L. Tweedy, P.A. Thomason, P.I. Paschke, K. Martin, L.M. Machesky, M. Zagnoni, R.H. Insall, Seeing around corners: Cells solve mazes and respond at a distance using attractant breakdown, 9792 (2020).
During development and metastasis, cells migrate large distances through complex environments. Migration is often guided by chemotaxis, but simple chemoattractant gradients between a source and sink cannot direct cells over such ranges. We describe how self-generated gradients, created by cells locally degrading attractant, allow single cells to navigate long, tortuous paths and make accurate choices between live channels and dead ends. This allows cells to solve complex mazes efficiently. Cells’ accuracy at finding live channels was determined by attractant diffusivity, cell speed, and path complexity. Manipulating these parameters directed cells in mathematically predictable ways; specific combinations can even actively misdirect them. We propose that the length and complexity of many long-range migratory processes, including inflammation and germ cell migration, means that self-generated gradients are needed for successful navigation.
概述
细胞在胚胎形成、免疫反应和神经寻路等方面的迁移是由于趋化性，即向趋化因子高浓度梯度方向移动。简单的趋化性是在局部引诱剂源与外部吸收体间建立梯度，仅能提供短距离的引导。当距离超过500μm时，它变得效率低下，无法解析复杂的路径，并且仅在小范围内有效。这篇文章主要阐述细胞如何在长距离、复杂路径中进行决策。
We found that cells using self-generated gradients could make accurate choices about paths they had not yet encountered.
结果与讨论
Self-generated gradients promote long-range chemotaxis 长距离趋化
Chemotactic cells detect attractant gradients by comparing receptor occupancy at different places. Cells can resolve 1% differences between the occupancy at their fronts and rears, but this is only enough to navigate short distances. 细胞通过感受前后的浓度差来决定迁移方向
However, cells can make sharp, local gradients by breaking down attractants. 降解趋化因子能产生更陡峭的局部梯度
By contrast, the self-generated gradient gives robust chemotaxis throughout because the gradient is always sharp and local to the group of cells that makes it, resulting in a nonsaturating attractant concentration around the cells.
Self-generated gradients allow cells to make long-range route decisions 路径决策
For dynamic gradients such as self-generated gradients, diffusion is a key determinant. 通常的趋化性研究是基于一个静态的浓度梯度场，而self-generated gradients中扩散是一个关键因素。
In the static gradient, each cell chose a route randomly. The self-generated gradient, on the other hand, robustly directed equal numbers of cells into each branch. Stochastic variations were balanced out; branches containing more cells evolved shallower attractant gradients, so newly arriving cells were directed into the other branch.
动态梯度使得细胞较为平衡地分布在两个分支中。
If one of the branches was closed off from the reservoir (Fig. 1D), then the number of cells entering the closed branch was small because the first arrivals rapidly depleted the attractant and prevented further recruitment. 封闭分支中的趋化因子会被迅速消耗，从而阻止新的细胞进入。
The effect depended strongly on the length of the dead end. 效果取决于封闭路径的长度，
Self-generated gradients allow cells to navigate mazes
使用不可降解的趋化因子，让细胞走相同的迷宫，细胞几乎不能寻路，说明趋化因子的降解是驱动力
Accuracy of decisions is controlled by length and complexity of paths决策的准确性由路径长度和复杂性决定
设计了三种不同的迷宫”simple” mazes，”short” mazes，”long” mazes。利用两种细胞进行了测试：D. discoideum cells and mouse pancreatic cancer cells
方法
细胞运动的模拟方法
The persistent, random element comes from drawing a new direction at each step from wrapped normal distribution centered on the current direction of motion. The attractant gradient direction was estimated from grid points that overlapped the cell (all those grid points within 6 mm of the cell centroid) and used to generate a bias vector. The bias vector was added to the persistent, randomvector to choose a final direction of motion, and the cell moved in this direction at its current speed unless it collided with a wall, in which case its movement distance was reduced.
扩散使用semi-implicit DuFort-Frankel method，用Java.Diffusion写成。细胞模拟采用基于agent的模型。每次运动以细胞当前方向为中心，用warpped normal distribution产生一组方向向量，再叠加6μm内的梯度方向产生的偏置向量，得到总的方向向量，用来选择移动方向。
细胞消耗趋化因子用米氏方程模拟，消耗掉的量均匀地从细胞占据的格点上去除。