Mathematical Strategies to Uncover the Molecular Basis of Prion Transitions

看似相同的细胞群体在表型上往往是高度可变的，但这种变异的定量基础很少被理解。本提案的目标是开发和实验验证多尺度随机和确定性数学模型，包括这种变异的来源：细胞分裂和细胞内成分。为此，我们的研究将利用并寻求解释酵母中亚稳态朊病毒表型，这是一种实验可处理和生物学相关的模型。朊病毒是一种仅含蛋白质的遗传元素，在这种遗传元素中，同一蛋白质的不同功能状态是通过聚合体中三维构象的自模板变化而产生的。哺乳动物中的朊病毒通常与致命的神经退行性疾病有关，但酵母朊病毒通过利用生物异质性的操作出现和消失。在目标1中，我们开发了一个具有随机调控两个阶段的朊病毒外观模型：初始聚合首先必须出现，然后随着细胞分裂在群体中持续存在。我们将通过直接求解化学主方程（CME）来分析我们的模型，这是我们为蛋白质聚集开发的一种新的状态空间截断。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，直至系统内存的大小。在目标2中，我们开发了一个多尺度结构种群模型（MS-SPM），其中聚集体在细胞的生命周期中在大小和数量上进化，并与影响这些动力学的其他细胞成分一起分布，根据细胞分裂的不对称性。为了解决MS-SPM -一个具有非局部边界条件的耦合偏微分方程系统-我们将推广用于年龄结构人口模型的数值方法。我们将使用我们的模型来研究细胞年龄和聚集成分之间的关系，并发现朊病毒显性阴性突变体诱导的朊病毒消失的分子基础。这些模型将用于解释数据，估计参数和发展假设，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.