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Live-cell microscopy is used to infer dynamics in single cells. Here, ERK signaling was monitored using four different biosensors in a common cell context. Each responds with unique kinetics, reflecting differences in ERK localization and activity. Mathematical modeling offers an interpretation of the data and may be used to guide biosensor design.

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.

We used particle-based computer simulations to study the emergent properties of the actomyosin cytoskeleton. Our model accounted for biophysical interactions between filamentous actin and non-muscle myosin II and was motivated by recent experiments demonstrating that spatial regulation of myosin activity is required for fibroblasts responding to spatial gradients of platelet derived growth factor (PDGF) to undergo chemotaxis. Our simulations revealed the spontaneous formation of actin asters, consistent with the punctate actin structures observed in chemotacting fibroblasts. We performed a systematic analysis of model parameters to identify biochemical steps in myosin activity that significantly affect aster formation and performed simulations in which model parameter values vary spatially to investigate how the model responds to chemical gradients. Interestingly, spatial variations in motor stiffness generated time-dependent behavior of the actomyosin network, in which actin asters continued to spontaneously form and dissociate in different regions of the gradient. Our results should serve as a guide for future experimental investigations.

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.

Phospholipase C-γ1 (PLC-γ1) is a receptor-proximal enzyme that promotes signal transduction through PKC in mammalian cells. Because of the complexity of PLC-γ1 regulation, a two-state (inactive/active) model does not account for the intricacy of activation and inactivation steps at the plasma membrane. Here, we introduce a structure-based kinetic model of PLC-γ1, considering interactions of its regulatory Src homology 2 (SH2) domains and perturbation of those dynamics upon phosphorylation of Tyr783, a hallmark of activation. For PLC-γ1 phosphorylation to dramatically enhance enzyme activation as observed, we found that high intramolecular affinity of the C-terminal SH2 (cSH2) domain-pTyr783 interaction is critical, but this affinity need not outcompete the autoinhibitory interaction of the cSH2 domain. Under conditions for which steady-state PLC-γ1 activity is sensitive to the rate of Tyr783 phosphorylation, maintenance of the active state is surprisingly insensitive to the phosphorylation rate, since pTyr783 is well protected by the cSH2 domain while the enzyme is active. In contrast, maintenance of enzyme activity is sensitive to the rate of PLC-γ1 membrane (re)binding. Accordingly, we found that hypothetical PLC-γ1 mutations that either weaken autoinhibition or strengthen membrane binding influence the activation kinetics differently, which could inform the characterization of oncogenic variants. Finally, we used this newly informed kinetic scheme to refine a spatial model of PLC/PKC polarization during chemotaxis. The refined model showed improved stability of the polarized pattern while corroborating previous qualitative predictions. As demonstrated here for PLC-γ1, this approach may be adapted to model the dynamics of other receptor- and membrane-proximal enzymes.

Chemotaxis of fibroblasts and other mesenchymal cells is critical for embryonic development and wound healing. Fibroblast chemotaxis directed by a gradient of platelet-derived growth factor (PDGF) requires signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway. Diacylglycerol (DAG), the lipid product of PLC that activates conventional PKCs, is focally enriched at the up-gradient leading edge of fibroblasts responding to a shallow gradient of PDGF, signifying polarization. To explain the underlying mechanisms, we formulated reaction-diffusion models including as many as three putative feedback loops based on known biochemistry. These include the previously analyzed mechanism of substrate-buffering by myristoylated alanine-rich C kinase substrate (MARCKS) and two newly considered feedback loops involving the lipid, phosphatidic acid (PA). DAG kinases and phospholipase D, the enzymes that produce PA, are identified as key regulators in the models. Paradoxically, increasing DAG kinase activity can enhance the robustness of DAG/active PKC polarization with respect to chemoattractant concentration while decreasing their whole-cell levels. Finally, in simulations of wound invasion, efficient collective migration is achieved with thresholds for chemotaxis matching those of polarization in the reaction-diffusion models. This multi-scale modeling framework offers testable predictions to guide further study of signal transduction and cell behavior that affect mesenchymal chemotaxis., Author summary Cell movement directed by external gradients of chemical composition is critical for immune responses, wound healing, and development. Although theoretical concepts explaining how shallow external gradients might definitively polarize a cell’s motility have been offered over the past two decades, mathematical models cast in terms of defined molecules and mechanisms are uncommon in this context. Based on both recent and older insights from the literature, we offer mechanistic models that are able to explain experimentally observed polarization of signal transduction elicited by shallow attractant gradients. A novel insight of our models is the implicated role of phosphatidic acid, a membrane lipid produced by at least two enzymatic pathways, in two positive feedback loops that amplify signal transduction locally. In separate simulations, we explored the implications of polarization for efficient cell invasion during wound healing. We expected that the ability to polarize in response to shallow gradients would enhance the speed of wound invasion, but an unexpected finding is that this property can promote intermittent polarization throughout the wound.

Live-cell fluorescence microscopy is broadly applied to study the dynamics of receptor-mediated cell signaling, but the availability of intracellular biosensors is limited. A biosensor based on the tandem SH2 domains from phospholipase C γ1 (PLCγ1), tSH2-WT, has been used to measure phosphorylation of the epidermal growth factor receptor (EGFR). Here, we found that tSH2-WT lacked specificity for phosphorylated EGFR, consistent with the known promiscuity of SH2 domains. Further, EGF-stimulated membrane recruitment of tSH2-WT differed qualitatively from the expected kinetics of EGFR phosphorylation. Analysis of a mathematical model suggested, and experiments confirmed, that the high avidity of tSH2-WT resulted in saturation of its target and interference with EGFR endocytosis. To overcome the apparent target specificity and saturation issues, we implemented two protein engineering strategies. In the first, we screened a combinatorial library generated by random mutagenesis of the C-terminal SH2 domain (cSH2) of PLCγ1 and isolated a mutant form (mSH2) with enhanced specificity for phosphorylated Tyr(992) (pTyr(992)) of EGFR. A biosensor based on mSH2 faithfully reported the kinetics of EGFR phosphorylation but retained cross-reactivity similar to tSH2-WT. In the second approach, we isolated a pTyr(992)-binding protein (SPY992) from a combinatorial library generated by mutagenesis of the Sso7d protein scaffold. Compared to tSH2-WT and mSH2, SPY992 exhibited superior performance as a specific, moderate-affinity biosensor. We extended this approach to isolate a biosensor for EGFR pTyr(1148) (SPY1148). This approach of integrating theoretical considerations with protein engineering strategies can be generalized to design and evaluate suitable biosensors for various phospho-specific targets.

Filopodia are thin, fingerlike structures that contain bundled actin filaments and project from the cell periphery. These structures are dogmatically endowed with the ability to sense cues in the microenvironment, implying that filopodia foster local signal transduction, yet their small diameter hampers the imaging of dynamic processes therein. To overcome this challenge, we analyzed total internal reflection fluorescence images of migrating fibroblasts coexpressing either a plasma membrane marker or tagged AktPH domain, a translocation biosensor for signaling through the phosphoinositide 3-kinase pathway, along with a cytosolic volume marker. We devised a scheme to estimate the radii of filopodia using either the membrane marker or volume marker data, and we used that information to account for geometry effects in the biosensor data. With conservative estimates of relative target molecule abundance, it is revealed that filopodia typically harbor higher densities of 3' phosphoinositides than adjacent regions at the cell periphery. In this context at least, the analysis supports the filopodial signaling hypothesis.

SUMMARYLysophophatidic acid (LPA), a biologically active phospholipid that is ubiquitously present in tissues and organs, provokes cellular responses such as proliferation, apoptosis, differentiation and migration via activation of G-protein coupled receptors. These receptors activate a broad range of intracellular signaling cascades to mediate these responses. Using microfluidic chambers that generate and maintain stable gradients, we observed that chemotaxis of fibroblasts to LPA has higher directional fidelity than chemotaxis provoked by the receptor tyrosine kinase (RTK) ligand platelet-derived growth factor (PDGF). Unlike fast moving amoeboid cells, mesenchymal cells such as fibroblasts do not require PI3K for chemotaxis to a GPCR ligand. In addition, the Arp2/3 complex is not required for fibroblast GPCR-based chemotaxis in either 2D or 3D environments. Our data indicate that combinatorial regulation of myosin II involving global activation by RhoA/ROCK and local inhibition of myosin II at the leading edge by PKC results in highly efficient chemotaxis of fibroblasts to LPA. Based on these observations, we develop a simple mathematical model to explain how dual regulation of myosin II is responsible for enhanced chemotaxis in LPA gradients relative to PDGF. Using pharmacological approaches, we test predictions of this model and modulate the fidelity of LPA and PDGF chemotaxis.

Phosphorylation is an important post-translational modification that is involved in regulating many signaling pathways. Of particular interest are the growth factor mediated Ras and phosphoinositide 3-kinase (PI3K) signaling pathways which, if misregulated, can contribute to the progression of cancer. Phosphoproteomic methods have been developed to study regulation of signaling pathways; however, due to the low stoichiometry of phosphorylation, understanding these pathways is still a challenge. In this study, we have developed a multi-dimensional method incorporating electrostatic repulsion-hydrophilic interaction chromatography (ERLIC) with tandem IMAC/TiO2 enrichment for subsequent phosphopeptide identification by LC/MS/MS. We applied this method to PDGF-stimulated NIH 3T3 cells to provide over 11,000 unique phosphopeptide identifications. Upon motif analysis, IMAC was found to enrich for basophilic kinase substrates while the subsequent TiO2 step enriched for acidophilic kinase substrates, suggesting that both enrichment methods are necessary to capture the full complement of kinase substrates. Biological functions that were over-represented at each PDGF stimulation time point, together with the phosphorylation dynamics of several phosphopeptides containing known kinase phosphorylation sites, illustrate the feasibility of this approach in quantitative phosphoproteomic studies.

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.

Kinase cascades, in which enzymes are sequentially activated by phosphorylation, are quintessential signaling pathways. Signal transduction is not always achieved by direct activation, however. Often, kinases activate pathways by deactivation of a negative regulator; this indirect mechanism, pervasive in Akt signaling, has yet to be systematically explored. Here, we show that the indirect mechanism has properties that are distinct from direct activation. With comparable parameters, the indirect mechanism yields a broader range of sensitivity to the input, beyond saturation of regulator phosphorylation, and kinetics that become progressively slower, not faster, with increasing input strength. These properties can be integrated in network motifs to produce desired responses, as in the case of feedforward loops.

A bioactive platform for the quantitative observation of cell migration is presented by (1) presenting migration factors in a well-defined manner on 2-D substrates, and (2) enabling continuous cell tracking. Well-defined substrate presentation is achieved by correctly orienting immobilized proteins (chemokines and cell adhesion molecules), such that the active site is accessible to cell surface receptors. A thiol-terminated self-assembled monolayer on a silica slide was used as a base substrate for subsequent chemistry. The thiol-terminated surface was converted to an immobilized metal ion surface using a maleimido-nitrilotriacetic acid (NTA) cross-linker that bound Histidine-tagged recombinant proteins on the surface with uniform distribution and specific orientation. This platform was used to study the influence of surface-immobilized chemokine SDF-1α and cell adhesion molecule ICAM-1 on murine splenic B lymphocyte migration. While soluble SDF-1α induced trans-migration in a Boyden Chamber type chemotaxis assay, immobilized SDF-1α alone did not elicit significant surface-migration on our test-platform surface. Surface-immobilized cell adhesion protein, ICAM-1, in conjunction with activation enabled migration of this cell type on our surface. Controlled exposure to UV light was used to produce stable linear gradients of His-tagged recombinant SDF-1α co-immobilized with ICAM-1 following our surface chemistry approach. XPS and antibody staining showed defined gradients of outwardly oriented SDF-1α active sites. This test platform can be especially valuable for investigators interested in studying the influence of surface-immobilized factors on cell behavior and may also be used as a cell migration enabling platform for testing the effects of various diffusible agents.

Cell migration directed by spatial cues, or taxis, is a primary mechanism for orchestrating concerted and collective cell movements during development, wound repair, and immune responses. Compared with the classic example of amoeboid chemotaxis, in which fast-moving cells such as neutrophils are directed by gradients of soluble factors, directed migration of slow-moving mesenchymal cells such as fibroblasts is poorly understood. Mesenchymal cells possess a distinctive organization of the actin cytoskeleton and associated adhesion complexes as its primary mechanical system, generating the asymmetric forces required for locomotion without strong polarization. The emerging hypothesis is that the molecular underpinnings of mesenchymal taxis involve distinct signaling pathways and diverse requirements for regulation.

A physicochemical model is used to describe the coupling of adhesion, cytoskeletal, and signaling dynamics during cell migration. Analysis of stochastic simulations predicts relationships between measurable quantities that reflect partitioning of stress between F-actin–bound adhesions, which act as a molecular clutch, and retrograde F-actin flow., Animal cell migration is a complex process characterized by the coupling of adhesion, cytoskeletal, and signaling dynamics. Here we model local protrusion of the cell edge as a function of the load-bearing properties of integrin-based adhesions, actin polymerization fostered by adhesion-mediated signaling, and mechanosensitive activation of RhoA that promotes myosin II–generated stress on the lamellipodial F-actin network. Analysis of stochastic model simulations illustrates how these pleiotropic functions of nascent adhesions may be integrated to govern temporal persistence and frequency of protrusions. The simulations give mechanistic insight into the documented effects of extracellular matrix density and myosin abundance, and they show characteristic, nonnormal distributions of protrusion duration times that are similar to those extracted from live-cell imaging experiments. Analysis of the model further predicts relationships between measurable quantities that reflect the partitioning of stress between tension on F-actin–bound adhesions, which act as a molecular clutch, and dissipation by retrograde F-actin flow.

B-lymphocyte migration, directed by chemokine gradients, is essential for homing to sites of antigen presentation. B cells move rapidly, exhibiting amoeboid morphology like other leukocytes, yet quantitative studies addressing B-cell migration are currently lacking relative to neutrophils, macrophages, and T cells. Here, we used total internal reflection fluorescence (TIRF) microscopy to characterize the changes in shape (morphodynamics) of primary, murine B cells as they migrated on surfaces with adsorbed chemokine, CXCL13, and the adhesive ligand, ICAM-1. B cells exhibited frequent, spontaneous dilation and shrinking events at the sides of the leading membrane edge, a phenomenon that was predictive of turning versus directional persistence. To characterize directed B-cell migration, a microfluidic device was implemented to generate gradients of adsorbed CXCL13 gradients. Haptotaxis assays revealed a modest yet consistently positive bias of the cell's persistent random walk behavior towards CXCL13 gradients. Quantification of tactic fidelity showed that bias is optimized by steeper gradients without excessive midpoint density of adsorbed chemokine. Under these conditions, B-cell migration is more persistent when the direction of migration is better aligned with the gradient.

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.

Migrating fibroblasts reorient directionality by PI3K-dependent branching and pivoting of protrusions, a mechanism that allows fibroblasts to align with an external chemotactic gradient., Mesenchymal cell migration as exhibited by fibroblasts is distinct from amoeboid cell migration and is characterized by dynamic competition among multiple protrusions, which determines directional persistence and responses to spatial cues. Localization of phosphoinositide 3-kinase (PI3K) signaling is thought to play a broadly important role in cell motility, yet the context-dependent functions of this pathway have not been adequately elucidated. By mapping the spatiotemporal dynamics of cell protrusion/retraction and PI3K signaling monitored by total internal reflection fluorescence microscopy, we show that randomly migrating fibroblasts reorient polarity through PI3K-dependent branching and pivoting of protrusions. PI3K inhibition did not affect the initiation of newly branched protrusions, nor did it prevent protrusion induced by photoactivation of Rac. Rather, PI3K signaling increased after, not before, the onset of local protrusion and was required for the lateral spreading and stabilization of nascent branches. During chemotaxis, the branch experiencing the higher chemoattractant concentration was favored, and, thus, the cell reoriented so as to align with the external gradient.

Signal transduction networks in mammalian cells, comprising a limited set of interacting biochemical pathways, are accessed by various growth factor and cytokine receptors to elicit distinct cell responses. This raises the question as to how specificity of the stimulus–response relationship is encoded at the molecular level. It has been proposed that specificity arises not only from the activation of unique signalling pathways, but also from quantitative differences in the activation and regulation of shared receptor-proximal signalling proteins. To address such hypotheses, data sets with greater precision and coverage of experimental conditions will need to be acquired, and rigorous frameworks that codify and parameterize the inherently non-linear relationships among signalling activities will need to be developed. In the present study we apply a systematic approach combining quantitative measurements and mathematical modelling to compare the signalling networks accessed by FGF (fibroblast growth factor) and PDGF (platelet-derived growth factor) receptors in mouse fibroblasts, in which the ERK (extracellular-signal-regulated kinase) cascade is activated by Ras- and PI3K (phosphoinositide 3-kinase)-dependent pathways. We show that, whereas the FGF stimulation of PI3K signalling is relatively weak, this deficiency is compensated for by a more potent Ras-dependent activation of ERK. Thus, as the modelling would predict, the ERK pathway is activated to a greater extent in cells co-stimulated with FGF and PDGF, relative to the saturated levels achieved with either ligand alone. It is envisaged that similar approaches will prove valuable in the elucidation of quantitative differences among other closely related receptor signalling networks.

Cell migration is central to physiological responses to injury and infection and in the design of biomaterial implants. The ability to tune the properties of adhesive materials and relate those properties in a quantitative way to the dynamics of intracellular processes remains a definite challenge in the manipulation of cell migration. Here, we propose the use of poly(vinylmethylsiloxane) (PVMS) networks as novel substrata for cell adhesion and migration. These materials offer the ability to tune independently chemical functionality and elastic modulus. Importantly, PVMS networks are compatible with total internal reflection fluorescence (TIRF) microscopy, which is ideal for interrogating the cell-substratum interface; this latter characteristic presents a distinct advantage over polyacrylamide gels and other materials that swell with water. To demonstrate these capabilities, adhesive peptides containing the arginyl-glycyl-aspartic acid (RGD) tripeptide motif were successfully grafted to the surface of PVMS network using a carboxyl-terminated thiol as a linker. Peptide-specific adhesion, spreading, and random migration of NIH 3T3 mouse fibroblasts were characterized. These experiments show that a peptide containing the synergy sequence of fibronectin (PHSRN) in addition to RGD promotes more productive cell migration without markedly enhancing cell adhesion strength. Using TIRF microscopy, the dynamics of signal transduction through the phosphoinositide 3-kinase pathway were monitored in cells as they migrated on peptide-grafted PVMS surfaces. This approach offers a promising avenue for studies of directed migration and mechanotransduction at the level of intracellular processes.

Cell migration is regulated by processes that control adhesion to extracellular matrix (ECM) and force generation. While our fundamental understanding of how these control mechanisms are actuated at the molecular level (signal transduction) has been refined over many years, appreciation of their dynamics has grown more recently. Here, we formulate and analyze by stochastic simulation a quantitative model of signaling mediated by the integrin family of adhesion receptors. Nascent adhesions foster the activation of the small GTPase Rac by at least two distinct signaling pathways, one of which involves tyrosine phosphorylation of the scaffold protein paxillin and formation of multiprotein complexes containing the guanine nucleotide exchange factor DOCK180. Active Rac promotes protrusion of the cell’s leading edge, which in turn enhances the rate of nascent adhesion nucleation; we call this feedback mechanism the core protrusion cycle. Protrusion is antagonized by stable adhesions, which form by myosin-dependent maturation of nascent adhesions, and we propose here a feedforward mechanism mediated by the tyrosine kinase c-Src by which this antagonism is regulated so as to allow transient protrusion at higher densities of ECM. We show that this “buffering of inhibition” mechanism, coupled with the core protrusion cycle, is capable of tuning the frequencies of protrusion and adhesion maturation events.

It has long been appreciated that spatiotemporal dynamics of cell migration are under the control of intracellular signaling pathways, which are mediated by adhesion receptors and other transducers of extracellular cues. Further, there is ample evidence that aspects of cell migration are stochastic: how else could it exhibit directional persistence over timescales much longer than typical signal transduction processes, punctuated by abrupt changes in direction? Yet the mechanisms by which signaling processes affect those behaviors remain unclear. We have developed analytical methods for relating parallel live-cell microscopy measurements of cell migration dynamics to the intracellular signaling processes that govern them. In this analysis of phosphoinositide 3-kinase signaling in randomly migrating fibroblasts, we observe that hot spots of intense signaling coincide with localized cell protrusion and endure with characteristic lifetimes that correspond to those of cell migration persistence. We further show that distant hot spots are dynamically and stochastically coupled. These results are indicative of a mechanism by which changes in a cell's direction of migration are determined by a fragile balance of relatively rapid intracellular signaling processes.

During directed cell migration (chemotaxis), cytoskeletal dynamics are stimulated and spatially biased by phosphoinositide 3-kinase (PI3K) and other signal transduction pathways. Live-cell imaging using total internal reflection fluorescence (TIRF) microscopy revealed that, in the absence of soluble cues, 3′-phosphoinositides are enriched in a localized and dynamic fashion during active spreading and random migration of mouse fibroblasts on adhesive surfaces. Surprisingly, we found that PI3K activation is uncoupled from classical integrin-mediated pathways and feedback from the actin cytoskeleton. Inhibiting PI3K significantly impairs cell motility, both in the context of normal spreading and when microtubules are dissociated, which induces a dynamic protrusion phenotype as seen by TIRF in our cells. Accordingly, during random migration, 3′-phosphoinositides are frequently localized to regions of membrane protrusion and correlate quantitatively with the direction and persistence of cell movement. These results underscore the importance of localized PI3K signaling not only in chemotaxis but also in basal motility/migration of fibroblasts.

The plasma membrane provides a physical platform for the orchestration of molecular interactions and biochemical conversions involved in the early stages of receptor-mediated signal transduction in living cells. In that context, we introduce here the concept of spatial coupling, wherein simultaneous recruitment of different enzymes to the same receptor scaffold facilitates crosstalk between different signaling pathways through the local release and capture of activated signaling molecules. To study the spatiotemporal dynamics of this mechanism, we have developed a Brownian dynamics modeling approach and applied it to the receptor-mediated activation of Ras and the cooperative recruitment of phosphoinositide 3-kinase (PI3K) by activated receptors and Ras. Various analyses of the model simulations show that cooperative assembly of multimolecular complexes nucleated by activated receptors is facilitated by the local release and capture of membrane-anchored signaling molecules (such as active Ras) from/by receptor-bound signaling proteins. In the case of Ras/PI3K crosstalk, the model predicts that PI3K is more likely to be recruited by activated receptors bound or recently visited by the enzyme that activates Ras. By this mechanism, receptor-bound PI3K is stabilized through short-range, diffusion-controlled capture of active Ras and Ras/PI3K complexes released from the receptor complex. We contend that this mechanism is a means by which signaling pathways are propagated and spatially coordinated for efficient crosstalk between them.

Intracellular signal transduction proteins typically utilize multiple interaction domains for proper targeting, and thus a broad diversity of distinct signaling complexes may be assembled. Considering the coordination of only two such domains, as in tandem Src homology 2 (SH2) domain constructs, gives rise to a kinetic scheme that is not adequately described by simple models used routinely to interpret in vitro binding measurements. To analyze the interactions between tandem SH2 domains and bisphosphorylated peptides, we formulated detailed kinetic models and applied them to the phosphoinositide 3-kinase p85 regulatory subunit/platelet-derived growth factor β-receptor system. Data for this system from different in vitro assay platforms, including surface plasmon resonance, competition binding, and isothermal titration calorimetry, were reconciled to estimate the magnitude of the cooperativity characterizing the sequential binding of the high and low affinity SH2 domains (C-SH2 and N-SH2, respectively). Compared with values based on an effective volume approximation, the estimated cooperativity is 3 orders of magnitude lower, indicative of significant structural constraints. Homodimerization of full-length p85 was found to be an alternative mechanism for high avidity binding to phosphorylated platelet-derived growth factor receptors, which would render the N-SH2 domain dispensable for receptor binding.

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.

We consider the steady-state pattern of messenger molecules produced in the membrane of a cell perceiving and responding to an extracellular gradient of chemoattractant, which directs cell movement towards the chemoattractant source. Specifically, we analyze the undesirable effect of lateral diffusion in blurring the intracellular messenger profile. The concept of an effectiveness factor, akin to the analysis of reactions in porous catalysts, is applied to the spatial gradient sensing problem, with the distinction that slow, not fast, diffusion is required for effective gradient sensing. Analytical effectiveness factor expressions are derived for ideal geometries and then generalized to arbitrary cell shapes. In the case of mouse fibroblasts responding to gradients of platelet-derived growth factor, we conclude that the cell morphology and orientation with respect to the gradient can dictate whether messenger diffusion obliterates gradient sensing or has very little effect. The analysis outlined here allows the effect of intracellular messenger diffusion on spatial gradient sensing to be quantified for individual cells.

Directed cell migration is critical for normal development, immune responses, and wound healing and plays a prominent role in tumor metastasis. In eukaryotes, cell orientation is biased by an external chemoattractant gradient through a spatial contrast in chemoattractant receptor-mediated signal transduction processes that differentially affect cytoskeletal dynamics at the cell front and rear. Mechanisms of spatial gradient sensing and chemotaxis have been studied extensively in the social amoeba Dictyostelium discoideum and mammalian leukocytes (neutrophils), which are similar in their remarkable sensitivity to shallow gradients and robustness of response over a broad range of chemoattractant concentration. Recently, we have quantitatively characterized a different gradient sensing system, that of platelet-derived growth factor-stimulated fibroblasts, an important component of dermal wound healing. The marked differences between this system and the others have led us to speculate on the diversity of gradient sensing mechanisms and their biological implications.

In growth-factor-stimulated signal transduction, cell-surface receptors recruit PI3Ks (phosphoinositide 3-kinases) and Ras-specific GEFs (guanine nucleotide-exchange factors) to the plasma membrane, where they produce 3′-phosphorylated phosphoinositide lipids and Ras-GTP respectively. As a direct example of pathway networking, Ras-GTP also recruits and activates PI3Ks. To refine the mechanism of Ras–PI3K cross-talk and analyse its quantitative implications, we offer a theoretical model describing the assembly of complexes involving receptors, PI3K and Ras-GTP. While the model poses the possibility that a ternary receptor–PI3K–Ras complex forms in two steps, it also encompasses the possibility that receptor–PI3K and Ras–PI3K interactions are competitive. In support of this analysis, experiments with platelet-derived growth factor-stimulated fibroblasts revealed that Ras apparently enhances the affinity of PI3K for receptors; in the context of the model, this suggests that a ternary complex does indeed form, with the second step greatly enhanced through membrane localization and possibly allosteric effects. The apparent contribution of Ras to PI3K activation depends strongly on the quantities and binding affinities of the interacting molecules, which vary across different cell types and stimuli, and thus the model could be used to predict conditions under which PI3K signalling is sensitive to interventions targeting Ras.

Migration of eukaryotic cells toward a chemoattractant often relies on their ability to distinguish receptor-mediated signaling at different subcellular locations, a phenomenon known as spatial sensing. A prominent example that is seen during wound healing is fibroblast migration in platelet-derived growth factor (PDGF) gradients. As in the well-characterized chemotactic cells Dictyostelium discoideum and neutrophils, signaling to the cytoskeleton via the phosphoinositide 3-kinase pathway in fibroblasts is spatially polarized by a PDGF gradient; however, the sensitivity of this process and how it is regulated are unknown. Through a quantitative analysis of mathematical models and live cell total internal reflection fluorescence microscopy experiments, we demonstrate that PDGF detection is governed by mechanisms that are fundamentally different from those in D. discoideum and neutrophils. Robust PDGF sensing requires steeper gradients and a much narrower range of absolute chemoattractant concentration, which is consistent with a simpler system lacking the feedback loops that yield signal amplification and adaptation in amoeboid cells.

Fluorescent protein probes now permit spatial distributions of specific intracellular signaling molecules to be observed in real time. Mathematical models have been used to simulate molecular gradients and other spatial patterns within cells, and the output of such models may be compared directly with experiments if the binding of the fluorescent probe and the physics of the imaging technique are each incorporated. Here we present a comprehensive model describing the dynamics of 3' phosphoinositides (PIs), lipid second messengers produced in the plasma membrane in response to stimulation of the PI 3-kinase signaling pathway, as monitored in the cell-substratum contact area using total internal reflection fluorescence microscopy. With this technique it was previously shown that uniform stimulation of fibroblasts with platelet-derived growth factor elicits the formation of axisymmetric 3' PI gradients, which we now characterize in the context of our model. We find that upper and lower bounds on the relevant dimensionless model parameter values for an individual cell can be calculated from four well-defined fluorescence measurements. Based on our analysis, we expect that the key dimensionless group, the ratio of 3' PI turnover and diffusion rates, can be estimated within approximately 20% or less.

Isoforms of the serine-threonine kinase Akt coordinate multiple cell survival pathways in response to stimuli such as platelet-derived growth factor (PDGF). Activation of Akt is a multistep process, which relies on the production of 3'-phosphorylated phosphoinositide (PI) lipids by PI 3-kinases. To quantitatively assess the kinetics of PDGF receptor/PI 3-kinase/Akt signaling in fibroblasts, a systematic study of this pathway was performed, and a mechanistic mathematical model that describes its operation was formulated. We find that PDGF receptor phosphorylation exhibits positive cooperativity with respect to PDGF concentration, and its kinetics are quantitatively consistent with a mechanism in which receptor dimerization is initially mediated by the association of two 1:1 PDGF/PDGF receptor complexes. Receptor phosphorylation is transient at high concentrations of PDGF, consistent with the loss of activated receptors upon endocytosis. By comparison, Akt activation responds to lower PDGF concentrations and exhibits more sustained kinetics. Further analysis and modeling suggest that the pathway is saturated at the level of PI 3-kinase activation, and that the p110alpha catalytic subunit of PI 3-kinase contributes most to PDGF-stimulated 3'-PI production. Thus, at high concentrations of PDGF the kinetics of 3'-PI production are limited by the turnover rate of these lipids, while the Akt response is additionally influenced by the rate of Akt deactivation.

In our previously published article, we described a computational model and analysis investigating the stochastic dynamics of cell protrusion during cell migration. In that work, we presented results of stochastic simulations plotted in two-dimensional parameter space. To supplement this analysis, the associated region of model bistability was identified by analysis of the deterministic model equations, and this region was plotted on the same graphs (panels a & b in each of Figs. 2–6). Since publication of our article, we became aware that certain parameter combinations thought to lie in the bistable region are, in fact, monostable. We wish to thank Dr. Michael Savageau (Biomedical Engineering, UC Davis), who studied our model during the preparation of his review article, for bringing the matter to our attention. We traced the error to the use of incorrect values of certain parameters in the bistability analysis. Whereas the values reported in the paper are correct for the stochastic model results, the bistability analysis was performed using three incorrect parameter values as shown in Table C1. Shown below as Fig. C1 are the corrected figure panels, which now show the bistability regions using the correct parameter values as used in the stochastic simulations. One of our previous conclusions concerned the lack of a definitive relationship between phenotypic switching in the stochastic simulations and model bistability. This conclusion was based, in part, on stochastic simulations for parameter sets that were supposed to lie in regions of bistability (Fig. 2e and Fig. 5e of the paper). Since the corrected results show that the parameter sets in question do not lie in the bistable regime, we have performed additional simulations to confirm that the original conclusions are valid (Figure C2). In these simulations, the analysis shown in Fig. 5 of the original paper was repeated with a larger value of the Cs parameter in order to expand the region of bistability. Comparison of stochastic runs on either side of the bistability region, as originally intended, confirms that although switching between protrusion and adhesion phenotypes is likely to occur in regions of parameter space that are close to the region of bistability, model bistability is not required for this behavior. As explained in the original article, bistable regions of parameter space usually lie between those regions that give monostable low and monostable high protrusion, and in the vicinity of the interface between the two, the stochastic model readily produces transient departures from the stable state.

Although prolonged cell signaling is attenuated by internalization and downregulation of active receptors, it is now appreciated that many receptors continue to signal in intracellular compartments. Employing enhanced green fluorescent protein fusion probes, we have investigated the hypothesis that multiple signaling pathways are affected by the differential trafficking of membrane substrates such as PtdIns(4,5)P2. A phosphotyrosine-specific probe, but not a PtdIns(4,5)P2-specific probe, colocalized with internalized EGF as well as transferrin in EGF-stimulated living cells expressing autophosphorylation-competent EGF receptors. Neither probe colocalized with transferrin in the absence of EGF, demonstrating that the reduced level of accessible PtdIns(4,5)P2 in endosomes is constitutive. Finally, a PtdIns(3,4,5)P3-specific probe, which monitors phosphorylation of PtdIns(4,5)P2 by phosphoinositide 3-kinases, was recruited to the plasma membrane but not to EGF- or transferrin-containing endosomes in response to EGF stimulation. These results suggest that while many internalized receptors continue to engage intracellular enzymes, the phospholipase C and phosphoinositide 3-kinase signaling pathways are abrogated by the constitutive lack of accessible PtdIns(4,5)P2 in endosomes.

The directed movement of fibroblasts towards locally released platelet-derived growth factor (PDGF) is a critical event in wound healing. Although recent studies have implicated polarized activation of phosphoinositide (PI) 3-kinase in G protein-mediated chemotaxis, the role of 3′ PI lipids in tyrosine kinase-triggered chemotaxis is not well understood. Using evanescent wave microscopy and green fluorescent protein–tagged Akt pleckstrin homology domain (GFP–AktPH) as a molecular sensor, we show that application of a shallow PDGF gradient triggers a markedly steeper gradient in 3′ PI lipids in the adhesion zone of fibroblasts. Polar GFP–AktPH gradients, as well as a new type of radial gradient, were measured from front to rear and from the periphery to the center of the adhesion zone, respectively. A strong spatial correlation between polarized 3′ PI production and rapid membrane spreading implicates 3′ PI lipids as a direct mediator of polarized migration. Analysis of the temporal changes of 3′ PI gradients in the adhesion zone revealed a fast diffusion coefficient (0.5 μm2/s) and short lifetime of 3′ PIs of

Combining engineering analyses and mathematical modeling with intervention and detection methodologies at the molecular level will allow manipulation of intracellular signal transduction pathways, and therefore rational control of functional processes central to medicine and biotechnology. We have formulated a simple mathematical model of a key signaling pathway required for regulated migration of fibroblasts and other cell types: activation of the intracellular enzyme phospholipase C (PLC) mediated by epidermal growth factor receptor (EGFR) and a multitude of other transmembrane receptors. One of the interesting features of this pathway is that the substrate of PLC, the lipid phosphatidylinositol (4,5)-bisphosphate (PIP(2)), is turned over quite rapidly and must be constantly resupplied to the plasma membrane by a known transfer mechanism. The model, which accounts for regulation of PIP(2) concentration, is sufficiently detailed to explain unique quantitative features of recent experimental data. We find that competitive pathways that deplete PIP(2) from the membrane, as well as receptor-mediated enhancement of PIP(2) supply, must be significant for agreement between model and experiment. Importantly, the mechanistic nature of the model also allowed us to predict the efficacy of various molecular intervention strategies, including overexpression of wild-type and variant proteins in the pathway as well as treatment with specific drug inhibitors. For many parameter conditions the intuitive strategy of targeting the enzyme itself is actually predicted to be relatively inefficient, with a novel and potentially useful alternative being disruption of the reactant supply mechanism.

Regulated activation of the highly conserved Ras GTPase is a central event in the stimulation of cell proliferation, motility, and differentiation elicited by receptor tyrosine kinases, such as the epidermal growth factor receptor (EGFR). In fibroblasts, this involves formation and membrane localization of Shc.Grb2.Sos complexes, which increases the rate of Ras guanine nucleotide exchange. In order to control Ras-mediated cell responses, this activity is regulated by receptor down-regulation and a feedback loop involving the dual specificity kinase mitogen-activated protein kinase/extracellular signal-regulated kinase kinase (MEK). We investigated the role of EGFR endocytosis in the regulation of Ras activation. Of fundamental interest is whether activated receptors in endosomes can participate in the stimulation of Ras guanine nucleotide exchange, because the constitutive membrane localization of Ras may affect its compartmentalization. By exploiting the differences in postendocytic signaling of two EGFR ligands, epidermal growth factor and transforming growth factor-alpha, we found that activated EGFR located at the cell surface and in internal compartments contribute equally to the membrane recruitment and tyrosine phosphorylation of Shc in NR6 fibroblasts expressing wild-type EGFR. Importantly, both the rate of Ras-specific guanine nucleotide exchange and the level of Ras-GTP were depressed to near basal values on the time scale of receptor trafficking. Using the selective MEK inhibitor PD098059, we were able to block the feedback desensitization pathway and maintain activation of Ras. Under these conditions, the generation of Ras-GTP was not significantly affected by the subcellular location of activated EGFR. In conjunction with our previous analysis of the phospholipase C pathway in the same cell line, this suggests a selective continuation of specific signaling activities and cessation of others upon receptor endocytosis.

A mechanism for cell shape control of intracellular signal transduction, whereby the average concentration of activated proteins in the cytosol increases as the height of the cell decreases, has been described recently. An important modification of this analysis is offered, recognizing that signaling proteins are not only activated at the plasma membrane but must first form complexes with signaling molecules that reside there, such as receptors and lipids. With these more realistic boundary conditions, it is shown that the region of parameter space where cell shape amplifies the average cytosolic activity is greatly expanded. Moreover, this model allows for amplification of the activated protein bound at the membrane, which is considered more relevant for certain, spatially driven signaling processes in cell migration.