Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as "fluidization" of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D'Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D'Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D'Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

Dissection of MKK6 and p38 Signaling Using Light-Activated Protein Kinases

Stress-activated signaling pathways orchestrate cellular behaviors and fates. Studying the precise role(s) of stress-activated protein kinases is challenging, because stress conditions induce adaptation and impose selection pressure. To meet this challenge, we have applied an optogenetic system with a single plasmid to express light-activated p38α or its upstream activator, MKK6, in conjunction with live-cell fluorescence microscopy. In starved cells, decaging of constitutively active p38α or MKK6 by brief exposure to UV light elicits rapid p38-mediated signaling, release of cytochrome c from mitochondria, and apoptosis with different kinetics. In parallel, light activation of p38α also suppresses autophagosome formation, similarly to stimulation with growth factors that activate PI3K/Akt/mTORC1 signaling. Active MKK6 negatively regulates serum-induced ERK activity, which is p38-independent as previously reported. Here, we reproduce that result with the one plasmid system and show that although decaging active p38α does not reduce basal ERK activity in our cells, it can block growth factor-stimulated ERK signaling in serum-starved cells. These results clarify the roles of MKK6 and p38α in dynamic signaling programs, which act in concert to actuate apoptotic death while suppressing cell survival mechanisms.

Isoform-specific optical activation of kinase function reveals p38-ERK signaling crosstalk

Evolution has diversified the mammalian proteome by the generation of protein isoforms that originate from identical genes, e.g., through alternative gene splicing or post-translational modifications, or very similar genes found in gene families. Protein isoforms can have either overlapping or unique functions and traditional chemical, biochemical, and genetic techniques are often limited in their ability to differentiate between isoforms due to their high similarity. This is particularly true in the context of highly dynamic cell signaling cascades, which often require acute spatiotemporal perturbation to assess mechanistic details. To that end, we describe a method for the selective perturbation of the individual protein isoforms of the mitogen-activated protein kinase (MAPK) p38. The genetic installation of a photocaging group at a conserved active site lysine enables the precise light-controlled initiation of kinase signaling, followed by investigation of downstream events. Through optical control, we have identified a novel point of crosstalk between two major signaling cascades: the p38/MAPK pathway and the extracellular signal-regulated kinase (ERK)/MAPK pathway. Specifically, using the photoactivated p38 isoforms, we have found the p38γ and p38δ variants to be positive regulators of the ERK signaling cascade, while confirming the p38α and p38β variants as negative regulators.

G-actin diffusion is insufficient to achieve F-actin assembly in fast-treadmilling protrusions

To generate forces that drive migration of a eukaryotic cell, arrays of actin filaments (F-actin) are assembled at the cell's leading membrane edge. To maintain cell propulsion and respond to dynamic external cues, actin filaments must be disassembled to regenerate the actin monomers (G-actin), and transport of G-actin from sites of disassembly back to the leading edge completes the treadmilling cycle and limits the flux of F-actin assembly. Whether or not molecular diffusion is sufficient for G-actin transport has been a long-standing topic of debate, in part because the dynamic nature of cell motility and migration hinders the estimation of transport parameters. In this work, we applied an experimental system in which cells adopt an approximately constant and symmetrical shape; they cannot migrate but exhibit fast, steady treadmilling in the thin region protruding from the cell. Using fluorescence recovery after photobleaching, we quantified the relative concentrations and corresponding fluxes of F- and G-actin in this system. In conjunction with mathematical modeling, constrained by measured features of each region of interest, this approach revealed that diffusion alone cannot account for the transport of G-actin to the leading edge. Although G-actin diffusion and vectorial transport might vary with position in the protruding region, good agreement with the fluorescence recovery after photobleaching measurements was achieved by a model with constant G-actin diffusivity ∼2 μm2/s and anterograde G-actin velocity less than 1 μm/s.

Semi-autonomous wound invasion via matrix-deposited, haptotactic cues

Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFβ, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFβ, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.

On the inference of ERK signaling dynamics from protein biosensor measurements

The extracellular signal-regulated kinase (ERK) signaling pathway plays prominent roles in cell growth, proliferation, and differentiation. ERK signaling is dynamic, involving phosphorylation/dephosphorylation, nucleocytoplasmic shuttling, and interactions with scores of protein substrates in the cytosol and in the nucleus. Live-cell fluorescence microscopy using genetically encoded ERK biosensors offers the potential to infer those dynamics in individual cells. In this study, we have monitored ERK signaling using four commonly used translocation- and FRET-based biosensors in a common cell stimulation context. Consistent with previous reports, we found that each biosensor responds with unique kinetics; it is clear that there is not a single dynamic signature characterizing the complexity of ERK phosphorylation, translocation, and kinase activity. In particular, the widely adopted ERK Kinase Translocation Reporter (ERKKTR) gives a readout that reflects ERK activity in both compartments. Mathematical modeling offers an interpretation of the measured ERKKTR kinetics, in relation to cytosolic and nuclear ERK activity, and suggests that biosensor-specific dynamics substantially influence the measured output.

A kinetic model of phospholipase C-γ1 linking structure-based insights to dynamics of enzyme autoinhibition and activation

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.

Modeling cell protrusion predicts how myosin II and actin turnover affect adhesion-based signaling

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.

Microfluidic devices fitted with "flowver" paper pumps generate steady, tunable gradients for extended observation of chemotactic cell migration

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.

Optical control of MAP kinase kinase 6 (MKK6) reveals that it has divergent roles in pro-apoptotic and anti-proliferative signaling

The selective pressure imposed by extrinsic death signals and stressors adds to the challenge of isolating and interpreting the roles of proteins in stress-activated signaling networks. By expressing a kinase with activating mutations and a caged lysine blocking the active site, we can rapidly switch on catalytic activity with light and monitor the ensuing dynamics. Applying this approach to MAP kinase 6 (MKK6), which activates the p38 subfamily of MAPKs, we found that decaging active MKK6 in fibroblasts is sufficient to trigger apoptosis in a p38-dependent manner. Both in fibroblasts and in a murine melanoma cell line expressing mutant B-Raf, MKK6 activation rapidly and potently inhibited the pro-proliferative extracellular signal-regulated kinase (ERK) pathway; to our surprise, this negative cross-regulation was equally robust when all p38 isoforms were inhibited. These results position MKK6 as a new pleiotropic signal transducer that promotes both pro-apoptotic and anti-proliferative signaling, and they highlight the utility of caged, light-activated kinases for dissecting stress-activated signaling networks.

Design and evaluation of engineered protein biosensors for live-cell imaging of EGFR phosphorylation

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 approach, 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 Tyr992 (pTyr992) of EGFR. A biosensor based on mSH2 closely reported the kinetics of EGFR phosphorylation but retained cross-reactivity similar to tSH2-WT. In the second approach, we isolated a pTyr992-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 pTyr1148 (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.

Emergent spatiotemporal dynamics of the actomyosin network in the presence of chemical gradients

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.

A Reaction-Diffusion Model Explains Amplification of the PLC/PKC Pathway in Fibroblast Chemotaxis

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.

Kinetic Modeling and Analysis of the Akt/Mechanistic Target of Rapamycin Complex 1 (mTORC1) Signaling Axis Reveals Cooperative, Feedforward Regulation

Mechanistic target of rapamycin complex 1 (mTORC1) controls biosynthesis and has been implicated in uncontrolled cell growth in cancer. Although many details of mTORC1 regulation are well understood, a systems-level, predictive framework synthesizing those details is currently lacking. We constructed various mathematical models of mTORC1 activation mediated by Akt and aligned the model outputs to kinetic data acquired for growth factor-stimulated cells. A model based on a putative feedforward loop orchestrated by Akt consistently predicted how the pathway was altered by depletion of key regulatory proteins. Analysis of the successful model also elucidates two dynamical motifs: neutralization of a negative regulator, which characterizes how Akt indirectly activates mTORC1, and seesaw enzyme regulation, which describes how activated and inhibited states of mTORC1 are controlled in concert to produce a nonlinear, ultrasensitive response. Such insights lend quantitative understanding of signaling networks and their precise manipulation in various contexts.

Are Filopodia Privileged Signaling Structures in Migrating Cells?

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.

Quantitative analysis of B-lymphocyte migration directed by CXCL13

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.

Lamellipodia are crucial for haptotactic sensing and response

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.

Linking morphodynamics and directional persistence of T lymphocyte migration

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.

GMFβ controls branched actin content and lamellipodial retraction in fibroblasts

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.

Development of a tandem affinity phosphoproteomic method with motif selectivity and its application in analysis of signal transduction networks

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.

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.

Profilin-1 serves as a gatekeeper for actin assembly by Arp2/3-dependent and -independent pathways

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

Bi-ligand surfaces with oriented and patterned protein for real-time tracking of cell migration

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.

Data-driven modeling reconciles kinetics of ERK phosphorylation, localization, and activity states

The extracellular signal‐regulated kinase (ERK) signaling pathway controls cell proliferation and differentiation in metazoans. Two hallmarks of its dynamics are adaptation of ERK phosphorylation, which has been linked to negative feedback, and nucleocytoplasmic shuttling, which allows active ERK to phosphorylate protein substrates in the nucleus and cytosol. To integrate these complex features, we acquired quantitative biochemical and live‐cell microscopy data to reconcile phosphorylation, localization, and activity states of ERK. While maximal growth factor stimulation elicits transient ERK phosphorylation and nuclear translocation responses, ERK activities available to phosphorylate substrates in the cytosol and nuclei show relatively little or no adaptation. Free ERK activity in the nucleus temporally lags the peak in nuclear translocation, indicating a slow process. Additional experiments, guided by kinetic modeling, show that this process is consistent with ERK's modification of and release from nuclear substrate anchors. Thus, adaptation of whole‐cell ERK phosphorylation is a by‐product of transient protection from phosphatases. Consistent with this interpretation, predictions concerning the dose‐dependence of the pathway response and its interruption by inhibition of MEK were experimentally confirmed.

Quantitative analysis of phosphoinositide 3-kinase (PI3K) signaling using live-cell total internal reflection fluorescence (TIRF) microscopy

This unit focuses on the use of total internal reflection fluorescence (TIRF) microscopy and image analysis methods to study the dynamics of signal transduction mediated by class I phosphoinositide 3-kinases (PI3Ks) in mammalian cells. The first four protocols cover live-cell imaging experiments, image acquisition parameters, and basic image processing and segmentation. These methods are generally applicable to live-cell TIRF experiments. The remaining protocols outline more advanced image analysis methods, which were developed in our laboratory for the purpose of characterizing the spatiotemporal dynamics of PI3K signaling. These methods may be extended to analyze other cellular processes monitored using fluorescent biosensors.

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.