Mathematical Modeling of Neural Populations

当我们伸手去触摸一个视觉对象时，从视觉区域到控制手臂和手部运动的运动电路有一个精确而连续的信息流。但过一会儿，我们可能会抓耳朵，同样的运动回路现在由触觉引导，与视觉分离。这个研究项目提出了一些基本问题，关于神经回路如何在控制和自适应行为中执行如此复杂的转换功能来重新路由信息流。增益调制可能在功能切换中发挥关键作用，其中突触中的一种“音量控制”机制调节神经反应。一个重要的新组成部分是一个可测试的假设的特定生物物理机制的增益调制。神经元和神经群的数学模型将建立在详细的解剖和生理数据的基础上，这些模型产生的结果将与涉及视觉、辨别和运动任务的实验进行比较。拟议的研究结果将揭示神经回路的一些复杂特征，这些特征使动物和人类能够控制自己的行为，并根据特定条件修改和调整自己的行为。科学目标是将神经回路的这些行为方面与产生它们的潜在细胞和生物物理机制联系起来，使用数学建模来弥合我们在细胞和行为层面的知识之间的差距。此外，拟议的研究将通过课堂作业，荣誉和轮转项目以及论文研究，将数学和生物学融入本科生和研究生的教育和培训中发挥关键作用。本项目由计算神经科学（BIO）和应用数学（MPS）联合资助。

When we reach toward a visual object, there is a precise and continuous flow of information from the visual areas to the motor circuits that control arm and hand movements. But a moment later, we may be engaged in scratching an ear, with the same motor circuits now guided by tactile sensation and uncoupled from vision. This research project asks fundamental questions about how neural circuits perform such complex switching functions to re-route the flow of information during controlled and adaptive behaviors. A critical role in functional switching may be played by gain modulation, in which a type of "volume-control" mechanism at synapses adjusts neural responses. An important novel component is a testable hypothesis of a specific biophysical mechanism for gain modulation. Mathematical models of neurons and neural populations will be constructed based on detailed anatomical and physiological data, and the results arising from these models will be compared with experiments involving visual, discrimination, and motor tasks. Results of the proposed research will shed light on some of the complex features of neural circuitry that allow animals and people to control their actions and modify and tune their behaviors to specific conditions. The scientific goal is to relate these behavioral aspects of neural circuitry to the underlying cellular and biophysical mechanisms that generate them, using mathematical modeling to bridge the gaps between our knowledge at the cellular and behavioral levels. In addition, the proposed research will play a critical role integrating mathematics and biology into the education and training of undergraduate and graduate students, through classroom work, honors and rotation projects, and thesis research. This project is jointly supported between Computational Neuroscience (BIO) and Applied Mathematics (MPS).