Poznanski R R, Cacha L A, Ali J, Rizvi Z H, Yupapin P, Salleh S H, Bandyopadhyay A
Faculty of Bioscience and Medical Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia.
Laser Centre, Ibnu Sina ISIR, Universiti Teknologi Malaysia, 81310 Johor Bahru, Malaysia.
PLoS One. 2017 Sep 7;12(9):e0183677. doi: 10.1371/journal.pone.0183677. eCollection 2017.
A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge 'soakage' is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge 'soakage') have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell's equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.
我们推导了一个包含极化感应电容电流的电缆模型，用于模拟具有内质网微观结构的神经元小分支中电紧张电位的孤子传导。通过对含裂隙细胞内介质的非线性电缆方程进行求解，并引入一个表示电荷“吸收”的源项，以展示线粒体内膜内结合电荷的细胞内电容效应如何影响以孤立波形式表达的电紧张信号。两个孤立波正面碰撞产生的弹性碰撞会导致由源项非线性产生的局部化且非色散的电孤子。研究表明，与没有内质网的具有微观结构的神经元中的孤子相比，具有线粒体膜且微观结构存在电荷准静电相互作用（即电荷“吸收”）的神经元中的孤子传播速度较慢。当平衡电位相对于静息电位有小偏差时，非欧姆电导起到漏电通道的作用，此时孤子较小；而当平衡电位较大且线粒体外膜起到放大器作用时，会增强内源性产生的孤子的幅度。这些发现表明，微观结构所保持的结合电荷的准静电相互作用在通过线粒体膜平衡电位的变化维持孤子幅度的稳健自我调节方面具有功能性作用。我们结果的意义在于，离子电流的现象学描述可以成功地用麦克斯韦方程组中的位移电流作为涉及准静电相互作用而不包含扩散电流的传导过程来建模。这是第一项研究表明电紧张电位的孤子传导是由微观结构中的极化感应电容电流和非欧姆线粒体膜电流产生的。
