Curvature-driven pore growth in charged membranes during charge-pulse and voltage-clamp experiments

Phase-field model of bilipid membrane electroporation

This paper proposes a new model of membrane electropermeabilisation that combines the water content of the membrane and the transmembrane voltage. Interestingly, thanks to a well defined free-energy of the membrane, we somehow generalise the seminal approach of Chizmadzhev, Weaver and Krassowska, getting rid of the geometrical cylindrical assumption upon which most of the current electroporation models are based. Our approach is physically relevant and we recover a surface diffusion equation of the lipid phase proposed by Leguèbe et al. in a previous phenomenological model. We also perform a fine analysis of the involved nonlocal operators in two simple configurations (a spherical membrane and a flat periodic membrane) that enables us to compare the time constants of the phenomenon in spherical and flat membranes. An accurate splitting scheme combined with Fast Fourier Transforms is developed for efficient computations of the model. Our numerical results enable us to make a link between the molecular dynamics simulations of membrane permeabilisation and the experimental observations on vesicles and cells.

Modeling and simulation of current-clamp electroporation

Current-Clamp electroporation refers to the application of a constant current across a membrane which results in voltage fluctuations due to the creation of electropores. This method allows for the measurement of electroporation across a long timescale (minutes) and facilitates the comparison between experimental and theoretical studies. Of particular interest is the claim in the literature that current-clamp electroporation results in the creation of a single pore. We simulated current-clamp electroporation using the Smoluchowski and Langevin equations and identified two possible mechanisms to explain the observed voltage fluctuations. The voltage fluctuations may be due to a single pore or a few pores growing and shrinking via a negative feedback mechanism or the opening and closing of pores in a larger population of pores. Our results suggest that current-clamp conditions do not necessarily result in the creation of a single pore. Additionally, we showed that the Langevin model is more accurate than the Smoluchowski model under conditions where there are only a few pores.

Response characteristics and optimization of electroporation: simulation based on finite element method

Electroporation has been widely used in biology, medicine, and the food industry as a means to transport various molecules through the cell membrane. The phenomenon of electroporation is the result of cell membrane damage caused by the application of an electric field. In order to understand more precisely how cells function, we established a dielectric model of a spherical cell and analyzed its characteristics by the finite element method. The effects of altering different electrical parameters were determined. The results showed that the electric field strength was positively related to the transmembrane voltage (TMV) and pore density. There was a minimum electric field strength necessary to induce a critical TMV for the formation of pores. Pulse width also had to be long enough to charge the cell membrane, compared with the normal membrane charging time constant of about 1 μs. When the pulse width was shorter than the charging time constant, it was necessary to increase pulse frequency to create a high enough TMV. The rise-time of the electric pulse also affected electroporation: a fast rise-time pulse not only allowed penetration of the plasma membrane but also the organelle membrane. With slow rise-time pulse, the organelle was shielded from electroporation. This study defines the response characteristics of electrical parameters on the electric load cell and establishes the specificity of parameters for different purposes.

Characterizing the malignancy and drug resistance of cancer cells from their membrane resealing response

In this report, we showed that two tumor cell characteristics, namely the malignancy and drug-resistance status can be evaluated by their membrane resealing response. Specifically, membrane pores in a number of pairs of cancer and normal cell lines originated from nasopharynx, lung and intestine were introduced by nano-mechanical puncturing. Interestingly, such nanometer-sized holes in tumor cells can reseal ~2-3 times faster than those in the corresponding normal cells. Furthermore, the membrane resealing time in cancer cell lines exhibiting resistance to several leading chemotherapeutic drugs was also found to be substantially shorter than that in their drug-sensitive counterparts, demonstrating the potential of using this quantity as a novel marker for future cancer diagnosis and drug resistance detection. Finally, a simple model was proposed to explain the observed resealing dynamics of cells which suggested that the distinct response exhibited by normal, tumor and drug resistant cells is likely due to the different tension levels in their lipid membranes, a conclusion that is also supported by direct cortical tension measurement.

Estimation of activation energy for electroporation and pore growth rate in liquid crystalline and gel phases of lipid bilayers using molecular dynamics simulations

Molecular dynamics simulations of electroporation in POPC and DPPC lipid bilayers have been carried out at different temperatures ranging from 230 K to 350 K for varying electric fields. The dynamics of pore formation, including threshold field, pore initiation time, pore growth rate, and pore closure rate after the field is switched off, was studied in both the gel and liquid crystalline (Lα) phases of the bilayers. Using an Arrhenius model of pore initiation kinetics, the activation energy for pore opening was estimated to be 25.6 kJ mol(-1) and 32.6 kJ mol(-1) in the Lα phase of POPC and DPPC lipids respectively at a field strength of 0.32 V nm(-1). The activation energy decreases to 24.2 kJ mol(-1) and 23.7 kJ mol(-1) respectively at a higher field strength of 1.1 V nm(-1). At temperatures below the melting point, the activation energy in the gel phase of POPC and DPPC increases to 28.8 kJ mol(-1) and 34.4 kJ mol(-1) respectively at the same field of 1.1 V nm(-1). The pore closing time was found to be higher in the gel than in the Lα phase. The pore growth rate increases linearly with temperature and quadratically with field, consistent with viscosity limited growth models.

A model of plasma membrane flow and cytosis regulation in growing pollen tubes

A model of cytosis regulation in growing pollen tubes is developed and simulations presented. The authors address the question on the minimal assumptions needed to describe the pattern of exocytosis and endocytosis reported recently by experimental biologists. Biological implications of the model are also treated. Concepts of flow and conservation of membrane material are used to pose an equation system, which describes the movement of plasma membrane in the tip of growing pollen tubes. After obtaining the central equations, relations describing the rates of endocytosis and exocytosis are proposed. Two cytosis receptors (for exocytosis and endocytosis), which have different recycling rates and activation times, suffice to describe a stable growing tube. Simulations show a very good spatial separation between endocytosis and exocytosis, in which separation is shown to depend strongly on exocytic vesicle delivery. In accordance to measurements, most vesicles in the clear zone are predicted to be endocytic. Membrane flow is essential to maintain cell polarity, and bi-directional flow seems to be a natural consequence of the proposed mechanism. For the first time, a model addressing plasma membrane flow and cytosis regulation were posed. Therefore, it represents a missing piece in an integrative model of pollen tube growth, in which cell wall mechanics, hydrodynamic fluxes and regulation mechanisms are combined.

Theoretical and experimental analysis of electroporated membrane conductance in cell suspension

An intense electric field can be applied to increase the membrane conductance G(m) and consequently, the conductivity of cell suspension. This phenomenon is called electroporation. This mechanism is used in a wide range of medical applications, genetic engineering, and therapies. Conductivity measurements of cell suspensions were carried out during application of electric fields from 40 to 165 kV/m. Experimental results were analyzed with two electroporation models: the asymptotic electroporation model was used to estimate G(m) at the beginning and at the end of electric field pulse, and the extended Kinosita electroporation model to increase G(m) linearly in time. The maximum G(m) was 1-7 × 10(4) S/m(2), and the critical angle (when the G(m) is insignificant) was 50°-65°. In addition, the sensitivity of electroporated membrane conductance to extracellular and cytoplasmatic conductivity and cell radius has been studied. This study showed that external conductivity and cell radius are important parameters affecting the pore-opening phenomenon. However, if the cell radius is larger than 7 μm in low conductivity medium, the cell dimensions are not so important.