Directional search-and-capture model of cytoneme-based morphogenesis

TL;DR

This paper presents a mathematical model of how cytonemes search for and capture target cells to facilitate morphogen distribution, incorporating stochastic growth directions, resetting, and multiple search rounds.

Contribution

It introduces a novel search-and-capture model with stochastic resetting and calculates morphogen gradients based on search dynamics.

Findings

Derived splitting probabilities and MFPTs for target capture

Quantified how resetting rate affects morphogen gradient steepness

Extended the model to multiple cytonemes and layered target cells

Abstract

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 $\Omega_k\subset \R^d$, $k=1,\ldots,N$, 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.