Brenner M P, Levitov L S, Budrene E O
Department of Mathematics, Massachusetts Institute of Technology, Cambridge 02139, USA.
Biophys J. 1998 Apr;74(4):1677-93. doi: 10.1016/S0006-3495(98)77880-4.
This paper formulates a theory for chemotactic pattern formation by the bacteria Escherichia coli in the presence of excreted attractant. In a chemotactically neutral background, through chemoattractant signaling, the bacteria organize into swarm rings and aggregates. The analysis invokes only those physical processes that are both justifiable by known biochemistry and necessary and sufficient for swarm ring migration and aggregate formation. Swarm rings migrate in the absence of an external chemoattractant gradient. The ring motion is caused by the depletion of a substrate that is necessary to produce attractant. Several scaling laws are proposed and are demonstrated to be consistent with experimental data. Aggregate formation corresponds to finite time singularities in which the bacterial density diverges at a point. Instabilities of swarm rings leading to aggregate formation occur via a mechanism similar to aggregate formation itself: when the mass density of the swarm ring exceeds a threshold, the ring collapses cylindrically and then destabilizes into aggregates. This sequence of events is demonstrated both in the theoretical model and in the experiments.
本文阐述了一种理论，用于解释在存在排泄引诱剂的情况下，大肠杆菌的趋化模式形成。在化学趋化中性的背景下，通过化学引诱剂信号传导，细菌组织成群体环和聚集体。该分析仅涉及那些由已知生物化学证明合理且对群体环迁移和聚集体形成必要且充分的物理过程。群体环在没有外部化学引诱剂梯度的情况下迁移。环的运动是由产生引诱剂所需的底物耗尽引起的。提出了几个标度律，并证明它们与实验数据一致。聚集体形成对应于有限时间奇点，其中细菌密度在某一点发散。导致聚集体形成的群体环不稳定性通过类似于聚集体形成本身的机制发生：当群体环的质量密度超过阈值时，环会呈圆柱形坍塌，然后不稳定形成聚集体。这一系列事件在理论模型和实验中均得到了证明。
