Mathematical Strategies to Uncover the Molecular Basis of Prion Transitions

揭示朊病毒跃迁分子基础的数学策略

• 批准号: 9459439
• 负责人: Suzanne Sindi
• 金额: $ 21.36万
• 依托单位: UNIVERSITY OF CALIFORNIA, MERCED
• 依托单位国家: 美国
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2021-03-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/9459439
• 关键词: Age; Alpha Cell; Appearance; Biological; Cell division; Cells; Chemicals; Coupled; Data; Dimensions; Disease; Dominant-Negative Mutation; Equation; Future; Genetic; Goals; Human; Mammals; Mathematics; Memory; Methods; Mission; Modeling; Molecular; Molecular Conformation; Neurodegenerative Disorders; Non-Insulin-Dependent Diabetes Mellitus; Phenotype; Population; Prions; Proteins; Regulation; Source; Structure; System; United States National Institutes of Health; Variant; Yeasts; biological heterogeneity; experimental study; genetic element; human disease; insight; mathematical model; novel; prion-based; protein aggregation; yeast prion

Populations of seemingly identical cells are often highly variable with respect to phenotype, but the quantitative basis of this variation is rarely understood. The goal of this proposal is to develop and experimentally validate multiscale stochastic and deterministic mathematical models incorporating the sources of this variation: cell division and intracellular constituents. To do so, our studies will exploit and seek to explain metastable prion-based phenotypes in yeast, an experimentally tractable and biologically relevant model. Prions are protein-only genetic elements in which distinct functional states of the same protein are created by self-templating changes in its three-dimensional conformation within the context of an aggregate. Prions in mammals are commonly associated with fatal neurodegenerative disease, but yeast prions appear and disappear through manipulations that exploit biological heterogeneity. In Aim 1 we develop a model of prion appearance with two stages of stochastic regulation: an initial aggregate first must appear and then persist in the population as cells divide. We will analyze our model by directly solving the chemical master equation (CME) over a novel state-space truncation we developed for protein aggregation. We use generating functions to develop a matrix free implementation of the CME enabling us to consider biologically feasible state spaces up to the size of system memory. In Aim 2, we develop a multiscale structured population model (MS-SPM) where aggregates evolve in size and number during a cell's lifetime and are distributed, along with other cellular constituents impacting these dynamics, in accordance with asymmetries in cell division. To solve the MS-SPM - a system of coupled PDEs with non-local boundary conditions - we will generalize numerical methods developed for age-structured population models. We will use our model to study the relationship between cellular age and aggregate composition and to discovery the molecular basis of prion disappearance induced by prion dominant-negative mutants. These models will be used to explain data, estimate parameters and develop hypotheses to guide future experiments.

对于表型，看似相同的细胞的种群通常是高度可变的，但是这种变异的定量基础很少被理解。该提案的目的是开发和实验验证融合了这种变体来源的多尺度随机和确定性的数学模型：细胞分裂和细胞内成分。为此，我们的研究将利用并试图解释酵母中基于稳定的prion的表型，这是一种实验性的且具有生物学相关的模型。王室是仅蛋白质的遗传元素，其中同一蛋白质的不同功能状态是通过在骨料的背景下的三维构象中的自我测定变化而产生的。哺乳动物中的王室通常与致命的神经退行性疾病有关，但是通过利用生物异质性的操纵而出现酵母菌prions并消失。在AIM 1中，我们开发了一个具有两个随机调节阶段的prion外观模型：首先必须出现初始骨料，然后随着细胞分裂而在人群中持续存在。我们将通过直接求解用于蛋白质聚集的新型状态空间截断的化学主方程（CME）来分析我们的模型。我们使用生成功能来开发CME的矩阵免费实现，从而使我们能够考虑生物学上可行的状态空间，直到系统内存的大小。在AIM 2中，我们开发了一个多尺度结构化种群模型（MS-SPM），其中聚集体在单元的寿命期间的大小和数量演变，并根据细胞分裂的不对称性而分布以及其他影响这些动力学的细胞成分。为了解决MS-SPM - 具有非本地边界条件的耦合PDE系统 - 我们将推广为年龄结构群体模型开发的数值方法。我们将使用我们的模型研究细胞年龄与骨料组成之间的关系，并发现由王室显性阴性突变体引起的prion王消失的分子基础。这些模型将用于解释数据，估计参数并提出假设以指导未来的实验。