Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "back-propagate" effects upstream of the target, specifically resulting in increased steady-state upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.

Contact inhibition of proliferation is a hallmark of normal epithelial cells. By contrast, cancer cells over-ride this key constraint and proliferate in a contact-independent manner, leading to tumor formation (Hanahan and Weinberg, 2000). Contact inhibition is enforced in a rich microenvironment that includes conflicting mitogenic stimuli, such as soluble growth factors. Antagonistic interactions between growth factors and cell-cell contact are mediated through several mechanisms involving the atypical cadherin, Fat (protocadherin Fat 1), the ERM family proteins, Merlin and Expanded, the Hippo-YAP pathway and interactions between cadherins and growth factor receptors (Curto et al., 2007;Hamaratoglu et al., 2006;Lampugnani et al., 2003;Lampugnani et al., 2006;Yin and Pan, 2007).We recently demonstrated that this crosstalk has quantitative implications for contact inhibition in a microenvironment that includes the mitogen EGF (epidermal growth factor) (Kim et al., 2009). Cell-cell contact does not act as an autonomous switch and is titrated against the level of EGF to determine the net effect on cell proliferation. Only when the level of EGF is below a threshold amount does cell-cell contact inhibit proliferation, leading to a spatial pattern in proliferation in epithelial cell clusters. Furthermore, this threshold is a tuneable property. Enhancing cell-cell interactions either specifically by overexpressing E-cadherin or non-specifically by crowding cells in a micropatterned region elevates the EGF threshold. These quantitative features of contact inhibition are captured in a state diagram model (supplementary material Fig. S1).The state diagram model provides a quantitative framework for the contact dependence of cell proliferation. Cell cycle progression, however, is regulated by cell adhesion not only to its neighbors, but also to the ECM. In non-transformed cells, adhesion to the ECM is required for a full mitogenic response to growth factor stimulation (Lee and Juliano, 2004). The loss of ECM-dependent proliferation leads to anchorage-independent proliferation, another hallmark of cancer cells (Assoian, 1997). However, how anchoragedependent and contact-dependent proliferation are inter-related remains to be elucidated. This issue is particularly relevant in many physiological contexts in which epithelial cells are exposed to soluble growth factors while adhered to both an underlying ECM and to neighboring cells. How does the three-way crosstalk among cell-cell contact, ECM and growth factors quantitatively affect cell cycle regulation? How does the ECM factor into or modify the state diagram model?To begin to examine these questions, we focused on a physiologically significant property of the ECM: its mechanical compliance. Changes in ECM stiffness are associated with disease progression. A prominent example is the stiffening of the ECM during cancer progression and its role in metastasis and disruption of tissue architecture (Butcher et al., 2009;Levental et al., 2009). Matrix stiffness is now broadly app...

Because integrin-mediated signals are transferred through a physical architecture and synergistic biochemical network whose properties are not well defined, quantitative relationships between extracellular integrin-ligand binding events and key intracellular responses are poorly understood. We begin to address this by quantifying integrin-mediated FAK and ERK2 responses in CHO cells for varied ␣ 5 ␤ 1 expression level and substratum fibronectin density. Plating cells on fibronectin-coated surfaces initiated a transient, biphasic ERK2 response, the magnitude and kinetics of which depended on integrin-ligand binding properties. Whereas ERK2 activity initially increased with a rate proportional to integrin-ligand bond number for low fibronectin density, the desensitization rate was independent of integrin and fibronectin amount but proportional to the ERK2 activity level with an exponential decay constant of 0.3 (؎ 0.08) min ؊1. Unlike the ERK2 activation time course, FAK phosphorylation followed a superficially disparate time course. However, analysis of the early kinetics of the two signals revealed them to be correlated. The initial rates of FAK and ERK2 signal generation exhibited similar dependence on fibronectin surface density, with both rates monotonically increasing with fibronectin amount until saturating at high fibronectin density. Because of this similar initial rate dependence on integrin-ligand bond formation, the disparity in their time courses is attributed to differences in feedback regulation of these signals. Whereas FAK phosphorylation increased to a steady-state level as new integrin-ligand bond formation continued during cell spreading, ERK2 activity was decoupled from the integrin-ligand stimulus and decayed back to a basal level. Accordingly, we propose different functional metrics for representing these two disparate dynamic signals: the steady-state tyrosine phosphorylation level for FAK and the integral of the pulse response for ERK2. These measures of FAK and ERK2 activity were found to correlate with short term cell-substratum adhesivity, indicating that signaling via FAK and ERK2 is proportional to the number of integrin-fibronectin bonds.Integrins are adhesion receptors that not only provide the mechanical link between the cell and the extracellular matrix (ECM) 1 that is essential for adhesion, spreading, and migration (1, 2), but also generate intracellular signals that affect multiple cell functions (3-5). Altered cell behavior due to aberrant regulation of these signals results in pathologies, such as cancer, in which loss of integrin signaling-based control of cell cycle progression leads to anchorage-independent cell growth and tumor formation (6). Because of these significant and wideranging regulatory roles, modulating integrin-mediated signals may provide powerful targets for disease therapy. Furthermore, since integrins interface cells to biomaterials, biomimetic surfaces may be designed to instigate appropriate integrin-mediated signals to elicit desired cell behavior on...

Key Words biochemical circuits, biomolecular networks, biophysical interactions, mechanotransduction s Abstract Strategies for rationally manipulating cell behavior in cell-based technologies and molecular therapeutics and understanding effects of environmental agents on physiological systems may be derived from a mechanistic understanding of underlying signaling mechanisms that regulate cell functions. Three crucial attributes of signal transduction necessitate modeling approaches for analyzing these systems: an ever-expanding plethora of signaling molecules and interactions, a highly interconnected biochemical scheme, and concurrent biophysical regulation. Because signal flow is tightly regulated with positive and negative feedbacks and is bidirectional with commands traveling both from outside-in and inside-out, dynamic models that couple biophysical and biochemical elements are required to consider information processing both during transient and steady-state conditions. Unique mathematical frameworks will be needed to obtain an integrated perspective on these complex systems, which operate over wide length and time scales. These may involve a two-level hierarchical approach wherein the overall signaling network is modeled in terms of effective "circuit" or "algorithm" modules, and then each module is correspondingly modeled with more detailed incorporation of its actual underlying biochemical/biophysical molecular interactions.

The breast tumor microenvironment (TMEN) is a unique niche where protein fibers help to promote invasion and metastasis. Cells migrating along these fibers are constantly interacting with each other. How cells respond to these interactions has important implications. Cancer cells that circumnavigate or slide around other cells on protein fibers take a less tortuous path out of the primary tumor; conversely, cells that turn back upon encountering other cells invade less efficiently. The contact response of migrating cancer cells in a fibrillar TMEN is poorly understood. Here, using high-aspect ratio micropatterns as a model fibrillar platform, we show that metastatic cells overcome spatial constraints to slide effectively on narrow fiber-like dimensions, whereas nontransformed MCF-10A mammary epithelial cells require much wider micropatterns to achieve moderate levels of sliding. Downregulating the cell-cell adhesion protein, E-cadherin, enables MCF-10A cells to slide on narrower micropatterns; meanwhile, introducing exogenous E-cadherin in metastatic MDA-MB-231 cells increases the micropattern dimension at which they slide. We propose the characteristic fibrillar dimension (CFD) at which effective sliding is achieved as a metric of sliding ability under spatial confinement. Using this metric, we show that metastasis-promoting genetic perturbations enhance cell sliding and reduce CFD. Activation of ErbB2 combined with downregulation of the tumor suppressor and cell polarity regulator, PARD3, reduced the CFD, in agreement with their cooperative role in inducing metastasis in vivo. The CFD was further reduced by a combination of ErbB2 activation and transforming growth factor β stimulation, which is known to enhance invasive behavior. These findings demonstrate that sliding is a quantitative property and a decrease in CFD is an effective metric to understand how multiple genetic hits interact to change cell behavior in fibrillar environments. This quantitative framework sheds insights into how genetic perturbations conspire with fibrillar maturation in the TMEN to drive the invasive behavior of cancer cells.