论文标题
基于细胞素形态发生的定向搜索和捕捉模型
Directional search-and-capture model of cytoneme-based morphogenesis
论文作者
论文摘要
在本文中，我们开发了基于细胞素形态发生的定向搜索模型。我们考虑从源单元中进行单个细胞核定核的成核，并搜索一组$ n $ target细胞$ω_k\ subset \ r^d $，$ k = 1，\ ldots，n $，带有$ d \ geq 2 $。我们假设每次核定核会沿随机方向生长时，以$ \ sum_ {k = 1}^np_k <1 $而定向的概率为$ k $ -th目标。因此，除非有某种机制返回成核位点并随后在新方向上核定成核，否则未能找到目标的概率是非零的。我们将后者建模为一维搜索过程，并具有随机重置，有限的返回时间和难治期。我们使用一种续签方法来计算分裂概率和条件平均第一次通道时间（MFPTS），以通过给定目标细胞捕获的细胞。然后，在多轮搜索和捕获事件和形态学降解之后，我们确定了在靶细胞集上形态基因的稳态积累。然后，这会在整个靶细胞中产生相应的形态梯度，它们的陡度取决于重置速率。我们通过考虑单层靶细胞来说明理论，并讨论对多个细胞质的扩展。
In this paper we develop a directional search-and-capture model of cytoneme-based morphogenesis. We consider a single cytoneme nucleating from a source cell and searching for a set of $N$ target cells $Ω_k\subset \R^d$, $k=1,\ldots,N$, with $d\geq 2$. We assume that each time the cytoneme nucleates, it grows in a random direction so that the probability of being oriented towards the $k$-th target is $p_k$ with $\sum_{k=1}^Np_k<1$. Hence, there is a non-zero probability of failure to find a target unless there is some mechanism for returning to the nucleation site and subsequently nucleating in a new direction. We model the latter as a one-dimensional search process with stochastic resetting, finite returns times and refractory periods. We use a renewal method to calculate the splitting probabilities and conditional mean first passage times (MFPTs) for the cytoneme to be captured by a given target cell. We then determine the steady-state accumulation of morphogen over the set of target cells following multiple rounds of search-and-capture events and morphogen degradation. This then yields the corresponding morphogen gradient across the set of target cells, whose steepness depends on the resetting rate. We illustrate the theory by considering a single layer of target cells, and discuss the extension to multiple cytonemes.
