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

神经细胞内和细胞间的信息处理是通过沿分支和跨细胞膜的电扩散实现的。分支相对较差的轴向电导被无数穿过细胞膜的离子通道所抵消。神经细胞显著的物理性质，而不是几何性质，是它的轴向电导，它的膜的电容和对一种或多种离子的渗透性，以及底层通道的动力学（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，实验确定这些数量是一项艰巨的任务，鉴于最近的数据表明，渗透率随着树突树的位置而变化，除了最简单的几何形状外，所有这些都需要大量的投资。因此，研究者和他的同事们确定了神经元的物理特性可以从更容易获得的间接测量中推断出来的程度。这些间接测量是记录体细胞和远端膜电位后，已知电流刺激到体细胞。假设电流在远端密封，这两个潜在的记录导致霍奇金-赫胥黎方程的潜在退化抛物系统的横向超确定。研究者和他的同事们从这个过度确定的系统中推断出许多良好的问题，以及相关的算法（基于矩、不动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中提取的锥体神经元记录的数据来测试这些算法。为了修复或复制大脑，人们必须有一个零件清单和一个详细说明零件如何连接的蓝图。在最粗略的层面上，只有两种类型的部分，神经（神经元）和神经胶（胶质细胞）。尽管人类大脑中每一种细胞的数量都比银河系中恒星的数量还要多，但使大脑如此强大的不是它们的数量，而是相互联系和电学特性变化的微妙结合。“变异”一词意在表达这样一种认识，即神经元不仅仅是某个大脑中心内的开关，也不是连接两个大脑中心的导线，而是一棵由导线组成的树，其电学特性在每个分支上都有所不同。正是神经元传导大脑主要离子的能力的这种局部变异，被认为是单个神经元执行类似于基本计算机的任务的能力的原因。然而，考虑到单个神经元的微小尺寸和多样性，对其电学特性的直接实验测定尚未实现。因此，研究人员和他的同事们追求从数学上具有挑战性的任务，即通过更容易获得的间接实验测量来确定这些特性。这个过程类似于通过比较美国人和英国人听到的内容来确定跨大西洋电话电缆泄漏的大小和位置。他们的努力取得了成功，再加上神经元互连图像的分辨率越来越高，这将使研究者和他的同事们能够制作出足够准确的模型，供医学界从构建假神经回路到设计和测试药物和更好的治疗方法使用。

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.