Summary Activation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell fate decisions, although signals propagate through shared pathways. Using modeling and experiments, we unravel how EGF and HRG generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands.
Summary: Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing.Availability and implementation: Binary packages are available at http://imc.zih.tu-dresden.de/wiki/morpheus for Linux, Mac OSX and MS Windows.Contact: walter.deback@tu-dresden.deSupplementary information: Supplementary data are available at Bioinformatics online.
We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.
Key cellular functions and developmental processes rely on cascades of GTPases. GTPases of the Rab family provide a molecular ID code to the generation, maintenance and transport of intracellular compartments. Here, we addressed the molecular design principles of endocytosis by focusing on the conversion of early endosomes into late endosomes, which entails replacement of Rab5 by Rab7. We modelled this process as a cascade of functional modules of interacting Rab GTPases. We demonstrate that intermodule interactions share similarities with the toggle switch described for the cell cycle. However, Rab5-to-Rab7 conversion is rather based on a newly characterized 'cut-out switch' analogous to an electrical safety-breaker. Both designs require cooperativity of autoactivation loops when coupled to a large pool of cytoplasmic proteins. Live cell imaging and endosome tracking provide experimental support to the cut-out switch in cargo progression and conversion of endosome identity along the degradative pathway. We propose that, by reconciling module performance with progression of activity, the cut-out switch design could underlie the integration of modules in regulatory cascades from a broad range of biological processes.
The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We introduce and describe periodic coherent structures of the CGLE, called Modulated Amplitude Waves (MAWs). MAWs of various period P occur naturally in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures occur which evolve toward defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.PACS numbers: 47.52.+j, 03.40.Kf, 05.45.+b, 47.54.+r Spatially extended systems can exhibit, when driven away from equilibrium, irregular behavior in space and time: this phenomenon is commonly referred to as spatio-temporal chaos [1]. The one-dimensional complex Ginzburg-Landau equation (CGLE):describes pattern formation near a Hopf bifurcation and has become a popular model to study spatiotemporal chaos [1][2][3][4][5][6][7][8][9][10][11][12][13]. As a function of c 1 and c 3 , the CGLE exhibits two qualitatively different spatiotemporal chaotic states known as phase chaos (when A is bounded away from zero) and defect chaos (when the phase of A displays singularities where A = 0). The transition from phase to defect chaos can either be hysteretic or continuous; in the former case, it is referred to as L 3 , in the latter as L 1 (Fig. 1). Despite intensive studies [5][6][7][8][9][10][11][12][13], the phenomenology of the CGLE and in particular its "phase"-diagram [5,7] are far from being understood. Moreover, it is under dispute whether the L 1 transition is sharp, and whether a pure phase-chaotic (i.e. defect-free) state can exist in the thermodynamic limit [9]. It is the purpose of this paper to elucidate these issues by presenting the mechanism which creates defects in transient phase chaotic states. Our analysis consists of four parts: (i) We describe a family of Modulated Amplitude Waves (MAWs), i.e., pulse-like coherent structures with a characteristic spatial period P . (ii) A bifurcation analysis of these MAWs reveals that their range of existence is limited by a saddle-node (SN) bifurcation. For all c 1 , c 3 within a certain range, we define P SN as the period of the MAW for which this bifurcation occurs. (iii) We show that for P > P SN , i.e., beyond the SN bifurcation, near-MAW structures display a nonlinear evolution to defects. It is found that, in phase chaos, near-MAWs with various P 's are created and annihilated perpetually. L1, L2 and L3 transitions (after [7]). Between the L2 and L3 curves, there is the hysteretic regime where either phase or defect chaos can occur; in the latter case, defects persist up to the L2 transition. Notice how the L1 and L3 transitions to defect chaos lie above our lower (P → ∞) bounds. Also shown are the SN locations for P = 20, 50.The transition to def...
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