Structure-preserving model reduction of passive and quasi-active neurons
Structure-preserving model reduction of passive and quasi-active neurons
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DOI：
10.1007/s10827-012-0403-y
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发表时间：
2013-02-01
影响因子：
1.2
通讯作者：
Cox, Steven J.
中科院分区：
文献类型：
--
作者：
Hedrick, Kathryn R.;Cox, Steven J.
输入信号的空间分量通常携带对神经元功能至关重要的信息，但是将突触输入映射到跨膜电位的模型在计算上可能是昂贵的。神经元的现有简化模型要么合并隔室，从而牺牲输入的空间特异性，要么应用模型简化技术，牺牲模型的潜在电生理学。我们使用Krylov子空间投影方法来构建被动和准主动神经元的简化模型，该模型分别保留了输入的空间特异性和RC和RLC电路的电生理解释。每个简化模型精确地计算潜在的尖峰起始区（SIZ）给出了一个小得多的尺寸和模拟时间，正如我们所示的数值和理论。通过电路表示中的相似性来保留结构，为此我们提供电路元件的电路图和数学表达式。此外，从完整系统到简化系统的转换是直接的，并且取决于枝晶的固有性质。由于每个简化模型都是准确的，并且具有清晰的电生理学解释，因此简化模型不仅可以用于模拟形态学上准确的神经元，还可以用于检查在树突中执行的计算。
The spatial component of input signals often carries information crucial to a neuron's function, but models mapping synaptic inputs to the transmembrane potential can be computationally expensive. Existing reduced models of the neuron either merge compartments, thereby sacrificing the spatial specificity of inputs, or apply model reduction techniques that sacrifice the underlying electrophysiology of the model. We use Krylov subspace projection methods to construct reduced models of passive and quasi-active neurons that preserve both the spatial specificity of inputs and the electrophysiological interpretation as an RC and RLC circuit, respectively. Each reduced model accurately computes the potential at the spike initiation zone (SIZ) given a much smaller dimension and simulation time, as we show numerically and theoretically. The structure is preserved through the similarity in the circuit representations, for which we provide circuit diagrams and mathematical expressions for the circuit elements. Furthermore, the transformation from the full to the reduced system is straightforward and depends on intrinsic properties of the dendrite. As each reduced model is accurate and has a clear electrophysiological interpretation, the reduced models can be used not only to simulate morphologically accurate neurons but also to examine computations performed in dendrites.