Korogod Sergey M, Kaspirzhny Anton V
Laboratory of Biophysics and Bioelectronics, Dniepropetrovsk National University, 72 Gagarin Avenue, 49050 Dniepropetrovsk, Ukraine.
Biol Cybern. 2008 Feb;98(2):87-100. doi: 10.1007/s00422-007-0204-y. Epub 2007 Dec 21.
Geometry and membrane properties of the dendrites crucially determine input-output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise.
树突的几何形状和膜特性对神经元的输入-输出关系起着至关重要的决定作用。与通常可从计算机重建中详细获取的几何形状不同，膜电阻率即便有所了解也是支离破碎的。此外，它在持续活动过程中会发生变化。在本研究中，我们探讨这样一个问题：膜电阻率的变化对树突的传递特性有何影响？遵循控制系统理论的标准方法，我们推导并研究了与具有任意几何参数（长度和直径）及边界条件的无源树突传递函数互补的灵敏度函数。我们将位置依赖的向体细胞电流传递比（向胞体电压的倒数）用作传递函数，并将其对膜电阻率的导数用作灵敏度函数。在树突中，在距原点的每个路径距离处，通用形式的灵敏度函数将传递函数、膜电阻率、半无限电缆的特征输入电导以及给定内部位点和原点处的定向向胞体输入电导与长度联系起来。在膜电阻率与路径距离坐标中绘制的灵敏度函数呈现出共同特征：沿任何坐标都有低范围和高范围，其中灵敏度分别增加和降低。这些范围和相应的速率以一种特征性方式取决于形态和边界条件。这些特征预示着存在依赖于几何形状的膜电阻率范围（早期未被关注的中等电导状态），使得具有给定度量不对称性的树突在膜电阻率处于该范围内时，其传递特性和电状态最为显著，否则则不然。
