A Computational Study of The Electrical Response of Biological Cells with Realistic Three-Dimensional Morphologies

Abstract

One of the unique features of a biological cell is the cell membrane that protects the cell interior by establishing a physical barrier between the cytoplasm and the extracellular matrix and governs the distribution of the cytoskeleton to control the three-dimensional (3D) morphology of a cell. From an electrical standpoint, the cell membrane represents an insulating layer with selective ion permeability, thereby administering an ionic imbalance between the conductive extracellular and intracellular fluids. Consequently, the electrical characterization of a biological cell mostly focuses on the specific electrical properties of the cell membrane and the means to modulate its semipermeable nature. Previously reported research studies had revealed many characteristics of the cell membrane. However, they did not explore the morphological feature to its fullest, especially in three dimensions. Motivated by this knowledge gap, this work explores the effect of the 3D variations in cell morphology on the electrical response of biological cells. The most diverse and accurate 3D cell database developed to date by the National Institute of Standards and Technology was incorporated in this study, and an extensive investigation of these cells’ electrical characteristics was manifested by computational means. The cell database has hundreds of morphologies that were reconstructed from stem cells grown in different environments. To quantify how cell morphology affects the electrostatic properties of these complex cells, a validation study was conducted to study the polarizability tensors of stem cell morphologies, using three independent computational techniques. To draw accurate conclusions, the polarizability tensors of more than 1000 stem cells were calculated and statistical analysis was conducted to identify which growth environment generates cells with similar electric properties. Next, we studied the induced transmembrane voltage (ITV) across the cell membrane when it is subjected to a static and dynamic external electrical stimulus. The ITV generated across a cell’s membrane plays a significant role in the process of electroporation since the membrane permeability increases when the ITV exceeds a certain threshold. By setting an arbitrary ITV electroporation threshold, the electroporated area for each stem cell morphology at different orientations was calculated and significant differences were shown in comparison to spherical cells of similar size. The significance of morphological variation is more prominent for dynamic frequency-dependent excitation. Using computational experiments, it has been observed that as the frequency of the excitation increases, the ITV decreases beyond a certain cutoff frequency that varies with cell morphology. While the ITV study is vital in low-frequency applications, the nonlinear membrane dynamics must be taken into consideration in case of high intensity ultra-short electrical stimulus, commonly used in supra-electroporation techniques to penetrate the internal organelles’ (i.e. nucleus, mitochondria, etc.) membrane. As a consecutive step of this research, a computational testbed was developed upon the stem cell geometries to investigate the supra-electroporation phenomenon in realistic cell shapes. The results obtained from this study suggest that supra-electroporation is highly dependent on the cell membrane irregularity, especially the location of the internal organelle with respect to any protrusion on the cell surface. The results from this observation can be utilized to engineer selective targeting of the desired cell with specific morphology.