4B). Furthermore, the feature importance score suggested that knowing the distribution of these lipid groups is sufficient to predict poration sites. The densities of other lipids and other membrane properties including the area per lipid, thickness, …, and lipid tail order can be practically neglected. We confirmed this by training random forest using four most important features, that is the density of PU, GM, CHOL, and FS lipids. The accuracy of the prediction was indeed very similar (≥76%) as when using all features (Table 3, last column).

Electroporation kinetics depends on membrane composition and electric field polarity but can be described with a universal model

The analysis presented so far demonstrates that the pore location mainly depends on the local lipid arrangement, particularly the density of PU lipids, regardless of the type of membrane and electric field polarity. However, this does not necessarily mean that poration is equally likely or equally fast in all membranes. To investigate whether the membranes differ in poration kinetics we compared the distributions of first poration times for each membrane. These distributions were indeed found to depend both on membrane composition and electric field polarity (Figure 5A). APM membranes tend to porate faster than BPM, and hyperpolarizing fields tend to porate faster than depolarizing fields.

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A Bayesian survival model was then trained (1) to quantify and study the statistical significance of the differences in poration rates, (2) to investigate if an underlying universal model can be used to describe the poration kinetics, and (3) to parametrize the kinetic parameters. Cox’s proportional hazards survival model (Cox, 1972) is a suitable model for this purpose, since it allows for an arbitrary time dependence of the poration rate, and it allows to then compare different systems or situations. This model assumes that for a given system, i, the instantaneous probability of an event happening, λ_i(t) (the rate pore formation), is a function of time:

(1) ${\lambda }_i\left(t\right)={\lambda }_0\left(t\right)\mathrm{e}\mathrm{x}\mathrm{p}\left({\beta }_i\right)$

where λ₀(t) is a time-dependent and system-independent baseline rate of pore formation and β_i are regression coefficients accounting for the difference in poration kinetics between systems (APM-depolarization, APM-hyperpolarization, BPM-depolarization, BPM-hyperpolarization). The baseline rate captures the common time dependency whereas the regression coefficient captures the system specificity. The inferred model was able to successfully reproduce the measured data (Figure 5—figure supplement 1) highlighting its robustness and suggesting the existence of a common kinetic model for electroporation. To further test the model validity, we trained a more complex model which allowed the β_i coefficients to vary with time, allowing for a system-specific time variability of λ_i(t). The β_i(t) obtained were found to slightly drop in the interval 0 < t < 3 ns until becoming practically time independent (Figure 5—figure supplement 2). Given that the β_i(t) for all systems follow the same trend and that the time-dependent model only adds information in the initial stage of electroporation and has a high uncertainty, the time-independent model was selected for its easier interpretability and lower complexity.

The time-independent Bayesian survival model shows that the baseline poration rate λ₀(t) is initially zero and then increases, reaching a constant steady-state value after approximately 3 ns (Figure 5B). To determine the mechanistic basis for the initial transient kinetic regime, we performed additional simulations at non-porating electric fields. These simulations revealed that the electric field E causes the membrane to thin and expand its area, whereby the relative change in membrane thickness and area are proportional to E² (Figure 5—figure supplement 5 and Figure 5—figure supplement 6), as expected for Maxwell stress (Lewis, 2003). The membrane thickness and area reach a steady state ~3 ns after electric field onset (Figure 5—figure supplement 4), suggesting that the time scale of the initial transient kinetic regime is related to the progressive thinning and area expansion caused by Maxwell stress.

The calculated β_i credible intervals (Figure 5C, Figure 5—figure supplement 3) confirm that the differences in poration kinetics between different systems are statistically significant. APM membranes porate ~5 and ~2 times faster than BPM for hyperpolarizing and depolarizing fields, respectively. Hyperpolarizing fields porate membranes ~3 and ~2 times faster than depolarizing fields for APM and BPM membranes, respectively. We found that the values of β_i correlate with the ability of a membrane to thin and expand its area under electric field, that is, they corelate inversely with the membrane area compressibility (or stretching) modulus (Figure 5D, E).

In this study, we focused on lipid pores formed by electric field (electroporation) and we asked three main questions: Where do pores form in membranes with realistic plasma membrane lipid composition? Which membrane features/properties govern the most likely poration sites? Which membrane features/properties govern the poration kinetics?

The current manuscript is a computational study. Data required to reproduce the results is available at https://osf.io/fv98a/. Analysis codes are available at https://github.com/learems/Electroporation-CGmem-PoreLocalization (copy archived at swh:1:rev:af74428dc722ea4ecdb3e1f1c62178ea3f91b65b) , https://github.com/learems/Electroporation-CGmem-MemSurfer (copy archived at swh:1:rev:3e7d2d393b8ec98e04aa1e8915b55ee024840b97), https://github.com/learems/Electroporation-CGmem-MachineLearning, (copy archived at swh:1:rev:1e32cf42c04af4543fb101ece2c92f35d793d62e), and https://github.com/sperezconesa/electroporation_modeling, (copy archived at swh:1:rev:1cc26d28bd76b5c254b4cbbf85703b2394aff775).

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Author details

1. Lea Rems

   1. KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden
   2. University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia

   Contribution

   Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Supervision, Validation, Visualization, Writing – original draft, Writing - review and editing

   For correspondence

   lea.rems@fe.uni-lj.si

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7470-4367

2. Xinru Tang

   1. KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden
   2. University of Chinese Academy of Sciences, Beijing, China

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing – original draft

   Contributed equally with

   Fangwei Zhao

   Competing interests

   No competing interests declared

3. Fangwei Zhao

   1. KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden
   2. University of Chinese Academy of Sciences, Beijing, China

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing – original draft

   Contributed equally with

   Xinru Tang

   Competing interests

   No competing interests declared

4. Sergio Pérez-Conesa

   KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden

   Contribution

   Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing - review and editing

   Competing interests

   No competing interests declared

5. Ilaria Testa

   KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden

   Contribution

   Conceptualization, Funding acquisition, Investigation, Supervision, Validation, Writing - review and editing

   Competing interests

   Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-4005-4997

6. Lucie Delemotte

   KTH Royal Institute of Technology, Dept. Applied Physics, Science for Life Laboratory, Solna, Sweden

   Contribution

   Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Validation, Writing - review and editing

   For correspondence

   lucie.delemotte@scilifelab.se

   Competing interests

   Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0002-0828-3899

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