Modeling direct positive feedback between predators and prey

Predators can have positive impacts on their prey through such mechanisms as nutrient mineralization and prey transport. These positive feedbacks have the potential to change predictions based on food web theory, such as the assertion that enrichment is destabilizing. We present a model of a simple food web, consisting of a resource, a consumer, and its predator. We assume that the predator has a direct positive effect on the consumer, by increasing the rate at which the consumer acquires resources. We consider two cases: the feedback strength is a saturating function of predator density, or it is proportional to the encounter rate between predators and prey. In both cases, the positive feedback is stabilizing, delaying or preventing the onset of oscillations due to enrichment. Positive feedback can introduce an Allee effect for the predator population, yielding multiple stable equilibria. Strong positive feedback can yield counterintuitive results such as a transient increase in consumer density following the introduction of predators, and a decrease in the resource pool following enrichment.     

Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability

Cell signaling systems that contain positive-feedback loops or double-negative feedback loops can, in principle, convert graded inputs into switch-like, irreversible responses. Systems of this sort are termed "bistable". Recently, several groups have engineered artificial bistable systems into Escherichia coli and Saccharomyces cerevisiae, and have shown that the systems exhibit interesting and potentially useful properties. In addition, two naturally occurring signaling systems, the p42 mitogen-activated protein kinase and c-Jun amino-terminal kinase pathways in Xenopus oocytes, have been shown to exhibit bistable responses. Here we review the basic properties of bistable circuits, the requirements for construction of a satisfactory bistable switch, and the recent progress towards constructing and analysing bistable signaling systems.     

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.     

Ultrasensitivity and positive feedback to promote sharp mitotic entry

In this issue, Trunnell et?al. (2011) show that in mitotic entry the positive feedback that drives the activation of cyclin-dependent kinase (Cdk) involves a very ultrasensitive step of phosphorylation of Cdc25C by Cdk, thus strongly contributing to the switch-like behavior of this essential cell-cycle transition.     

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.     

Spatial positive feedback at the onset of mitosis

Mitosis is triggered by the activation of Cdk1-cyclin B1 and its translocation from the cytoplasm to the nucleus. Positive feedback loops regulate the activation of Cdk1-cyclin B1 and help make the process irreversible and all-or-none in character. Here we examine whether an analogous process, spatial positive feedback, regulates Cdk1-cyclin B1 redistribution. We used chemical biology approaches and live-cell microscopy to show that nuclear Cdk1-cyclin B1 promotes the translocation of Cdk1-cyclin B1 to the nucleus. Mechanistic studies suggest that cyclin B1 phosphorylation promotes nuclear translocation and, conversely, nuclear translocation promotes cyclin B1 phosphorylation, accounting for the feedback. Interfering with the abruptness of Cdk1-cyclin B1 translocation affects the timing and synchronicity of subsequent mitotic events, underscoring the functional importance of this feedback. We propose that spatial positive feedback ensures a rapid, complete, robust, and irreversible transition from interphase to mitosis and suggest that bistable spatiotemporal switches may be widespread in biological regulation.     

Temporally fluctuating prey and interfering predators: a positive feedback

Prey densities often show fluctuating patterns over various timescales. Focusing on short-term, within-generation fluctuating patterns of local prey availability, we suggest that prey that show synchronized and high-amplitude fluctuations in availability experience decreased risks of predation, but also enhance the maintenance of predator interference hierarchies by affecting the relative foraging success of unequal conspecific interferers. When predators interfere with each other, they forage less intensely on prey, which benefits prey in terms of decreased predation risk. The system hence involves a positive feedback. We thus argue that short-term temporal fluctuations in local prey availability could be an important mechanism behind how interference-structured social predator systems are developed and sustained. The temporal fluctuations also have implications for the phenotypic diversity of predators, and may be involved in speciation processes.     

Directional positive feedback and pattern at an alpine tree line

Abstract. The spatial pattern at alpine tree line may be part of a feedback process in which wind plays a central role. The basic aspects of such a feedback were embedded in a cellular automaton. Spatial metrics of the patterns generated by this simulation and those of observed patterns at a windy tree line site were ordinated using Principal Component Analysis. Only the simulations that included a directionally weighted feedback fell close to the observed sites in ordination space. MANOVA indicated that the directionally weighted feedback is most important in structuring the tree line pattern, but that random hotspots for establishment and the overall steepness of the environmental gradient from forest to tundra in space also have an effect. The importance of wind in determining feedback with the spatial pattern of a canopy indicates that nonlinear reactions to climatic change are likely.     

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.     

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.     

Synthetic robust perfect adaptation achieved by negative feedback coupling with linear weak positive feedback

Unlike their natural counterparts, synthetic genetic circuits are usually fragile in the face of environmental perturbations and genetic mutations. Several theoretical robust genetic circuits have been designed, but their performance under real-world conditions has not yet been carefully evaluated. Here, we designed and synthesized a new robust perfect adaptation circuit composed of two-node negative feedback coupling with linear positive feedback on the buffer node. As a key feature, the linear positive feedback was fine-tuned to evaluate its necessity. We found that the desired function was robustly achieved when genetic parameters were varied by systematically perturbing all interacting parts within the topology, and the necessity of the completeness of the topological structures was evaluated by destroying key circuit features. Furthermore, different environmental perturbances were imposed onto the circuit by changing growth rates, carbon metabolic strategies and even chassis cells, and the designed perfect adaptation function was still achieved under all conditions. The successful design of a robust perfect adaptation circuit indicated that the top-down design strategy is capable of predictably guiding bottom-up engineering for robust genetic circuits. This robust adaptation circuit could be integrated as a motif into more complex circuits to robustly implement more sophisticated and critical biological functions.     

Presence of positive feedback in males with Klinefelter's syndrome

This study examined the effect of 17 beta-estradiol (E2) on basal and luteinizing hormone (LH)-releasing hormone (LHRH)-stimulated gonadotropin secretion in 9 patients with Klinefelter's syndrome. Intramuscular injection of E2 (10 micrograms/kg/day during 5 days) induced a rapid decrease in follicle-stimulating hormone (FSH) and LH levels. The maximum suppression was observed on day 7 (D7) for FSH [median 9.7 mIU/ml (range 4.6-37.8) vs. 21.7 mIU/ml (range 12.2-56.9)] and on D2 for LH [median 13.6 mIU/ml (range 6.8-25.2) vs. 21.2 mIU/ml (range 13-54.7)]. E2 concentrations rose and reached their peak values on D3 [median 723 pmol/l (range 517-1,247.8) vs. 110.1 pmol/l (range 68.6-227.5) on D0]. These changes were followed by a subsequent rise in LH on D4 [36.7 mIU/ml (range 19.4-77.7)]. LH response to LHRH was higher during E2 treatment: median value of absolute peaks: 156.3 mIU/ml (range 56.7-188.6) on D4 vs. 64 mIU/ml (range 38.9-131) on DO. These results demonstrate the presence of a positive feedback in patients with Klinefelter's syndrome.     

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.     

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.     

Robust neuronal symmetry breaking by Ras-triggered local positive feedback

Neuronal polarity is initiated by a symmetry-breaking event whereby one out of multiple minor neurites undergoes rapid outgrowth and becomes the axon [1]. Axon formation is regulated by phosphatidylinositol 3-kinase (PI3K)-related signaling elements [2-10] that drive local actin [11] and microtubule reorganization [3, 12], but the upstream signaling circuit that causes symmetry breaking and guarantees the formation of a single axon is not known. Here, we use live FRET imaging in hippocampal neurons and show that the activity of the small GTPase HRas, an upstream regulator of PI3K, markedly increases in the nascent axonal growth cone upon symmetry breaking. This local increase in HRas activity results from a positive feedback loop between HRas and PI3K, locally reinforced by vesicular transport of HRas to the axonal growth cone. Recruitment of HRas to the axonal growth cone is paralleled by a decrease in HRas concentration in the remaining neurites, suggesting that competition for a limited pool of HRas guarantees that only one axon forms. Mathematical modeling demonstrates that local positive feedback between HRas and PI3K, coupled to recruitment of a limited pool of HRas, generates robust symmetry breaking and formation of a single axon in the absence of extrinsic spatial cues.