棒状聚合物的断裂和单体延长，朊病毒增殖的相关模型
Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation
摘要：
Greer、Pujo-Menjouet和Webb模型[Greer等人，理论生物学杂志，242（2006），598-606]，发现与无流动条件下的实验观察结果非常一致。这项工作的目的是概括的问题，一般的聚合-断裂流动运动下的框架，动机的事实，实验室工作往往涉及朊病毒动力学流动条件下，以观察更快的过程。此外，理解和建模的微观结构的宏观监测的非牛顿行为的影响是至关重要的传感器设计，其目标是提供有关正在进行的分子进化的实用信息。本文的结果，然后可以被认为是一个步骤，在数学上理解这样的模型，即证明的积极性和存在的解决方案，在适当的功能空间。为此，我们引入了一个新的模型的基础上的刚性杆聚合物理论占流动条件下的聚合物动力学。正如预期的那样，当应用于朊病毒问题时，在没有运动的情况下，它减少到Greer et al.（2006）中的情况。在任何聚合物动力学理论的核心，都有一个Fokker-Planck-Smoluchowski型的构型概率扩散偏微分方程（PDE）。本文的主要数学结果是证明了存在的正解，上述PDE的一类流量的实际利益，考虑到一般的聚合物，特别是朊病毒流诱导分裂/延长。
英文摘要：
The Greer, Pujo-Menjouet andWebb model [Greer et al., J. Theoret. Biol., 242 (2006), 598-606] for prion dynamics was found to be in good agreement with experimental observations under no-flow conditions. The objective of this work is to generalize the problem to the framework of general polymerization-fragmentation under flow motion, motivated by the fact that laboratory work often involves prion dynamics under flow conditions in order to observe faster processes. Moreover, understanding and modelling the microstructure influence of macroscopically monitored non-Newtonian behaviour is crucial for sensor design, with the goal to provide practical information about ongoing molecular evolution. This paper's results can then be considered as one step in the mathematical understanding of such models, namely the proof of positivity and existence of solutions in suitable functional spaces. To that purpose, we introduce a new model based on the rigid-rod polymer theory to account for the polymer dynamics under flow conditions. As expected, when applied to the prion problem, in the absence of motion it reduces to that in Greer et al. (2006). At the heart of any polymer kinetical theory there is a configurational probability diffusion partial differential equation (PDE) of Fokker-Planck-Smoluchowski type. The main mathematical result of this paper is the proof of existence of positive solutions to the aforementioned PDE for a class of flows of practical interest, taking into account the flow induced splitting/lengthening of polymers in general, and prions in particular.
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