ISC-CNR, Institute for Complex Systems, Piazzale Aldo Moro 2, 00185 Rome, Italy.
Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy.
Phys Rev E. 2019 Nov;100(5-1):052147. doi: 10.1103/PhysRevE.100.052147.
We consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case.
我们考虑一个具有空间相关速度的进行奔跑和翻滚的粒子。该模型具有生物学相关性，因为它描述了在不均匀环境中运动的细菌或细胞。我们给出了在无界空间中自由运动的情况下概率密度函数的精确表达式。然后，我们分析了在存在部分吸收边界的情况下粒子在受限区间内运动的情况，报告了拉普拉斯（时间）域中的概率密度和吸收的平均时间。我们还讨论了在存在反射边界的情况下限制与翻滚率方向相关的弛豫到稳态的情况，这模拟了细胞的趋化现象。具有空间变化扩散系数的扩散粒子的情况是作为一个极限情况得到的。
