A minimal model for poration induced electro deformation of Giant Vesicles

TL;DR

The paper delivers a minimal analytical framework that couples electrostatics, hydrodynamics, and membrane mechanics to describe poration-induced deformation of GUVs under pulsed DC fields. By explicitly modeling poration as a growing, angularly dependent membrane conductance and translating the resulting excess area into higher Legendre deformation modes ($P_2$, $P_4$, $P_6$), the authors predict prolate, oblate, cylindrical, and square-like vesicle shapes through Maxwell stresses that scale quadratically with the field. The model obtains qualitative and semi-quantitative agreement with experimental observations across varying conductivity ratios ($\beta$) and salt conditions, using a fitting parameter $\chi$ to scale the poration area $A_p(t)$. This work highlights poration-driven excess area as the key mechanism behind amplified deformation under porating fields and lays a foundation for future, more tightly coupled tension-poration models. The approach provides insight into the role of higher-order deformation modes and offers a tractable analytical route to interpret rapid electrohydrodynamic responses in GUVs.

Abstract

This work attempts to understand the mechanism of simultaneous electrodeformation and electroporation in Giant Unilamellar Vesicles (GUVs) using a minimal analytical model. In the small deformation limit, the coupled electroporation, electrohydrodynamics and membrane mechanics are solved. The excess membrane area generated by electroporation manifests as amplitudes of the second, fourth, and sixth Legendre modes, P2(cosθ), P4(cosθ), and P6(cosθ), respectively, which serves as the shape function. The proposed model reveals that accentuated deformation in GUVs under strong pulsed DC fields arises from the additional surface area introduced by membrane poration. Thus, the resulting GUV deformation, obtained as a result of a balance of electric stresses and the membrane and hydrodynamic stresses, is prolate or oblate cylindrical or square shaped instead of prolate or oblate ellipsoids, as otherwise seen under weak AC/DC fields. The origin of higher modes is essentially due to electropore-generated membrane conductance, which is approximated to angularly vary as 2/3(1/2+P2(cosθ)), to keep the calculations analytically tractable, whereby the electric potential varies as P3(cosθ) in addition to P1(cosθ) seen for unporated vesicles. The vesicle correspondingly admits P4(cosθ) and P6(cosθ) shape deformation modes, besides P2(cosθ) observed for unporated vesicles, on account of the quadratic dependence of Maxwell stresses on the electric field. The model qualitatively and semiquantitatively, with a correction factor (fitting parameter), captures the square shape modes for \b{eta} = 1, prolate ellipsoids (cylinders) for \b{eta} >1, and oblate cylinders for \b{eta} < 1, where \b{eta} =σi/σe is the ratio of the electrical conductivity of the inner fluid (σi) to the outer fluid (σe).

Figures (14)

• Figure 1: (i) Schematic of a Giant Unilamellar Vesicle (GUV) with radius $R$, depicting the conductivities ($\sigma_i, \sigma_e$) and permittivities ($\epsilon_i, \epsilon_e$) of the inner and outer fluids. (ii) Upon application of a DC pulse electric field along the $z$-direction, the schematic shows a GUV undergoing prolate deformation and membrane poration.
• Figure 2: Collage of images of low and high salt for 1.0 and 1.5 kV/cm for $\beta<1,=1,>1$, adapted from Maoyafikuddin et al maoyafikuddin2025synthesis; at the end of $1ms$.
• Figure 3: The fractional pore area data plotted with parameters in table \ref{['nalinifit']} using the electroporation model. 1 kV/cm, low salt- solid line (red), 1.5 kV/cm, low salt- dashed (blue), 1 kV/cm, high salt- dot dashed (black), and 1.5 kV/cm, high salt- dotted (green) in all three cases (a) $\beta<1$, (b) $\beta=1$, and (c) $\beta>1$.
• Figure 4: Plots for $\beta<1$, low salt. First column E=1 kV/cm, unporated, second column E=1 kV/cm, porated, third column E=1.5 kV/cm, porated. (a),(b),and (c) AR vs $t$ plot, (d),(e), and (f) $V_{mb}$ vs $t$, (g),(h), and (i) $V_{mb}$ vs $\theta$, $t=\tau_c/2$-red solid, $t=1.5 \tau_c$-blue dashed, $t=t_p$-black dotdashed, (j),(k), and (l) Normal electric stress ($\tau_n^e$) vs $\theta$, $t=\tau_c/2$-red solid, $t=1.5 \tau_c$ -blue dashed, $t=t_p$-black dotdashed, (m), (n) and (o) Tangential electric stress ($\tau_t^e$) vs $\theta$, $t=\tau_c/2$-red solid, $t=1.5 \tau_c$-blue dashed, $t=t_p$-black dotdashed, (p), (q) and (r) $s_2,s_4,s_6$ vs $t$, electric field directed left to right, $s_2$-red solid, $s_4$-blue dashed, $s_6$-black dotdashed, (s),(t) and (u) $r$ vs $z$ circle- black dotdashed, model prediction-red solid, experimental - blue dots
• Figure 5: Electric field ($V/m$) distribution for $\beta<1$, (a) and (d) 1 kV/cm unporated, (b) and (e) 1 kV/cm porated, all at low salt (c) and (f) 1kv porated at high salt (first-row at $t=\tau_c$, second-row at $t=t_{p}$). Electric field in the direction of the arrow (bottom to top).