At the leading edge of a crawling keratocyte

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Filaments, networks and the mechanics of whole cells

Problem

At the leading edge of a crawling keratocyte, the plasma membrane behaves as a flat sheet under tension advancing as an army of actin filaments beneath it polymerise, each acting as an independent Brownian ratchet. Electron micrographs show about ρ=100\rho = 100 filament ends engaged with the membrane per micrometre of leading-edge length. Model the membrane's resistance to advance as a force per unit length of the edge equal to its tension, so that the ρ\rho filaments in that length share this load equally. Take membrane tension γ=0.050 mN m−1\gamma = 0.050\,\mathrm{mN\,m^{-1}} (comparable in order to a neutrophil's cortical tension), free barbed-end actin monomer concentration c=10ccc = 10c_c with cc=0.12 μMc_c = 0.12\,\mu\mathrm{M}, barbed-end rate constants kon=11.6 μM−1 s−1k_{\rm on} = 11.6\,\mu\mathrm{M^{-1}\,s^{-1}} and koff=1.4 s−1k_{\rm off} = 1.4\,\mathrm{s^{-1}}, step size δ=2.7 nm\delta = 2.7\,\mathrm{nm}, and body temperature 310 K310\,\mathrm{K}, where kBT=4.28 pN nmk_BT = 4.28\,\mathrm{pN\,nm}. ((a)) Find the average opposing force carried by each filament. ((b)) Find the stall force of a single filament from the Brownian ratchet model at this monomer concentration. ((c)) Using the load-dependent growth rate v(f)=δ[konc e−fδ/kBT−koff]v(f) = \delta\big[k_{\rm on}c\,e^{-f\delta/k_BT} - k_{\rm off}\big], find the actual growth speed of a filament carrying the force found in part (a), and compare it with the unloaded growth speed.

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