Mathematical Modeling of Neural Populations

当我们靠近一个视觉物体时，有一个精确而持续的信息流从视觉区域流向控制手臂和手运动的马达电路。但过了一会儿，我们可能会抓挠耳朵，同样的马达电路现在由触觉引导，与视觉分离。这项研究项目提出了一些基本问题，即神经电路如何在受控和适应行为期间执行如此复杂的开关功能，以重新路由信息流。在功能转换中起关键作用的可能是增益调节，在这种调节中，突触的一种“音量控制”机制调节神经反应。一个重要的新组成部分是对增益调制的特定生物物理机制的可测试假说。我们将根据详细的解剖学和生理学数据建立神经元和神经细胞群体的数学模型，并将这些模型的结果与涉及视觉、辨别和运动任务的实验进行比较。这项拟议的研究结果将阐明神经回路的一些复杂功能，这些功能允许动物和人类控制他们的行为，并根据特定条件修改和调整他们的行为。科学目标是将神经电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，使用数学模型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、荣誉和轮换项目以及论文研究，将数学和生物学整合到本科生和研究生的教育和培训中，发挥关键作用。该项目由计算神经科学(BIO)和应用数学(MPS)共同支持。

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).