Mathematical Modeling of Neural Populations

拟议的研究是一个通用程序的一部分，该程序使用数学建模和计算分析来揭示神经元电路的功能特征是如何从基本的细胞机制产生的。这项研究是理论上的，但它是基于解剖学和生理学数据，结果为未来的实验提供了方向和预测。拟议的工作主要集中在视觉系统上。我们的目标是确定初级视觉皮层的回路如何产生对视觉图像的反应，并研究必要的回路元件如何在依赖活动的过程的基础上发展。关于初级视觉皮质中的神经元如何对视觉图像的空间模式做出反应，人们知道的很多，但对变化的图像反应的时间特征知之甚少。拟议研究中的一个项目将通过构建准确复制对瞬变、运动和振荡图像的视觉反应的模型来解决这一问题。许多影响时间反应特征的机制将被研究、比较和对比。初级视皮层细胞的反应通常取决于视觉图像移动的方向，这一现象的模型将被开发和深入研究。初级视觉皮质中的一些细胞表现出一种有趣的特性，这可能代表了我们识别物体的能力的第一阶段，即所谓的不变物体识别。另一项研究项目提出了一个新的模型，说明大脑皮层回路如何产生暂时性不变的视觉反应。该模型基于大脑皮层细胞之间相互连接的结构和强度，并对如果这些连接被调制或中断会发生什么做出明确的预测。该模型的预测可以在实验中得到验证。还将研究通过依赖活动的过程来发展模型中所需的突触互连。拟议的研究通过培训研究生应用数学和计算技术来分析和理解大脑的神经元电路，发挥了重要的教育作用。这种教育是跨学科的，涉及数学、物理、计算机科学和神经生物学方面的技能。

L.F.Abbott IBN 98-17194Mathematical Modeling of Neural PopulationsABSTRACTThe proposed research is part of a general program that uses mathematical modeling and computational analysis to reveal how the functional characteristics of neuronal circuits arise from basic cellular mechanisms. The research is theoretical, but it is based on anatomical and physiological data, and the results suggest directions and provide predictions for future experiments. The proposed work focuses primarily on the visual system. The goal is to determine how the circuits of the primary visual cortex generate responses to visual images, and to study how the necessary circuit elements could develop on the basis of activity-dependent processes.Much is known about how neurons in the primary visual cortex respond to the spatial pattern of a visual image, but less is known about the temporal characteristics of responses to changing images. One project in the proposed research will address this issue by constructing models that accurately duplicate visual responses to transient, moving, and oscillating images. A number of mechanisms that affect temporal response characteristics will be studied, compared, and contrasted. Responses of cells in primary visual cortex often depend on the direction that a visual image is moving, and a model of this phenomenon will be developed and investigated in depth.Some cells in the primary visual cortex exhibit an interesting property that may represent the first stage in our ability to identify objects irrespective of their position in the visual field, so-called invariant object recognition. Another research project proposes a new model for how transitionally invariant visual responses are generated by cortical circuitry. The model is based on the structure and strength of interconnections between cortical cells and makes definite predictions about what happens if these connections are modulated or disrupted. The predictions of the model can be tested experimentally. The development of the synaptic interconnections needed in the model through activity-dependent processes will also be studied.The proposed research serves an important educational function by training graduate students to apply mathematical and computation techniques to the analysis and understanding of neuronal circuits of the brain. This education is cross-disciplinary, involving skills in mathematics, physics, computer science, and neurobiology.