LEAPS-MPS: Mathematical Modeling of Brain Structure in Neurodegenerative Diseases Exhibiting Prion-Like Spreading

神经退行性疾病，如阿尔茨海默病和帕金森病，与大脑中神经毒性蛋白质的扩散和功能性脑细胞的逐渐丧失有关，根据损伤发生的部位产生症状。通常有毒蛋白质与健康蛋白质相互作用并将其转化为有毒蛋白质。有毒蛋白质和健康蛋白质都是通过复杂的途径在脑细胞之间运输的。目前，在关键领域缺乏对疾病进展期间这种传播的深入了解。参考临床和实验数据进行参数推断，研究者将建立数学模型，定性和定量地描述有毒蛋白质的传播，特别强调大脑结构。这项研究的结果将为治疗大脑疾病的实验和临床探索带来新的途径。该项目将在西班牙裔服务机构进行，并将提供研究培训和指导机会，包括教授与科学劳动力相关的计算和建模技能，在本科，研究生和博士后水平。该项目的重点是开发一个耦合的非线性微分方程模型系统，用于大脑不同连接体中蛋白质的生物化学及其相关途径，以及一个蛋白质运输的随机网络模型，以解释大脑之间的差异。微分方程组可以用科学的计算和渐近的方法从动力系统的角度来研究。模型结果将增强对潜在疾病轨迹、优化特定结果的策略和具有生物学意义的参数的理解。网络模型允许考虑参数分布和其他自然变化，量化不确定性，并添加所谓的基于生物学的逻辑条件，这些条件不能通过微分方程很好地处理。该项目将解决模型方程解的存在性问题，并建立这些解的性质。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Neurodegenerative diseases such as Alzheimer's Disease and Parkinson's Disease are associated with the spreading of neurotoxic proteins in the brain and the gradual loss of functional brain cells giving rise to symptoms according to where the damage takes place. Often the toxic proteins interact with and convert healthy proteins into toxic proteins. Both toxic and healthy proteins are transported between brain cells through complex pathways. Presently, an in-depth understanding of this spreading during disease progression is lacking in critical areas. With reference to clinical and experimental data for parameter inference, the investigator will develop mathematical models to describe the spread of toxic proteins qualitatively and quantitatively, with particular emphasis on brain structure. The results from this research will bring insights to new avenues of experimental and clinical exploration for treating disorders of the brain. The project will be conducted at a Hispanic Serving Institution and will provide research training and mentoring opportunities, including teaching computing and modeling skills relevant for the scientific workforce, at the undergraduate, graduate, and postdoctoral levels. The project is focused on the development of a model system of coupled, nonlinear differential equations for the biochemistry of proteins in different connectomes of the brain, with their associated pathways, and of a stochastic network model of protein transport to account for variations between brains. The system of differential equations can be studied from a dynamical systems perspective, with scientific computing, and asymptotic methods. The model results will enhance the understanding of potential disease trajectories, strategies for optimizing a particular outcome, and parameters that are of biological interest. The network model allows for considering distributions of parameters and other natural variations, quantifying uncertainty, and adding so-called logical conditions based in biology that are not well handled through differential equations. The project will address the question of existence of solutions to the model equations and establish properties of these solutions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.