Rotstein Horacio G, Nadim Farzan
Department of Mathematical Sciences, New Jersey Institute of Technology, 323 Martin Luther King Blvd., Newark, NJ, 07102, USA,
J Comput Neurosci. 2014 Aug;37(1):9-28. doi: 10.1007/s10827-013-0483-3. Epub 2013 Nov 20.
Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.
许多神经元类型在其电压幅度（共振）或对阈下振荡电流的相移方面表现出偏好频率响应，但生物物理参数对这些特性的影响尚未得到很好的理解。我们提出了一个通用框架，用于分析不同离子电流及其相互作用在塑造线性化生物物理模型中阻抗幅度和相位特性方面的作用，并在具有两个有效电导gL和g1的二维线性模型中演示了这种方法。我们在g(L) - g1参数空间中计算阻抗和相位的关键属性（共振频率和幅度、零相位频率、选择性等）。使用这些属性图，我们确定了产生共振的两种基本机制：随着g1增加且总阻抗降低时共振幅度增加，以及随着离子电流时间常数增加，在输入电阻不变的情况下最大阻抗增加。我们使用属性图来分析两个生物物理模型线性化的共振和相位，这两个模型包括共振电流（Ih或慢钾电流）和放大电流（持续性钠电流）。在没有放大电流的情况下，随着共振电流电导增加，这两个模型的行为相似；而在存在放大电流的情况下，这两个模型具有定性相反的响应。这项工作提供了一种通用方法，通过在预先构建的属性图中跟踪由相关生物物理参数参数化的轨迹，来解码生物物理参数对线性膜共振和相位的影响。
