Collaborative Research: Modelling the Integration of Multiple Synaptic Inputs

Baer 通过理论和实验，研究者和他的同事研究了多个电输入到可兴奋神经元结构中的整合。Baer和Rinzel（1991）为研究大量树突棘而提出的一种新的缆绳理论，被用来适应一个特定生物系统的现实：昆虫Manduca的多末端神经支配的肌肉纤维。 数学涉及多个群体的棘反应扩散模型的制定和分析，以模拟从多个突触簇接收同步输入的圆柱形结构（树突或肌纤维）中产生的电位的幅度和时程。 考虑的重要生物学特性是量子电流的幅度、突触后过程的形状、实际发生的输入的固有不确定性（释放的概率）以及电压门控通道的精确分布。 理论与实验数据相关，并推动新的实验。 所有可兴奋细胞的功能，包括神经和肌肉，都受到跨膜电位的精确调节。 该项目是数学家和神经生物学家之间的跨学科合作，使用实验和数学建模来研究复杂神经元结构中电位的空间和时间分布。 本文建立了一个数学模型，模拟了从多个突触簇接收同步输入的圆柱形结构（树突或肌纤维）中产生的电位的幅度和时程。研究人员使用多末端神经支配的肌肉纤维来测试模型的预测，反过来使用模型来增强他们对突触生理学的理解。 多终端神经支配的肌纤维允许一个不寻常的阵列的实验和形态测量，并具有额外的优势，是一个树突的拓扑等效输入棘的delivers。 因此，无论是模拟的结论和方法正在开发的中枢神经系统结构有广泛的应用。

Baer Using theory and experiment, the investigator and his colleague study the integration of multiple electrical inputs into excitable neuronal structures. A new cable theory, developed by Baer and Rinzel (1991) to study large populations of dendritic spines, is adapted to fit the reality of a particular biological system: the multiterminally innervated muscle fiber of the insect Manduca. The mathematics involves the formulation and analysis of reaction diffusion models for multiple populations of spines, to model the amplitude and timecourse of potentials arising in cylindrical structures (dendrite or muscle fiber) receiving synchronous input from multiple clusters of synapses. Important biological properties considered are the amplitude of the quantal currents, shape of the postsynaptic process, the inherent uncertainty of an input actually occurring (probability of release), and the precise distribution of voltage gated channels. Theory is related to experimental data and drives new experiments. The functions of all excitable cells, both nerve and muscle, are regulated with precision by transmembrane potentials. This project is an interdisciplinary collaboration between a mathematician and a neurobiologist to study, using experiments and mathematical modeling, the spatial and temporal distribution of electrical potentials in complex neuronal structures. A mathematical model is developed to simulate amplitude and timecourse of potentials arising in cylindrical structures (dendrite or muscle fiber) receiving synchronous input from multiple clusters of synapses. The investigators use multiterminally innervated muscle fibers to test the predictions of the model, and conversely use the model to augment their understanding of synaptic physiology. The multiterminally innervated muscle fiber allows an unusual array of experimental and morphometric measurements, and has the added advantage of being the topological equivalent of a dendrite having clust ers of input spines. Consequently, both the conclusions of the simulations and the methodology being developed have broad applications to central nervous system structures.