Determining Active, Nonuniform Dendritic Membrane Properties from Single and Multipoint Potential Readings

Cox0077728 信息处理沿着和神经细胞之间是通过电扩散沿着分支和跨细胞膜。 树枝相对较差的轴向传导性被覆盖细胞膜的无数离子通道所抵消。 一个神经细胞最显著的物理性质（与几何性质相反）是它的轴向电导、膜的电容和对一种或多种离子的渗透性以及潜在通道的动力学（控制其打开/关闭状态的规则）。 当然，数学模型的预测效用取决于已知这些物理性质的准确性。 不幸的是，这些量的实验测定是一项艰巨的任务，根据最近的数据表明，渗透率随树枝状树中的位置而变化，除了最简单的几何形状外，所有几何形状都需要大量投资。 因此，研究者和他的同事们确定了神经元的物理特性在多大程度上可以从更容易获得的间接测量中推断出来。 这些间接测量是在已知电流刺激索马后记录的体细胞和远端膜电位，假设电流在远端封闭，这两种电位记录导致了Hodgkin-Huxley方程的退化抛物系统的横向超定。 研究者和他的同事们从这个超定系统中推导出了一些很好的问题，以及相关的算法（基于矩，定点和输出最小二乘法），用于恢复一个或多个神经元的物理特性。 他们用从大鼠海马体提取的锥体神经元记录的数据测试这些算法。 为了修复或复制大脑，必须有一个单独的清单和一个蓝图，规定如何将各部分连接起来。 在粗糙的层面上，只有两种类型的部分，神经（神经元）和神经胶（神经胶质细胞）。 尽管人脑中的每一个都比银河系中的星星多，但这并不是它们的绝对数量，而是相互联系和电特性变化的微妙组合使大脑如此强大。 “变异”一词的意思是表达这样一种认识，即神经元不仅仅是某个大脑中心内的开关或连接两个这样的中心的电线，而是一棵电线树，电线的电特性沿着它的每个分支都不同。 正是这种神经元传导大脑主要离子的能力的局部变化，被认为是负责单个神经元执行任务的能力，让人想起初级计算机。 然而，考虑到单个神经元的微小尺寸和多样性，对其电特性的直接实验测定还有待实现。 因此，研究人员和他的同事们追求数学上具有挑战性的任务，即从更容易获得的间接实验测量中确定这些属性。 这个过程类似于通过比较美国人所说的和英国人听到的来确定跨大西洋电话电缆泄漏的大小和位置。 他们奋进的成功，再加上神经元相互连接的图像分辨率越来越高，将使研究者和他的同事能够制作出足够准确的模型，供医学界使用，从人工神经元回路的构建到药物和更好治疗的设计和测试。

Cox0077728 Information processing along and between nerve cells isachieved via electrodiffusion along branches and across cellmembranes. The relatively poor axial conductance of the branchesis offset by the myriad of ion channels that perforate the cellmembrane. A nerve cell's salient physical, as opposed togeometrical, properties are then its axial conductance, itsmembrane's capacitance and permeability to one or more ionicspecies and the kinetics (rules that govern its open/closedstate) of the underlying channels. The predictive utility of amathematical model of course hinges on the accuracy to whichthese physical properties are known. Unfortunately, theexperimental determination of each of these quantities is aformidable task that, in light of recent data suggesting that thepermeabilities vary with position in the dendritic tree, requiresgreat investment for all but the simplest geometries. Theinvestigator and his colleagues therefore determine the extent towhich the neuron's physical properties may be inferred from morereadily available indirect measurements. These indirectmeasurements are recordings of somatic and distal membranepotential following a known current stimulus to the soma.Assuming current seals at the distal ends, these two potentialrecordings result in lateral overdetermination of the underlyingdegenerate-parabolic system of Hodgkin-Huxley equations. Theinvestigator and his colleagues deduce from this overdeterminedsystem a number of well posed problems, and associated algorithms(based on moment, fixed-point and output least squares methods),for the recovery of one or more of the neuron's physicalproperties. They test these algorithms on data recorded frompyramidal neurons drawn from the rat's hippocampus. In order to repair or reproduce the brain one must have aparts list and a blueprint specifying how the parts are to beconnected. At the coarsest level there are but two types ofparts, nerves (neurons) and nerve glue (glial cells). Though thehuman brain has more of each than the Milky Way has stars, it isnot their sheer number but rather a subtle combination ofinterconnectedness and variation in electrical properties thatrender the brain so powerful. The term `variation' is meant toexpress the realization that a neuron is not simply a switchwithin a certain brain center or a wire connecting two suchcenters, but rather is a tree of wires with electrical propertiesvarying along each of its branches. It is this local variation ina neuron's ability to conduct the brain's principal ions that isthought to be responsible for an individual neuron's ability toperform tasks reminiscent of rudimentary computers. Given howeverthe minute size and variegated nature of a single neuron, thedirect experimental determination of its electrical propertieshas yet to be achieved. The investigator and his colleaguestherefore pursue the mathematically challenging task ofdetermining these properties from more readily available, thoughindirect, experimental measurements. This process is akin todetermining the size and location of a leak in a transatlantictelephone cable by comparing what the American said to what theEnglishman heard. The success of their endeavor, coupled with theincreasingly fine resolution of images of neuronalinterconnections, will permit the investigator and his colleaguesto produce models of sufficient veracity to be of use by themedical community from construction of prosthetic neuronalcircuits to the design and testing of drugs and bettertreatments.