Analyzing Neuronal Activity When Classical Reaction-Diffusion Breaks Down

直觉上，我们有理由认为，即使所有的反应物都是相同的，在实验室试管中发生的生化反应也应该与在高度复杂的神经元中发生的生化反应不同。该项目的目的是开发一个理论框架，以了解神经元的基本结构特性，这些特性可以完全改变作为学习和记忆基础的生化反应的结果。这个项目将利用计算机模拟来研究神经元的表面和内部结构如何影响参与记忆形成的分子反应。数学的一个分支，称为分数微积分，将被用来概括模拟的结果。同样的形式主义将被扩展到研究神经元如何表达蛋白质或神经元网络如何相互作用。该项目将产生知识，以研究旨在了解记忆形成，复杂蛋白质网络和小脑信息处理的实验结果;这项工作还将提供一个统一的数学框架，以了解生化信号与神经元复杂结构之间的微妙相互作用。所产生的知识将与计算工具箱一起传播，该工具箱可用于对复杂系统感兴趣的任何生物学领域，从生物化学到生态学。该提案将为少数民族双语本科生提供培训机会，不仅在该项目的科学方面，而且还开发西班牙语维基百科页面，以帮助美国西班牙裔人口更好地获得神经科学和生物物理学方面的科学信息。该项目还将允许研究生和博士后研究员的培训，这将丰富UTSA，西班牙裔服务机构的学术环境。

Intuitively it is reasonable to agree that even when all the reactants are the same the biochemical reactions that take place in a laboratory test tube should probably differ from those that take place in highly complex neurons. The purpose of this project is to develop a theoretical framework to understand the fundamental structural properties of neurons that can completely modify the outcome of the biochemical reactions that are at the foundation of learning and memory. This project will make use of computer simulations that to study how the structure of the surface and interior of neurons affects molecular reactions involved in memory formation. A branch of mathematics, called fractional calculus, will be used to generalize the findings of the simulations. The same formalism will be extended to study how neurons express proteins or how networks of neurons interact with each other. The project will generate knowledge to study the outcome of experiments aimed at understanding memory formation, complex proteins networks, and information processing in the cerebellum; this work will also provide a unified mathematical framework to understand the exquisite interaction between biochemical signals and the complex structure of neurons in which they take place. The knowledge generated will be disseminated with a computational toolbox that can be used in any area of biology interested in complex systems, from biochemistry to ecology. This proposal will provide training opportunities to minority bilingual undergraduates not only in the scientific aspects of the project but also to develop Wikipedia pages in Spanish to help the American Hispanic population get better access to scientific information in neuroscience and biophysics. The project will also allow the training of a graduate student and post-doctoral fellows which will enrich the academic environment of UTSA, a Hispanic serving institution.