The EGFR phosphatase RPTPγ is a redox-regulated suppressor of promigratory signaling.

Spatially organized reaction dynamics between proto-oncogenic epidermal growth factor receptor (EGFR) and protein tyrosine phosphatases determine EGFR phosphorylation dynamics in response to growth factors and thereby cellular behavior within developing tissues. We show that the reaction dynamics of mutual inhibition between RPTPγ phosphatase and autocatalytic ligandless EGFR phosphorylation enable highly sensitive promigratory EGFR signaling responses to subnanomolar EGF levels, when < 5% receptors are occupied by EGF. EGF thereby triggers an autocatalytic phospho-EGFR reaction by the initial production of small amounts of phospho-EGFR through transient, asymmetric EGF-EGFR2 dimers. Single cell RPTPγ oxidation imaging revealed that phospho-EGFR induces activation of NADPH oxidase, which in turn inhibits RPTPγ-mediated dephosphorylation of EGFR, tilting the autocatalytic RPTPγ/EGFR toggle switch reaction towards ligandless phosphorylated EGFR. Reversibility of this reaction to EGF is maintained by the constitutive phosphatase activity of endoplasmic reticulum-associated TCPTP. This RPTPγ/EGFR reaction at the plasma membrane causes promigratory signaling that is separated from proliferative signaling induced by accumulated, liganded, phosphorylated EGF-EGFR in endosomes. Accordingly, loss of RPTPγ results in constitutive promigratory signaling from phosphorylated EGFR monomers. RPTPγ is thus a suppressor of promigratory oncogenic but not of proliferative EGFR signaling.

Robustness and timing of cellular differentiation through population-based symmetry breaking.

During mammalian development and homeostasis, cells often transition from a multilineage primed state to one of several differentiated cell types that are marked by the expression of mutually exclusive genetic markers. These observations have been classically explained by single-cell multistability as the dynamical basis of differentiation, where robust cell-type proportioning relies on pre-existing cell-to-cell differences. We propose a conceptually different dynamical mechanism in which cell types emerge and are maintained collectively by cell-cell communication as a novel inhomogeneous state of the coupled system. Differentiation can be triggered by cell number increase as the population grows in size, through organisation of the initial homogeneous population before the symmetry-breaking bifurcation point. Robust proportioning and reliable recovery of the differentiated cell types following a perturbation is an inherent feature of the inhomogeneous state that is collectively maintained. This dynamical mechanism is valid for systems with steady-state or oscillatory single-cell dynamics. Therefore, our results suggest that timing and subsequent differentiation in robust cell-type proportions can emerge from the cooperative behaviour of growing cell populations during development.

Cell-cell communication through FGF4 generates and maintains robust proportions of differentiated cell types in embryonic stem cells.

During embryonic development and tissue homeostasis, reproducible proportions of differentiated cell types are specified from populations of multipotent precursor cells. Molecular mechanisms that enable both robust cell-type proportioning despite variable initial conditions in the precursor cells, and the re-establishment of these proportions upon perturbations in a developing tissue remain to be characterized. Here, we report that the differentiation of robust proportions of epiblast-like and primitive endoderm-like cells in mouse embryonic stem cell cultures emerges at the population level through cell-cell communication via a short-range fibroblast growth factor 4 (FGF4) signal. We characterize the molecular and dynamical properties of the communication mechanism and show how it controls both robust cell-type proportioning from a wide range of experimentally controlled initial conditions, as well as the autonomous re-establishment of these proportions following the isolation of one cell type. The generation and maintenance of reproducible proportions of discrete cell types is a new function for FGF signaling that might operate in a range of developing tissues.

Organization at criticality enables processing of time-varying signals by receptor networks.

How cells utilize surface receptors for chemoreception is a recurrent question spanning between physics and biology over the past few decades. However, the dynamical mechanism for processing time-varying signals is still unclear. Using dynamical systems formalism to describe criticality in non-equilibrium systems, we propose generic principle for temporal information processing through phase space trajectories using dynamic transient memory. In contrast to short-term memory, dynamic memory generated via "ghost" attractor enables signal integration depending on stimulus history and thereby uniquely promotes integrating and interpreting complex temporal growth factor signals. We argue that this is a generic feature of receptor networks, the first layer of the cell that senses the changing environment. Using the experimentally established epidermal growth factor sensing system, we propose how recycling could provide self-organized maintenance of the critical receptor concentration at the plasma membrane through a simple, fluctuation-sensing mechanism. Processing of non-stationary signals, a feature previously attributed only to neural networks, thus uniquely emerges for receptor networks organized at criticality.

Growth factor-dependent ErbB vesicular dynamics couple receptor signaling to spatially and functionally distinct Erk pools.

Growth factor-dependent vesicular dynamics allow cells to regulate the spatial distribution of growth factor receptors and thereby their coupling to downstream signaling effectors that guide cellular responses. We found that the ErbB ligands epidermal growth factor (EGF) and heregulin (HRG) generated distinct spatiotemporal patterns of cognate receptor activities to activate distinct subcellular pools of the extracellular signal-regulated kinase (Erk). Sustained plasma membrane activity of the receptor tyrosine kinases ErbB2/ErbB3 signaled to Erk complexed with the scaffold protein KSR to promote promigratory EphA2 phosphorylation and cellular motility upon HRG stimulation. In contrast, receptor-saturating EGF stimuli caused proliferation-inducing transient activation of cytoplasmic Erk due to the rapid internalization of EGF receptors (EGFR or ErbB1) toward endosomes. Paradoxically, promigratory signaling mediated by Erk complexed to KSR was sustained at low EGF concentrations by vesicular recycling that maintained steady-state amounts of active, phosphorylated EGFR at the plasma membrane. Thus, the effect of ligand identity and concentration on determining ErbB vesicular dynamics constitutes a mechanism by which cells can transduce growth factor composition through spatially distinct Erk pools to enable functionally diverse cellular responses.

Interdependence between EGFR and Phosphatases Spatially Established by Vesicular Dynamics Generates a Growth Factor Sensing and Responding Network.

The proto-oncogenic epidermal growth factor receptor (EGFR) is a tyrosine kinase whose sensitivity to growth factors and signal duration determines cellular behavior. We resolve how EGFR's response to epidermal growth factor (EGF) originates from dynamically established recursive interactions with spatially organized protein tyrosine phosphatases (PTPs). Reciprocal genetic PTP perturbations enabled identification of receptor-like PTPRG/J at the plasma membrane and ER-associated PTPN2 as the major EGFR dephosphorylating activities. Imaging spatial-temporal PTP reactivity revealed that vesicular trafficking establishes a spatially distributed negative feedback with PTPN2 that determines signal duration. On the other hand, single-cell dose-response analysis uncovered a reactive oxygen species-mediated toggle switch between autocatalytically activated monomeric EGFR and the tumor suppressor PTPRG that governs EGFR's sensitivity to EGF. Vesicular recycling of monomeric EGFR unifies the interactions with these PTPs on distinct membrane systems, dynamically generating a network architecture that can sense and respond to time-varying growth factor signals.

Spatial cycles mediated by UNC119 solubilisation maintain Src family kinases plasma membrane localisation.

The peripheral membrane proto-oncogene Src family protein tyrosine kinases relay growth factor signals to the cytoplasm of mammalian cells. We unravel the spatial cycles of solubilisation, trapping on perinuclear membrane compartments and vesicular transport that counter entropic equilibration to endomembranes for maintaining the enrichment and activity of Src family protein tyrosine kinases at the plasma membrane. The solubilising factor UNC119 sequesters myristoylated Src family protein tyrosine kinases from the cytoplasm, enhancing their diffusion to effectively release Src family protein tyrosine kinases on the recycling endosome by localised Arl2/3 activity. Src is then trapped on the recycling endosome via electrostatic interactions, whereas Fyn is quickly released to be kinetically trapped on the Golgi by palmitoyl acyl-transferase activity. Vesicular trafficking from these compartments restores enrichment of the Src family protein tyrosine kinases to the plasma membrane. Interference with these spatial cycles by UNC119 knockdown disrupts Src family protein tyrosine kinase localisation and signalling activity, indicating that UNC119 could be a drug target to affect oncogenic Src family protein tyrosine kinase signalling.The peripheral membrane proto-oncogene Src family protein tyrosine kinases (SFKs) transmit growth factor signals to the cytoplasm. Here the authors show that the solubilising factor UNC119 sequesters myristoylated SFKs to maintain its enrichment at the plasma membrane to enable signal transduction.

Ubiquitination switches EphA2 vesicular traffic from a continuous safeguard to a finite signalling mode.

Autocatalytic phosphorylation of receptor tyrosine kinases (RTKs) enables diverse, context-dependent responses to extracellular signals but comes at the price of autonomous, ligand-independent activation. Using a conformational biosensor that reports on the kinase activity of the cell guidance ephrin receptor type-A (EphA2) in living cells, we observe that autonomous EphA2 activation is suppressed by vesicular recycling and dephosphorylation by protein tyrosine phosphatases 1B (PTP1B) near the pericentriolar recycling endosome. This spatial segregation of catalytically superior PTPs from RTKs at the plasma membrane is essential to preserve ligand responsiveness. Ligand-induced clustering, on the other hand, promotes phosphorylation of a c-Cbl docking site and ubiquitination of the receptor, thereby redirecting it to the late endosome/lysosome. We show that this switch from cyclic to unidirectional receptor trafficking converts a continuous suppressive safeguard mechanism into a transient ligand-responsive signalling mode.

Modeling the spread of multiple concurrent contagions on networks.

Many contagions spread over various types of communication networks and their spreading dynamics have been extensively studied in the literature. Here we propose a general model for the concurrent spread of an arbitrary number of contagions in complex networks. The model is stochastic and runs in discrete time, and includes two widely used mechanisms by which a node can change its state. The first, termed the spontaneous state change mechanism, describes spontaneous transition to another state, while the second, termed the contact-induced state change mechanism, describes acquiring other contagions due to contact with the neighbors. We consider reactive discrete-time spreading processes of multiple concurrent contagions where time steps are of finite size without neglecting the possibility of multiple infecting events in a single time step. An essential element for making the model numerically tractable is the use of an approximation for the probability that a node transits to a specific state given any set of neighboring states. Different transmission probabilities may be present between each pair of states. We also derive corresponding continuous-time equations that are simple and intuitive. The model includes many well-known epidemic and rumor spreading models as a special case and it naturally captures spreading processes in multiplex networks.

Identifying communities by influence dynamics in social networks.

Communities are not static; they evolve, split and merge, appear and disappear, i.e., they are the product of dynamical processes that govern the evolution of a network. A good algorithm for community detection should not only quantify the topology of the network but incorporate the dynamical processes that take place on the network. We present an algorithm for community detection that combines network structure with processes that support the creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes the node's involvement in each community. This way, in addition to the overlapping communities, we can identify nodes that are good followers of their leader and also nodes with no clear community involvement that serve as proxies between several communities and that are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results, including other possible applications.