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.     

Coupling oscillations and switches in genetic networks

Switches (bistability) and oscillations (limit cycle) are omnipresent in biological networks. Synthetic genetic networks producing bistability and oscillations have been designed and constructed experimentally. However, in real biological systems, regulatory circuits are usually interconnected and the dynamics of those complex networks is often richer than the dynamics of simple modules. Here we couple the genetic Toggle switch and the Repressilator, two prototypic systems exhibiting bistability and oscillations, respectively. We study two types of coupling. In the first type, the bistable switch is under the control of the oscillator. Numerical simulation of this system allows us to determine the conditions under which a periodic switch between the two stable steady states of the Toggle switch occurs. In addition we show how birhythmicity characterized by the coexistence of two stable small-amplitude limit cycles, can easily be obtained in the system. In the second type of coupling, the oscillator is placed under the control of the Toggleswitch. Numerical simulation of this system shows that this construction could for example be exploited to generate a permanent transition from a stable steady state to self-sustained oscillations (and vice versa) after a transient external perturbation. Those results thus describe qualitative dynamical behaviors that can be generated through the coupling of two simple network modules. These results differ from the dynamical properties resulting from interlocked feedback loops systems in which a given variable is involved at the same time in both positive and negative feedbacks. Finally the models described here may be of interest in synthetic biology, as they give hints on how the coupling should be designed to get the required properties.     

Mitotic exit in two dimensions

Metaphase of mitosis is brought about in all eukaryotes by activation of cylin-dependent kinase (Cdk1), whereas exit from mitosis requires down-regulation of Cdk1 activity and dephosphorylation of its target proteins. In budding yeast, the completion of mitotic exit requires the release and activation of the Cdc14 protein-phosphatase, which is kept inactive in the nucleolus during most of the cell cycle. Activation of Cdc14 is controlled by two regulatory networks called FEAR (Cdc fourteen early anaphase release) and MEN (mitotic exit network). We have shown recently that the anaphase promoting protease (separase) is essential for Cdc14 activation, thereby it makes mitotic exit dependent on execution of anaphase. Based on this finding, we have proposed a new model for mitotic exit in budding yeast. Here we explain the essence of the model by phaseplane analysis, which reveals two underlying bistable switches in the regulatory network. One bistable switch is caused by mutual activation (positive feedback) between Cdc14 activating MEN and Cdc14 itself. The mitosis-inducing Cdk1 activity inhibits the activation of this positive feedback loop and thereby controlling this switch. The other irreversible switch is generated by a double-negative feedback (mutual antagonism) between mitosis inducing Cdk1 activity and its degradation machinery (APC(Cdh1)). The Cdc14 phosphatase helps turning this switch in favor of APC(Cdh1) side. Both of these bistable switches have characteristic thresholds, the first one for Cdk1 activity, while the second for Cdc14 activity. We show that the physiological behaviors of certain cell cycle mutants are suggestive for those Cdk1 and Cdc14 thresholds. The two bistable switches turn on in a well-defined order. In this paper, we explain how the activation of Cdc20 (which causes the activation of separase and a decrease of Cdk1 kinase activity) provides an initial trigger for the activation of the MEN-Cdc14 positive feedback loops, which in turn, flips the second irreversible Cdk-APC(Cdh1) switch on the APC(Cdh1) side).     

Coupled feedback loops form dynamic motifs of cellular networks

Cellular networks are composed of complicated interconnections among components, and some subnetworks of particular functioning are often identified as network motifs. Among such network motifs, feedback loops are thought to play important dynamical roles. Intriguingly, such feedback loops are very often found as a coupled structure in cellular circuits. Therefore, we integrated all the scattered information regarding the coupled feedbacks in various cellular circuits and investigated the dynamical role of each coupled structure. Finally, we discovered that coupled positive feedbacks enhance signal amplification and bistable characteristics; coupled negative feedbacks realize enhanced homeostasis; coupled positive and negative feedbacks enable reliable decision-making by properly modulating signal responses and effectively dealing with noise.     

The PAR network: redundancy and robustness in a symmetry-breaking system

To become polarized, cells must first ‘break symmetry’. Symmetry breaking is the process by which an unpolarized, symmetric cell develops a singularity, often at the cell periphery, that is used to develop a polarity axis. The Caenorhabditis elegans zygote breaks symmetry under the influence of the sperm-donated centrosome, which causes the PAR polarity regulators to sort into distinct anterior and posterior cortical domains. Modelling analyses have shown that cortical flows induced by the centrosome combined with antagonism between anterior and posterior PARs (mutual exclusion) are sufficient, in principle, to break symmetry, provided that anterior and posterior PAR activities are precisely balanced. Experimental evidence indicates, however, that the system is surprisingly robust to changes in cortical flows, mutual exclusion and PAR balance. We suggest that this robustness derives from redundant symmetry-breaking inputs that engage two positive feedback loops mediated by the anterior and posterior PAR proteins. In particular, the PAR-2 feedback loop stabilizes the polarized state by creating a domain where posterior PARs are immune to exclusion by anterior PARs. The two feedback loops in the PAR network share characteristics with the two feedback loops in the Cdc42 polarization network of Saccharomyces cerevisiae.     

Coupled positive feedbacks provoke slow induction plus fast switching in apoptosis

Apoptosis is a form of a programmed cell death for multicellular organisms to remove unwanted or damaged cells. This critical choice of cellular fate is an all-or-none process, but its dynamics remains unraveled. The switch-like apoptotic decision has to be reliable, and once a pro-apoptotic fate is determined it requires fast and irreversible execution. One of the key regulators in apoptosis is caspase-3. Interestingly, activated caspase-3 quickly executes apoptosis, but it takes considerable time to activate it. Here, we have analyzed this "slow induction plus fast switching" mechanism of caspase-3 through mathematical modeling and computational simulation. First, we have shown that two positive feedbacks, composed of caspase-8 and XIAP, are essential for the "slow induction plus fast switching" behavior of caspase-3. Second, we have found that XIAP in the feedback loops primarily regulates induction time of caspase-3. In many cancer cells activation of caspase-3 is suppressed. Our results suggest that reinforcement of the positive feedback by XIAP, which relieves XIAP-mediated caspase-3 inhibition, might favor a pro-apoptotic cellular fate.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2

In the early embryonic cell cycle, Cdc2-cyclin B functions like an autonomous oscillator, whose robust biochemical rhythm continues even when DNA replication or mitosis is blocked. At the core of the oscillator is a negative feedback loop; cyclins accumulate and produce active mitotic Cdc2-cyclin B; Cdc2 activates the anaphase-promoting complex (APC); the APC then promotes cyclin degradation and resets Cdc2 to its inactive, interphase state. Cdc2 regulation also involves positive feedback, with active Cdc2-cyclin B stimulating its activator Cdc25 (refs 5-7) and inactivating its inhibitors Wee1 and Myt1 (refs 8-11). Under the correct circumstances, these positive feedback loops could function as a bistable trigger for mitosis, and oscillators with bistable triggers may be particularly relevant to biological applications such as cell cycle regulation. Therefore, we examined whether Cdc2 activation is bistable. We confirm that the response of Cdc2 to non-degradable cyclin B is temporally abrupt and switch-like, as would be expected if Cdc2 activation were bistable. We also show that Cdc2 activation exhibits hysteresis, a property of bistable systems with particular relevance to biochemical oscillators. These findings help establish the basic systems-level logic of the mitotic oscillator.     

Robust,tunable genetic memory from protein sequestration combined with positive feedback

Natural regulatory networks contain many interacting components that allow for fine-tuning of switching and memory properties. Building simple bistable switches, synthetic biologists have learned the design principles of complex natural regulatory networks. However, most switches constructed so far are so simple (e.g. comprising two regulators) that they are functional only within a limited parameter range. Here, we report the construction of robust, tunable bistable switches in Escherichia coli using three heterologous protein regulators (ExsADC) that are sequestered into an inactive complex through a partner swapping mechanism. On the basis of mathematical modeling, we accurately predict and experimentally verify that the hysteretic region can be fine-tuned by controlling the interactions of the ExsADC regulatory cascade using the third member ExsC as a tuning knob. Additionally, we confirm that a dual-positive feedback switch can markedly increase the hysteretic region, compared to its single-positive feedback counterpart. The dual-positive feedback switch displays bistability over a 10⁶-fold range of inducer concentrations, to our knowledge, the largest range reported so far. This work demonstrates the successful interlocking of sequestration-based ultrasensitivity and positive feedback, a design principle that can be applied to the construction of robust, tunable, and predictable genetic programs to achieve increasingly sophisticated biological behaviors.     

Kernel Architecture of the Genetic Circuitry of the Arabidopsis Circadian System

A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that at least half of the total regulatory interactions must be present to express the circadian molecular profiles observed in wild-type plants. A set of those essential interactions is called herein a kernel of the circadian system. The kernel structure unbiasedly reveals four interlocked negative feedback loops contributing to circadian rhythms, and three feedback loops among them drive the autonomous oscillation itself. Strikingly, the kernel structure, as well as the whole clock circuitry, is overwhelmingly composed of inhibitory, rather than activating, interactions between genes. We found that this tendency underlies plant circadian molecular profiles which often exhibit sharply-shaped, cuspidate waveforms. Through the generation of these cuspidate profiles, inhibitory interactions may facilitate the global coordination of temporally-distant clock events that are markedly peaked at very specific times of day. Our systematic approach resulting in experimentally-testable predictions provides insights into a design principle of biological clockwork, with implications for synthetic biology.     

Emergence of robust regulatory motifs from in silico evolution of sustained oscillation

The relationship between robustness and evolvability (easiness to evolve), and the evolutionary emergence of robust genetic circuits in biology have attracted much attention in systems biology. This paper investigates in silico the influence of the cis-regulation logic and the coupling of feedback loops on the evolvability and robustness of gene regulatory motifs that can generate sustained oscillation. Our simulation results indicate that both evolvability and robustness of the considered regulatory motifs depend on the cis-regulation logic and the way in which positive and negative feedback loops are coupled. Most interestingly, our findings suggest that robust regulatory motifs can emerge from evolution without an explicit selection pressure on robustness and adding noise in the parameters during the evolution is likely to promote the evolution of sustained oscillation.