静电场调制椭球形细胞膜电位和一侧离子浓度的研究
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摘要
在对静电场与细胞相互作用建模和跨膜电位计算的基础上,基于能斯托公式和玻尔兹曼公式,给出静电场对椭球细胞离子跨膜迁移量影响的分析方法,并就静电场对不同类型椭球细胞离子跨膜迁移量变化的影响进行数值分析.研究发现:静电场在细胞表面不同位置引起的跨膜离子迁移量不同;随外场方向角α、椭球半轴比值ρ增加,静电场引起的细胞膜一侧离子浓度相对无外场作用,其比值的最大值逐渐减少,最大值对应位置θ_(max)逐渐增加;在外场强度、细胞表面积或体积一定条件下,ρ值越大,则对应的θ_(max)值越大;对于含乘性白噪声的静电场,场强度越大、信噪比越小,则离子浓度相对变化量越大.电场影响椭球细胞离子的跨膜迁移量引起细胞介质极化.
Based on the model setting is carried out to describe the interaction between static electric field and cell and the calculation of the transmembrane potential, and the Nernst formula and the Boltzmann formula, the method which to analyze the influence of the static field on the quantity across ellipsoid-cell membrane is investigated by using the theorem of electromagnetic induction. Furthermore,numerical studies were used to detect and verify the transition of ion exchange across the membrane. Some interesting results are approached as follows. The exchange of ions across the membrane and fluctuation of membrane potential are dependent on the position, orientation of electric field applied on the membrane of cell and the cell-shape. With the increasing of the field angle(between the direction of applied field and the direction of ellipsoid semi-major axis) and the semi-axis ratio ρ, it is found that the maximal ratio of ion concentration on the side of the ellipsoid-cell will reduce when external field is applied on the cell membrane,and its positions θ_(max) will increase. Under a certain cell superficial area or volume, θ_(max) is increased as ρ goes up. The larger field intensity for the electrostatic field with the noise, the smaller signal to noise ratio, as a result, the rate of relative change of the ion concentration will increase. The mechanism for transition in transmembrane ions could be that media or cell can be polarized when appropriate electric field is applied on ellipsoid cell even noise is considered.
Based on the model setting is carried out to describe the interaction between static electric field and cell and the calculation of the transmembrane potential, and the Nernst formula and the Boltzmann formula, the method which to analyze the influence of the static field on the quantity across ellipsoid-cell membrane is investigated by using the theorem of electromagnetic induction. Furthermore,numerical studies were used to detect and verify the transition of ion exchange across the membrane. Some interesting results are approached as follows. The exchange of ions across the membrane and fluctuation of membrane potential are dependent on the position, orientation of electric field applied on the membrane of cell and the cell-shape. With the increasing of the field angle(between the direction of applied field and the direction of ellipsoid semi-major axis) and the semi-axis ratio ρ, it is found that the maximal ratio of ion concentration on the side of the ellipsoid-cell will reduce when external field is applied on the cell membrane,and its positions θ_(max) will increase. Under a certain cell superficial area or volume, θ_(max) is increased as ρ goes up. The larger field intensity for the electrostatic field with the noise, the smaller signal to noise ratio, as a result, the rate of relative change of the ion concentration will increase. The mechanism for transition in transmembrane ions could be that media or cell can be polarized when appropriate electric field is applied on ellipsoid cell even noise is considered.
引文
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32 Kotnik T,Miklav?i?D.Analytical description of transmembrane voltage induced by electric fields on spheroidal cells.Biophys J,2000,79:670–679
33牛中奇,王海彬,侯建强,等.电磁波对细胞内外离子浓度影响的基本理论.中国生物医学工程学报,2002,21:552-556
34 李辑熙,牛中奇.生物电磁剂量学概论.西安:西安电子科技大学出版社,1990
35 覃玉荣.外电场作用下悬液中细胞电压变化建模研究.博士学位论文.广州:华南理工大学,2005
2 Titushkin I,Cho M.Regulation of cell cytoskeleton and membrane mechanics by electric field:Role of linker proteins.Biophys J,2009,96:717–728
3 Sheikh A Q,Taghian T,Hemingway B,et al.Regulation of endothelial MAPK/ERK signalling and capillary morphogenesis by low-amplitude electric field.J R Soc Interface,2013,10:20120548
4 Zhang J,Ren R,Luo X,et al.A small physiological electric field mediated responses of extravillous trophoblasts derived from HTR8/SVneo cells:Involvement of activation of focal adhesion kinase signaling.PLo S ONE,2014,9:e92252
5 Rackauskas G,Saygili E,Rana O R,et al.Subthreshold high-frequency electrical field stimulation induces VEGF expression in cardiomyocytes.Cell Transplant,2015,24:1653–1659
6 Hernández-Bule M L,Paíno C L,Trillo Má,et al.Electric stimulation at 448 k Hz promotes proliferation of human mesenchymal stem cells.Cell Physiol Biochem,2014,34:1741–1755
7 Llucià-Valldeperas A,Sanchez B,Soler-Botija C,et al.Physiological conditioning by electric field stimulation promotes cardiomyogenic gene expression in human cardiomyocyte progenitor cells.Stem Cell Res Ther,2014,5:93
8 Kobelt L J,Wilkinson A E,Mc Cormick A M,et al.Short duration electrical stimulation to enhance neurite outgrowth and maturation of adult neural stem progenitor cells.Ann Biomed Eng,2014,42:2164–2176
9 Meng S,Rouabhia M,Zhang Z.Electrical stimulation modulates osteoblast proliferation and bone protein production through heparinbioactivated conductive scaffolds.Bioelectromagnetics,2013,34:189–199
10 Khodabukus A,Baar K.Defined electrical stimulation emphasizing excitability for the development and testing of engineered skeletal muscle.Tissue Eng Part C-Methods,2011,18:349–357
11 Chiu L L Y,Iyer R K,King J P,et al.Biphasic electrical field stimulation aids in tissue engineering of multicell-type cardiac organoids.Tissue Eng Part A,2011,17:1465–1477
12 Ahadian S,Ostrovidov S,Hosseini V,et al.Electrical stimulation as a biomimicry tool for regulating muscle cell behavior.Organogenesis,2013,9 :87–92
13 Cohen D J,Nelson W J,Maharbiz M M.Galvanotactic control of collective cell migration in epithelial monolayers.Nat Mater,2014,13:409–417
14 Yi G S,Wang J,Han C X,et al.Spiking patterns of a minimal neuron to ELF sinusoidal electric field.Appl Math Model,2012,36:3673–3684
15 Che Y Q,Wang J,Si W J,et al.Phase-locking and chaos in a silent Hodgkin-Huxley neuron exposed to sinusoidal electric field.Chaos Solitons Fractals,2009,39:454–462
16 Che Y,Wang J,Deng B,et al.Bifurcations in the Hodgkin-Huxley model exposed to DC electric fields.Neurocomputing,2012,81:41–48
17 Yi G,Wang J,Wei X,et al.Dynamic analysis of Hodgkin’s three classes of neurons exposed to extremely low-frequency sinusoidal induced electric field.Appl Math Comput,2014,231:100–110
18 伊国胜,王江,魏熙乐,等.无创式脑调制的神经效应研究进展.科学通报,2016,61:819-834
19 Wang H,Chen Y.Spatiotemporal activities of neural network exposed to external electric fields.Nonlinear Dyn,2016,85:881–891
20 Li J,Liu S,Liu W,et al.Suppression of firing activities in neuron and neurons of network induced by electromagnetic radiation.Nonlinear Dyn,2016,83:801–810
21 Ma J,Tang J.A review for dynamics of collective behaviors of network of neurons.Sci China Tech Sci,2015,58:2038–2045
22 张辉,许家栋,牛中奇.离子跨膜迁移的几率波理论.生物医学工程学杂志,2007,24:257-261
23 张辉,许家栋,牛中奇,等.离子跨膜迁移几率对电磁波的响应.中国医学物理学杂志,2004,21:179-181
24 张辉,许家栋,牛中奇,等.极低频磁场对胞内钙振荡影响的机理分析.中国医学物理学杂志,2007,24:189-192
25 张辉,张小娣,张淑荣,等.电磁场生物学效应的分子机制分析.中国组织工程研究与临床康复,2008,12:643-646
26 Schwan H P.Electrical properties of tissue and cell suspensions.Adv Biol Med Phys,1957,5:147-209
27 Grosse C,Schwan H P.Cellular membrane potentials induced by alternating fields.Biophys J,1992,63:1632–1642
28 Kotnik T,Bobanovi?F,Miklav?i?D.Sensitivity of transmembrane voltage induced by applied electric fields—A theoretical analysis.Bioelectrochem Bioenergetics,1997,43:285–291
29 Valic B,Golzio M,Pavlin M,et al.Effect of electric field induced transmembrane potential on spheroidal cells:Theory and experiment.Eur Biophys J,2003,32:519–528
30 Gimsa J,Wachner D.Analytical description of the transmembrane voltage induced on arbitrarily oriented ellipsoidal and cylindrical cells.Biophys J,2001,81:1888–1896
31 Pavlin M,Miklav?i?D.Effective conductivity of a suspension of permeabilized cells:A theoretical analysis.Biophys J,2003,85:719–729
32 Kotnik T,Miklav?i?D.Analytical description of transmembrane voltage induced by electric fields on spheroidal cells.Biophys J,2000,79:670–679
33牛中奇,王海彬,侯建强,等.电磁波对细胞内外离子浓度影响的基本理论.中国生物医学工程学报,2002,21:552-556
34 李辑熙,牛中奇.生物电磁剂量学概论.西安:西安电子科技大学出版社,1990
35 覃玉荣.外电场作用下悬液中细胞电压变化建模研究.博士学位论文.广州:华南理工大学,2005