### abstract ###
Productive cell migration requires the spatiotemporal coordination of cell adhesion, membrane protrusion, and actomyosin-mediated contraction.
Integrins, engaged by the extracellular matrix, nucleate the formation of adhesive contacts at the cell's leading edge, and maturation of nascent adhesions to form stable focal adhesions constitutes a functional switch between protrusive and contractile activities.
To shed additional light on the coupling between integrin-mediated adhesion and membrane protrusion, we have formulated a quantitative model of leading edge dynamics combining mechanistic and phenomenological elements and studied its features through classical bifurcation analysis and stochastic simulation.
The model describes in mathematical terms the feedback loops driving, on the one hand, Rac-mediated membrane protrusion and rapid turnover of nascent adhesions, and on the other, myosin-dependent maturation of adhesions that inhibit protrusion at high ECM density.
Our results show that the qualitative behavior of the model is most sensitive to parameters characterizing the influence of stable adhesions and myosin.
The major predictions of the model, which we subsequently confirmed, are that persistent leading edge protrusion is optimal at an intermediate ECM density, whereas depletion of myosin IIA relieves the repression of protrusion at higher ECM density.
### introduction ###
In multicellular organisms, cell migration is of paramount importance for physiological processes such as tissue homeostasis and repair, immune surveillance and response, and developmental patterning.
In culture, the crawling of mammalian cells on a surface coated with extracellular matrix protein such as fibronectin is classically described as a cycle of distinct subprocesses: membrane protrusion and formation of new adhesive bonds with the underlying substratum at the cell's leading edge, followed by contraction of the cell body forwards, and finally detachment of adhesions at the cell's rear CITATION.
The primary molecular hubs for the integration of these subprocesses are integrins, adhesion receptors that recognize specific ECM proteins.
Upon ligation, integrins cluster to form adhesive contacts that orchestrate the activation of a host of signal transduction pathways and the anchorage of actin filaments inside the cell CITATION, CITATION.
Thus, they provide not only physical linkages between the ECM and actin cytoskeleton, through which myosin II motors generate contractile force, but also platforms for localizing biochemical signals that govern leading edge protrusion CITATION, CITATION.
Of particular importance in that regard is the integrin-mediated activation of Rac.
Its isoforms are small GTPases of the Rho family that, among other cellular functions, promote cell spreading and formation of broad, flat membrane structures called lamellipodia CITATION.
Despite these molecular insights, the bases for the dynamics of cell migration subprocesses, seemingly stochastic on the one hand, yet spatiotemporally coordinated on the other, are only beginning to be clarified CITATION .
One of the most mechanistically telling aspects of cell migration is its dependence on ECM density.
The general observation is that overall migration speed, determined from the movement of the cell centroid, is optimal at an intermediate ECM density CITATION, CITATION.
The physical interpretation of this finding was that the optimal ECM density corresponds to a density of integrin-ECM bonds that allows for both productive motility at the cell front and detachment of older adhesions at the rear of the cell, through myosin-dependent contractility.
More recently, this conceptual model has been refined based on detailed measurements of F-actin dynamics and myosin II recruitment in PtK 1 cells, revealing an optimal myosin II/F-actin density ratio at intermediate ECM density CITATION .
Further insight came through the implication that not all adhesions actively contribute to membrane protrusion signaling; apparently, only newer adhesions formed at the cell's leading edges do CITATION.
It seems that maturation of a nascent adhesion to form a stable, focal adhesion, marked by actomyosin-dependent growth of the complex perpendicular to the leading edge CITATION, is accompanied by loss of its ability to mediate protrusion signaling.
In Chinese hamster ovary .K1 cells expressing paxillin-enhanced green fluorescent protein, total internal reflection fluorescence microscopy has revealed that, during steady protrusion, the small nascent adhesions are rapidly formed and turned over CITATION, in proportion to the protrusion velocity CITATION.
This phenotype is mediated by signaling through Rac, which can be activated in a variety of ways, one of them involving the Rac effector, p21-activated kinase.
Among its various functions, active PAK phosphorylates the focal adhesion protein paxillin on Ser 273, providing a binding site for the recruitment of the scaffold protein GIT1; GIT1 binds both PIX, a guanine-nucleotide exchange factor that activates Rac, and PAK, which is activated in turn by Rac.
Thus, the pathway constitutes a positive feedback circuit.
Disrupting the circuit, for example through expression of paxillin with Ser 273 Ala mutation or kinase-dead PAK, abrogates protrusion and nascent adhesion formation, whereas expression of paxillin with phosphorylation-mimicked Ser 273 Asp mutation or constitutively active PAK enhances these responses CITATION.
Myosin II opposes the influence of Rac/PAK signaling in this context, promotes adhesion maturation, and strongly inhibits the protrusion phenotype CITATION, CITATION ; this effect is expected to be more prominent at higher ECM density CITATION .
Here, through computational modeling and stochastic simulations, we develop new ideas about mechanisms that might give rise to the dynamical interplay between cell protrusion and adhesion at the cell's leading edge CITATION CITATION.
Analysis of the model suggests that protrusion signaling mediated by nascent adhesions is inherently sensitive because of positive feedback but also susceptible to regulation by other feedback loops involving stable adhesions and myosin II.
These regulatory mechanisms shape the dependence of the protrusion/adhesion phenotypic balance on ECM density, which we compare to experimentally observed dynamics in CHO.K1 cells.
