Electromagnetic field investigation on different cancer cell lines

Pulsed Electromagnetic Fields (PEMFs) Trigger Cell Death and Senescence in Cancer Cells

The currently available anti-cancer therapies, such as gamma-radiation and chemotherapeutic agents, induce cell death and cellular senescence not only in cancer cells but also in the adjacent normal tissue. New anti-tumor approaches focus on limiting the side effects on normal cells. In this frame, the potential anti-tumor properties of Pulsed Electromagnetic Fields (PEMFs) through the irradiation of breast cancer epithelial cells (MCF-7 and MDA-MB-231) and normal fibroblasts (FF95) were investigated. PEMFs had a frequency of 8 Hz, full-square wave type and magnetic flux density of 0.011 T and were applied twice daily for 5 days. The data collected showcase that PEMF application decreases the proliferation rate and viability of breast cancer cells while having the opposite effect on normal fibroblasts. Moreover, PEMF irradiation induces cell death and cellular senescence only in breast cancer cells without any effect in the non-cancerous cells. These findings suggest PEMF irradiation as a novel, non-invasive anti-cancer strategy that, when combined with senolytic drugs, may eliminate both cancer and the remaining senescent cells, while simultaneously avoiding the side effects of the current treatments.

P53 status, and G2/M cell cycle arrest, are determining factors in cell-death induction mediated by ELF-EMF in glioblastoma

The average survival of patients with glioblastoma is 12-15 months. Therefore, finding a new treatment method is important, especially in cases that show resistance to treatment. Extremely low-frequency electromagnetic fields (ELF-EMF) have characteristics and capabilities that can be proposed as a new cancer treatment method with low side effects. This research examines the antitumor effect of ELF-EMF on U87 and U251 glioblastoma cell lines. Flowcytometry determined the viability/apoptosis and distribution of cells in different phases of the cell cycle. The size of cells was assessed by TEM. Important cell cycle regulation genes mRNA expression levels were investigated by real-time PCR. ELF-EMF induced apoptosis in U87cells much more than U251 (15% against 2.43%) and increased G2/M cell population in U87 (2.56%, p value < 0.05), and S phase in U251 (2.4%) (data are normalized to their sham exposure). The size of U87 cells increased significantly after ELF-EMF exposure (overexpressing P53 in U251 cells increased the apoptosis induction by ELF-EMF). The expression level of P53, P21, and MDM2 increased and CCNB1 decreased in U87. Among the studied genes, MCM6 expression decreased in U251. Increasing expression of P53, P21 and decreasing CCNB1, induction of cell G2/M cycle arrest, and consequently increase in the cell size can be suggested as one of the main mechanisms of apoptosis induction by ELF-EMF; furthermore, our results demonstrate the possible footprint of P53 in the apoptosis induction by ELF-EMF, as U87 carry the wild type of P53 and U251 has the mutated form of this gene.

Cross-talk between non-ionizing electromagnetic fields and metastasis; EMT and hybrid E/M may explain the anticancer role of EMFs

Recent studies have shown that non-ionizing electromagnetic fields (NIEMFs) in a specific frequency, intensity, and exposure time can have anti-cancer effects on various cancer cells; however, the underlying precise mechanism of action is not transparent. Most cancer deaths are due to metastasis. This important phenomenon plays an inevitable role in different steps of cancer including progression and development. It has different stages including invasion, intravasation, migration, extravasation, and homing. Epithelial-mesenchymal transition (EMT), as well as hybrid E/M state, are biological processes, that involve both natural embryogenesis and tissue regeneration, and abnormal conditions including organ fibrosis or metastasis. In this context, some evidence reveals possible footprints of the important EMT-related pathways which may be affected in different EMFs treatments. In this article, critical EMT molecules and/or pathways which can be potentially affected by EMFs (e.g., VEGFR, ROS, P53, PI3K/AKT, MAPK, Cyclin B1, and NF-кB) are discussed to shed light on the mechanism of EMFs anti-cancer effect.

A mechanistically approached review upon assorted cell lines stimulated by athermal electromagnetic irradiation

The probable influence of electromagnetic irradiation on cancer treatment has been deduced from the interaction of artificial electromagnetic emissions with biological organisms. Nonetheless, the suspected health effects induced by electromagnetic-based technology imply that such a treatment may contaminate the adjacent healthy cells. Thus, gaining mechanistic insights into the problem is required to avoid athermal health hazards. To tackle that, the current review, based upon in vitro studies into assorted cell lines, depicts the alterations in physiological processes triggered by electromagnetic irradiation via addressing gene regulatory cascades. Furthermore, decisive factors in the hypothesized cause-effect linkage in terms of the cell line-associated, exposure-associated, or endpoint-associated parameters are highlighted. As a result, subcellular structures such as aberrant Ca2+ channels, rich glycocalyx charge, or high water content in cancerous cells, which have attracted a great deal of attention, can explain their higher susceptibility compared with healthy cells under irradiation. Affected by cell components or geometry, the cellular biological window correlates with the metabolic or cell cycle status and determines the irradiation that causes the maximum influence. For instance, correlations between the frequency (or intensity) of irradiation and cell excitability or between the duration of irradiation and cell doubling time are observed. There are unspecified signaling pathways such as the pathway of PPAR-γ or MAPKs, and also proteins devoid of any investigation such as p14, or S phase-related and G2 phase-related proteins. Other chains, such as the cAMP connection with mitochondrial ATP or ERK signaling, the association of Hsps releases with signaling pathways of MAPKs, or the role of different ion channels in regulating various cell processes, require further investigation.

Synergistic cytotoxic effects of an extremely low-frequency electromagnetic field with doxorubicin on MCF-7 cell line

Breast cancer is one of the leading causes of cancer deaths in women worldwide. Magnetic fields have shown anti-tumor effects in vitro and in vivo as a non-invasive therapy method that can affect cellular metabolism remotely. Doxorubicin (DOX) is one of the most commonly used drugs for treating breast cancer patients. It can be assumed that combining chemotherapy and magnetotherapy is one of the most effective treatments for breast cancer. This study aimed to investigate the potential cytotoxic effect of DOX at low concentrations in combination with extremely low-frequency electromagnetic fields (ELF-EMF; 50 Hz; 20 mT). The breast cancer cell line MCF-7 was examined for oxidative stress, cell cycle, and apoptosis. MCF-7 cells were treated with various concentrations of DOX as an apoptosis-inducing agent and ELF-EMF. Cytotoxicity was examined using the MTT colorimetric assay at 12, 24, and 48 h. Consequently, concentration- and time-dependent cytotoxicity was observed in MCF-7 cells for DOX within 24 h. The MTT assay results used showed that a 2 μM concentration of DOX reduced cell viability to 50% compared with control, and as well, the combination of ELF-EMF and DOX reduced cell viability to 50% compared with control at > 0.25 μM doses for 24 h. In MCF-7 cells, combining 0.25 μM DOX with ELF-EMF resulted in increased ROS levels and DOX-induced apoptosis. Flow cytometry analysis, on the other hand, revealed enhanced arrest of MCF-7 cells in the G0-G1 phase of the cell cycle, as well as inducing apoptotic cell death in MCF-7 cells, implying that the synergistic effects of 0.25 μM DOX and ELF-EMF may represent a novel and effective agent against breast cancer.

An overview of the biological effects of extremely low frequency electromagnetic fields combined with ionizing radiation

By growing the electrical power networks and electronic devices, electromagnetic fields (EMF) have become an inseparable part of the modern world. Considering the inevitable exposure to a various range of EMFs, especially at extremely low frequencies (ELF-EMF), investigating the biological effects of ELF-EMFs on biological systems became a global issue. The possible adverse consequences of these exposures were studied, along with their potential therapeutic capabilities. Also, their biological impacts in combination with other chemical and physical agents, specifically ionizing radiation (IR), as a co-carcinogen or as adjuvant therapy in combination with radiotherapy were explored. Here, we review the results of several in-vitro and in-vivo studies and discuss some proposed possible mechanisms of ELF-EMFs' actions in combination with IR. The results of these experiments could be fruitful to develop more precise safety standards for environmental ELF-EMFs exposures. Furthermore, it could evaluate the therapeutic capacities of ELF-EMFs alone or as an improver of radiotherapy.

Cancer on-target: Selective enhancement of 3-bromopyruvate action by an electromagnetic field in vitro

Cancer is one of the leading causes of death in the modern world. Nowadays, most often treatment methods used in clinical oncology are drug therapies applied as monotherapy or combined therapy. Additionally, recent studies focus on developing approaches with the use of a drug in combination with other factors, not only chemical, to improve the probability and magnitude of therapeutic responses and reduce the possibility of chemoresistance. Such a promising factor seems to be an electromagnetic field (EMF) application. Here, we tested the effect of continuous or pulsed EMF on human cancer cells of different origin treated or not with 3-bromopyruvate, a small and powerful alkylating agent with a broad spectrum of anticancer activities. We provide strong evidence suggesting that ELF-EMF potentiates the anti-cancer activity of 3BP in human cancer cells through inhibition of TNFα secretion leading to irreversible p21/p27-dependent G2/M cell cycle arrest and finally cancer cell death. Our findings suggest a novel approach combining pharmacotherapy with ELF-EMF. In conclusion, electromagnetic field seems to be a potential modulator of anti-cancer efficacy of 3BP while combined therapy offers off-target activity. These features contribute to the development of innovative therapeutic strategies for cancer treatment.

Effects of repeated exposure to 50 Hz electromagnetic field on breast cancer cells

The extremely low frequency electromagnetic field (ELF-EMF) is emerging as a novel approach in cancer treatment. This study evaluated the impact of daily exposure to 50 Hz EMF on breast cancer cells in vitro. The MDA-MB-231 and MCF-7 cells were exposed to EMF (50 Hz 20 mT, for 3 hours per day for up to four days) and examined for cell vaibility. The effect of daily ELF-EMF exposure on cell cycle progression and cell death was further investigated. The result revealed that the consecutive exposure to 50 Hz EMF at 20 mT remarkably decreased the viability of MDA-MB-231 compared to the non-exposed group, while it had no significant effect on MCF-7 cells. The ELF-EMF exposure induced G1 phase arrest along with the increase in sub-G1 cell population in MDA-MB-231. Moreover, repeated exposure to 50 Hz EMF promoted cell cycle progression in MCF-7 by increasing the percentage of cells in the S phase. The fluorescent staining revealed that daily exposure of ELF-EMF induced apoptotic cell death in MDA-MB-231, but no morphological change was observed in MCF-7 cells. The results showed that repeated daily exposure to 50 Hz EMF exhibited anti-proliferative activity against invasive breast cancer cells by impairing cell cycle progression and inducing cell death.

Up-regulation of miR-144 and miR-375 in the human gastric cancer cell line following the exposure to extremely low-frequency electromagnetic fields

PURPOSE

Recently, therapeutic effects of extremely low-frequency electromagnetic field (ELF-EMF) as complementary and alternative medicine, used in the oncology field to control disease symptoms. Micro RNAs (miRs) are responsible for the post-transcriptional regulation of gene expression in the cell. This study aimed to evaluate the expression changes of miR-144 and miR-375 in the human gastric adenocarcinoma cell line (AGS) under the exposure of ELF-EMF.

MATERIALS AND METHODS

AGS cells were exposed to magnetic flux densities of 0.2 and 2 mT for 18 h, continuously and discontinuously (1.5 h on/1.5 h off). Cell viability was evaluated by MTT assay. Changes of miR-144 expression levels in AGS cells immediately after exposure and 18 and 36 h after the exposure cut-off was calculated by QRT-PCR.

RESULTS

The cell viability of AGS cells was decreased under the exposure of 0.2 and 2 mT EMFs when compared to the control. Up-regulation of miR-144 and miR-375 were observed in AGS cells under the exposure of magnetic fields.

CONCLUSIONS

The results indicated that the miR levels were significantly decreased 18 and 36 h after finishing the exposure, but not reached the normal range. The results of this investigation indicated that weak and moderate intermittent 50 Hz ELF-EMFs can induce changes in miRNA expression.

Progressive Study on the Non-thermal Effects of Magnetic Field Therapy in Oncology

Cancer is one of the most common causes of death worldwide. Although the existing therapies have made great progress and significantly improved the prognosis of patients, it is undeniable that these treatment measures still cause some serious side effects. In this context, a new treatment method is needed to address these shortcomings. In recent years, the magnetic fields have been proposed as a novel treatment method with the advantages of less side effects, high efficiency, wide applications, and low costs without forming scars. Previous studies reported that static magnetic fields (SMFs) and low-frequency magnetic fields (LF-MFs, frequency below 300 Hz) exert anti-tumor function, independent of thermal effects. Magnetic fields (MFs) could inhibit cell growth and proliferation; induce cell cycle arrest, apoptosis, autophagy, and differentiation; regulate the immune system; and suppress angiogenesis and metastasis via various signaling pathways. In addition, they are effective in combination therapies: MFs not only promote the absorption of chemotherapy drugs by producing small holes on the surface of cell membrane but also enhance the inhibitory effects by regulating apoptosis and cell cycle related proteins. At present, MFs can be used as drug delivery systems to target magnetic nanoparticles (MNPs) to tumors. This review aims to summarize and analyze the current knowledge of the pre-clinical studies of anti-tumor effects and their underlying mechanisms and discuss the prospects of the application of MF therapy in cancer prevention and treatment.

Evaluation of frequency magnetic field, static field, and Temozolomide on viability, free radical production and gene expression (p53) in the human glioblastoma cell line (A172)

Thirteen million cancer deaths and 21.7 million new cancer cases are expected in the world by 2030. Glioblastoma is the most common primary malignant tumor of the central nervous system which is the most lethal type of primary brain tumor in adults with the survival time of 12-15 months after the initial diagnosis. Glioblastoma is the most common and most malignant type of brain tumor, and despite surgery, chemotherapy and radiation treatment, the average survival of patients is about 14 months. The current research showed that the frequency magnetic field (FMF) and static magnetic field (SMF) can influence cancer cell proliferation and coupled with anticancer drugs may provide a new strategy for cancer therapy. At the present study, we investigated the effects of FMF (10 Hz, 50 G), SMF (50 G) and Temozolomide (200 μm) on viability, free radical production, and p53 followed by p53 protein expression in the human glioblastoma cell line (A172) by MTT, NBT, RT-PCR and Western blot. Results showed that the effect of Temozolomide (TMZ) with SMF and FMF together increased the cytotoxicity, free radical production, and p53 followed by p53 protein expression in the human glioblastoma cell line (A172).

Low-Frequency Magnetic Fields (LF-MFs) Inhibit Proliferation by Triggering Apoptosis and Altering Cell Cycle Distribution in Breast Cancer Cells

Breast cancer is a common malignancy threatening women’s health around the world. Despite improved treatments for different subtypes of breast tumors that have been put forward, there still exists a poor therapeutic response and prognosis. Magnetic fields, as a non-invasive therapy, have shown anti-tumor effects in vitro and in vivo; however, the detailed mechanisms involved are still not clear. In this study, we found that in exposure to low-frequency magnetic fields (LF-MFs) with an intensity of 1 mT and frequencies of 50, 125, 200, and 275 Hz, separately, the proliferation of breast cancer cells was inhibited and LF-MF with 200 Hz reached the optimum inhibition effect, on exposure time-dependently. Notably, we found that exposure to LF-MF led to MCF-7 and ZR-75-1 cell apoptosis and cell cycle arrest. Moreover, we also discovered that LF-MF effectively increased the level of reactive oxygen species (ROS), suppressed the PI3K/AKT signaling pathway, and activated glycogen synthase kinase-3β (GSK-3β). We demonstrated that the GSK3β activity contributed to LF-MF-induced cell proliferation inhibition and apoptosis, while the underlying mechanism was associated with the inhibition of PI3K/AKT through increasing the intracellular ROS accumulation. These results indicate that LF-MF with a specific frequency may be an attractive therapy to treat breast cancers.

Anticancer Activities of Cu(II) Complex-Schiff Base and Low-Frequency Electromagnetic Fields and the Interaction Between Cu(II) Complex-Schiff Base with Bovine Serum Albumin by Spectroscopy

Cancer is the consequence of abnormal cell proliferation, which leads to the formation of abnormal mass. In this study, we aimed to determine the anticancer properties of Cu(II)-Schiff base complex and low-frequency electromagnetic field, and the interaction between BSA and Cu(II) complex. Firstly, Schiff base of the Cu(II) complex in the N,N'-dipyridoxyl(1,2 diaminobenzene) was originally synthesized. Following, the breast cancer was transplanted with the TUBO cells in vivo. Then, treatment of the cancerous mice was done by low-frequency electromagnetic field and the Cu(II)-Schiff base complex. In this project, antiproliferative activity on breast cancer cells was tested by TUBO cells using MTT assay and apoptosis properties were studied by flow cytometry. The interaction between the Cu(II)-Schiff base complex and bovine serum albumin (BSA) was checked by fluorescence and UV-vis absorbance spectroscopy. Tumor tissue investigation demonstrated that the low-frequency electromagnetic field and Cu(II)-Schiff base complex induce apoptosis and inhibit tumor growth. MTT results unveiled a cytotoxic impact on breast cancer cells. Flow cytometry analysis demonstrates that the anticancer effect of Cu(II)-Schiff base complex on breast cancer cells (MCF7) was associated with the cell cycle arrest. The results of fluorescence spectra and UV-vis absorption spectra showed that the conformation of bovine serum albumin has been changed in the presence of Cu(II)-Schiff base complex. Cu(II)-Schiff base complex and low-frequency electromagnetic field have anticancer properties. The spectroscopy method indicates the binding between Cu(II)-Schiff base complex and BSA.

A high throughput screening system of coils for ELF magnetic fields experiments: proof of concept on the proliferation of cancer cell lines

Background

It has been demonstrated that relatively small variations of the parameters of exposure to extremely low frequency magnetic fields (ELF-MF) can change significantly the outcome of experiments. Hence, either in trying to elucidate if these fields are carcinogenic, or in exploring their possible therapeutic use, it is desirable to screen through as many different exposures as possible. The purpose of this work is to provide a proof of concept of how a recently reported system of coils allows testing different field exposures, in a single experiment.

Methods

Using a novel exposure system, we subjected a glioblastoma cancer cell line (U251) to three different time modulations of an ELF-MF at 60 different combinations of the alternated current (AC) and direct current (DC) components of the field. One of those three time modulations was also tested on another cell line, MDA-MB-231 (breast cancer). After exposure, proliferation was assessed by colorimetric assays.

Results

For the U251 cells, a total of 180 different exposures were tested in three different experiments. Depending on exposure modulation and AC field intensity (but, remarkably, not on DC intensity), we found the three possible outcomes: increase (14.3% above control, p < 0.01), decrease (16.6% below control, p < 0.001), and also no-effect on proliferation with respect to control. Only the time modulation that inhibited proliferation of U251 was also tested on MDA-MB-231 cells which, in contrast, showed no alteration of their proliferation on any of the 60 AC/DC field combinations tested.

Conclusions

We demonstrated, for the first time, the use of a novel system of coils for magnetobiology research, which allowed us to find that differences of only a few μT resulted in statistically different results. Not only does our study demonstrate the relevance of the time modulation and the importance of finely sweeping through the AC and DC amplitudes, but also, and most importantly, provides a proof of concept of a system that sensibly reduces the time and costs of screening.

Electronic supplementary material

The online version of this article (10.1186/s12885-019-5376-z) contains supplementary material, which is available to authorized users.

A review on the use of magnetic fields and ultrasound for non-invasive cancer treatment

Current popular cancer treatment options, include tumor surgery, chemotherapy, and hormonal treatment. These treatments are often associated with some inherent limitations. For instances, tumor surgery is not effective in mitigating metastases; the anticancer drugs used for chemotherapy can quickly spread throughout the body and is ineffective in killing metastatic cancer cells. Therefore, several drug delivery systems (DDS) have been developed to target tumor cells, and release active biomolecule at specific site to eliminate the side effects of anticancer drugs. However, common challenges of DDS used for cancer treatment, include poor site-specific accumulation, difficulties in entering the tumor microenvironment, poor metastases and treatment efficiency. In this context, non-invasive cancer treatment approaches, with or without DDS, involving the use of light, heat, magnetic field, electrical field and ultrasound appears to be very attractive. These approaches can potentially improve treatment efficiency, reduce recovery time, eliminate infections and scar formation. In this review we focus on the effects of magnetic fields and ultrasound on cancer cells and their application for cancer treatment in the presence of drugs or DDS.

Cytotoxicity of temozolomide on human glioblastoma cells is enhanced by the concomitant exposure to an extremely low-frequency electromagnetic field (100Hz, 100G)

Glioblastoma multiforme (GBM) is the most malignant brain cancer that causes high mortality in humans. It responds poorly to the most common cancer treatments, such as surgery, chemo- and radiation therapy. Temozolomide (TMZ) is an alkylating agent that has been widely used to treat GBM; resistance to this drug is often found. One unexplored possibility for overcoming this resistance is a treatment based on concomitant exposure to electromagnetic fields (EMF) and TMZ. Indeed, many evidences show that EMF affects cancer cells and drug performance. In this study, we evaluated the potential synergistic effect of 100μM TMZ and EMF (100Hz, 100G) on two human glioma cells line, i.e., U87 and T98G above single treatments, TMZ or EMF. Co-treatment synergistically enhanced apoptosis in U87 and T98G cells, by increasing the expression of P53, Bax, and Caspase-3 and decreasing that of Bcl-2 and Cyclin-D1. We also observed an increase in reactive oxygen species (ROS) production and the overexpression of the heme oxygenase-1 (HO-1) gene in comparison to controls. In conclusion, since EMF enhanced the apoptotic effect of TMZ, possibly through a redox regulation mechanism, the TMZ/EMF combination may be effective for glioma cancer treating. Further studies are needed to reveal the action mechanism of this possible novel therapeutic approach.

Effects of extremely low-frequency pulsed electromagnetic fields (ELF-PEMFs) on glioblastoma cells (U87)

The impact of extremely low-frequency pulsed electromagnetic fields (ELF-PEMFs) at various frequencies and amplitudes was investigated on cell cycle, apoptosis and viability of the Glioblastoma Multiforme (GBM) cell line (U87), in vitro. The GBM is a malignant brain tumor with high mortality in humans and poorly responsive to the most common type of cancer treatments, such as surgery, chemotherapy and radiation therapy. U87 cells with five experimental groups (I-V) were exposed to various ELF-PEMFs for 2, 4 and 24 h, as follows: (I) no exposure, control; (II) 50 Hz 100 ± 15 G; (III) 100 Hz 100 ± 15 G; (IV) 10 Hz 50 ± 10 G; (V) 50 Hz 50 ± 10 G. The morphology properties, cell viability and gene expression of proteins involved in cell cycle regulation (Cyclin-D1 and P53) and apoptosis (Caspase-3) were investigated. After 24 h, the cell viability and Cyclin-D1 expression increased in Group II (30%, 45%), whereas they decreased in Groups III (29%, 31%) and IV (21%, 34%); P53 and Caspase-3 elevated only in Group III; and no significant difference was observed in Group V, respectively, compared with the control (p < 0.05). The data suggest that the proliferation and apoptosis of human GBM are influenced by exposure to ELF-PEMFs in different time-dependent frequencies and amplitudes. The fact that some of the ELF-PEMFs frequencies and amplitudes favor U87 cells proliferation indicates precaution for the use of medical devices related to the MFs on cancer patients. On the other hand, some other ELF-PEMFs frequencies and intensities arresting U87 cells growth could open the way to develop novel therapeutic approaches.

Mechanisms and therapeutic effectiveness of pulsed electromagnetic field therapy in oncology

Cancer is one of the most common causes of death worldwide. Available treatments are associated with numerous side effects and only a low percentage of patients achieve complete remission. Therefore, there is a strong need for new therapeutic strategies. In this regard, pulsed electromagnetic field (PEMF) therapy presents several potential advantages including non-invasiveness, safety, lack of toxicity for non-cancerous cells, and the possibility of being combined with other available therapies. Indeed, PEMF stimulation has already been used in the context of various cancer types including skin, breast, prostate, hepatocellular, lung, ovarian, pancreatic, bladder, thyroid, and colon cancer in vitro and in vivo. At present, only limited application of PEMF in cancer has been documented in humans. In this article, we review the experimental and clinical evidence of PEMF therapy discussing future perspectives in its use in oncology.

Response of single cell with acute angle exposed to an external electric field

It is known that the electric field incurs effects on the living cells. Predicting the response of single cell or multilayer cells to induced alternative or static eclectic field has permanently been a challenge. In the present study a first order single cell with acute angle under the influence of external electric field is considered. The cell division stage or the special condition of reshaping is modelled with a cone being connected. In the case of cell divisions, anaphase, it can be considered with two cones that connected nose-to-nose. Each cone consists of two regions. The first is the membrane modelled with a superficial layer, and the second is cytoplasm at the core. A Laplace equation is written for this model and the distribution of its electric field is a sharp point in the single cell for which an acute angle model is calculated.