Mechano-chemical feedbacks regulate actin mesh growth in lamellipodial protrusions

Abstract

During cell motion on a substratum, eukaryotic cells project sheetlike lamellipodia which contain a dynamically remodeling three-dimensional actin mesh. A number of regulatory proteins and subtle mechano-chemical couplings determine the lamellipodial protrusion dynamics. To study these processes, we constructed a microscopic physico-chemical computational model, which incorporates a number of fundamental reaction and diffusion processes, treated in a fully stochastic manner. Our work sheds light on the way lamellipodial protrusion dynamics is affected by the concentrations of actin and actin-binding proteins. In particular, we found that protrusion speed saturates at very high actin concentrations, where filament nucleation does not keep up with protrusion. This results in sparse filamentous networks, and, consequently, high resistance forces on individual filaments. We also observed maxima in lamellipodial growth rates as a function of Arp2/3, a nucleating protein, and capping proteins. We provide detailed physical explanations behind these effects. In particular, our work supports the actin-funneling-hypothesis explanation of protrusion speed enhancement at low capping protein concentrations. Our computational results are in agreement with a number of related experiments. Overall, our work emphasizes that elongation and nucleation processes work highly cooperatively in determining the optimal protrusion speed for the actin mesh in lamellipodia.

Figure 1

(a) Schematic drawing of our lamellipodial model is shown. (b) A snapshot from the simulation output showing the branched filamentous network. During simulation, both the front and the back of the membrane (shown as ribbons) move, and the region between them is the active reaction front. Filaments (shown as narrow tubes) are branched with branching points (shown as spheres; i.e., nucleated by Arp2/3 binding).

Figure 2

Actin concentration-dependence of (a) the protrusion speed and (b) the nucleation rate is shown. The concentrations of Arp2/3 and capping proteins were kept at 50 nM.

Figure 3

(a) Density of filaments along protrusion leading edge is shown as a function of G-actin concentration. Leading-edge filaments are defined as those close to the membrane (with distance no larger than 2.7 nm, the effective size of one monomeric actin). (b) The ratio of the nucleation rate to the protrusion speed (i.e., the density of new filaments) is shown. The curve indicates that new filament density decreases with actin concentration.

Figure 4

(a) Average local concentration [A] of monomeric G-actins available for polymerization near the membrane is shown as a function of G-actin concentration in the rear of the reaction front (i.e., bulk G-actin concentration). Local actins are these actins within the particular compartment in which a polymerization event occurs. (b) The average load 〈w〉 experienced by polymerizing filaments as a function of rear G-actin concentration. The load w diminishes the polymerization rate through the term $e^{-w/K_{\text{B}}T}$.

Figure 5

(a) Arp2/3 concentration dependence of the protrusion speed at different actin concentrations is shown. There exists an optimal Arp2/3 concentration at which the protrusion speed is maximal. (b) The nucleation rate grows with Arp2/3 concentration.

Figure 6

Capping proteins promote actin-based motility. There exists an optimal capping protein concentration at which the protrusion speed is maximal. The rate of nucleation grows with increasing capping protein concentration, being as it is correlated with the increase in protrusion speed. The concentrations of actin and Arp2/3 were kept at 5 μM and 100 nM, respectively.

Figure 7

Average local concentration [A] of monomeric G-actins available for polymerization and average load on filaments along the leading edge is shown.

Figure 8

Density of filaments along the leading edge, some of which are uncapped, is shown. Both densities decrease with increasing capping protein concentration. The fraction of uncapped filaments also decreases with capping protein concentration (data not shown).