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

Quantitative investigation of MDA-MB-231 breast cancer cell motility: dependence on epidermal growth factor concentration and its gradient

Enhanced cell motility is one of the primary features of cancer. Accumulated evidence demonstrates that Epidermal Growth Factor Receptor (EGFR) mediated pathways play an important role in breast cancer cell proliferation and migration. We have quantified the MDA-MB-231 breast cancer cell migration in response to the stimulation of EGFR pathways with their ligand EGF to determine how the cell motility of MDA-MB-231 cells depends on the ligand concentration and gradient. Analysis at the single cell level combined with mathematical modeling and the ability to vary the ligand concentration and gradients locally using microfluidic devices allowed us to separate the unique contributions of ligand concentration and ligand gradient to cell motility. We tracked the motility of 6600 cells individually using time lapse imaging under varying EGF stimulation conditions. Trajectory analysis of the tracked cells using non-linear multivariate regression models showed that: (i) cell migration of MDA-MB-231 breast cancer cells depends on the ligand gradient but not on the ligand concentration. This observation was valid for both the total (direction independent) and directed (along gradient direction) cell velocities. Although the dependence of the directed motility on ligand gradient is to be expected, the dependence of the total velocity solely on ligand gradient was an unexpected novel observation. (ii) Enhancement of the motilities of individual cells in a population upon exposure to the ligand was highly heterogeneous, and only a very small percentage of cells responded strongly to the external stimuli. Separating out the non-responding cells using quantitative analysis of individual cell motilities enabled us to establish that enhanced motility of the responding cells indeed increases monotonically with increasing EGF gradient. (iii) A large proportion of cells in a population were unresponsive to ligand stimulation, and their presence introduced considerable random intrinsic variability to the observations. This indicated that studying cell motilities at the individual cell level is necessary to better capture the biological reality and that population averaging methods should be avoided. Studying motilities at the individual cell level is particularly important to understand the biological processes that are possibly driven by the action of a small portion of cells in a population, such as metastasis. We discuss the implications of our results on the total and chemotactic movement of cancer cells in the tumor microenvironment.

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.

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.

Vibrio coralliilyticus search patterns across an oxygen gradient

The coral pathogen, Vibrio coralliilyticus shows specific chemotactic search pattern preference for oxic and anoxic conditions, with the newly identified 3-step flick search pattern dominating the patterns used in oxic conditions. We analyzed motile V. coralliilyticus cells for behavioral changes with varying oxygen concentrations to mimic the natural coral environment exhibited during light and dark conditions. Results showed that 3-step flicks were 1.4× (P = 0.006) more likely to occur in oxic conditions than anoxic conditions with mean values of 18 flicks (95% CI = 0.4, n = 53) identified in oxic regions compared to 13 (95% CI = 0.5, n = 38) at anoxic areas. In contrast, run and reverse search patterns were more frequent in anoxic regions with a mean value of 15 (95% CI = 0.7, n = 46), compared to a mean value of 10 (95% CI = 0.8, n = 29) at oxic regions. Straight swimming search patterns remained similar across oxic and anoxic regions with a mean value of 13 (95% CI = 0.7, n = oxic: 13, anoxic: 14). V. coralliilyticus remained motile in oxic and anoxic conditions, however, the 3-step flick search pattern occurred in oxic conditions. This result provides an approach to further investigate the 3-step flick.

The role of diatom nanostructures in biasing diffusion to improve uptake in a patchy nutrient environment

BACKGROUND

Diatoms are important single-celled autotrophs that dominate most lit aquatic environments and are distinguished by surficial frustules with intricate designs of unknown function.

PRINCIPAL FINDINGS

We show that some frustule designs constrain diffusion to positively alter nutrient uptake. In nutrient gradients of 4 to 160 times over <5 cm, the screened-chambered morphology of Coscincodiscus sp. biases the nutrient diffusion towards the cell by at least 3.8 times the diffusion to the seawater. In contrast, the open-chambers of Thalassiosira eccentrica produce at least a 1.3 times diffusion advantage to the membrane over Coscincodiscus sp. when nutrients are homogeneous.

SIGNIFICANCE

Diffusion constraint explains the success of particular diatom species at given times and the overall success of diatoms. The results help answer the unresolved question of how adjacent microplankton compete. Furthermore, diffusion constraint by supramembrane nanostructures to alter molecular diffusion suggests that microbes compete via supramembrane topology, a competitive mechanism not considered by the standard smooth-surface equations used for nutrient uptake nor in microbial ecology and cell physiology.

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.

Phosphoinositides in chemotaxis

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

Investigating circular dorsal ruffles through varying substrate stiffness and mathematical modeling

Circular dorsal ruffles (CDRs) are transient actin-rich ringlike structures that form on the dorsal surface of growth-factor stimulated cells. However, the dynamics and mechanism of formation of CDRs are still unknown. It has been observed that CDR formation leads to stress fibers disappearing near the CDRs. Because stress fiber formation can be modified by substrate stiffness, we examined the effect of substrate stiffness on CDR formation by seeding NIH 3T3 fibroblasts on glass and polydimethylsiloxane substrates of varying stiffnesses from 20 kPa to 1800 kPa. We found that increasing substrate stiffness increased the lifetime of the CDRs. We developed a mathematical model of the signaling pathways involved in CDR formation to provide insight into this lifetime and size dependence that is linked to substrate stiffness via Rac-Rho antagonism. From the model, increasing stiffness raised mDia1-nucleated stress fiber formation due to Rho activation. The increased stress fibers present increased replenishment of the G-actin pool, therefore prolonging Arp2/3-nucleated CDR formation due to Rac activation. Negative feedback by WAVE-related RacGAP on Rac explained how CDR actin propagates as an excitable wave, much like wave propagation in other excitable medium, e.g., nerve signal transmission.

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

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

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

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

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.

A Cut Cell Method for Simulating Spatial Models of Biochemical Reaction Networks in Arbitrary Geometries

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells and is second order in space and time. We use our method to simulate several models of signaling systems in realistic cell morphologies obtained from live cell images and examine the effects of geometry on signal transduction.

SIMULATING BIOCHEMICAL SIGNALING NETWORKS IN COMPLEX MOVING GEOMETRIES

Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast.

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.

Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks

The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

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.

Histone Deacetylase 7 Silencing Alters Endothelial Cell Migration, a Key Step in Angiogenesis

Global inhibition of class I and II histone deacetylases (HDACs) impairs angiogenesis. Herein, we have undertaken the identification of the specific HDAC(s) with activity that is necessary for the development of blood vessels. Using small interfering RNAs, we observed that HDAC7 silencing in endothelial cells altered their morphology, their migration, and their capacity to form capillary tube-like structures in vitro but did not affect cell adhesion, proliferation, or apoptosis. Among several factors known to be involved in angiogenesis, platelet-derived growth factor-B ( PDGF-B ) and its receptor ( PDGFR -β) were the most upregulated genes following HDAC7 silencing. We demonstrated that their increased expression induced by HDAC7 silencing was partially responsible for the inhibition of endothelial cell migration. In addition, we have also shown that treatment of endothelial cells with phorbol 12-myristate 13-acetate resulted in the exportation of HDAC7 out of the nucleus through a protein kinase C/protein kinase D activation pathway and induced, similarly to HDAC7 silencing, an increase in PDGF-B expression, as well as a partial inhibition of endothelial cell migration. Collectively, these data identified HDAC7 as a key modulator of endothelial cell migration and hence angiogenesis, at least in part, by regulating PDGF-B/PDGFR-β gene expression. Because angiogenesis is required for tumor progression, HDAC7 may represent a rational target for therapeutic intervention against cancer.

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.

Key role of local regulation in chemosensing revealed by a new molecular interaction-based modeling method

The signaling network underlying eukaryotic chemosensing is a complex combination of receptor-mediated transmembrane signals, lipid modifications, protein translocations, and differential activation/deactivation of membrane-bound and cytosolic components. As such, it provides particularly interesting challenges for a combined computational and experimental analysis. We developed a novel detailed molecular signaling model that, when used to simulate the response to the attractant cyclic adenosine monophosphate (cAMP), made nontrivial predictions about Dictyostelium chemosensing. These predictions, including the unexpected existence of spatially asymmetrical, multiphasic, cyclic adenosine monophosphate–induced PTEN translocation and phosphatidylinositol-(3,4,5)P₃ generation, were experimentally verified by quantitative single-cell microscopy leading us to propose significant modifications to the current standard model for chemoattractant-induced biochemical polarization in this organism. Key to this successful modeling effort was the use of “Simmune,” a new software package that supports the facile development and testing of detailed computational representations of cellular behavior. An intuitive interface allows user definition of complex signaling networks based on the definition of specific molecular binding site interactions and the subcellular localization of molecules. It automatically translates such inputs into spatially resolved simulations and dynamic graphical representations of the resulting signaling network that can be explored in a manner that closely parallels wet lab experimental procedures. These features of Simmune were critical to the model development and analysis presented here and are likely to be useful in the computational investigation of many aspects of cell biology.

Cells can orient their migration in response to small local differences in the concentration of extracellular chemicals (chemoattractants). Understanding this process (chemosensing) requires analyzing the time and position-dependent behavior of the signaling molecules within the responding cell, making it an especially interesting challenge for both experimental and computational investigation. Here, the authors report the development and testing of a new detailed molecular model of the chemosensing apparatus of the amoeba Dictyostelium discoidium reacting to the chemoattractant cyclic adenosine monophosphate. Computer simulations performed using this model predicted unexpected and previously unreported patterns of changes in the concentration and location of two important intracellular signaling molecules. These predictions were experimentally verified using microscopy, suggesting the need for modifications to the current “standard” model of eukaryotic chemosensing. The high degree of detail in their model was made possible by a new software suite called “Simmune,” which allows biologists to enter information about molecular interactions using a graphical interface. Without requiring the user to write any equations, the software automatically constructs the overall reaction network, simulates the model, and provides several ways to view the biochemistry of simulated cells. This new tool should help biologists to translate qualitative representations of cell biological processes into quantitative, predictive models.

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

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

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

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