AI 中文总结
本研究结合理论与数值模拟，解析球形膜囊泡局部电流驱动的电荷重组时空动力学，推导非局部电缆方程，为电紧张紧凑细胞的电生理学简化提供第一性原理基础。
AI 中文摘要
离子通道和离子泵在局部位点驱动离子选择性电流穿过细胞膜，然而细胞的电状态通常用单一跨膜电压来概括。结合理论和数值模拟，我们解析了球形膜囊泡上局部电流驱动的电荷重组的时空动力学。早期阶段，该响应对膜几何形状不敏感：与平坦膜的情况（arXiv:2407.11947；arXiv:2508.14001）类似，跨膜电压以单极方式衰减，与距源的距离成反比，并过渡到与距离的立方成反比的偶极尾。在持续电流作用下，该单极响应从源向外扩散。由于囊泡是闭合的，该响应无法无限持续；一旦单极前沿遍历整个囊泡，后续的充电动力学由对应于膜电容充电的空间均匀模式主导。我们进一步将体电势分解为产生体电场的静电镜像电荷分量和可表示为等效电路的空间均匀电容模式。我们还推导了控制跨膜电压动力学的非局部电缆方程，并表明均匀模式是其长时间解。本工作为电紧张紧凑细胞的电生理学简化提供了第一性原理基础。
英文摘要
Ion channels and pumps drive ion-selective currents through cell membranes at localized sites, yet a cell's electrical state is routinely summarized by a single transmembrane voltage. Combining theory and numerical simulations, we resolve the spatiotemporal dynamics of charge reorganization driven by a localized current on a spherical membrane vesicle. At early times, the response is insensitive to membrane geometry: as in the case of a flat membrane (arXiv:2407.11947; arXiv:2508.14001), the transmembrane voltage decays in a monopolar fashion, varying inversely with distance from the source, and crosses over to a dipolar tail that scales as the inverse cube of distance. Under sustained current, this monopolar response spreads outward from the source. Because the vesicle is closed, this response cannot persist indefinitely; once the monopolar front traverses the entire vesicle, the subsequent charging dynamics is dominated by a spatially uniform mode corresponding to capacitive charging of the membrane. We further decompose the bulk potentials into an electrostatic image-charge component that generates the bulk electric fields and a spatially uniform capacitive mode that can be represented as an equivalent circuit. We also derive a nonlocal cable equation governing the transmembrane voltage dynamics and show that the uniform mode is its long-time solution. This work provides a first-principles basis for the electrophysiological simplification of an electrotonically compact cell.
Comments10 pages, 6 figures
