Mathematical Strategies to Uncover the Molecular Basis of Prion Transitions

看似相同的细胞群体在表型方面往往是高度可变的，但这种变化的定量基础很少被理解。该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，将这种变化的来源：细胞分裂和细胞内成分。为了做到这一点，我们的研究将利用并试图解释酵母中基于亚稳态朊病毒的表型，这是一种实验上易于处理的生物学相关模型。朊病毒是蛋白质唯一的遗传元件，其中相同蛋白质的不同功能状态是通过在聚集体的背景下其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，我们开发了一个模型的朊病毒外观与两个阶段的随机调节：一个初始的聚集体首先必须出现，然后坚持在人口中的细胞分裂。我们将通过直接求解化学主方程（CME）来分析我们的模型，该方程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一个矩阵自由实现的CME，使我们能够考虑生物学上可行的状态空间的系统内存的大小。在目标2中，我们开发了一个多尺度结构种群模型（MS-SPM），聚集体在细胞的生命周期中在大小和数量上发生变化，并与其他影响这些动态的细胞成分一起沿着，与细胞分裂中的不对称性一致。为了解决MS-SPM -一个系统的耦合偏微分方程与非局部边界条件-我们将推广数值方法开发的年龄结构人口模型。我们将利用我们的模型来研究细胞年龄和聚集体组成之间的关系，并发现由朊病毒显性阴性突变体引起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.