The prerequisite of any form of directed force transmission is an initial symmetry breaking step, which determines the future front and rear end of the cell (Lauffenburger and Horwitz, 1996). Symmetry breaking is fueled by various internal and external signaling cues (Drubin and Nelson, 1996). One of the main sensors for polarized chemotactic signaling cues are G protein-coupled receptors (Rodríguez-Frade et al., 1999). At the molecular level, receptor activation converges into the polarization of commonly used secondary messengers. For instance, the LE displays increased phosphotyrosine kinase activity and elevated levels of PI (3,4,5) P₃ and DAG, while cytosolic Ca²⁺ levels are lowered (Tsai et al., 2014). This polarized distribution of secondary messengers is associated with a non-isotropic distribution of small Rho GTPase activity that either promotes actin polymerization (e.g., Rac, Cdc42) or actomyosin contractility (e.g., RhoA). Importantly, as small GTPases transition between an active and inactive state, such a polarized activity does not necessarily rely on a redistribution of the GTPase itself, but may also be coordinated through relocation of actuators (i.e., GTPase exchange factors, GEFs) and inhibitors (i.e., Guanine nucleotide exchange factors, GEFs) of the respective Rho GTPase. Analysis of Rho GTPase activation presents an intriguing spatio-temporal pattern, with high levels of GTP-Rac and GTP-Cdc42 at protruding sites, while contractile regions show increased GTP-RhoA levels (Kraynov et al., 2000; Nalbant et al., 2004; Pertz et al., 2006; Machacek et al., 2009). Strikingly, as many receptor-based systems rely on secondary messengers that are mutually exclusive, initial symmetry breaking can also occur in the absence of external signaling inputs (Kirschner et al., 2000). One example, how this may be achieved, is the so-called local excitation global inhibition (LEGI) model (Xiong et al., 2010), an extension of the classical reaction-diffusion systems initially described by Alan Turing (Turing, 1952) and later by Meinhardt and Gierer (Gierer and Meinhardt, 1972), where two mutually exclusive states take advantage of minor fluctuations to stochastically induce stable polarized structures.

Cell polarization translates into directed cell motion. A result of polarized GTPase activity is a non-isotropic change in actin polymerization dynamics (Peskin et al., 1993) and actin branching (Small et al., 1995), causing cell-wide rearrangements of the cytoskeleton (Figure 1A). Of particular importance for cell motion are changes in actin dynamics at the LE. Considering that the LE has over the last decades been the subject of extensive research, we refer readers interested in this topic to reviews written elsewhere (Pollard and Borisy, 2003; Krause and Gautreau, 2014). Here, we only note that the polymerization rates of individual actin filaments at the LE can reach rates of up to 7 μm/min (Kiuchi et al., 2011), while the LE extends at a rate of only 1–2 μm/min (Begemann et al., 2019). The difference between the polymerization rate of actin and the net forward motion of the LE results in a retrograde actin flow (Lin et al., 1997). This continuous actin treadmilling, further augmented by inward directed actomyosin pulling (Gardel et al., 2008), provides the basic force used for cell propulsion.

Transfer of tractile forces from the cell to the substrate is accomplished by Integrin molecules (Izzard and Lochner, 1976). Integrins are transmembrane receptors, consisting of non-covalently interacting α and ß subunits. To date, over 20 unique combinations of α (18 types) and ß (8 types) subunits have been described that differ in selectivity to extracellular matrix (ECM) components (Humphries et al., 2006). Common to all Integrins is the ability of participating in bidirectional signaling. Inside-out signaling describes the conformational change in the extracellular domain (i.e., activation) upon binding of Talin to the cytoplasmatic tail of Integrin (Tadokoro et al., 2003). In addition, Integrins also engage in outside-in signaling. Here, Integrins become activated upon force application from outside, which induces conformational changes in Integrin and increased ligand binding affinity (Friedland et al., 2009). In response to this external stimulation, Integrins trigger activation of FAK and other signaling pathways on its cytosolic site (reviewed in Hamidi and Ivaska, 2018). The two central elements for successful force-transduction through Integrins are on the extracellular site the binding of the heterodimer head to the ligand, and on the cytosolic site the unfolding of Talin (del Rio et al., 2009). As individual Integrins display ligand selectivity [e.g., αMβ2 binds ICAM1 (Rosetti et al., 2015); α3β1 binds VCAM1 (Chen et al., 2010)], the former element may give rise to selective cell-ECM interactions. The latter element refers to the fact that Talin only unfolds and binds to Vinculin and to actin in the presence of tensile forces. Hence, only under strain are mechanical forces transmitted from the cytoskeleton to the substrate, a mechanism called the ‘molecular clutch’ (Mitchison and Kirschner, 1988) (Figure 1B). Ultimately, the resulting force asymmetry along the planar cell axis yields forward propulsion, which is further augmented by de-adhesion of focal adhesions (FAs) and retraction at the rear of the cell (Abercrombie, 1980).

Importantly, the LE in most cells is not a stable structure but repeatedly transitions through cycles consisting of extension, adhesion and contraction (Lauffenburger and Horwitz, 1996; Ridley et al., 2003; Stock and Pauli, 2021). With each cycle, the cells crawl only a few micrometers forward. Hence, to efficiently migrate over a long distance in a persistent manner, the LE needs to be continuously reinitiated in the same direction. The need to repeatedly reinitiate the LE is not a design flaw, but a beneficial feature, as periodic extinguishing of activity permits a system to adapt more readily to changing external directional stimuli (Meinhardt and Gierer, 1974; Jilkine and Edelstein-Keshet, 2011). As will be discussed in more detail later, pairing these extension-retraction cycles with differential Integrin activation, caused by environmental factors, can gives rise to distinct changes in LE dynamics.

The literature presented to this point establishes a mechanism that allows cells to spontaneously polarize and migrate in an arbitrary direction, even in the absence of polarized signaling cues. To properly discuss the relevance of such cell motion, we first need to introduce the concept of self-organization. Following the physico-chemical definition, according to Ilya Prigogine (Nicolis and Prigogine, 1977), self-organization describes the ability of a system to create a spatial or temporal pattern at the macro-scale upon interactions of its components at the micro-scale. Importantly, to qualify for this definition, the emerging properties at the macro-scale need to be fundamentally different than the interactions that drive the pattern formation at the micro-scale, and the system needs to operate far off the thermodynamic equilibrium. Examples that meet these requirements are the animal swarm dynamics (Tunstrøm et al., 2013), and certain patterns arising from reaction-diffusion systems (Turing, 1952). Self-assembling structures, such as crystals, lipid bilayers or polypeptides, which operate near or at the thermodynamic equilibrium, however, do not qualify. Readers interested in learning more about the concept of self-organization, we refer to reviews written elsewhere (Kondo and Miura, 2010; Saha and Galic, 2018; Mancinelli and Galic, 2020).

As summarized above, cells initiate symmetry breaking spontaneously or in response to a polarized input. In the terminology of self-organization, cells employ at the micro-scale cytoskeletal forces at the LE to migrate for a certain amount of time in one direction. At the macro-scale, this causes cells to transition between phases of random and directed motion (Figure 1C). Strikingly, these emerging motion pattern strongly resembles the swimming pattern of E. coli, which also transitions stochastically between phases of random and ballistic propulsion (Berg, 1975). As proposed half a century ago, and revisited more recently theoretically, random transitions between phases of persistent and random motion present a search strategy to find sparsely distributed objects in a planar system (Bénichou et al., 2006; Harris et al., 2012). Notably, such a search strategy can also be found in foraging animals (Viswanathan et al., 1996). Here, depending on the distance between individual targets and the detection sensitivity of the searching agent, the lifetime of the persistent phase is adjusted to maximize the search efficiency (Bénichou et al., 2006). Hence, motion patterns arising at the micro-scale from stochastically formed LE can be interpreted at the macro-scale as a search strategy used by cells in pursuit of polarized signaling cues. Importantly, once a chemotactic signal is detected, cellular motion pattern become biased towards the source but maintain a random element (Arrieumerlou and Meyer, 2005), suggesting that stochastic search pattern act as a basic element that is fine-tuned by polarized signaling inputs.

Cell migration in a planar system relies on mechanical forces exerted by the actomyosin network (Gardel et al., 2008). Within the LE, individual actin filaments are facing the cell periphery with their barbed ends (Urban et al., 2010), bringing this heavily regulated end of actin filaments in close proximity to the plasma membrane. This proximity to the site of action provides the system with an intriguing control unit. For one, it allows regulatory elements to be limited to the plasma membrane. More relevant for this review, however, it allows to couple actin dynamics directly to the shape of the membrane itself, thereby bypassing the need for receptor-based signaling cascades.

Cell migration is associated with outward (i.e., negative) and inward (i.e., positive) deformations of the plasma membrane. Such highly curved membrane sections per se are energetically not favorable and will rapidly return to their lowest energy state, unless additional circuits are in place to maintain these membrane deformations. Intriguingly, studies identified a protein family consisting of over 70 members that are capable of sensing inward (i.e., positive) and outward (i.e., negative) membrane curvature with the help of a BAR domain (Peter et al., 2004; Bhatia et al., 2009; Galic et al., 2012). Within this protein family, 17 members carry actin-regulatory domains, allowing changes in actin polymerization dynamics in a curvature-dependent manner. Examples regulating actin dynamics at positively curved membrane sites include Arhgap17 and Arhgap44 that accomplish this through its RhoGAP domains (Richnau and Aspenström, 2001; Galic et al., 2014). Complementing these proteins, several I-BAR domain proteins regulate actin polymerization at negatively curved membrane sections through binding of Rho GTPases to the CRIB domain (Zhang et al., 1997), or of actin monomers to the WH2 domain (Marchand et al., 2001). By coupling membrane curvature to actin polymerization dynamics, distinct emerging properties can be achieved. Prominent examples based on stochastic curvature-dependent feedback loops include the emergence of travelling waves (Wu et al., 2018), or the formation of exploratory filopodia in developing neurons (Mancinelli et al., 2021). Intriguingly, recent work established that actin polymerization may depend on the membrane geometry itself. From theoretical (Peskin et al., 1993) and experimental (Bieling et al., 2016) work, we know that individual actin filaments can exert a forced of up to 6 pN. Since forming a protrusion requires more force (Helfrich, 1973; Raucher and Sheetz, 1999), a single filament will only cause shallow membrane deformations. If, however, two (or more) such minor deformations occur in close proximity, membrane tension will cause bundling of individual actin filaments, which may cause the formation of protrusions with multiple actin filaments over time (Liu et al., 2008). In addition, experimental and numerical analysis showed that the shape of the plasma membrane changes the local polymerization rates of branched actin filaments, thus causing the outgrowth of finger-like protrusions (Simon et al., 2019). While limited in number, these experimental and theoretical considerations show the ability of membrane shape to influence actin dynamics and in consequence cell shape and function. Notably, similar self-organization circuits were also described for microtubules (Singh et al., 2018; Gavriljuk et al., 2021).

Keeping in mind the ability of subcellular systems to self-organize in a curvature-dependent manner, we now focus on the LE of migrating cells. Outgrowth of the LE yields outward (i.e., negative) plasma membrane deformations with a curvature of 200–300 nm along the Z-axis (Urban et al., 2010). This local negative curvature was reported to trigger assembly of a self-organizing circuit at the tip of the LE (Begemann et al., 2019), which leads to increased actin polymerization and therefore to LE extension (Figure 3A). At the molecular level, this is accomplished through the recruitment of the curvature-sensitive I-BAR domain protein Baiap2 to negative membrane deformation sites. Baiap2 interacts through its CRIB and WH2 domain with actuators of actin polymerization dynamics. Hence, Baiap2 recruitment locally increases actin polymerization dynamics, leading to outgrowth of the LE. While this presents a mechanism for LE extension, it does not explain how the cell terminates this process. One factor, which likely limits the positive feedback loop, is a local increase in membrane tension at the LE (Shi et al., 2018). Published work demonstrates that an increase in membrane tension reduces actin polymerization (Raucher and Sheetz, 2000; Tsujita et al., 2015; Diz-Muñoz et al., 2016). At the same time, increase in membrane tension may also induce mechanically activated ion channels (Coste et al., 2010) to mediate transition from extension to collapsing the LE. Strikingly, the collapse of a retracting LE will cause to the formation of a highly curved membrane site adjacent to adhesion complexes, triggering the enrichment of the signaling machinery and re-initiation of the next LE protrusion. With this mechanochemical feedback loop, the maintenance of the polarization is ensured and therefore the longevity of the LE increased.

This curvature-dependent feedback loop is likely to interface with other regulatory circuits present at the LE. For instance, recent work showed that the retrograde flow of actin filaments at the LE maintains cell polarity, whereby increased polymerization speed (e.g., at higher temperatures) yields faster and more persistent migration (Maiuri et al., 2015). As just mentioned, increased membrane curvature augments recruitment of I-BAR domain proteins, likely resulting in higher actin polymerization rates that will further increase membrane curvature. At the same time, elevated temperatures will reduce membrane rigidity (Lamparter and Galic, 2020), which will lead to an increase in membrane curvature in response to a constant force. It is thus plausible to envision that a curvature-dependent feedback loop may contribute to previously described correlation of actin dynamics and motion persistence of the cell. Yet, published work demonstrates that the retrograde flow does not decrease but increases when Integrin binding is abolished due to actin slippage (Renkawitz and Sixt, 2010), arguing for the presence of additional (compensatory) circuits that work in parallel with the curvature-dependent signaling circuit at the LE.

At the macro-scale, increasing the longevity of LE through repeated re-initiation and other parameters leads to augmented motion persistence (Figure 3B). Augmented persistence, as discussed above, yields increased search efficiency, as it reduces oversampling of the very same position (Begemann et al., 2019).

We next discuss how 3D material properties affect this particular self-organizing circuit at the micro- and macro-scale. The LE of mesenchymal cells in 3D resembles structurally the situation in 2D (Thievessen et al., 2015; Doyle et al., 2021). While it remains elusive whether contraction and coordination with subsequent LE extensions occurs in 3D, it is plausible to envision a similar mechanism (Figure 3C). Consistently, the LE of mesenchymal cells grown in a 3D system relies on extension-retraction cycles for forward movement (Doyle et al., 2021). However, LE outgrowth in 3D is not restricted to a plane, but stochastically distributed in all dimensions (Thievessen et al., 2015), thus allowing cells to sample its entire environment for optimal migration conditions (Doyle et al., 2021). Notably, contractile forces are independent of matrix properties (Feld et al., 2020), and single FAs were shown to act as rigidity sensors (Plotnikov et al., 2012). However, while the LE in 2D and 3D both grow out as planar sheets, reduced traction due to lower substrate stiffness is likely to delay and/or reduce membrane curvature at the tip of the LE. Changes in membrane curvature, in turn, may alter protein and isoform composition at the LE. Considering that individual curvature-sensitive proteins bind to distinct target proteins (Safari and Suetsugu, 2012), shape-dependent changes in protein stoichiometry may arise at the LE. Noteworthy, altered protrusion dynamics can be observed in some cell types when transitioning from a stiff 2D to a soft 3D environment (Santos et al., 2020). In the absence of mature FAs, for instance at sites where the ECM surrounding the cell is not suitable to build up sufficient tension, no mesenchymal migration is possible (Thievessen et al., 2015; Doyle et al., 2021). Here, Integrin-independent mechanisms, as shown for a number of cell types (Paluch et al., 2006; Lämmermann et al., 2008), promote cell locomotion. Strikingly, recent work showed that force-induced membrane deformations can lead to Talin-independent activation of integrins (Kim et al., 2020), raising the possibility that Integrins activate upon LE outgrowth to test the strength of the bond by actomyosin contractions. If true, this would leave only the connections that have the optimal conditions for further migration in this direction. For a full understanding of this process, the activation status of Integrins could be imaged during 3D cell migration with focus on the protrusion-adhesion-contraction cycle at the LE.

At the macro-scale, the self-organizing circuit is likely to influence motion pattern as described for the planar system (Begemann et al., 2019). In support of such a notion, published work showed that 3D mesenchymal migration depends on the relative LE adhesiveness (Caballero et al., 2015), whereby FAs will dictate the direction (Lo Vecchio et al., 2020) and the speed (Kim and Wirtz, 2013) of motion. Consistently, ablating collagen fibers 20 µm in front of the LE, which precludes among others re-initiation of the self-organizing circuit, was shown to avoid further migration in this direction (Doyle et al., 2021). How exactly FAs (size, number, maturity, stability, and density) and ECM (composition, density, rigidity, orientation) properties alter LE dynamics and in consequence cell migration, remains elusive. As that the self-organizing circuit is well suited to detect gradients in adhesion strength (haptotaxis), ECM stiffness (durotaxis), and fiber orientation (ratchetaxis), it raises the possibility that it may not only contribute to persistent cell migration but also bias stochastic 3D motion pattern in a particular direction (Figure 3C).

Finally, changing mechanical properties of a 3D system may not only influence motion pattern, but could also yield additional emerging features of the self-organizing circuit. As mentioned above, a cell pulling on the substrate will deform the adjacent matrix (Doyle et al., 2021). For two neighboring cells that adhere to the same fiber, this means that one cell will sense the other cell tugging the fiber (Figure 3D). As pulling the fiber away from a cell will form an outward membrane deformation, this may trigger activation of the self-organizing circuit and LE extension in that direction. Hence, it is plausible to envision that pulling on the same fiber may yield self-organization of cells into equidistant cell aggregates, which has been observed in vitro (Trappmann et al., 2017) and in vivo (Biggs et al., 2018; Trela et al., 2021). To determine this putative emerging property, the activation status of Integrins in neighboring cells could be imaged, and corresponding motion pattern determined.