The potential for filopodia to emerge from the lamellipodium near the plasma membrane ( Figure 2A) raised the question of how a structure made of parallel actin bundles can arise from a densely branched actin network. Two overlapping theoretical models have attempted to explain this transition: the convergent elongation model and the nucleation model ^{23, 48, 49} .

According to the convergent elongation model, filopodia are initiated by the reorganization of the branched actin network due to a fine-tuning of actin filament elongation at their growing ends ²⁵ . The branched actin filaments of the lamellipodium are short due to the regulation of their growth by capping proteins ^{50, 51} . An attractive hypothesis to explain the transition between short filaments in the lamellipodium and the longer filaments driving filopodium formation is that some of the barbed actin filament ends in the lamellipodium are protected from capping proteins by cellular elongation factors such as Ena/VASP proteins ^{52, 53} or formins ⁵⁴ and will therefore grow longer. In support of this hypothesis, Ena/VASP and formin proteins have been observed at filopodia tips ^{30, 55} and can induce filopodia formation ^{56, 57} .

Moreover, depletion of capping protein promotes filopodia formation at the expense of lamellipodium extension, and Ena/VASP proteins have been shown to play an important role in filopodia formation ⁵⁸ . Indeed, Ena/VASP proteins promote the convergence of filament barbed ends and have an enhanced activity when bound to trailing barbed ends in a fascin bundle, thus allowing the trailing ends to catch up with the leading barbed ends ⁵⁹ . Longer actin filaments can, after positional fluctuations and bending, be captured and aligned into bundles by fascin ( Figure 2), depending on the angle of their association ^{60, 61} . These initial thin bundles can be further reinforced by other actin filaments to form a rigid body that is necessary for filopodium growth ²⁹ . Convergence of actin network filaments into filopodia-like bundles can be recapitulated by both in vitro reconstitution ^{23, 62} and Monte Carlo simulation ⁶³ .

The nucleation model is supported by the observation that filopodia can form even when the lamellipodium is absent as a consequence of lack of the Arp2/3 complex or its activation ^{64– 67} . In this model, formin and/or Ena/VASP promoting de novo tip nucleation form actin filaments in filopodium. Further support for this model comes from the recent observation that fibroblasts lacking Arp2/3 complex produce more prominent filopodia than wild-type cells ⁶⁸ . However, it is not yet clear how precisely filaments are initiated in the absence of the Arp2/3 complex. In a very elegant study using fission yeast, inhibition of the Arp2/3 complex disturbed the balance of different actin structures that were, in effect, competing for actin monomers from the same reservoir and resulted in the enhanced formation of formin-dependent structures ⁶⁹ . The abundance of filopodia when the Arp2/3 complex is knocked down might also be explained by the disruption of actin homeostasis causing an increased incidence of spontaneous assembly of actin filaments in the cytoplasm ⁶⁸ . A proportion of these spontaneously formed actin filaments may be capped by Ena/VASP and/or formins, whose activities are enhanced by the absence of the Arp2/3 complex, to promote filopodia formation ⁴⁹ . Together, the two models are not necessarily mutually exclusive and might be reconciled by a capture elongation model mediated by Ena/VASP or formins.

To interrogate and illustrate the dynamic transition from lamellipodium to filopodia, we performed mathematical simulations using the cytoskeleton simulation software Cytosim ⁷⁰ . In the simulation, a lamellipodium-like branched network was grown by distributing the Arp2/3 complex-like nucleators within a broad, two-dimensional area ( Figure 3A, top and 61). To create the variation of lengths among those actin filaments, formin-like (could also be Ena/VASP-like) entities were added to capture the barbed ends of growing actin filaments and accelerate filament elongation. The growing actin filaments then extended out of the lamellipodium network and merged into bundled filaments by fascin-like crosslinkers. In the simulation, a synergy between the modulation of actin filament elongation at growing barbed ends by Ena/VASP and/or formin and actin filament crosslinking into tight bundles is sufficient ( Figure 3A, top) and necessary to induce filopodium formation ( Figure 3A, bottom panel).

Although the principle of the transition from lamellipodium to filopodia may be simple, it is quite difficult to identify exactly which proteins or pathways are involved in the formation of a filopodium. There exists potential competition or redundancy between different cellular actors, illustrated by formins that constitute a large family of different isoforms ⁷¹ . Moreover, the interactions between filaments and the membrane could also regulate this transition. The tension produced by the membrane can determine filopodia dimensions ²⁹ and can induce filament alignment in protrusions, even in the absence of crosslinkers ⁷² .

A considerable amount of information about the assembly mechanisms of contractile structures has been obtained from numerous studies using live cell imaging ^{36, 38, 46, 73, 74} . The current model for the assembly of radial fibers is based on a simple mechanism of initiation, whereby the fibers are generated by formin-mediated nucleation at focal adhesions ⁷⁵ . Following this initiation step, the growing actin filaments are brushed into parallel bundles by the retrograde flow toward the cell center ³⁸ . Radial fibers further recruit crosslinked filaments from the lamella, giving rise to an organization of filaments with graded polarity ³⁶ .

The model for the formation of transverse arcs is clearly different to that of radial fibers ³⁸ . Transverse arcs are assembled by the end-to-end annealing of myosin filaments and actin bundles that have come from the reorganization of the Arp2/3 complex branched network at the back of the lamellipodium ( Figure 2 and 46). The reorganization of a branched network into actin bundles of mixed polarity includes several steps. First, disassembly factors such as ADF/cofilin and glia maturation factor (GMF) disconnect the network by debranching the Arp2/3 complex links ^{76– 78} . Second, the released short filaments are captured by myosin and actin filament crosslinkers such as α-actinin, which are present in the lamella to trigger the formation of small bundles ( Figure 2B). Third, the alignment of the filaments is enforced by the high mechanical stress produced by the interaction between focal adhesions and the ECM, and by centripetal flow at the lamellipodium/lamella interface ⁷⁹ . Fourth, the nascent bundles are pushed away from the cell edge by the actin centripetal flow ⁷⁴ , while condensing and forming transverse arcs, until they encounter focal adhesions and pre-formed radial fibers ^{38, 80} . The radial fibers and transverse arcs will then associate with crosslinked actin bundles incorporating into the ends of radial fibers through the activity of myosin filaments.

We have also performed simulations of the transition from a branched actin network to a contractile fiber using Cytosim and the same simulation starting point using Arp2/3 complex-like nucleators as described above ( Figure 3A). To mimic focal adhesions nucleating the radial fibers, two small zones of adherence (friction points) with a few parallel filaments growing toward the cell center were placed at the bottom of a growing branched network. Arp2/3 complex connections were removed to simulate the lamellipodium debranching effect mediated by ADF/cofilin or GMF, and then motors (to simulate myosins) and crosslinkers (to simulate α-actinin) were added. A slow, directed flow was added to simulate the effect of centripetal actin flow. With only these few ingredients, the transition from a branched, non-contractile network to a mixed polarity, contractile fiber emerged from numerical simulations ( Figure 3B, top panel). These ingredients all seem essential, since removal of the motors, crosslinkers, or friction points all prevented the efficient formation of the contractile cable ( Figure 3B, bottom panel).

Radial fibers can associate with transverse arcs by the incorporation of myosin II filaments and subsequently develop into ventral fibers ^{37, 38} . During this process, first, two independent radial fibers connect with a pre-existing transverse arc that is pushed to the trailing edge of the motile cell by the flow. As a consequence, arc contractile forces get transmitted to radial fibers. Second, the distal parts of the transverse arc dissociate because of local stress relaxation ( Figure 2C). Finally, the radial fibers fuse with what remains of the contracting transverse arc to form a ventral stress fiber that is attached to focal adhesions at both ends ³⁸ .

In addition, a ventral stress fiber could be formed by the fusion of two dorsal stress fibers, without transverse arc incorporation ⁸⁰ . This latter case has been observed in Arp2/3 complex knockdown cells ³⁸ .

The mechanisms by which filopodia disassemble remain to be determined. However, stationary filopodia can be disassembled into small bundles by ADF/cofilin ⁸¹ . Filopodia may also develop kinks after a decrease and/or change of direction of the actin flow between the lamellipodium and lamella leading to their integration into the lamella ^{73, 74, 82} . In both scenarios, short actin bundles generated by filopodia disassembly would then participate in the formation of contractile structures, by feeding pre-existing contractile fibers with actin filaments.