Directed cell migration poses a rich set of theoretical challenges. Broadly, these are concerned with (1) how cells sense external signal gradients and adapt; (2) how actin polymerisation is localised to drive the leading cell edge and Myosin-II molecular motors retract the cell rear; and (3) how the combined action of cellular forces and cell adhesion results in cell shape changes and net migration. Reaction–diffusion models for biological pattern formation going back to Turing have long been used to explain generic principles of gradient sensing and cell polarisation in simple, static geometries like a circle. In this minireview, we focus on recent research which aims at coupling the biochemistry with cellular mechanics and modelling cell shape changes. In particular, we want to contrast two principal modelling approaches: (1) interface tracking where the cell membrane, interfacing cell interior and exterior, is explicitly represented by a set of moving points in 2D or 3D space and (2) interface capturing. In interface capturing, the membrane is implicitly modelled analogously to a level line in a hilly landscape whose topology changes according to forces acting on the membrane. With the increased availability of high-quality 3D microscopy data of complex cell shapes, such methods will become increasingly important in data-driven, image-based modelling to better understand the mechanochemistry underpinning cell motion.
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Cover Image
Cover Image
The cover shows a metaphorical representation of the anti-CRISPR AcrIIA6, represented as handcuffs, sequestering two Streptococcus thermophilus CRISPR1-Cas9 (St1Cas9) molecules at a time and preventing conformational changes associated with DNA recognition and binding. In the absence of AcrIIA6, St1Cas9 tightly binds to its target DNA, and can proceed to target cleavage. For further information, see the article by Hardouin and Goulet in this issue (pp. 507–516). This cover artwork has been made by Beata Edyta Mierzwa (www.BeataScienceArt.com).
Mathematical modelling in cell migration: tackling biochemistry in changing geometries
Björn Stinner, Till Bretschneider; Mathematical modelling in cell migration: tackling biochemistry in changing geometries. Biochem Soc Trans 29 April 2020; 48 (2): 419–428. doi: https://doi.org/10.1042/BST20190311
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