Low-dimensional, morphologically accurate models of subthreshold membrane potential.
Low-dimensional, morphologically accurate models of subthreshold membrane potential.
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DOI：
10.1007/s10827-008-0134-2
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发表时间：
2009-10
影响因子：
1.2
通讯作者：
Cox, Steven J.
中科院分区：
文献类型：
--
作者：
Kellems, Anthony R.;Roos, Derrick;Xiao, Nan;Cox, Steven J.
关键词：
神经元整合分布式突触输入的能力的精确模拟通常需要同时求解数万个常微分方程。因为，为了理解细胞如何区分输入模式，我们显然需要一个模型，该模型在生物病理学上精确到单个脊柱的空间尺度，即，1 μm。我们在这里认为，如果满足于在少量位置准确地再现相关的膜电位，则可以保留这种高度详细的输入结构，同时显著降低整个系统的维度，例如，在阈下刺激下，在动作电位起始部位。后者的假设允许我们近似的活性细胞模型与相关的准活性模型，这反过来又减少了时域（平衡截断）和频域（传递函数的近似）的方法。我们应用和对比这些方法在一套典型的细胞，实现了四个数量级的降维和相关的加速树突民主化和共振的模拟。我们还附加了一个阈值机制，并表明这种减少有可能提供一个准确的准集成和消防模型。
The accurate simulation of a neuron’s ability to integrate distributed synaptic input typically requires the simultaneous solution of tens of thousands of ordinary differential equations. For, in order to understand how a cell distinguishes between input patterns we apparently need a model that is biophysically accurate down to the space scale of a single spine, i.e., 1 μm. We argue here that one can retain this highly detailed input structure while dramatically reducing the overall system dimension if one is content to accurately reproduce the associated membrane potential at a small number of places, e.g., at the site of action potential initiation, under subthreshold stimulation. The latter hypothesis permits us to approximate the active cell model with an associated quasi-active model, which in turn we reduce by both time-domain (Balanced Truncation) and frequency-domain (ℋ2 approximation of the transfer function) methods. We apply and contrast these methods on a suite of typical cells, achieving up to four orders of magnitude in dimension reduction and an associated speed-up in the simulation of dendritic democratization and resonance. We also append a threshold mechanism and indicate that this reduction has the potential to deliver an accurate quasi-integrate and fire model.
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