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How nematode sperm crawl

Dean Bottino^1,*, Alexander Mogilner², Tom Roberts³, Murray Stewart⁴ and George Oster^1,

¹ Department of Molecular and Cellular Biology, University of California, Berkeley, CA 94720-3112, USA
² Department of Mathematics, University of California, Davis, CA 95616, USA
³ Department of Biological Science, Florida State University, Tallahassee, FL 32306-3050, USA
⁴ MRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, England
^* Present address: Physiome Sciences, 150 College Road West, Princeton, NJ 08540-6608

View larger version (50K): [in a new window]   Fig. 1. (A) Top view of a crawling Ascaris sperm. The lamellipod can be divided into three major regions: (LE), the leading edge where polymerization and gel condensation into macrofibers and ribs takes place. In Ascaris, but not in other nematode sperm, hyper-complexed branched MSP ‘ribs’ are prominent and originate in protuberances called villipodia. (PR) the perinuclear region where the MSP gel solates and generates a contractile stress. (IR) the intermediate region between the LE and PR where the gel density is nearly constant. The proximal-to-distal pH gradient affects the polymerization and depolymerization rates at the LE and in the PR. (B) Schematic diagram showing the Ascaris sperm lamellipod in cross section. The ventral-fiber complexes branch dorsally. The MSP gel forms at the leading edge and is connected mechanically to the substratum through the membrane. As the cell moves forwards, the gel remains stationary with respect to the substratum, eventually entering the perinuclear region where it solates and contracts. (C) The graphs show how the pH, adhesion, gel density and the elastic stress vary with position in the lamellipod.

View larger version (44K): [in a new window]   Fig. 2. (A) The continuum model of a 1D cytogel strip representing the lamellipod (see Appendix). (B) The finite element model of the lamellipod. The lamellipod is triangulated so that each node represents a mass of cytoskeleton contained in the surrounding (Voronoi) polygon. (C) Detail of a finite element consisting of an elastic element in parallel with a tensile element. The dashpot with damping coefficient µ connected to the substratum accounts for the viscous dissipation associated with making and breaking attachments as well as the dissipation associated with cytoskeleton-fluid friction.

View larger version (36K): [in a new window]   Fig. 3. Frames from the simulation movie showing the progression of the MSP cytoskeleton as the cell moves forward. The same time interval elapses between successive shaded cell ‘shadows’. Bottom, simulation of translocation with ‘normal’ substrate friction. Top, simulation with the cell body friction increased four-fold over the normal run. Note that the cell body moves much more slowly, but the lamellipod shape changes very little.

View larger version (19K): [in a new window]   Fig. 4. A vector field plot of forces at nodes computed after the cell moved two body lengths. The interior node forces (red) are applied to the substrate; the cell body interface node forces (blue) are applied throughout the substrate beneath the cell body. The magnitude of the forces are proportional to the lengths of the arrows. The forces applied to the center of the cell body interface are 100 pN. The total forward translocation force on the cell body is 1000 pN. The traction forces at the rear of the lamellipod are 10 pN per node. Because of the strong substrate adhesion and because there is no gradient in the bundling stress, the traction forces decrease to 1 pN per node at the leading edge. There is also no noticeable anisotropy in the traction forces.

View larger version (28K): [in a new window]   Fig. 5. A study of effects of extracellular pHext on the simulated cell. In all figures, the red filled region is the original outline of the cell. The final position of the cell in all three cases is shown after the same amount of simulation time has elapsed (1 sec of real time). Bottom, pHext=7.6. This is the case of normal motility. At the front, pH reaches the value of >6.15, so that both the storage of elastic energy, cytoskeletal assembly and adhesion are strong at the leading edge. Middle, pHext=6.75. At this pH motility is impaired. At the front, pH drops to less than 6.15, but both the storage of elastic energy and adhesion are still strong at the leading edge. However, the cytoskeletal assembly is attenuated significantly. The cell body moves forward, but the leading edge is nearly stationary. Top, at pHext=6.35 this motility ceases. At the front the pH decreases to less than 6.1, so that all of the protrusion-supporting processes – adhesion, storage of elastic energy and cytoskeletal assembly – are inhibited. The contraction of the lamellipod takes place transiently owing to the elastic energy stored prior to the change in extracellular pH. This contraction moves the cell body forward slightly, at the same time pulling the leading edge backward significantly. The adhesion of the cell body is now greater than the adhesion of the lamellipod.

View larger version (8K): [in a new window]   Fig. 6.

View larger version (12K): [in a new window]   Fig. 7.

View larger version (37K): [in a new window]   Fig. 8.