Different effects of redundant feedback loops on a bistable switch

Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as “signed activation time”. We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.

Markevich et al. developed a computational model for a mechanism, not previously described, whereby signaling pathways can exhibit bistable behavior and switch between stable "on" and "off" states. Mitogen-activated protein kinase (MAPK) signaling pathways, which play critical roles in cell proliferation, differentiation, and apoptosis, generally function as a three-tiered cascade in which an activated (phosphorylated) kinase at one level phosphorylates and thereby activates the kinase at the subsequent level. To be fully activated, these MAPKs, MAPK kinases (MAPKKs), and MAPKK kinases must be phosphorylated at two sites. The MAPK cascades are regulated by multiple feedback loops, and the existence of either positive or double-negative feedback regulation is generally thought to be necessary for a cascade to function as a bistable system. Markevich et al. , however, present a model in which bistability of the MAPK signaling pathway arises from a distributive kinetic mechanism for the dual phosphorylation and dephosphorylation of the kinase and is independent of feedback regulation. (A distributive mechanism implies that the kinase or phosphatase releases the monophosphorylated intermediate, which must then interact with enzyme again before it is converted into the final doubly phosphorylated or completely dephosphorylated state.) Their model was consistent with the reported kinetic properties of the extracellular signal-regulated kinase (ERK) kinase (MEK) and phosphatase (MKP3). The authors suggest that multisite phosphorylation, which takes place on proteins involved in many signaling systems, may represent a widespread mechanism for conferring switch-like behavior on various signaling systems. N. I. Markevich, J. B. Hoek, B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J. Cell Biol . 164 , 353-359 (2004). [Abstract] [Full Text]

A graph-theoretic analysis of metabolic regulation in linear pathways with multiple feedback loops and branched pathways

KRAS, YAP, and obesity in pancreatic cancer: A signaling network with multiple loops.

Control of cell fraction and population recovery during tissue regeneration in stem cell lineages

Boolean Dynamics of Biological Networks with Multiple Coupled Feedback Loops

Multiple feedback loops achieve robust localization of wingless expression in Drosophila notum development

We demonstrated broadening of the comb bandwidth by constructing a feedback loop in a Mach-Zehnder-modulator-based flat comb generator. By multiple-modulation using the feedback loop, a broadband comb signal was generated.

Integration of nutrient and growth factor signaling pathways through mammalian TOR (mTOR) plays a central role in the regulation of cell growth. However, the mechanism of integration of these two signals in mTOR activation is largely unknown. Moreover, the nutritional input involving amino acids is yet to be characterized. Excess amino acid conditions, such as in obesity and protein-rich diets, are known to regulate insulin signaling through mTOR activation resulting in insulin resistance. Here, we develop a dynamic model to identify the regulatory role of amino acids in mTOR activation and to study its effect on insulin signaling in relation to multiple feedback loops present in the insulin signaling pathway. The analysis revealed that amino acids bring about multiple effects in the regulation of mTOR that might be represented by a single mechanism. Insulin signaling was demonstrated to operate between two extreme conditions involving tumor growth and insulin resistance, with multiple feedback loops tightly controlling and maintaining a robust insulin response. The state of insulin resistance was characterized by a decrease in the time lag or an increase in the magnitude of the negative feedback loop facilitated through perturbations such as excess input of amino acids. Such a condition disturbs the delicate balance between positive and negative feedback loops to yield an insulin-resistant state.

The G1/S transition is a crucial decision point in the cell cycle. At G1/S, there is an abrupt switch from a state of high cyclin-dependent kinases (CDK) inhibitor (CKI) levels and low S-phase CDK activity to a state of high S-phase CDK activity and degraded CKI. In budding yeast, this transition is triggered by phosphorylation of the Cdk1 inhibitor Sic1 at multiple sites by G1-phase CDK (Cln1,2-Cdk1) and S-phase CDK (Clb5,6-Cdk1) complexes. Using mathematical modeling we demonstrate that the mechanistic basis for the abruptness of the G1/S transition is the highly specific phosphorylation of Sic1 by S-phase CDK complex. This switch is generated by a double-negative feedback loop in which S-CDK1 phosphorylates Sic1, thus targeting it for destruction, and thereby liberating further S-CDK1 from the inhibitory Sic1-S-CDK1 complex. Our model predicts that the abruptness of the switch depends upon a strong binding affinity within the Sic1-S-CDK inhibitory complex. In vitro phosphorylation analysis using purified yeast proteins revealed that free Clb5-Cdk1 can create positive feedback by phosphorylating Sic1 that is bound in the inhibitory complex, and that Sic1 inhibits Clb5-Cdk1 with a sub-nanomolar inhibition constant. Our model also predicts that if the G1-phase CDK complex is too efficient at targeting Sic1 for destruction, then G1/S becomes a smooth and readily reversible transition. We propose that the optimal role for the G1-phase CDK in the switch would not be to act as a kinase activity directly responsible for abrupt degradation of CKI, but rather to act as a priming signal that initiates a positive feedback loop driven by emerging free S-phase CDK.

The characterization of multiport networks generalized analysis of linear networks estimation of network response single loop feedback single loop feedback amplifier design dual loop feedback current mode feedback electrical noise multiple loop feedback networks.

Feedback loop reasoning is an important stepping-stone toward systems thinking.To date, studies on feedback loop reasoning in ecology have focused on college students, while only a limited effort has been made to investigate a more general systems thinking of students at the lower elementary level.The goal of this study is to investigate how elementary students reason about feedback loop relationships among interdependent organisms (predator-prey), and address the knowledge sources of students as part of context of reasoning about this topic.This study was conducted in three countries, with 128 first through fourth grader participants from Japan, Lebanon, and the United States.These students participated in semi-structured clinical interviews focusing on the predator-and-prey relationships.We found that the majority of students used one-way causal reasoning, and only a few students reasoned using twoway causality with multiple feedback loops in the predator-prey relationship.

Multiple feedback loops are key to a robust dynamic performance of tryptophan regulation in Escherichia coli

After approximately 50 years of circadian research, especially in selected circadian model systems (Drosophila, Neurospora, Gonyaulax and, more recently, cyanobacteria and mammals), we appreciate the enormous complexity of the circadian programme in organisms and cells, as well as in physiological and molecular circuits. Many of our insights into this complexity stem from experimental reductionism that goes as far as testing the interaction of molecular clock components in heterologous systems or in vitro. The results of this enormous endeavour show circadian systems that involve several oscillators, multiple input pathways and feedback loops that contribute to specific circadian qualities but not necessarily to the generation of circadian rhythmicity. For a full appreciation of the circadian programme, the results from different levels of the system eventually have to be put into the context of the organism as a whole and its specific temporal environment. This review summarizes some of the complexities found at the level of organisms, cells and molecules, and highlights similar strategies that apparently solve similar problems at the different levels of the circadian system.

We present a dynamical model of the gene network controlling flower development in Arabidopsis thaliana. The network is centered at the regulation of the floral organ identity genes (AP1, AP2, AP3, PI and AG) and ends with the transcription factor complexes responsible for differentiation of floral organs. We built and simulated the regulatory interactions that determine organ specificity using an extension of hybrid Petri nets as implemented in Cell Illustrator. The network topology is characterized by two main features: (1) the presence of multiple autoregulatory feedback loops requiring the formation of protein complexes, and (2) the role of spatial regulators determining floral patterning. The resulting network shows biologically coherent expression patterns for the involved genes, and simulated mutants produce experimentally validated changes in organ expression patterns. The requirement of heteromeric higher-order protein complex formation for positive autoregulatory feedback loops attenuates stochastic fluctuations in gene expression, enabling robust organ-specific gene expression patterns. If autoregulation is mediated by monomers or homodimers of proteins, small variations in initial protein levels can lead to biased production of homeotic proteins, ultimately resulting in homeosis. We also suggest regulatory feedback loops involving miRNA loci by which homeotic genes control the activity of their spatial regulators.