蛋白质转位布朗棘轮的渐近性
Asymptotics of a Brownian ratchet for Protein Translocation
摘要：
细胞中的蛋白质易位已通过\emph{Brownian ratchets}建模。在这样的模型中，蛋白质通过纳米孔扩散。在孔的一侧，棘轮分子与蛋白质结合并阻止其扩散出孔。利用反射布朗运动$(X_t)_{t\geq 0}$的反射点$(R_t)_{t\geq 0}$的变化来研究布朗棘轮. $R_t$的变化率为$γ(X_t-R_t)$，新的反射边界均匀分布在$R_{t-}$和$X_t$之间。棘轮的渐近速度与$γ^{1/3}$成比例，渐近方差与$γ$无关。
英文摘要：
Protein translocation in cells has been modelled by \emph{Brownian ratchets}. In such models, the protein diffuses through a nanopore. On one side of the pore, ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a Brownian ratchet by means of a reflected Brownian motion $(X_t)_{t\geq 0}$ with a changing reflection point $(R_t)_{t\geq 0}$. The rate of change of $R_t$ is $γ(X_t-R_t)$ and the new reflection boundary is distributed uniformly between $R_{t-}$ and $X_t$. The asymptotic speed of the ratchet scales with $γ^{1/3}$ and the asymptotic variance is independent of $γ$.
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