Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: II. Parameter estimates for individual cells from experiments

PLEKHG3 enhances polarized cell migration by activating actin filaments at the cell front

Cells migrate by directing Ras-related C3 botulinum toxin substrate 1 (Rac1) and cell division control protein 42 (Cdc42) activities and by polymerizing actin toward the leading edge of the cell. Previous studies have proposed that this polarization process requires a local positive feedback in the leading edge involving Rac small GTPase and actin polymerization with PI3K likely playing a coordinating role. Here, we show that the pleckstrin homology and RhoGEF domain containing G3 (PLEKHG3) is a PI3K-regulated Rho guanine nucleotide exchange factor (RhoGEF) for Rac1 and Cdc42 that selectively binds to newly polymerized actin at the leading edge of migrating fibroblasts. Optogenetic inactivation of PLEKHG3 showed that PLEKHG3 is indispensable both for inducing and for maintaining cell polarity. By selectively binding to newly polymerized actin, PLEKHG3 promotes local Rac1/Cdc42 activation to induce more local actin polymerization, which in turn promotes the recruitment of more PLEKHG3 to induce and maintain cell front. Thus, autocatalytic reinforcement of PLEKHG3 localization to the leading edge of the cell provides a molecular basis for the proposed positive feedback loop that is required for cell polarization and directed migration.

F-actin bundles direct the initiation and orientation of lamellipodia through adhesion-based 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.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Live-cell fluorescence microscopy with molecular biosensors: what are we really measuring?

Engineered protein biosensors, such as those based on Förster resonance energy transfer, membrane translocation, or solvatochromic shift, are being used in combination with live-cell fluorescence microscopy to reveal kinetics and spatial localization of intracellular processes as they occur. Progress in the application of this approach has been steady, yet its general suitability for quantitative measurements remains unclear. To address the pitfalls of the biosensor approach in quantitative terms, simple reaction-diffusion models were analyzed. The analysis shows that although high-affinity molecular recognition allows robust detection of the fluorescence readout, either of two detrimental effects is fostered. Binding of an intramolecular biosensor or of a relatively abundant intermolecular biosensor introduces observer effects in which the dynamics of the target molecule under study are significantly perturbed, whereas binding of a sparingly expressed intermolecular biosensor is subject to a saturation effect, where the pool of unbound biosensor is significantly depleted. The analysis explores how these effects are manifest in the kinetics and spatial gradients of the biosensor-target complex. A sobering insight emerges: the observer or saturation effect is always significant; the question is whether or not it can be tolerated or accounted for. The challenge in managing the adverse effects is that specification of the biosensor-target affinity to within a certain order of magnitude is required.

Migrating fibroblasts reorient directionality by a metastable, PI3K-dependent mechanism

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.

How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility

To regulate shape changes, motility and chemotaxis in eukaryotic cells, signal transduction pathways channel extracellular stimuli to the reorganization of the actin cytoskeleton. The complexity of such networks makes it difficult to understand the roles of individual components, let alone their interactions and multiple feedbacks within a given layer and between layers of signalling. Even more challenging is the question of if and how the shape of the cell affects and is affected by this internal spatiotemporal reorganization. Here we build on our previous 2D cell motility model where signalling from the Rho family GTPases (Cdc42, Rac, and Rho) was shown to organize the cell polarization, actin reorganization, shape change, and motility in simple gradients. We extend this work in two ways: First, we investigate the effects of the feedback between the phosphoinositides (PIs) , and Rho family GTPases. We show how that feedback increases heights and breadths of zones of Cdc42 activity, facilitating global communication between competing cell “fronts”. This hastens the commitment to a single lamellipodium initiated in response to multiple, complex, or rapidly changing stimuli. Second, we show how cell shape feeds back on internal distribution of GTPases. Constraints on chemical isocline curvature imposed by boundary conditions results in the fact that dynamic cell shape leads to faster biochemical redistribution when the cell is repolarized. Cells with frozen cytoskeleton, and static shapes, consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes, the degree of the shape-induced effects being proportional to the extent of cell deformation. We explain these concepts in the context of several in silico experiments using our 2D computational cell model.

Single cells, such as amoeba and white blood cells, change shape and move in response to environmental stimuli. Their behaviour is a consequence of the intracellular properties balanced by external forces. The internal regulation is modulated by several proteins that interact with one another and with membrane lipids. We examine, through in silico experiments using a computational model of a moving cell, the interactions of an important class of such proteins (Rho GTPases) and lipids (phosphoinositides, PIs), their spatial redistribution, and how they affect and are affected by cell shape. Certain GTPases promote the assembly of the actin cytoskeleton. This then leads to the formation of a cell protrusion, the leading edge. The feedback between PIs and GTPases facilitates global communication across the cell, ensuring that multiple, complex, or rapidly changing stimuli can be resolved into a single decision for positioning the leading edge. Interestingly, the cell shape itself affects the intracellular biochemistry, resulting from interactions between the curvature of the chemical fronts and the cell edge. Cells with static shapes consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes. This potential to respond more rapidly to external stimuli depends on the degree of cellular shape deformation.

Phosphoinositides in chemotaxis

Phosphatidylinositol lipids generated through the action of phosphinositide 3-kinase (PI3K) are key mediators of a wide array of biological responses. In particular, their role in the regulation of cell migration has been extensively studied and extends to amoeboid as well as mesenchymal migration. Through the emergence of fluorescent probes that target PI3K products as well as the use of specific inhibitors and knockout technologies, the spatio-temporal distribution of PI3K products in chemotaxing cells has been shown to represent a key anterior polarity signal that targets downstream effectors to actin polymerization. In addition, through intricate cross-talk networks PI3K products have been shown to regulate signals that control posterior effectors. Yet, in more complex environments or in conditions where chemoattractant gradients are steep, a variety of cell types can still chemotax in the absence of PI3K signals. Indeed, parallel signal transduction pathways have been shown to coordinately regulate cell polarity and directed movement. In this chapter, we will review the current role PI3K products play in the regulation of directed cell migration in various cell types, highlight the importance of mathematical modeling in the study of chemotaxis, and end with a brief overview of other signaling cascades known to also regulate chemotaxis.

In chemotaxing fibroblasts, both high-fidelity and weakly biased cell movements track the localization of PI3K signaling

Cell movement biased by a chemical gradient, or chemotaxis, coordinates the recruitment of cells and collective migration of cell populations. During wound healing, chemotaxis of fibroblasts is stimulated by platelet-derived growth factor (PDGF) and certain other chemoattractants. Whereas the immediate PDGF gradient sensing response has been characterized previously at the level of phosphoinositide 3-kinase (PI3K) signaling, the sensitivity of the response at the level of cell migration bias has not yet been studied quantitatively. In this work, we used live-cell total internal reflection fluorescence microscopy to monitor PI3K signaling dynamics and cell movements for extended periods. We show that persistent and properly aligned (i.e., high-fidelity) fibroblast migration does indeed correlate with polarized PI3K signaling; accordingly, this behavior is seen only under conditions of high gradient steepness (>10% across a typical cell length of 50 μm) and a certain range of PDGF concentrations. Under suboptimal conditions, cells execute a random or biased random walk, but nonetheless move in a predictable fashion according to the changing pattern of PI3K signaling. Inhibition of PI3K during chemotaxis is accompanied by loss of both cell-substratum contact and morphological polarity, but after a recovery period, PI3K-inhibited fibroblasts often regain the ability to orient toward the PDGF gradient.

Computational analysis of the spatiotemporal coordination of polarized PI3K and Rac1 activities in micro-patterned live cells

Polarized molecular activities play important roles in guiding the cell toward persistent and directional migration. In this study, the polarized distributions of the activities of phosphatidylinositol 3-kinase (PI3K) and the Rac1 small GTPase were monitored using chimeric fluorescent proteins (FPs) in cells constrained on micro-patterned strips, with one end connecting to a neighboring cell (junction end) and the other end free of cell-cell contact (free end). The recorded spatiotemporal dynamics of the fluorescent intensity from different cells was scaled into a uniform coordinate system and applied to compute the molecular activity landscapes in space and time. The results revealed different polarization patterns of PI3K and Rac1 activity induced by the growth factor stimulation. The maximal intensity of different FPs, and the edge position and velocity at the free end were further quantified to analyze their correlation and decipher the underlying signaling sequence. The results suggest that the initiation of the edge extension occurred before the activation of PI3K, which led to a stable extension of the free end followed by the Rac1 activation. Therefore, the results support a concerted coordination of sequential signaling events and edge dynamics, underscoring the important roles played by PI3K activity at the free end in regulating the stable lamellipodia extension and cell migration. Meanwhile, the quantification methods and accompanying software developed can provide a convenient and powerful computational analysis platform for the study of spatiotemporal molecular distribution and hierarchy in live cells based on fluorescence images.

A comparison of mathematical models for polarization of single eukaryotic cells in response to guided cues

Polarization, a primary step in the response of an individual eukaryotic cell to a spatial stimulus, has attracted numerous theoretical treatments complementing experimental studies in a variety of cell types. While the phenomenon itself is universal, details differ across cell types, and across classes of models that have been proposed. Most models address how symmetry breaking leads to polarization, some in abstract settings, others based on specific biochemistry. Here, we compare polarization in response to a stimulus (e.g., a chemoattractant) in cells typically used in experiments (yeast, amoebae, leukocytes, keratocytes, fibroblasts, and neurons), and, in parallel, responses of several prototypical models to typical stimulation protocols. We find that the diversity of cell behaviors is reflected by a diversity of models, and that some, but not all models, can account for amplification of stimulus, maintenance of polarity, adaptation, sensitivity to new signals, and robustness.

Systematic quantification of negative feedback mechanisms in the extracellular signal-regulated kinase (ERK) signaling network

Cell responses are actuated by tightly controlled signal transduction pathways. Although the concept of an integrated signaling network replete with interpathway cross-talk and feedback regulation is broadly appreciated, kinetic data of the type needed to characterize such interactions in conjunction with mathematical models are lacking. In mammalian cells, the Ras/ERK pathway controls cell proliferation and other responses stimulated by growth factors, and several cross-talk and feedback mechanisms affecting its activation have been identified. In this work, we take a systematic approach to parse the magnitudes of multiple regulatory mechanisms that attenuate ERK activation through canonical (Ras-dependent) and non-canonical (PI3K-dependent) pathways. In addition to regulation of receptor and ligand levels, we consider three layers of ERK-dependent feedback: desensitization of Ras activation, negative regulation of MEK kinase (e.g. Raf) activities, and up-regulation of dual-specificity ERK phosphatases. Our results establish the second of these as the dominant mode of ERK self-regulation in mouse fibroblasts. We further demonstrate that kinetic models of signaling networks, trained on a sufficient diversity of quantitative data, can be reasonably comprehensive, accurate, and predictive in the dynamical sense.

Directional persistence of cell migration coincides with stability of asymmetric intracellular signaling

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.

Spontaneous phosphoinositide 3-kinase signaling dynamics drive spreading and random migration of fibroblasts

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.

Modelling cellular signalling systems

Cell signalling pathways and networks are complex and often non-linear. Signalling pathways can be represented as systems of biochemical reactions that can be modelled using differential equations. Computational modelling of cell signalling pathways is emerging as a tool that facilitates mechanistic understanding of complex biological systems. Mathematical models are also used to generate predictions that may be tested experimentally. In the present chapter, the various steps involved in building models of cell signalling pathways are discussed. Depending on the nature of the process being modelled and the scale of the model, different mathematical formulations, ranging from stochastic representations to ordinary and partial differential equations are discussed. This is followed by a brief summary of some recent modelling successes and the state of future models.

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.

Mathematical Models of Cell Motility

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Imaging and manipulating phosphoinositides in living cells

Phosphoinositides are minor phospholipid constituents of virtually every biological membrane yet they play fundamental roles in controlling membrane-bound signalling events. Phosphoinositides are produced from phosphatidylinositol (PtdIns) by phosphorylation of one or more of three positions (3, 4 and 5) of the inositol headgroup located at the membrane cytoplasmic interface by distinct families of inositol lipid kinases. Intriguingly, many of the kinase reactions are catalysed by more than one form of the kinases even in simple organisms and these enzymes often assume non-redundant functions. A similar diversity is seen with inositide phosphatases, the enzymes that dephosphorylate phosphoinositides with a certain degree of specificity and the impairments of which are often linked to human diseases. This degree of multiplicity at the enzyme level together with the universal roles of these lipids in cell regulation assumes that inositol lipids are spatially and functionally restricted in specific membrane compartments. Studying the compartmentalized roles of these lipids at the cellular level represents a major methodological challenge. Over the last 10 years significant progress has been made in creating reagents that can monitor inositol lipid changes in live cells with fluorescence or confocal microscopy. New methods are also being developed to manipulate these lipids in specific membrane compartments in a regulated fashion. This article recalls some historical aspects of inositide research and describes the new methodological advances highlighting their great potential as well as the problems one can encounter with their use.

Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a one-dimensional model of a motile cell

Gradient sensing, polarization, and chemotaxis of motile cells involve the actin cytoskeleton, and regulatory modules, including the phosphoinositides (PIs), their kinases/phosphatases, and small GTPases (Rho proteins). Here we model their individual components (PIP1, PIP2, PIP3; PTEN, PI3K, PI5K; Cdc42, Rac, Rho; Arp2/3, and actin), their interconversions, interactions, and modular functions in the context of a one-dimensional dynamic model for protrusive cell motility, with parameter values derived from in vitro and in vivo studies. In response to a spatially graded stimulus, the model produces stable amplified internal profiles of regulatory components, and initiates persistent motility (consistent with experimental observations). By connecting the modules, we find that Rho GTPases work as a spatial switch, and that the PIs filter noise, and define the front versus back. Relatively fast PI diffusion also leads to selection of a unique pattern of Rho distribution from a collection of possible patterns. We use the model to explore the importance of specific hypothesized interactions, to explore mutant phenotypes, and to study the role of actin polymerization in the maintenance of the PI asymmetry. We also suggest a mechanism to explain the spatial exclusion of Cdc42 and PTEN and the inability of cells lacking active Cdc42 to properly detect chemoattractant gradients.

Regulation of the epithelial Na+ channel (ENaC) by phosphatidylinositides

The epithelial Na(+) channel (ENaC) is an end-effector of diverse cellular signaling cascades, including those with phosphatidylinositide second messengers. Recent evidence also suggests that in some instances, phospatidylinositides can directly interact with ENaC to increase channel activity by increasing channel open probability and/or membrane localization. We review here findings relevant to regulation of ENaC by phosphatidylinositol 4,5-bisphosphate (PIP(2)) and phosphatidylinositol 3,4,5-triphosphate (PIP(3)). Similar to its actions on other ion channels, PIP(2) is permissive for ENaC openings having a direct effect on gating. The PIP(2) binding site in ENaC involved in this regulation is most likely localized to the NH(2) terminus of beta-ENaC. PIP(3) also affects ENaC gating but, rather than being permissive, augments open probability. The PIP(3) binding site in ENaC involved in this regulation is localized to the proximal region of the COOH terminus of gamma-ENaC just following the second transmembrane domain. In complementary pathways, PIP(3) also impacts ENaC membrane levels through both direct actions on the channel and via a signaling cascade involving phosphoinositide 3-OH kinase (PI3-K) and the aldosterone-induced gene product serum and glucocorticoid-inducible kinase. The putative PIP(3) binding site in ENaC involved in direct regulation of channel membrane levels has not yet been identified.

Quantitative model of Ras-phosphoinositide 3-kinase signalling cross-talk based on co-operative molecular assembly

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.

Imaging signaling processes in platelets

Unraveling the complex signaling processes regulating platelet adhesion has been a longstanding goal for those in the field of platelet research. Advances in high-speed live cell imaging techniques, taking advantage of developments in the area of fluorescent probe design hold considerable promise for the investigation of the dynamic signaling processes governing platelet activation and function, both physiologically and pathologically. This review broadly covers the application of existing imaging techniques to the investigation of platelet function and examines new developments in the area of live cell imaging that may have future applications in the field.

Deterministic model of dermal wound invasion incorporating receptor-mediated signal transduction and spatial gradient sensing

During dermal wound healing, platelet-derived growth factor (PDGF) serves as both a chemoattractant and mitogen for fibroblasts, potently stimulating their invasion of the fibrin clot over a period of several days. A mathematical model of this process is presented, which accurately accounts for the sensitivity of PDGF gradient sensing through PDGF receptor/phosphoinositide 3-kinase-mediated signal transduction. Analysis of the model suggests that PDGF receptor-mediated endocytosis and degradation of PDGF allows a constant PDGF concentration profile to be maintained at the leading front of the fibroblast density profile as it propagates, at a constant rate, into the clot. Thus, the constant PDGF gradient can span the optimal concentration range for asymmetric phosphoinositide 3-kinase signaling and fibroblast chemotaxis, with near-maximal invasion rates elicited over a relatively broad range of PDGF secretion rates. A somewhat surprising finding was that extremely sharp PDGF gradients do not necessarily stimulate faster progression through the clot, because maintaining such a gradient through PDGF consumption is a potentially rate-limiting process.

Spontaneous polarization in eukaryotic gradient sensing: a mathematical model based on mutual inhibition of frontness and backness pathways

A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at the front end of the cell, and backness molecules, such as Rho and myosin II, accumulate at the back of the cell. Importantly, this frontness-backness polarization occurs spontaneously even if the cells are exposed to uniform chemoattractant profiles. The spontaneous polarization suggests that the gradient sensing machinery undergoes a Turing bifurcation. This has led to several classical activator-inhibitor and activator-substrate models which identify the frontness molecules with the activator. Conspicuously absent from these models is any accounting of the backness molecules. This stands in sharp contrast to experiments which show that the backness pathways inhibit the frontness pathways. Here, we formulate a model based on the mutually inhibitory interaction between the frontness and backness pathways. The model builds upon the mutual inhibition model proposed by Bourne and coworkers [Xu et al., 2003. Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils. Cell 114, 201-214.]. We show that mutual inhibition alone, without the help of any positive feedback (autocatalysis), can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhibition and activation of the frontness and backness pathways are consistent with those observed in experiments. Furthermore, depending on the parameter values, the model yields spatial distributions corresponding to chemoattraction (frontness pathways in-phase with the external gradient) and chemorepulsion (frontness pathways out-of-phase with the external gradient). Analysis of the model suggests a mechanism for the chemorepulsion-to-chemoattraction transition observed in neurons.

Quantitative elucidation of a distinct spatial gradient-sensing mechanism in fibroblasts

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.

Distinguishing modes of eukaryotic gradient sensing

We develop a mathematical model of phosphoinositide-mediated gradient sensing that can be applied to chemotactic behavior in highly motile eukaryotic cells such as Dictyostelium and neutrophils. We generate four variants of our model by adjusting parameters that control the strengths of coupled positive feedbacks and the importance of molecules that translocate from the cytosol to the membrane. Each variant exhibits a qualitatively different mode of gradient sensing. Simulations of characteristic behaviors suggest that differences between the variants are most evident at transitions between efficient gradient detection and failure. Based on these results, we propose criteria to distinguish between possible modes of gradient sensing in real cells, where many biochemical parameters may be unknown. We also identify constraints on parameters required for efficient gradient detection. Finally, our analysis suggests how a cell might transition between responsiveness and nonresponsiveness, and between different modes of gradient sensing, by adjusting its biochemical parameters.

Stable activation of phosphatidylinositol 3-kinase in the T cell immunological synapse stimulates Akt signaling to FoxO1 nuclear exclusion and cell growth control

We have previously reported at the single cell level that PI3K is activated after conjugate formation between T lymphocytes and APCs. However, in contrast to cells exposed to an asymmetrical signal that usually increase 3'-phosphoinositides (3'-PI) transiently in the region of the activated receptors, T cells contacting APC accumulate 3'-PI across their whole plasma membrane far beyond the region of the immunological synapse (IS). Importantly, this effect is maintained over time, for hours, and although PI3K-dependent pathways translate in various cell types extracellular stimuli into a wide range of biological events, in primary T cells this stability is mostly required for cell division induced by Ag. Using imaging methodologies, the present article elucidates the molecular mechanisms responsible for this particular functioning of the PI3K pathway in primary human T lymphocytes interacting with APCs, especially with dendritic cells. The results reveal that the IS unremittingly recruits PI3K to maintain high 3'-PI levels in T cells through phosphotyrosine-dependent mechanisms, suggesting a major participation of class Ia PI3K. This persistent activation of PI3K results in the Akt-dependent sequestration of the FoxO transcription factor, FoxO1, outside the nucleus of T cells interacting with APCs. Using an active form of FoxO1, we demonstrate that this compartmentalization process can affect T cell growth after Ag recognition. We conclude that the need for sustained PI3K signaling within the consolidated IS is probably an undemanding tactic used by primary T cells critical for initiating cell cycle progression through the prolonged inactivation of FoxO1, one important factor that can control cell quiescence.

Spatial analysis of 3' phosphoinositide signaling in living fibroblasts, III: influence of cell morphology and morphological Polarity

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.

Computational approaches for modeling regulatory cellular networks

Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.

A mechanistic model for eukaryotic gradient sensing: spontaneous and induced phosphoinositide polarization

The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of gradient sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. The increased understanding of this step has been driven by the discovery that within 5-10 s of applying a weak chemoattractant gradient, membrane phosphoinositides such as PIP(3) localize at the front end of the cell. It is currently believed that the gradient sensing mechanism is precisely the mechanism leading to this localization. We have formulated a reaction-diffusion model based on the phosphoinositide cycle which predicts various responses of motile cells in addition to the phosphoinositide polarization induced by chemoattractant gradients. The responses include: (a) Polarized sensitivity wherein a polarized cell responds to a change in the direction of the gradient by turning its existing front. (b) Spontaneous polarization wherein cells polarize in a random direction even if the surrounding chemoattractant concentration is uniform. (c) Unique localization which refers to the formation of a unique polarity even in the face of multiple chemoattractant sources. The above responses preclude the hypothesis that the cell merely amplifies the external signal. Our model indicates that the cell must be viewed as a system that nonlinearly processes chemoattractant inputs. We show in particular that these seemingly complex dynamics can be explained very simply in terms of the instabilities and wavefront dynamics that are characteristic of the activator-inhibitor class of models.