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author:("well, Erik S")
1.  Stochastic models of cell protrusion arising from spatiotemporal signaling and adhesion dynamics 
Methods in cell biology  2012;110:223-241.
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 stochastic simulations results are shown, and implications of this analysis for understanding cell protrusion behavior are offered.
PMCID: PMC4117837  PMID: 22482951
2.  Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility 
Molecular Biology of the Cell  2013;24(24):3945-3955.
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.
PMCID: PMC3861089  PMID: 24152734
3.  Migrating fibroblasts reorient directionality by a metastable, PI3K-dependent mechanism 
The Journal of Cell Biology  2012;197(1):105-114.
Migrating fibroblasts reorient directionality by PI3K-dependent branching and pivoting of protrusions, a mechanism that allows fibroblasts to align with an external chemotactic gradient.
Mesenchymal cell migration as exhibited by fibroblasts is distinct from amoeboid cell migration and is characterized by dynamic competition among multiple protrusions, which determines directional persistence and responses to spatial cues. Localization of phosphoinositide 3-kinase (PI3K) signaling is thought to play a broadly important role in cell motility, yet the context-dependent functions of this pathway have not been adequately elucidated. By mapping the spatiotemporal dynamics of cell protrusion/retraction and PI3K signaling monitored by total internal reflection fluorescence microscopy, we show that randomly migrating fibroblasts reorient polarity through PI3K-dependent branching and pivoting of protrusions. PI3K inhibition did not affect the initiation of newly branched protrusions, nor did it prevent protrusion induced by photoactivation of Rac. Rather, PI3K signaling increased after, not before, the onset of local protrusion and was required for the lateral spreading and stabilization of nascent branches. During chemotaxis, the branch experiencing the higher chemoattractant concentration was favored, and, thus, the cell reoriented so as to align with the external gradient.
PMCID: PMC3317800  PMID: 22472441
4.  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 whilst ignoring or coarse-graining others, it is clear that the challenge ahead will be to characterize the couplings between them in an integrated framework.
PMCID: PMC3052860  PMID: 21305705
Cell motility; signal transduction; actin cytoskeleton; focal adhesion; mechanotransduction
5.  Probabilistic modeling and analysis of the effects of extra-cellular matrix density on the sizes, shapes, and locations of integrin clusters in adherent cells 
BMC Biophysics  2011;4:15.
Regulation of integrin binding to the specific complementary sites on extra-cellular matrix (ECM) proteins plays a major role in cell adhesion and migration. In addition to regulating single integrin-ligand bonds by affinity modulation, cells regulate their adhesiveness by forming integrin clusters. Although it is clear that cells exhibit different adhesion and migration behaviors on surfaces coated with different concentrations of ECM proteins, it is not clear if this response is mediated by changes in the availability of integrin binding sites or by differential intracellular signaling that may affect integrin binding and clustering.
To quantify how the concentration of ECM affects integrin clustering, we seeded cells expressing the integrin αIIbβ3 on different concentrations of the complementary ECM protein fibrinogen (Fg) and measured the resulting integrin cluster properties. We observed heterogeneity in the properties of integrin clusters, and to characterize this population heterogeneity we use a probabilistic modeling approach to quantify changes to the distributions of integrin cluster size, shape, and location.
Our results indicate that in response to increasing ECM density cells form smaller integrin clusters that are less elongated and closer to the cell periphery. These results suggest that cells can sense the availability of ECM binding sites and consequently regulate integrin clustering as a function of ECM density.
PMCID: PMC3179437  PMID: 21827670
6.  Stochastic Dynamics of Membrane Protrusion Mediated by the DOCK180/Rac Pathway in Migrating Cells 
Cell migration is regulated by processes that control adhesion to extracellular matrix (ECM) and force generation. While our fundamental understanding of how these control mechanisms are actuated at the molecular level (signal transduction) has been refined over many years, appreciation of their dynamics has grown more recently. Here, we formulate and analyze by stochastic simulation a quantitative model of signaling mediated by the integrin family of adhesion receptors. Nascent adhesions foster the activation of the small GTPase Rac by at least two distinct signaling pathways, one of which involves tyrosine phosphorylation of the scaffold protein paxillin and formation of multiprotein complexes containing the guanine nucleotide exchange factor DOCK180. Active Rac promotes protrusion of the cell’s leading edge, which in turn enhances the rate of nascent adhesion nucleation; we call this feedback mechanism the core protrusion cycle. Protrusion is antagonized by stable adhesions, which form by myosin-dependent maturation of nascent adhesions, and we propose here a feedforward mechanism mediated by the tyrosine kinase c-Src by which this antagonism is regulated so as to allow transient protrusion at higher densities of ECM. We show that this “buffering of inhibition” mechanism, coupled with the core protrusion cycle, is capable of tuning the frequencies of protrusion and adhesion maturation events.
PMCID: PMC2869102  PMID: 20473365
Integrins; Focal adhesions; Signal transduction; Paxillin; Src-family kinases; Myosin
7.  Stochastic Model of Integrin-Mediated Signaling and Adhesion Dynamics at the Leading Edges of Migrating Cells 
PLoS Computational Biology  2010;6(2):e1000688.
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.
Author Summary
Cell migration is fundamental to human physiology and a phenomenon of long-standing interest in cell biology. It requires the concerted regulation of several dynamic processes that mediate physical anchorage of the cell and productive generation of protrusion and traction forces that propel the cell forward. In this work, we have developed a mathematical model that describes this interplay, cast at the level of biochemical signaling pathways activated at the front of a moving cell. Based on our analysis of the model and experimental confirmation of its basic predictions, we assert that coupled, counteracting feedback loops constitute a functional switch between maintenance and stalling of the cell protrusion speed. Our model successfully explains the dependence of this switch on the abundance of adhesive molecules in the cell's immediate surroundings and sheds light on how non-muscle myosin shapes that dependence.
PMCID: PMC2829041  PMID: 20195494

Results 1-7 (7)