Buttenschön Andreas, Edelstein-Keshet Leah
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada.
J Math Biol. 2019 Oct;79(5):1953-1972. doi: 10.1007/s00285-019-01416-6. Epub 2019 Aug 17.
Correlated random walks (CRW) have been explored in many settings, most notably in the motion of individuals in a swarm or flock. But some subcellular systems such as growth or disassembly of bio-polymers can also be described with similar models and understood using related mathematical methods. Here we consider two examples of growing cytoskeletal elements, actin and microtubules. We use CRW or generalized CRW-like PDEs to model their spatial distributions. In each case, the linear models can be reduced to a Telegrapher's equation. A combination of explicit solutions (in one case) and numerical solutions (in the other) demonstrates that the approach to steady state can be accompanied by (decaying) waves.
相关随机游走（CRW）已在许多场景中得到研究，最显著的是在群体或鱼群中个体的运动。但一些亚细胞系统，如生物聚合物的生长或解聚，也可以用类似的模型来描述，并使用相关的数学方法来理解。在这里，我们考虑两个生长中的细胞骨架成分的例子，肌动蛋白和微管。我们使用CRW或广义的类似CRW的偏微分方程来模拟它们的空间分布。在每种情况下，线性模型都可以简化为电报方程。（在一种情况下）显式解和（在另一种情况下）数值解的结合表明，达到稳态的过程可能伴随着（衰减的）波。
