A continuum model of actin waves in Dictyostelium discoideum

Abstract

Actin waves are complex dynamical patterns of the dendritic network of filamentous actin in eukaryotes. We developed a model of actin waves in PTEN-deficient Dictyostelium discoideum by deriving an approximation of the dynamics of discrete actin filaments and combining it with a signaling pathway that controls filament branching. This signaling pathway, together with the actin network, contains a positive feedback loop that drives the actin waves. Our model predicts the structure, composition, and dynamics of waves that are consistent with existing experimental evidence, as well as the biochemical dependence on various protein partners. Simulation suggests that actin waves are initiated when local actin network activity, caused by an independent process, exceeds a certain threshold. Moreover, diffusion of proteins that form a positive feedback loop with the actin network alone is sufficient for propagation of actin waves at the observed speed of * 6 mm/min. Decay of the wave back can be caused by scarcity of network components, and the shape of actin waves is highly dependent on the filament disassembly rate. The model allows retraction of actin waves and captures formation of new wave fronts in broken waves. Our results demonstrate that a delicate balance between a positive feedback, filament disassembly, and local availability of network components is essential for the complex dynamics of actin waves.

Figure 1. Actin waves in normal and LatA-treated cells.

Evolution of actin waves in a LatA-treated cell imaged by TIRF displays expansion, retraction, separation, and collapse of the waves. The cell comes in contact with another cell between and .

Figure 2. The spatial localization of components in an actin wave network, modified from .

The diagram represents F-actin and densities along a TIRF line scan through a closed actin wave in a cell attached on a glass surface. The wave fronts are propagating outwards while localization coincides with the dendritic network comprising the actin wave.

Figure 3. A simplified diagram for the feedback between F-actin and PI3K.

This diagram shows regulation of molecular activity related to branching of actin filaments. Arrows represent activation, except for the conversion between and . The actin wave model developed herein describes the dynamics of boxed components, and the condensed network captures the essential features of wave propagation.

Figure 4. A schematic of the network structure and molecular interactions in the model.

Figure 5. The development of actin waves from localized F-actin activity.

The time course of the F-actin concentration (in ) shows accumulation of F-actin at a spot, spot expansion, and separation of the wave fronts.

Figure 6. Shape of actin waves.

(Left) A z-scan of an actin wave from , showing F-actin (red) and coronin (green). The dashed grey line approximates the bottom surface. Bars are . (Right) F-actin concentration within a simulated actin wave.

Figure 7. Localization of F-actin (red) and Arp2/3 (green) in actin waves.

TIRF intensity along a line scan shows the relative localization of F-actin and Arp2/3 near the contact surface. (Upper) Experimental observation from . (Lower) Simulation on a domain.

Figure 8. Dependence of actin-wave development on the precursor strength.

Time required for actin waves to develop and propagate away from the nucleation center is plotted as a function of precursor activity. is normalized around the value used in other simulations.

Figure 9. Scarcity of free Arp2/3 within actin waves.

The distributions of free Arp2/3 (bottom) and G-actin (middle) are depicted with the corresponding F-acin density (top). The Arp2/3 profile displays large spatial variation with low concentration near the contact region covered by the wave.

Figure 10. Actin waves at higher Arp2/3 concentration.

The distributions of free Arp2/3 (bottom) and G-actin (middle) from a simulation on a domain with initial Arp2/3 concentration are depicted with the corresponding F-actin density (top). Membrane diffusion of WASP and its complexes is incorporated in the simulation. , , , and .

Figure 11. Annihilation of actin waves.

Two wave fronts annihilate when they collide, combining the regions they enclose. The actin waves are initiated apart at and on a domain. The image sequence displays evolution of the pointed end density.

Figure 12. Relative coronin localization on the F-actin network in actin waves.

Concentration of F-actin (right bar) and coronin-bound pointed ends (left bar) is plotted together, showing relative localization on the actin waves. The height displays relative concentration levels.

Figure 13. F-actin structures without coronin activity.

Lower effective debranching rates caused by lack of coronin activity lead to altered actin structures. (Left) 3-fold reduction. (Right) 5-fold reduction.

Figure 14. Relative localization of activity.

TIRF images show localization of activity within the region enclosed by actin waves. (Left) Experimentally-observed TIRF image from . (Right) Simulated Rac concentration is used to represent activity.

Figure 15. Standing and retracting actin waves.

The surface density of pointed ends (in ) at a sequence of times. The actin waves stall between , upon reaching the boundary of the PTEN region . The PTEN region is stationary for and then translates to the right at a speed of , causing the wave to retract at the left and advance at the right.

Figure 16. Actin structure of retracting waves.

The actin density (upper) of the retracting actin waves at in Figure 15 corresponding to the total pointed-end density of the waves (lower).

Figure 17. PTEN ingression and separated enclosed areas.

(Upper left) PTEN ingression. PTEN (green) appears from the upper area of the cell-substrate contact, cutting through a portion of actin (red) wave front (adapted from [34]). (Upper right) Separated regions surrounded by actin waves. A TIRF image depicts F-actin (red) and Arp2/3 (green) density near the contact surface. A connected region is split into two regions after the wave front is broken at the bottom right of the cell (see [21]). New wave fronts are subsequently formed, connecting broken fronts with the existing wave front at the top left region and forming two separated regions. Dotted lines note the cell boundary. (Lower) A region enclosed by actin waves is divided and new wave fronts are formed by PTEN activity. New wave fronts are formed after introduction of PTEN.