SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 919-938, January 2021.
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 $\Omega_k\subset {\mathbb R}^d$, $k=1,\ldots,N$, 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 toward the $k$th target is $p_k$ with $\sum_{k=1}^Np_k<1$. Hence, there is a nonzero 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 1D search process with stochastic resetting, finite return times, and refractory periods. We use a renewal method to calculate the splitting probabilities and conditional mean first passage times 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.

中文翻译：

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基于音素的形态发生的定向搜索和捕获模型

SIAM应用数学杂志，第81卷，第3期，第919-938页，2021年1月。
在本文中，我们开发了基于细胞因子的形态发生的定向搜索和捕获模型。我们考虑单个细胞因子从源细胞中成核并搜索一组$ N $目标细胞$ \ Omega_k \ subset {\ mathbb R} ^ d $，$ k = 1，\ ldots，N $，其中有$ d \ geq 2 $。我们假设每次细胞因子成核时，细胞因子都会沿随机方向生长，因此朝向$ k $目标的概率为$ p_k $，其中$ \ sum_ {k = 1} ^ Np_k <1 $。因此，除非有某种机制可以返回成核位置并随后沿新方向成核，否则无法找到目标的可能性为非零。我们将后者建模为具有随机重置，有限返回时间和不应期的一维搜索过程。我们使用一种更新方法来计算分裂概率和有条件的平均第一次通过时间，以得到给定靶细胞捕获的细胞因子。然后，我们在多轮搜索和捕获事件以及形态发生子降解之后，确定了目标细胞组上形态发生子的稳态积累。然后，这会在整个目标细胞的集合中产生相应的形态发生子梯度，这些目标细胞的陡度取决于重置速率。我们通过考虑目标细胞的单层来说明该理论，并讨论对多个细胞因子的扩展。然后，这会在目标细胞组中产生相应的形态发生子梯度，其陡度取决于重置速率。我们通过考虑目标细胞的单层来说明该理论，并讨论对多个细胞因子的扩展。然后，这会在目标细胞组中产生相应的形态发生子梯度，其陡度取决于重置速率。我们通过考虑目标细胞的单层来说明该理论，并讨论对多个细胞因子的扩展。