UMPA, ENS-Lyon, 46, allée d'Italie, 69000, Lyon, France.
J Biol Dyn. 2010 Jan;4(1):28-42. doi: 10.1080/17513750902935208.
Models for the polymerization process involved in prion self-replication are well-established and studied [H. Engler, J. Pruss, and G.F. Webb, Analysis of a model for the dynamics of prions II, J. Math. Anal. Appl. 324 (2006), pp. 98-117; M.L. Greer, L. Pujo-Menjouet, and G.F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoret. Biol. 242 (2006), pp. 598-606; J. Pruss, L. Pujo-Menjouet, G.F. Webb, and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Cont. Dyn. Sys. Ser. B 6(1) (2006), pp. 215-225] in the case where the dynamics coefficients do not depend on the size of polymers. However, several experimental studies indicate that the structure and size of the prion aggregates are determinant for their pathological effect. This motivated the analysis in Calvez et al. [Size distribution dependence of prion aggregates infectivity, Math Biosci. 217 (2009), pp. 88-99] where the authors take into account size-dependent replicative properties of prion aggregates. We first improve a result concerning the dynamics of prion aggregates when a pathological state exists (high production of the normal protein). Then we study the strain phenomena and more specifically we wonder what specific replicative properties are determinant in strain propagation. We propose to interpret it also as a dynamical property of size repartitions.
涉及朊病毒自我复制的聚合过程模型已经得到很好的确立和研究[H. Engler、J. Pruss 和 G.F. Webb，分析朊病毒动力学模型 II，J. Math. Anal. Appl. 324 (2006)，第 98-117 页；M.L. Greer、L. Pujo-Menjouet 和 G.F. Webb，朊病毒增殖的数学分析，J. Theoret. Biol. 242 (2006)，第 598-606 页；J. Pruss、L. Pujo-Menjouet、G.F. Webb 和 R. Zacher，朊病毒动力学模型分析，Discrete Cont. Dyn. Sys. Ser. B 6(1) (2006)，第 215-225 页]，在这种情况下，动力学系数不依赖于聚合物的大小。然而，几项实验研究表明，朊病毒聚集体的结构和大小对其病理效应起决定性作用。这促使 Calvez 等人进行了分析[朊病毒聚集体感染性的大小分布依赖性，Math Biosci. 217 (2009)，第 88-99 页]，作者在其中考虑了朊病毒聚集体的复制特性与大小相关。我们首先改进了一个关于朊病毒聚集体动力学的结果，即存在病理状态（正常蛋白大量产生）时。然后，我们研究了菌株现象，更具体地说，我们想知道在菌株传播中哪些特定的复制特性是决定性的。我们建议将其也解释为大小分布的动态特性。
