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Orchestration of cell migration is essential for development, tissue regeneration, and the immune response. This dynamic process integrates adhesion, signaling, and cytoskeletal subprocesses across spatial and temporal scales. In mesenchymal cells, adhesion complexes bound to extracellular matrix mediate both biochemical signal transduction and physical interaction with the F-actin cytoskeleton. Here, we present a mathematical model that offers insight into both aspects, considering spatiotemporal dynamics of nascent adhesions, active signaling molecules, mechanical clutching, actin treadmilling, and nonmuscle myosin II contractility. At the core of the model is a positive feedback loop, whereby adhesion-based signaling promotes generation of barbed ends at, and protrusion of, the cell's leading edge, which in turn promotes formation and stabilization of nascent adhesions. The model predicts a switch-like transition and optimality of membrane protrusion, determined by the balance of actin polymerization and retrograde flow, with respect to extracellular matrix density. The model, together with new experimental measurements, explains how protrusion can be modulated by mechanical effects (nonmuscle myosin II contractility and adhesive bond stiffness) and F-actin turnover.

Microfluidics approaches have gained popularity in the field of directed cell migration, enabling control of the extracellular environment and integration with live-cell microscopy; however, technical hurdles remain. Among the challenges are the stability and predictability of the environment, which are especially critical for the observation of fibroblasts and other slow-moving cells. Such experiments require several hours and are typically plagued by the introduction of bubbles and other disturbances that naturally arise in standard microfluidics protocols. Here, we report on the development of a passive pumping strategy, driven by the high capillary pressure and evaporative capacity of paper, and its application to study fibroblast chemotaxis. The paper pumps—flowvers (flow + clover)—are inexpensive, compact, and scalable, and they allow nearly bubble-free operation, with a predictable volumetric flow rate on the order of μl/min, for several hours. To demonstrate the utility of this approach, we combined the flowver pumping strategy with a Y-junction microfluidic device to generate a chemoattractant gradient landscape that is both stable (6+ h) and predictable (by finite-element modeling calculations). Integrated with fluorescence microscopy, we were able to recapitulate previous, live-cell imaging studies of fibroblast chemotaxis to platelet derived growth factor (PDGF), with an order-of-magnitude gain in throughput. The increased throughput of single-cell analysis allowed us to more precisely define PDGF gradient conditions conducive for chemotaxis; we were also able to interpret how the orientation of signaling through the phosphoinositide 3-kinase pathway affects the cells’ sensing of and response to conducive gradients.

The primary activity of GMFβ in vivo is actin branch disassembly (and not inhibition of Arp2/3 activation), and this activity plays an important role in lamellipodial dynamics and directional migration toward ECM cues., The lamellipodium is an important structure for cell migration containing branched actin nucleated via the Arp2/3 complex. The formation of branched actin is relatively well studied, but less is known about its disassembly and how this influences migration. GMF is implicated in both Arp2/3 debranching and inhibition of Arp2/3 activation. Modulation of GMFβ, a ubiquitous GMF isoform, by depletion or overexpression resulted in changes in lamellipodial dynamics, branched actin content, and migration. Acute pharmacological inhibition of Arp2/3 by CK-666, coupled to quantitative live-cell imaging of the complex, showed that depletion of GMFβ decreased the rate of branched actin disassembly. These data, along with mutagenesis studies, suggest that debranching (not inhibition of Arp2/3 activation) is a primary activity of GMFβ in vivo. Furthermore, depletion or overexpression of GMFβ disrupted the ability of cells to directionally migrate to a gradient of fibronectin (haptotaxis). These data suggest that debranching by GMFβ plays an important role in branched actin regulation, lamellipodial dynamics, and directional migration.

During cell migration, F-actin bundles/filopodia serve as templates for formation and orientation of lamellipodia and prime their stabilization by adhesion-based PI3K signaling., Mesenchymal cells such as fibroblasts are weakly polarized and reorient directionality by a lamellipodial branching mechanism that is stabilized by phosphoinositide 3-kinase (PI3K) signaling. However, the mechanisms by which new lamellipodia are initiated and directed are unknown. Using total internal reflection fluorescence microscopy to monitor cytoskeletal and signaling dynamics in migrating cells, we show that peripheral F-actin bundles/filopodia containing fascin-1 serve as templates for formation and orientation of lamellipodia. Accordingly, modulation of fascin-1 expression tunes cell shape, quantified as the number of morphological extensions. Ratiometric imaging reveals that F-actin bundles/filopodia play both structural and signaling roles, as they prime the activation of PI3K signaling mediated by integrins and focal adhesion kinase. Depletion of fascin-1 ablated fibroblast haptotaxis on fibronectin but not platelet-derived growth factor chemotaxis. Based on these findings, we conceptualize haptotactic sensing as an exploration, with F-actin bundles directing and lamellipodia propagating the process and with signaling mediated by adhesions playing the role of integrator.

During the proliferative phase of cutaneous wound healing, dermal fibroblasts are recruited into the clotted wound by a concentration gradient of platelet-derived growth factor (PDGF), together with other spatial cues. Despite the importance of this chemotactic process, the mechanisms controlling the directed migration of slow-moving mesenchymal cells such as fibroblasts are not well understood. Here, we develop and analyze a reaction-diffusion model of phospholipase C/protein kinase C (PKC) signaling, which was recently identified as a requisite PDGF-gradient-sensing pathway, with the goal of identifying mechanisms that can amplify its sensitivity in the shallow external gradients typical of chemotaxis experiments. We show that phosphorylation of myristoylated alanine-rich C kinase substrate by membrane-localized PKC constitutes a positive feedback that is sufficient for local pathway amplification. The release of phosphorylated myristoylated alanine-rich C kinase substrate and its subsequent diffusion and dephosphorylation in the cytosol also serves to suppress the pathway in down-gradient regions of the cell. By itself, this mechanism only weakly amplifies signaling in a shallow PDGF gradient, but it synergizes with other feedback mechanisms to enhance amplification. This model offers a framework for a mechanistic understanding of phospholipase C/PKC signaling in chemotactic gradient sensing and can guide the design of experiments to assess the roles of putative feedback loops.

Haptotaxis is the process by which cells respond to gradients of substrate-bound cues, such as extracellular matrix proteins (ECM); however, the cellular mechanism of this response remains poorly understood and has mainly been studied by comparing cell behavior on uniform ECMs with different concentrations of components. To study haptotaxis in response to gradients, we utilized microfluidic chambers to generate gradients of the ECM protein fibronectin, and imaged the cell migration response. Lamellipodia are fan-shaped protrusions that are common in migrating cells. Here, we define a new function for lamellipodia and the cellular mechanism required for haptotaxis – differential actin and lamellipodial protrusion dynamics lead to biased cell migration. Modest differences in lamellipodial dynamics occurring over time periods of seconds to minutes are summed over hours to produce differential whole cell movement towards higher concentrations of fibronectin. We identify a specific subset of lamellipodia regulators as being crucial for haptotaxis. Numerous studies have linked components of this pathway to cancer metastasis and, consistent with this, we find that expression of the oncogenic Rac1 P29S mutation abrogates haptotaxis. Finally, we show that haptotaxis also operates through this pathway in 3D environments.

T cells play a central role in the adaptive immune response, and their directed migration is essential for homing to sites of antigen presentation. Like neutrophils, T lymphocytes are rapidly moving cells that exhibit amoeboid movement, characterized by a definitive polarity with F-actin concentrated at the front and myosin II elsewhere. In this study, we used total internal reflection fluorescence (TIRF) microscopy to monitor the cells' areas of contact with a surface presenting adhesive ICAM-1 and the chemokine, CXCL12/SDF-1. Our analysis reveals that T-cell migration and reorientation are achieved by bifurcation and lateral separation of protrusions along the leading membrane edge, followed by cessation of one of the protrusions, which acts as a pivot for cell turning. We show that the distribution of bifurcation frequencies exhibits characteristics of a random, spontaneous process; yet, the waiting time between bifurcation events depends on whether or not the pivot point remains on the same side of the migration axis. Our analysis further suggests that switching of the dominant protrusion between the two sides of the migration axis is associated with persistent migration, whereas the opposite is true of cell turning. To help explain the bifurcation phenomenon and how distinct migration behaviours might arise, a spatio-temporal, stochastic model describing F-actin dynamics is offered.

SummaryChemotaxis, migration toward soluble chemical cues, is critical for processes such as wound healing and immune surveillance and is exhibited by various cell types, from rapidly migrating leukocytes to slow-moving mesenchymal cells. To study mesenchymal chemotaxis, we observed cell migration in microfluidic chambers that generate stable gradients of platelet-derived growth factor (PDGF). Surprisingly, we found that pathways implicated in amoeboid chemotaxis, such as PI3K and mammalian target of rapamycin signaling, are dispensable for PDGF chemotaxis. Instead, we find that local inactivation of Myosin IIA, through a noncanonical Ser1/2 phosphorylation of the regulatory light chain, is essential. This site is phosphorylated by PKCα, which is activated by an intracellular gradient of diacylglycerol generated by PLCγ. Using a combination of live imaging and gradients of activators/inhibitors in the microfluidic chambers, we demonstrate that this signaling pathway and subsequent inhibition of Myosin II activity at the leading edge are required for mesenchymal chemotaxis.

Dissecting the intracellular signaling mechanisms that govern the movement of eukaryotic cells presents a major challenge, not only because of the large number of molecular players involved, but even more so because of the dynamic nature of their regulation by both biochemical and mechanical interactions. Computational modeling and analysis have emerged as useful tools for understanding how the physical properties of cells and their microenvironment are coupled with certain biochemical pathways to actuate and control cell motility. In this focused review, we highlight some of the more recent applications of quantitative modeling and analysis in the field of cell migration. Both in modeling and experiment, it has been prudent to follow a reductionist approach in order to characterize what are arguably the principal modules: spatial polarization of signaling pathways, regulation of the actin cytoskeleton, and dynamics of focal adhesions. While it is important that we “cut our teeth” on these subsystems, focusing on the details of certain aspects whilst ignoring or coarse-graining others, it is clear that the challenge ahead will be to characterize the couplings between them in an integrated framework.

Productive cell migration requires the spatiotemporal coordination of cell adhesion, membrane protrusion, and actomyosin-mediated contraction. Integrins, engaged by the extracellular matrix (ECM), nucleate the formation of adhesive contacts at the cell's leading edge(s), 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., Author Summary Cell migration is fundamental to human physiology and a phenomenon of long-standing interest in cell biology. It requires the concerted regulation of several dynamic processes that mediate physical anchorage of the cell and productive generation of protrusion and traction forces that propel the cell forward. In this work, we have developed a mathematical model that describes this interplay, cast at the level of biochemical signaling pathways activated at the front of a moving cell. Based on our analysis of the model and experimental confirmation of its basic predictions, we assert that coupled, counteracting feedback loops constitute a functional switch between maintenance and stalling of the cell protrusion speed. Our model successfully explains the dependence of this switch on the abundance of adhesive molecules in the cell's immediate surroundings and sheds light on how non-muscle myosin shapes that dependence.

Most cell surface receptors for growth factors and cytokines dimerize in order to mediate signal transduction. For many such receptors, the Janus kinase (Jak) family of non-receptor protein tyrosine kinases are recruited in pairs and juxtaposed by dimerized receptor complexes in order to activate one another by trans-phosphorylation. An alternative mechanism for Jak trans-phosphorylation has been proposed in which the phosphorylated kinase interacts with the Src homology 2 (SH2) domain of SH2-B, a unique adaptor protein with the capacity to homo-dimerize. Building on a rule-based kinetic modeling approach that considers the concerted nature and combinatorial complexity of modular protein domain interactions, we examine these mechanisms in detail, focusing on the growth hormone (GH) receptor/Jak2/SH2-Bβ system. The modeling results suggest that, whereas Jak2-(SH2-Bβ)2-Jak2 heterotetramers are scarcely expected to affect Jak2 phosphorylation, SH2-Bβ and dimerized receptors synergistically promote Jak2 trans-activation in the context of intracellular signaling. Analysis of the results revealed a unique mechanism whereby SH2-B and receptor dimers constitute a bipolar ‘clamp’ that stabilizes the active configuration of two Jak2 molecules in the same macro-complex., Author Summary Janus kinases (Jaks) interact with and activate receptors on the cell surface that mediate changes in gene expression. How these interactions are promoted and regulated is of central interest in fields such as cellular endocrinology and immunology. Here, detailed computational models of Jak activation are offered at the level of protein modification states and interaction domains, wherein the specification of only a handful of binding/reaction rules can produce networks comprised of thousands of differential equations. Specifically, we investigated the role of an adaptor protein, SH2-B, revealing a novel mechanism whereby it cooperates with receptors to form a stable complex that juxtaposes two Jak molecules for efficient activation. We refer to this mode of molecular assembly as the bipolar clamp mechanism.

The cytokines interleukin (IL)-2 and IL-4 are important regulators of the adaptive immune response, due in part to their effects on clonal expansion and differentiation of T cells. When IL-2 and IL-4 are administered together, both antagonistic and synergistic effects have been reported, but little is known in general concerning the mechanisms underlying such combinatorial effects. We found evidence for both effects in the proliferation responses of the IL-2 and IL-4 responsive T cell line, HT-2; IL-4 delays the onset of cell growth yet ultimately allows a higher cell density to be achieved in static culture. At the level of signal transduction pathways, we found that IL-4 partially inhibits IL-2 receptor-mediated pathways (PI3K/Akt, Ras/Erk, and STAT5a/b) and does not prolong their transient kinetics. This mode of antagonism, but not the effects on cell proliferation, is overcome at higher concentrations of IL-2 that are sufficient to saturate the signaling responses. By comparison, IL-4-stimulated activation of STAT6 is unaffected by IL-2 and shows sustained kinetics, and we speculate that this or another IL-4 receptor-specific pathway is responsible for the effects of IL-4 on IL-2-stimulated proliferation. A possibly related observation is that IL-4 induces a dramatic cell adhesion phenotype.

Fibroblast migration is directed by gradients of platelet-derived growth factor (PDGF) during wound healing. As in other chemotactic systems, it has been shown recently that localized stimulation of intracellular phosphoinositide (PI) 3-kinase activity and production of 3' PI lipids in the plasma membrane are important events in the signaling of spatially biased motility processes. In turn, 3' PI localization depends on the effective diffusion coefficient, D, and turnover rate constant, k, of these lipids. Here we present a systematic and direct comparison of mathematical model calculations and experimental measurements to estimate the values of the effective 3' PI diffusion coefficient, D, turnover rate constant, k, and other parameters in individual fibroblasts stimulated uniformly with PDGF. In the context of our uniform stimulation model, the values of D and k in each cell were typically estimated within 10-20% or less, and the mean values across all of the cells analyzed were D = 0.37 +/- 0.25 microm2/s and k = 1.18 +/- 0.54 min(-1). In addition, we report that 3' PI turnover is not affected by PDGF receptor signaling in our cells, allowing us to focus our attention on the regulation of 3' PI production as this system is studied further.

Cytokines can be engineered for greater potency in stimulating cellular functions. An obvious test criterion for an improved cytokine is receptor-binding affinity, but this does not always correlate with improved biological response. By combining protein-engineering techniques with studies of receptor trafficking and signaling, it might be possible to identify the ligand receptor-binding properties that should be sought.

Summary Cells contain multiple F-actin assembly pathways, including the Arp2/3 complex, formins, and Ena/VASP, which have largely been analyzed separately. They collectively generate the bulk of F-actin from a common pool of G-actin; however, the interplay and/or competition between these pathways remains poorly understood. Using fibroblast lines derived from an Arpc2 conditional knockout mouse, we established matched-pair cells with and without the Arp2/3 complex. Arpc2 −/− cells lack lamellipodia and migrate more slowly than WT cells but have F-actin levels indistinguishable from controls. Actin assembly in Arpc2 −/− cells was resistant to cytochalasin-D and was highly dependent on profilin-1 and Ena/VASP but not formins. Profilin-1 depletion in WT cells increased F-actin and Arp2/3 complex in lamellipodia. Conversely, addition of exogenous profilin-1 inhibited Arp2/3 complex actin nucleation in vitro and in vivo. Antagonism of the Arp2/3 complex by profilin-1 in cells appears to maintain actin homeostasis by balancing Arp2/3 complex-dependent and -independent actin assembly pathways.

Activation of phosphoinositide (PI) 3-kinase is a required signaling pathway in fibroblast migration directed by platelet-derived growth factor. The pattern of 3′ PI lipids in the plasma membrane, integrating local PI 3-kinase activity as well as 3′ PI diffusion and turnover, influences the spatiotemporal regulation of the cytoskeleton. In fibroblasts stimulated uniformly with platelet-derived growth factor, visualized using total internal reflection fluorescence microscopy, we consistently observed localized regions with significantly higher or lower 3′ PI levels than adjacent regions (hot and cold spots, respectively). A typical cell contained multiple hot spots, coinciding with apparent leading edge structures, and at most one cold spot at the rear. Using a framework for finite-element modeling with actual cell contact area geometries, we find that although the 3′ PI pattern is affected by irregular contact area shape, cell morphology alone cannot explain the presence of hot or cold spots. Our results and analysis instead suggest that these regions reflect different local 3′ PI dynamics, specifically through a combination of mechanisms: enhanced PI 3-kinase activity, reduced 3′ PI turnover, and possibly slow/constrained 3′ PI diffusion. The morphological polarity of the cell may thus bias 3′ PI signaling to promote persistent migration in fibroblasts.