A cell's shape changes as it moves along a surface. The forward-thinking cytoskeletal elements are all for progress, but the conservative cell membrane keeps them under control by physically opposing their movement.
The ability of living cells to move affects the way our bodies develop, fight off infections and heal wounds. Moreover, cell migration is an extremely complex process, which explains why it has captured the collective imaginations of a variety of fields, from the biological and the physical sciences. This is good news, because cell motility is determined in equal parts by biochemistry and mechanics1,2, and so understanding and manipulating it require the sort of clever approach that comes only from the integration of multiple scientific disciplines. On page 475 of this issue, Keren et al.3 combine approaches familiar to cell biology with those familiar to applied mathematics and physics to address how the forces generated by specific molecular processes in a cell produce its observed shape.
The starting point for the authors' analysis was the characterization of variability in the shapes adopted by epithelial keratocytes from fish skin in culture. These cells serve as a unique model system for studying cell migration, because they crawl rapidly and without frequent changes in direction, and maintain a nearly constant shape as they move. Their stereotypical shape, often described as an 'inverted canoe', is characterized by a broad membrane structure at its front, the lamellipodium, which protrudes forward in concert with forces that act at the rear of the cell. The authors determined that most of the shape variability could be attributed to differences in cell size and, to a lesser extent, the aspect ratio of its characteristic dimensions (the ratio of its width to its height).
The key insight by Keren et al. was to relate two independent observations: the cell's shape and its distribution of actin filaments. Actin filaments are structural elements inside the cell that, through the energy-intensive process of adding (and later removing) protein subunits, produce the mechanical work required to push the cell forward. New, growing filaments are formed by the branching off of existing ones, a process that is well understood in keratocytes4,5.
Building on previous work6, the authors propose a mathematical model to explain the observation that the filament density at the cell front is graded, with the highest density at its centre (Fig. 1). The importance of this approach is that it incorporates known molecular mechanisms, and hence the model could be used to predict what might happen if the functions of the molecules involved were perturbed. The authors next invoked what is known as the force–velocity relationship, which states that the rate at which the membrane can be pushed forward by the growing actin filaments decreases as the force resisting them increases, and above a critical value — the stall force — protrusion stops completely.
Although the mechanisms that give rise to this relationship are actively debated, it is strongly grounded by empirical observations7. Keren et al.3 reasoned that the load force per actin filament must increase as the filament density decreases from the centre of the cell, and thus the 'sides' of the cell represent the regions of the lamellipodium where the actin filaments are stalled (and/or buckled under pressure; Fig. 1). A specific prediction followed, which the authors confirmed: the steepness of the actin-filament gradient from the cell centre to the front edges is directly related to the cell's aspect ratio. Furthermore, with the specification of the cell shape and the force–velocity relationship, Keren et al. showed that they could predict, in a consistent way, the curvature of the cell front and the cell-migration speed.
The elegance of the authors' model, which exemplifies the combined use of quantitative cell biology and mathematical analysis8, lies in its ability to relate molecular and physical processes with very few or in some cases no adjustable parameters. One unresolved issue that warrants further study concerns the mechanistic implications for the variability in cell size. Although Keren et al. were not able to address this point directly, their model suggests that it ought to affect either the rate of actin-filament branching or the tension of the cell membrane, or possibly both.
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