Autocrine loops with positive feedback enable context-dependent cell signaling

We describe a mechanism for context-dependent cell signaling mediated by autocrine loops with positive feedback. We demonstrate that the composition of the extracellular medium can critically influence the intracellular signaling dynamics induced by extracellular stimuli. Specifically, in the epidermal growth factor receptor (EGFR) system, amplitude and duration of mitogen-activated protein kinase (MAPK) activation are modulated by the positive-feedback loop formed by the EGFR, the Ras-MAPK signaling pathway, and a ligand-releasing protease. The signaling response to a transient input is short-lived when most of the released ligand is lost to the cellular microenvironment by diffusion and/or interaction with an extracellular ligand-binding component. In contrast, the response is prolonged or persistent in a cell that is efficient in recapturing the endogenous ligand. To study functional capabilities of autocrine loops, we have developed a mathematical model that accounts for ligand release, transport, binding, and intracellular signaling. We find that context-dependent signaling arises as a result of dynamic interaction between the parts of an autocrine loop. Using the model, we can directly interpret experimental observations on context-dependent responses of autocrine cells to ionizing radiation. In human carcinoma cells, MAPK signaling patterns induced by a short pulse of ionizing radiation can be transient or sustained, depending on cell type and composition of the extracellular medium. On the basis of our model, we propose that autocrine loops in this, and potentially other, growth factor and cytokine systems may serve as modules for context-dependent cell signaling.     

Homeostatic signaling: the positive side of negative feedback

Synaptic homeostasis provides a means for neurons and circuits to maintain stable function in the face of perturbations such as developmental or activity-dependent changes in synapse number or strength. These forms of plasticity are thought to utilize negative feedback signaling to sense some aspect of activity, compare this with an internal set point, and then adjust synaptic properties to keep activity close to this set point. However, the molecular identity of these signaling components has not been firmly established. Recent work suggests that there are likely to be multiple forms of synaptic homeostasis, mediated by distinct signaling pathways and with distinct expression mechanisms. These include presynaptic forms that depend on retrograde signaling to presynaptic Ca(2+) channels, and postsynaptic forms influenced by BDNF, TNFalpha and Arc signaling. Current challenges include matching signaling elements to their functions (i.e. as detectors of activity, as part of the set-point mechanism and/or as effectors of synaptic change), and fitting these molecular candidates into a unified view of the signaling pathways that underlie synaptic homeostasis.     

Modeling genetic switches with positive feedback loops

In this paper, we develop a new methodology to design synthetic genetic switch networks with multiple genes and time delays, by using monotone dynamical systems. We show that the networks with only positive feedback loops have no stable oscillation but stable equilibria whose stability is independent of the time delays. In other words, such systems have ideal properties for switch networks and can be designed without consideration of time delays, because the systems can be reduced from functional spaces to Euclidian spaces. Therefore, we can ensure that the designed switches function correctly even with uncertain delays. We first prove the basic properties of the genetic networks composed of only positive feedback loops, and then propose a procedure to design the switches, which drastically simplifies analysis of the switches and makes theoretical analysis and design tractable even for large-scaled systems. Finally, to demonstrate our theoretical results, we show biologically plausible examples by designing a synthetic genetic switch with experimentally well investigated lacI, tetR, and cI genes for numerical simulation.     

Sprouty: a common antagonist of FGF and EGF signaling pathways in Drosophila

Extracellular factors such as FGF and EGF control various aspects of morphogenesis, patterning and cellular proliferation in both invertebrates and vertebrates. In most systems, it is primarily the distribution of these factors that controls the differential behavior of the responding cells. Here we describe the role of Sprouty in eye development. Sprouty is an extracellular protein that has been shown to antagonize FGF signaling during tracheal branching in Drosophila. It is a novel type of protein with a highly conserved cysteine-rich region. In addition to the embryonic tracheal system, sprouty is also expressed in other tissues including the developing eye imaginal disc, embryonic chordotonal organ precursors and the midline glia. In each of these tissues, EGF receptor signaling is known to participate in the control of the correct number of neurons or glia. We show that, in all three tissues, the loss of sprouty results in supernumerary neurons or glia, respectively. Furthermore, overexpression of sprouty in wing veins and ovarian follicle cells, two other tissues where EGF signaling is required for patterning, results in phenotypes that resemble the loss-of-function phenotypes of Egf receptor. These results suggest that Sprouty acts as an antagonist of EGF as well as FGF signaling pathways. These receptor tyrosine kinase-mediated pathways may share not only intracellular signaling components but also extracellular factors that modulate the strength of the signal.     

The interaction of positive and negative sensory feedback loops in dynamic regulation of a motor pattern

In many rhythmic behaviors, phasic sensory feedback modifies the motor pattern. This modification is assumed to depend on feedback sign (positive vs. negative). While on a phenomenological level feedback sign is well defined, many sensory pathways also process antagonistic, and possibly contradictory, sensory information. We here model the locust flight pattern generator and proprioceptive feedback provided by the tegula wing receptor to test the functional significance of sensory pathways processing antagonistic information. We demonstrate that the tegula provides delayed positive feedback via interneuron 301, while all other pathways provide negative feedback. Contradictory to previous assumptions, the increase of wing beat frequency when the tegula is activated during flight is due to the positive feedback. By use of an abstract model we reveal that the regulation of motor pattern frequency by sensory feedback critically depends on the interaction of positive and negative feedback, and thus on the weighting of antagonistic pathways.     

Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops

ABSTRACT: BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.     

DSulfatase-1 fine-tunes Hedgehog patterning activity through a novel regulatory feedback loop

Sulfs are secreted sulfatases that catalyse removal of sulfate from Heparan Sulfate Proteoglycans (HSPGs) in the extracellular space. These enzymes are well known to regulate a number of crucial signalling pathways during development. In this study, we report that DSulfatase-1 (DSulf1), the unique Drosophila Sulf protein, is a regulator of Hedgehog (Hh) signalling during wing development. DSulf1 activity is required in both Hh source and Hh receiving cells for proper positioning of Hh target gene expression boundaries. As assessed by loss- and gain-of-function experiments in specific compartments, DSulf1 displays dual functions with respect to Hh signalling, acting as a positive regulator in Hh producing cells and a negative regulator in Hh receiving cells. In either domain, DSulf1 modulates Hh distribution by locally lowering the concentration of the morphogen at the apical pole of wing disc cells. Thus, we propose that DSulf1, by its desulfation catalytic activity, lowers Hh/HSPG interaction in both Hh source and target fields, thereby enhancing Hh release from its source of production and reducing Hh signalling activity in responding cells. Finally, we show that Dsulf1 pattern of expression is temporally regulated and depends on EGFR signalling, a Hh-dependent secondary signal in this tissue. Our data reveal a novel Hh regulatory feedback loop, involving DSulf1, which contributes to maintain and stabilise expression domains of Hh target genes during wing disc development.     

Equilibria and stability of a class of positive feedback loops

Positive feedback loops are common regulatory elements in metabolic and protein signalling pathways. The length of such feedback loops determines stability and sensitivity to network perturbations. Here we provide a mathematical analysis of arbitrary length positive feedback loops with protein production and degradation. These loops serve as an abstraction of typical regulation patterns in protein signalling pathways. We first perform a steady state analysis and, independently of the chain length, identify exactly two steady states that represent either biological activity or inactivity. We thereby provide two formulas for the steady state protein concentrations as a function of feedback length, strength of feedback, as well as protein production and degradation rates. Using a control theory approach, analysing the frequency response of the linearisation of the system and exploiting the Small Gain Theorem, we provide conditions for local stability for both steady states. Our results demonstrate that, under some parameter relationships, once a biological meaningful on steady state arises, it is stable, while the off steady state, where all proteins are inactive, becomes unstable. We apply our results to a three-tier feedback of caspase activation in apoptosis and demonstrate how an intermediary protein in such a loop may be used as a signal amplifier within the cascade. Our results provide a rigorous mathematical analysis of positive feedback chains of arbitrary length, thereby relating pathway structure and stability.     

Cytokinesis through biochemical–mechanical feedback loops

Cytokinesis is emerging as a control system defined by interacting biochemical and mechanical modules, which form a system of feedback loops. This integrated system accounts for the regulation and kinetics of cytokinesis furrowing and demonstrates that cytokinesis is a whole-cell process in which the global and equatorial cortices and cytoplasm are active players in the system. Though originally defined in Dictyostelium, features of the control system are recognizable in other organisms, suggesting a universal mechanism for cytokinesis regulation and contractility.     

Roles of positive and negative feedback in biological systems

We discuss the influence of positive and negative feedback on the stability of a system, which is not clear-cut, and involves complex, mathematical problems. We show in particular that positive feedback can have a stabilising effect on some systems. We also point out the role that positive feedback plays in the digital treatment of signals required by cellular signalling, drawing on analogies from electronics, and the role that negative feedback plays in making a system robust against alteration of its parameters. Both positive and negative feedback can be seen as important enhancers of the properties of biological systems.     

Delay model of circadian gene expression with two negative feedback loops

In this theoretical paper we propose a quantitative minimal model for circadian gene expression based on two negative feedback loops. We perform numerical simulations to analyse its dynamics and parameter sensitivities in free-running conditions, and verify the entrainability by a single periodic driver. We furthermore apply two simultaneously acting external drivers, leading to aperiodic oscillations in the case of a single-loop system. These can be turned into regular periodic oscillations by introduction of a second loop. Our studies confirm the increasing evidence that multiple feedback loops increase the robustness of regulatory systems, and stress the particular situation of systems that are close to transition from free-running oscillation to steady-state behaviour. We discuss possible molecular realisations of the featured feedback loops and suggest the application of complex patterns of external stimulation as a generally useful approach to assess the functionality of models of circadian systems.     

Scaffolding protein Grb2-associated binder 1 sustains epidermal growth factor-induced mitogenic and survival signaling by multiple positive feedback loops

Grb2-associated binder 1 (GAB1) is a scaffold protein involved in numerous interactions that propagate signaling by growth factor and cytokine receptors. Here we explore in silico and validate in vivo the role of GAB1 in the control of mitogenic (Ras/MAPK) and survival (phosphatidylinositol 3-kinase (PI3K)/Akt) signaling stimulated by epidermal growth factor (EGF). We built a comprehensive mechanistic model that allows for reliable predictions of temporal patterns of cellular responses to EGF under diverse perturbations, including different EGF doses, GAB1 suppression, expression of mutant proteins, and pharmacological inhibitors. We show that the temporal dynamics of GAB1 tyrosine phosphorylation is significantly controlled by positive GAB1-PI3K feedback and negative MAPK-GAB1 feedback. Our experimental and computational results demonstrate that the essential function of GAB1 is to enhance PI3K/Akt activation and extend the duration of Ras/MAPK signaling. By amplifying positive interactions between survival and mitogenic pathways, GAB1 plays the critical role in cell proliferation and tumorigenesis.     

Differential effects of aging on estrogen negative and positive feedback

Recent studies have demonstrated an age-related decline in gonadotropins and a decrease in pituitary responsiveness to GnRH, indicating that aging influences the neuroendocrine components of the female reproductive axis independently of changes in ovarian function. To determine whether aging might also affect the luteinizing hormone (LH) negative and positive feedback responses to gonadal steroids, we administered a controlled, graded sex steroid infusion to 11 younger (45-56 yr) and nine older (70-80 yr) postmenopausal women (PMW) in whom endogenous ovarian steroids and peptides are uniformly low. The doses of estradiol (E(2)) and progesterone (P) were chosen to mimic levels across the normal follicular phase and have been shown previously to induce negative followed by positive feedback on LH. Similar E(2) and P levels were achieved in younger and older PMW (P = 0.4 and 0.3, respectively) and produced a biphasic LH response in all subjects. The early decline in LH to 53% of baseline was not different in older vs. younger PMW. However, the positive feedback effect was attenuated in older compared with younger PMW (peak LH 144.4 ± 19.5 vs. 226.8 ± 22.3 IU/l, respectively, P = 0.01). In conclusion, these studies in PMW demonstrate preservation of short-term steroid negative and positive feedback in response to exogenous E(2) and P with aging. Attenuation of positive feedback in older compared with younger PMW is consistent with previous reports of declining GnRH responsiveness with aging.