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

Cox0077728沿着神经细胞和神经细胞之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导电性被穿透细胞膜的无数离子通道所抵消。神经细胞显著的物理性质，与共同计量学相反，则是它的轴向电导，它的膜对一个或多个离子物种的电容和渗透性，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精确度。不幸的是，这些量的实验测定是一项艰巨的任务，鉴于最近的数据表明，渗透率在树枝状树中的位置不同，除了最简单的几何形状外，所有这些都需要巨大的投资。因此，这位研究人员和他的同事们确定了从更容易获得的间接测量中推断神经元物理性质的程度。这些间接测量是对躯体和远端膜电位的记录，在已知的体细胞电流刺激后，这两个电位记录在远端有电流密封，这两个电位记录导致下面的退化-抛物型Hodgkin-Huxley方程系统的横向超定。这位研究人员和他的同事从这个超定系统中推导出一些适定的问题，以及相关的算法(基于矩、不动点和输出最小二乘法)，以恢复神经元的一个或多个物理属性。他们用从大鼠海马区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，一个人必须有一个分离清单和一份蓝图，说明如何将各个部分连接起来。在最粗略的水平上，只有两种类型的部分，神经(神经元)和神经胶(神经胶质细胞)。虽然人类大脑中的每一颗恒星都比银河系中的恒星多，但这并不是它们的绝对数量，而是相互关联和电学特性变化的微妙组合，使大脑变得如此强大。术语“变异”旨在表达这样一种认识，即神经元不是某个大脑中心内的开关或连接两个这样的中心的电线，而是一棵电特性沿其每个分支变化的电线树。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任务的能力的原因，这让人联想到初级计算机。然而，考虑到单个神经元的微小尺寸和多种多样的性质，还没有实现对其电学性质的直接实验确定。因此，研究人员和他的同事进行了一项具有数学挑战性的任务，即从更容易获得的、尽管是间接的实验测量中确定这些性质。这一过程类似于通过比较美国人所说的和英国人所听到的来确定跨大西洋电话电缆泄漏的大小和位置。他们的努力的成功，再加上神经元互联图像的日益精细的分辨率，将使研究人员和他的同事能够生产出足够准确的模型，供医学界使用，从构建假体神经元电路到药物的设计和测试以及更好的治疗。

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.