Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility

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.

Fibroblast Migration Is Regulated by Myristoylated Alanine-Rich C-Kinase Substrate (MARCKS) Protein

Myristoylated alanine-rich C-kinase substrate (MARCKS) is a ubiquitously expressed substrate of protein kinase C (PKC) that is involved in reorganization of the actin cytoskeleton. We hypothesized that MARCKS is involved in regulation of fibroblast migration and addressed this hypothesis by utilizing a unique reagent developed in this laboratory, the MANS peptide. The MANS peptide is a myristoylated cell permeable peptide corresponding to the first 24-amino acids of MARCKS that inhibits MARCKS function. Treatment of NIH-3T3 fibroblasts with the MANS peptide attenuated cell migration in scratch wounding assays, while a myristoylated, missense control peptide (RNS) had no effect. Neither MANS nor RNS peptide treatment altered NIH-3T3 cell proliferation within the parameters of the scratch assay. MANS peptide treatment also resulted in inhibited NIH-3T3 chemotaxis towards the chemoattractant platelet-derived growth factor-BB (PDGF-BB), with no effect observed with RNS treatment. Live cell imaging of PDGF-BB induced chemotaxis demonstrated that MANS peptide treatment resulted in weak chemotactic fidelity compared to RNS treated cells. MANS and RNS peptides did not affect PDGF-BB induced phosphorylation of MARCKS or phosphoinositide 3-kinase (PI3K) signaling, as measured by Akt phosphorylation. Further, no difference in cell migration was observed in NIH-3T3 fibroblasts that were transfected with MARCKS siRNAs with or without MANS peptide treatment. Genetic structure-function analysis revealed that MANS peptide-mediated attenuation of NIH-3T3 cell migration does not require the presence of the myristic acid moiety on the amino-terminus. Expression of either MANS or unmyristoylated MANS (UMANS) C-terminal EGFP fusion proteins resulted in similar levels of attenuated cell migration as observed with MANS peptide treatment. These data demonstrate that MARCKS regulates cell migration and suggests that MARCKS-mediated regulation of fibroblast migration involves the MARCKS amino-terminus. Further, this data demonstrates that MANS peptide treatment inhibits MARCKS function during fibroblast migration and that MANS mediated inhibition occurs independent of myristoylation.

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.

Stochastic models of cell protrusion arising from spatiotemporal signaling and adhesion dynamics

During cell migration, local protrusion events are regulated by biochemical and physical processes that are in turn coordinated with the dynamic properties of cell-substratum adhesion structures. In this chapter, we present a modeling approach for integrating the apparent stochasticity and spatial dependence of signal transduction pathways that promote protrusion in tandem with adhesion dynamics. We describe our modeling framework, as well as its abstraction, parameterization, and validation against experimental data. Analytical techniques for identifying and evaluating the effects of model bistability on simulation simulation results are shown, and implications of this analysis for understanding cell protrusion behavior are offered.

Quantitative models of signal transduction networks: How detailed should they be?

Receptor-mediated signal transduction networks, comprised of multiple biochemical pathways, control cell responses and are therefore central to normal and aberrant physiological processes. An appreciation for the inherent complexities of these networks has matured in recent years, to the point where it is now apparent that experimental measurements will need to be combined with computational modeling and analysis to best interpret and predict how individual mechanisms (proteinprotein interactions, enzymatic reactions, etc.,) are integrated at the network level. To progress along these lines, there is a major barrier to overcome: although a deep mechanistic understanding of signal transduction has been achieved, data sets of a suitably quantitative nature are still lacking. Based on our efforts to systematically acquire and analyze such measurements, we contend that the level of detail in models of signaling networks ought to be limited by the availability of quantitative data, rather than by the much greater availability of qualitative information about signaling interactions. Although this approach is sensible from a data-driven modeling perspective, it is controversial because it gives the false impression that molecular-level details are being ignored.

Guidelines for visualizing and annotating rule-based models

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.

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.

Signaling pathways that control cell migration: models and analysis

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

Allosteric modulation of Ras-GTP is linked to signal transduction through RAF kinase

Ras is a key signal transduction protein in the cell. Mutants of Gly(12) and Gln(61) impair GTPase activity and are found prominently in cancers. In wild type Ras-GTP, an allosteric switch promotes disorder to order transition in switch II, placing Gln(61) in the active site. We show that the "on" and "off" conformations of the allosteric switch can also be attained in RasG12V and RasQ61L. Although both mutants have similarly impaired active sites in the on state, RasQ61L stabilizes an anti-catalytic conformation of switch II in the off state of the allosteric switch when bound to Raf. This translates into more potent activation of the MAPK pathway involving Ras, Raf kinase, MEK, and ERK (Ras/Raf/MEK/ERK) in cells transfected with RasQ61L relative to RasG12V. This differential is not observed in the Raf-independent pathway involving Ras, phosphoinositide 3-kinase (PI3K), and Akt (Ras/PI3K/Akt). Using a combination of structural analysis, hydrolysis rates, and experiments in NIH-3T3 cells, we link the allosteric switch to the control of signaling in the Ras/Raf/MEK/ERK pathway, supporting a GTPase-activating protein-independent model for duration of the Ras-Raf complex.

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.

Stochastic model of integrin-mediated signaling and adhesion dynamics at the leading edges of migrating cells

Productive cell migration requires the spatiotemporal coordination of cell adhesion, membrane protrusion, and actomyosin-mediated contraction. Integrins, engaged by the extracellular matrix (ECM), nucleate the formation of adhesive contacts at the cell's leading edge(s), and maturation of nascent adhesions to form stable focal adhesions constitutes a functional switch between protrusive and contractile activities. To shed additional light on the coupling between integrin-mediated adhesion and membrane protrusion, we have formulated a quantitative model of leading edge dynamics combining mechanistic and phenomenological elements and studied its features through classical bifurcation analysis and stochastic simulation. The model describes in mathematical terms the feedback loops driving, on the one hand, Rac-mediated membrane protrusion and rapid turnover of nascent adhesions, and on the other, myosin-dependent maturation of adhesions that inhibit protrusion at high ECM density. Our results show that the qualitative behavior of the model is most sensitive to parameters characterizing the influence of stable adhesions and myosin. The major predictions of the model, which we subsequently confirmed, are that persistent leading edge protrusion is optimal at an intermediate ECM density, whereas depletion of myosin IIA relieves the repression of protrusion at higher ECM density.

Analysis of reaction-diffusion systems with anomalous subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.

A bipolar clamp mechanism for activation of Jak-family protein tyrosine kinases

Most cell surface receptors for growth factors and cytokines dimerize in order to mediate signal transduction. For many such receptors, the Janus kinase (Jak) family of non-receptor protein tyrosine kinases are recruited in pairs and juxtaposed by dimerized receptor complexes in order to activate one another by trans-phosphorylation. An alternative mechanism for Jak trans-phosphorylation has been proposed in which the phosphorylated kinase interacts with the Src homology 2 (SH2) domain of SH2-B, a unique adaptor protein with the capacity to homo-dimerize. Building on a rule-based kinetic modeling approach that considers the concerted nature and combinatorial complexity of modular protein domain interactions, we examine these mechanisms in detail, focusing on the growth hormone (GH) receptor/Jak2/SH2-Bβ system. The modeling results suggest that, whereas Jak2-(SH2-Bβ)₂-Jak2 heterotetramers are scarcely expected to affect Jak2 phosphorylation, SH2-Bβ and dimerized receptors synergistically promote Jak2 trans-activation in the context of intracellular signaling. Analysis of the results revealed a unique mechanism whereby SH2-B and receptor dimers constitute a bipolar ‘clamp’ that stabilizes the active configuration of two Jak2 molecules in the same macro-complex.

Janus kinases (Jaks) interact with and activate receptors on the cell surface that mediate changes in gene expression. How these interactions are promoted and regulated is of central interest in fields such as cellular endocrinology and immunology. Here, detailed computational models of Jak activation are offered at the level of protein modification states and interaction domains, wherein the specification of only a handful of binding/reaction rules can produce networks comprised of thousands of differential equations. Specifically, we investigated the role of an adaptor protein, SH2-B, revealing a novel mechanism whereby it cooperates with receptors to form a stable complex that juxtaposes two Jak molecules for efficient activation. We refer to this mode of molecular assembly as the bipolar clamp mechanism.

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.

Combinatorial Signal Transduction Responses Mediated by Interleukin-2 and -4 Receptors in a Helper TH2 Cell Line

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

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.

Computational models of tandem SRC homology 2 domain interactions and application to phosphoinositide 3-kinase

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 beta-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.

Membrane-binding/modification model of signaling protein activation and analysis of its control by cell morphology

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.

Structure-based kinetic models of modular signaling protein function: focus on Shp2

We present here a computational, rule-based model to study the function of the SH2 domain-containing protein tyrosine phosphatase, Shp2, in intracellular signal transduction. The two SH2 domains of Shp2 differentially regulate the enzymatic activity by a well-characterized mechanism, but they also affect the targeting of Shp2 to signaling receptors in cells. Our kinetic model integrates these potentially competing effects by considering the intra- and intermolecular interactions of the Shp2 SH2 domains and catalytic site as well as the effect of Shp2 phosphorylation. Even for the isolated Shp2/receptor system, which may seem simple by certain standards, we find that the network of possible binding and phosphorylation states is composed of over 1000 members. To our knowledge, this is the first kinetic model to fully consider the modular, multifunctional structure of a signaling protein, and the computational approach should be generally applicable to other complex intermolecular interactions.