Mathematical Strategies to Uncover the Molecular Basis of Prion Transitions

看似相同的细胞群体通常在表型上有很大的差异，但这种差异的数量基础很少被理解。这项提议的目标是开发和实验验证多尺度、随机和确定性的数学模型，其中包括这种变异的来源：细胞分裂和细胞内成分。为了做到这一点，我们的研究将开发并试图解释酵母中亚稳态的基于Pron的表型，这是一个实验上容易处理的和生物相关的模型。Prion是纯蛋白质遗传元件，在这种遗传元件中，同一蛋白质的不同功能状态是通过自模板化在聚集体环境中其三维构象的变化而产生的。哺乳动物中的Prion通常与致命的神经退行性疾病有关，但酵母Prion通过利用生物异质性的操纵而出现和消失。在目标1中，我们建立了一个带有两个随机调节阶段的普利子出现模型：首先必须出现一个初始聚集体，然后随着细胞分裂而持续存在于种群中。我们将通过在我们为蛋白质聚集开发的新的状态空间截断上直接求解化学主方程(CME)来分析我们的模型。我们使用生成函数来开发CME的无矩阵实现，使我们能够考虑生物上可行的状态空间，直到系统内存的大小。在目标2中，我们开发了一个多尺度结构化种群模型(MS-SPM)，其中聚集体在细胞生命周期中在大小和数量上进化，并根据细胞分裂的不对称性与影响这些动态的其他细胞成分一起分布。为了求解MS-SPM--一个具有非局部边界条件的耦合偏微分方程组--我们将推广为年龄结构人口模型开发的数值方法。我们将使用我们的模型来研究细胞年龄和聚集体组成之间的关系，并发现由Prion显性-负性突变体诱导的Prion消失的分子基础。这些模型将被用来解释数据、估计参数和开发假说，以指导未来的实验。

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.