Feedback Loop Model Research Articles

Evidence for a cell cycle checkpoint that senses branched actin in the lamellipodium

Recent evidence indicates that branched actin might control cell progression through G1 in addition to lamellipodium protrusion.

Molecular mechanism of the “feedback loop” model of carcinogenesis

It is commonly accepted that cancer is a genetic disease. The current prevailing theory of carcinogenesis is the somatic mutation theory of carcinogenesis and metastasis (SMT). This theory postulates that mutations in epithelial cells lead to uncontrolled proliferation of tumor cells in a cell-autonomous fashion. This cell-autonomy is increasingly criticized. Current data suggest that the tumor microenvironment is also strongly involved in carcinogenesis. Recently, we published a hypothesis that considers the important contribution of the tumor microenvironment in carcinogenesis and complements the classical clonal evolution model.Essentially, this “feedback loop model” (FBM) postulates that the physiological communication between cancer cells and stromal cells in inflammatory or proliferative conditions is altered by anomalous signal processing within the parenchymal cells. The inability of parenchymal cells to correctly finalize the intercellular communication might result in a perpetuation of the activated state of cells and the tumor micromilieu. The FBM is unique among the tissue-based models because in this model tumor and stromal cells interact together in a reciprocal manner to form the cancer phenotype. Contrary to the SMT, the FBM postulates that mutated genes act in a cell-heteronomous fashion, not in a cell-autonomously fashion.

Abstract PR7: Visualizing the dynamic and heterogeneous responses of single cells to inhibitors of the growth factor signaling network

Abstract The growth factor signaling network, including the Akt, ERK, mTOR and other pathways, is deregulated in many diseases and is a prominent target for therapeutic inhibitors. The effectiveness of these inhibitors is limited by the existence of homeostatic feedback loops that act to restore signaling and attenuate the effects of inhibition. To obtain the single-cell data necessary to fully characterize these rapid and heterogeneous responses, we developed a library of mammary epithelial cells stably expressing over 90 fluorescent protein-based reporters. This library comprises reporters for: cellular processes including cell death, cell cycle, protein translation, and metabolism; kinases including ERK, Akt and AMPK; and microRNAs involved in the regulation of cellular differentiation and stress response. Using high-throughput live-cell microscopy and computational image analysis, we monitored the responses of these pathways to inhibitors of EGFR, ErbB2, PI3K, mTOR, MEK, Raf, and Bcl-2. This analysis revealed unexpectedly dynamic fluctuations in key pathways including ERK, Akt, and glycolysis. In one example, inhibition of EGFR transformed constitutive ERK activity into intermittent bursts of activity ranging in duration from 20-90 minutes with high cell-to-cell variability. Characterization of ERK activity pulses revealed that their frequency depended on the level of EGF receptor activity and that their duration was essential for controlling the commitment to cell proliferation. In sharp contrast, inhibition of MEK altered the amplitude, rather than the frequency, of ERK activity. Using these live-cell measurements in combination with high content immunofluorescence, we constructed a computational model of feedback loops controlling ERK activity pulses. Quantitative mapping of ERK output to proliferation rate revealed a distinct and exquisitely sensitive threshold of ERK output required for proliferation. Potential strategies for reducing ERK output below this threshold and effectively blocking proliferation include dual inhibition of upstream regulators or intermittent high-dose inhibition. Single-cell quantitative analysis of inhibitor responses is now being extended to other pathways to identify signaling dynamics and information transfer properties that enable effective therapeutic targeting of the network. This proffered talk is also presented as Poster A19. Citation Format: John Albeck, Yin P. Hung, Gregory Leya, Gary Yellen, Gordon Mills, Joan Brugge. Visualizing the dynamic and heterogeneous responses of single cells to inhibitors of the growth factor signaling network [abstract]. In: Proceedings of the AACR Special Conference on Chemical Systems Biology: Assembling and Interrogating Computational Models of the Cancer Cell by Chemical Perturbations; 2012 Jun 27-30; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2012;72(13 Suppl):Abstract nr PR7.

Regulation of thyroid hormone sensitivity by differential expression of the thyroid hormone receptor during Xenopus metamorphosis

During amphibian metamorphosis, a series of dynamic changes occur in a predetermined order. Hind limb morphogenesis begins in response to low levels of thyroid hormone (TH) in early prometamorphosis, but tail muscle cell death is delayed until climax, when TH levels are high. It takes about 20 days for tadpoles to grow from early prometamorphosis to climax. To study the molecular basis of the timing of tissue-specific transformations, we introduced thyroid hormone receptor (TR) expression constructs into tail muscle cells of Xenopus tadpoles. The TR-transfected tail muscle cells died upon exposure to a low level of thyroxine (T4). This cell death was suggested to be mediated by type 2 iodothyronine deiodinase (D2) that converts T4 to T3-the more active form of TH. D2 mRNA was induced in the TR-overexpressing cells by low levels of TH. D2 promoter contains a TH-response element (TRE) with a lower affinity for TR. These results show that the TR transfection confers the ability to respond to physiological concentrations of TH at early prometamorphosis to tail muscle cells through D2 activity and promotes TH signaling. We propose the positive feedback loop model to amplify the cell's ability to respond to low levels of T4.

Antiinflammatory Role of MUC1 Mucin during Infection with NontypeableHaemophilus influenzae

MUC1 (or Muc1 in nonhuman species) is a membrane-tethered mucin expressed on the apical surface of mucosal epithelia (including those of the airways) that suppresses Toll-like receptor (TLR) signaling. We sought to determine whether the anti-inflammatory effect of MUC1 is operative during infection with nontypeable Haemophilus influenzae (NTHi), and if so, which TLR pathway was affected. Our results showed that: (1) a lysate of NTHi increased the early release of IL-8 and later production of MUC1 protein by A549 cells in dose-dependent and time-dependent manners, compared with vehicle control; (2) both effects were attenuated after transfection of the cells with a TLR2-targeting small interfering (si) RNA, compared with a control siRNA; (3) the NTHi-induced release of IL-8 was suppressed by an overexpression of MUC1, and was enhanced by the knockdown of MUC1; (4) the TNF-α released after treatment with NTHi was sufficient to up-regulate MUC1, which was completely inhibited by pretreatment with a soluble TNF-α receptor; and (5) primary murine tracheal surface epithelial (MTSE) cells from Muc1 knockout mice exhibited an increased in vitro production of NTHi-stimulated keratinocyte chemoattractant compared with MTSE cells from Muc1-expressing animals. These results suggest a hypothetical feedback loop model whereby NTHi activates TLRs (mainly TLR2) in airway epithelial cells, leading to the increased production of TNF-α and IL-8, which subsequently up-regulate the expression of MUC1, resulting in suppressed TLR signaling and decreased production of IL-8. This report is the first, to the best of our knowledge, demonstrating that the inflammatory response in airway epithelial cells during infection with NTHi is controlled by MUC1 mucin, mainly through the suppression of TLR2 signaling.

Service innovation and competitive advantage with the perspective of system dynamics - using China Mobile as an example

To explore the mutual strategic and conditional relationship between service innovation and competitive advantage, this paper used case studies and a literature research to explore how competitive advantage can be reached through service innovation. Making use of system dynamics, (suitable for the analysis of dynamic, complex non-linear relationships), the analysis of systematic behaviour and the causal feedback loop model, this paper summarised the key driving factors that shape competitive edge into three core competencies: the ability to respond to the environment, strategy adaptation, and learning and innovation capacities. In this study, the tactical actions of the China Mobile Communications Corporation (CMCC), whose service innovation surpasses that of its competitors, is used as an example. The path of its development services, strategic choices and innovation performance are used as a case study to verify this study’s argument and to offer a reference to the speculation on academic research and v...

Neuroendocrine regulation of food intake

Despite a global obesity epidemic suggesting that human physiology is unable to prevent unhealthy gains in body weight, ample evidence indicates that weight can be tightly regulated. Food intake regulation is complex and in this article we will present a basic endocrine feedback loop model of energy homeostasis. Next, integration of long-term regulation with short-term, meal specific regulation and satiety will be discussed. Finally, the role of adiposity signals in modulation of food reward will be highlighted. A basic understanding of the structure-function of these systems will inform the challenges of clinical care for those with disorders of energy balance.

A fluorescence spotlight on the clockwork development and metabolism of bone

Biological phenomena that exhibit periodic activity are often referred as biorhythms or biological clocks. Among these, circadian rhythms, cyclic patterns reflecting a 24-h cycle, are the most obvious in many physiological activities including bone growth and metabolism. In the late 1990s, several clock genes were isolated and their primary structures and functions were identified. The feedback loop model of transcriptional factors was proposed to work as a circadian core oscillator not only in the suprachiasmatic nuclei of the anterior hypothalamus, which is recognized as the mammalian central clock, but also in various peripheral tissues including cartilage and bone. Looking back to embryonic development, the fundamental architecture of skeletal patterning is regulated by ultradian clocks that are defined as biorhythms that cycle more than once every 24 h. As post-genomic approaches, transcriptome analysis by micro-array and bioimaging assays to detect luminescent and fluorescent signals have been exploited to uncover a more comprehensive set of genes and spatio-temporal regulation of the clockwork machinery in animal models. In this review paper, we provide an overview of topics related to these molecular clocks in skeletal biology and medicine, and discuss how fluorescence imaging approaches can contribute to widening our views of this realm of biomedical science.

Definition of a Diagnostic Window Prior to the Onset of Clinically Apparent Acute Graft-Versus-Host Disease.

AbstractAbstract 3746Acute graft-versus-host disease (aGvHD) is an immune syndrome after allogeneic hematopoietic cell transplantation (allo-HCT) caused by alloreactive donor T cells that attack the gastrointestinal tract, liver and skin. Thus, early T cell migration patterns to these organs could provide first cues for the onset of aGvHD. Hence, a unique surface marker profile of donor T cells at early time points after allo-HCT may be an indicator for patients at risk of aGVHD. Therefore, we analyzed the course of donor T cell activation, proliferation and homing in a clinical relevant murine MHC minor mismatch (miHAg) allo-HCT model to define critical time points and marker profiles for the detection of alloreactive T cells.Luciferase-labeled C57Bl/6 (H-2b) T cells plus bone marrow cells were transplanted into conditioned (8 Gy) MHC major mismatched Balb/c (H-2d) or miHAg Balb/b (H-2b) recipients. Donor T cell migration was visualized by in vivo bioluminescence imaging (BLI) and cells were characterized by multiparameter flow cytometry for 30 consecutive days after allo-HCT. GVHD scoring was performed by histopathology. Donor T cells proliferated exclusively in secondary lymphoid organs until day+3 (initiation phase) before migrating via the peripheral blood into target organs (effector phase). This occured in both models, MHC major mismatch and miHAg allo-HCT, which resulted in hyper-acute (starting at day+6) or acute GVHD (starting at day+21), respectively. In the hyper-acute scenario one wave of T cell migration starting at day+4 sufficed to cause lethal aGVHD. We detected a 4000-fold increase in CD4 and a 1500-fold increase in CD8 donor T cell numbers in the peripheral blood between day+3 and day+6 in this model. In contrast, in the more clinical relevant miHAg allo-HCT model we found 3 waves of T cell migration with peaks at days +6, +11 and +15 after allo-HCT. In the peripheral blood CD4 T cells increased 20-fold, CD8 T cells 50-fold between day+3 and day+6, but more than 40-fold (CD4) and 400-fold (CD8) between day+3 and day+11. After the third peak on day+15 a period followed when we could only detect very few migrating donor T cells in the peripheral blood before aGvHD became clinically apparent on day+21. Next, we asked whether we could identify alloreactive T cells by testing a large panel of surface markers at the defined migration peaks. Indeed, allogeneic T cells upregulated certain homing receptors at these peaks (e.g. at day+11: α4β7 integrin: 27% of CD4 T cells, 3.4×104/ml, 60% of CD8 T cells, 1.6×105/ml; P-selectin ligand: 28% of CD4 T cells, 3.5×104/ml, 35% of CD8 T cells, 9.1×104/ml). In contrast, syngeneic transplanted mice only showed a constant low expression level of those receptors (e.g. at day+11: α4β7 integrin: 20% of CD4 T cells, 9.6×103/ml, 5% of CD8 T cells, 3.1×103/ml; P-selectin ligand: 17% of CD4 T cells, 8.5×103/ml, 10% of CD8 T cells, 6.6×103/ml). However, other markers such as CD44 could be found on more than 80% of all donor T cells in allogeneic or syngeneic recipients.Our results in this clinical relevant mouse model show accelerating waves of T cell migration consistent with an enhancing feedback loop model of aGvHD pathogenesis. The homing receptor expression profile of donor T cells correlated with critical migration waves and clearly differed between mice with or without aGvHD. The assessment of critical time points frame a diagnostic window for a potential predictive test based on the dynamic change of the T cell homing receptor profile after allo-HCT. This preclinical study now awaits to be evaluated in patients undergoing allo-HCT. Disclosures:No relevant conflicts of interest to declare.

Induction of SENP1 in Endothelial Cells Contributes to Hypoxia-driven VEGF Expression and Angiogenesis

SENP1 (SUMO-specific protease 1) has been shown to be essential for the stability and activity of hypoxia-inducible factor 1 (HIF-1α) under hypoxia conditions. However, it is unknown how SENP1 activation and hypoxia signaling are coordinated in the cellular response to hypoxia. Here, we report the essential role of SENP1 in endothelial cells as a positive regulator of hypoxia-driven VEGF production and angiogenesis. SENP1 expression is increased in endothelial cells following exposure to hypoxia. Silencing of HIF-1α blocks SENP1 expression in cell response to hypoxia. Mutation of the hypoxia response element (HRE) on the Senp1 promoter abolishes its transactivation in response to hypoxia. Moreover, silencing of SENP1 expression decreases VEGF production and abrogates the angiogenic functions of endothelial cell. We also find that the elongated endothelial cells in embryonic brain section and vascular endothelial cells in embryonic renal glomeruli in Senp1(-/-) mice are markedly reduced than those in wild-type. Thus, these results show that hypoxia implies a positive feedback loop mediated by SENP1. This feedback loop is important in VEGF production, which is essential for angiogenesis in endothelial cells.

Using theories of behaviour change to inform interventions for addictive behaviours

This paper reviews a set of theories of behaviour change that are used outside the field of addiction and considers their relevance for this field. Ten theories are reviewed in terms of (i) the main tenets of each theory, (ii) the implications of the theory for promoting change in addictive behaviours and (iii) studies in the field of addiction that have used the theory. An augmented feedback loop model based on Control Theory is used to organize the theories and to show how different interventions might achieve behaviour change. Briefly, each theory provided the following recommendations for intervention: Control Theory: prompt behavioural monitoring, Goal-Setting Theory: set specific and challenging goals, Model of Action Phases: form 'implementation intentions', Strength Model of Self-Control: bolster self-control resources, Social Cognition Models (Protection Motivation Theory, Theory of Planned Behaviour, Health Belief Model): modify relevant cognitions, Elaboration Likelihood Model: consider targets' motivation and ability to process information, Prototype Willingness Model: change perceptions of the prototypical person who engages in behaviour and Social Cognitive Theory: modify self-efficacy. There are a range of theories in the field of behaviour change that can be applied usefully to addiction, each one pointing to a different set of modifiable determinants and/or behaviour change techniques. Studies reporting interventions should describe theoretical basis, behaviour change techniques and mode of delivery accurately so that effective interventions can be understood and replicated.

Cytoplasmic Ca2+ Dynamics under the Interplay between the Different IP3R Gating Models and the Plasma Membrane Ca2+ Influx

The cytoplasmic Ca oscillations are investigated under the effect of CRAC channels in non-excitable cells (especially in T cells). The oscillatory Ca2+ signals can be modulated as the amplitude-, frequency- and mixed amplitude-frequency modulation modes dependent on the different IP3R gating models. Bifurcation analyses show that Ca2+ signals in the single positive feedback loop model is a mixed modulation mode. In contrast, Ca2+ signals in the Mak–McBride–Foskett model demonstrates approximately the frequency modulation mode only with slight amplitude shifts.

The making of a bushy grass with a branched flowering stem

In Arabidopsis thaliana, a eudicot species, the transcription factor LFY is expressed throughout the floral meristem and promotes their formation. The expression pattern of the rice LFY homolog-RFL shows distinct differences from that of its Arabidopsis counterpart. In the March issue of PNAS (2008) we have shown the temporally-regulated high-level expression of RFL in the apical meristem is necessary for its transition to an inflorescence meristem and thus to initiate flowering. RFL controls the time taken for flowering, by activating integrators of flowering signals such as OsSOC1 and RFT1. Further, the dynamic pattern of RFL expression in the branching inflorescence meristem (panicle) and in vegetative axillary meristems (tiller buds) is required for panicle branching and tiller outgrowth. Thus RFL functions determine the architecture of the rice plant. Here we propose a plausible model for a regulatory feedback loop between RFL and OsSOC1/RFT1 in controlling the vegetative to flowering phase transition. We discuss the possibility that non-cell autonomous RFL functions may also regulate signaling the net outcome of which determines the rice plant body plan.Addendum to: Rao NN, Prasad K, Kumar PR, Vijayraghavan U. Distinct regulatory role for RFL, the rice LFY homolog, in determining flowering time and plant architecture. Proc Natl Acad Sci USA 2008; 105:3646-51.

Feedback loop of immune regulation by CD4 +CD25 + Treg

Naturally occurring regulatory T cells (Tregs), residing in CD4 +CD25 + fraction, are important in the maintenance of immune homeostasis. One of the functional characteristics of Tregs is close relationship between suppressive activity and anergy in vitro. Meanwhile, many in vitro assays have observed Treg proliferation and suppressive activities in different settings, i.e., in the absence and presence of CD25 − responder cells. If the presence of responder cells affect the proliferation of Tregs, comparison between the two settings would be inappropriate. In the present study, we traced proliferation as well as suppressive activities of Tregs in the same setting of coculture in response to varying concentrations of anti-CD3 and anti-CD28. Quantitative analysis using two parameters, precursor frequency and CD25 mean fluorescence intensity, reflecting early and late proliferative responsiveness, respectively, showed that proliferation of Tregs was dependent on the responder cells and proliferating Tregs preserved suppressive activities. Transwell assay and neutralization assay showed that the enhancement of Treg proliferation by the responder cells was mediated through secreted IL-2. Quantitative analysis also showed distinct mode of suppression by Tregs according to the presence or absence of anti-CD28. In the absence of anti-CD28, Tregs suppressed the initial proliferation, whereas in the presence of anti-CD28, Tregs suppressed only the late expansion of the responder cells by lowering CD25 expression. Considering that Tregs cannot produce IL-2 by themselves while they constitutively express CD25 (IL-2R α), dependency of Tregs on their target of suppression (responder cells) for proliferation supports the model for feedback loop of immune regulation by Tregs.

A Positive Feedback Signal Transduction Loop Determines Timing of Cerebellar Long-Term Depression

Synaptic activity produces short-lived second messengers that ultimately yield a long-term depression (LTD) of cerebellar Purkinje cells. Here, we test the hypothesis that these brief second messenger signals are translated into long-lasting biochemical signals by a positive feedback loop that includes protein kinase C (PKC) and mitogen-activated protein kinase. Histochemical "epistasis" experiments demonstrate the reciprocal activation of these kinases, and physiological experiments--including the use of a light-activated protein kinase--demonstrate that such reciprocal activation is required for LTD. Timed application of enzyme inhibitors reveals that this positive feedback loop causes PKC to be active for more than 20 min, allowing sufficient time for LTD expression. Such regenerative mechanisms may sustain other long-lasting forms of synaptic plasticity and could be a general mechanism for prolonging signal transduction networks.

A role for neurological memory feedback loops in psychiatric depression

This hypothesis proposes a neurological system model of memory feedback loops which demonstrates the difference in specific memory processing between depressed and non-depressed people. It is suggested that non-depressed people have a functioning neurological memory feedback loop system which enables them to re-appraise and be more circumspect with given situations. In contrast to this, it is suggested that depressed people do not have a functioning memory feedback loop and it is this that leads to the deficit of circumspect and considered thinking. This could explain why depressed people commonly exhibit instantaneous negative reactions to events that pre-morbidity were considered to be pleasurable or interesting.

Towards manipulative neuroscience based on brain-network -interface

Event Abstract Back to Event Towards manipulative neuroscience based on brain-network -interface Mitsuo Kawato1* 1 ATR Computational Neuroscience Labs, Japan The cerebellar internal model theory postulates that the cerebellar cortex acquires many internal models of controlled objects, dynamical processes in the external world dependent on long-term depression (LTD) of Purkinje cells. It predicts that the climbing fiber inputs to Purkinje cells carry the feedback motor command and can supervise learning of inverse dynamics models. Many experimental supports were obtained from the ventral paraflocculus of the cerebellum during monkey control of ocular following responses. fMRI studies mapped forward and inverse models of manipulated objects and tools in the cerebellar cortex. Kinetic models of LTD [1,2] suggest a cascade of excitable and bistable dynamical processes, which may resolve plasticity-stability dilemma at single spine level. That is, even a single pulse of climbing fiber input combined with an early train of several parallel fiber pulses can induce Ca2+ induced Ca2+ release via IP3 receptors on ER. The MAPK positive feedback loop leaky integrates resulting large Ca2+ elevation and if it crosses the threshold then the state moves to the depressed equilibrium. These models explain diverse LTD experiments and clearly demonstrate that LTD is a supervised learning rule, and not anti-Hebbian as erroneously characterized. The MAPK positive feedback loop model [1] was recently supported by a Ca2+ photo-uncaging and imaging experiment [3] that supports LTD all-or-none character. In [3], the most important information within the system, Ca2+ can be measured and manipulated directly, thus the theory was quite rigorously proved. At the system level, the cerebellar internal models for arm movements are still debated and we need to develop a method to directly manipulate information. In our "Understanding brain by Creating Brain"-approach, high-performance humanoid robots have been developed, and sensory-motor coordination problems were investigated. We explored several computational theories such as MOSAIC, imitation learning, biologically motivated robot biped locomotion, modular and hierarchical reinforcement learning models. Our paradigms include computational-model based imaging and non-invasive decoding of neural representations. However, we got frustrated that most experiments can show just temporal correlation between data and theory but not causality, unlike the above spine-level LTD story. We hope that manipulative neuroscience based on real time feedback of decoded neural information could be a resolution to this difficulty. Hierarchical Bayesian approach to combine fMRI and MEG, or NIRS and EEG, or neural decoding with machine learning techniques, and real-time control of robots with decoded information are expected to be key technological elements. Demonstrations of real-time robot hand control by decoded information from fMRI (http://www.atr.jp/html/topics/press_060526_e.html) in collaboration with Honda, control of a humanoid robot locomotion-like movements from monkey brain in collaboration with Miguel Nicolelis [4], prediction of wrist joint angular acceleration from the primary motor cortex currents estimated by hierarchical Bayesian MEG, or estimation of visual target velocity from MST currents, etc could be technical bases for this new approach.

Modeling the Hes1 Oscillator

Somitogenesis describes the segmentation of vertebrate embryonic bodies, which is thought to be induced by ultradian clocks (i.e., clocks with relatively short cycles compared to circadian clocks). One candidate for such a clock is the bHLH factor Hes1, forming dimers which repress the transcription of its own encoding gene. Most models for such small autoregulative networks are based on delay equations where a Hill function represents the regulation of transcription. The aim of the present paper is to estimate the Hill coefficient in the switch of an Hes1 oscillator and to suggest a more detailed model of the autoregulative network. The promoter of Hes1 consists of three to four binding sites for Hes1 dimers. Using the sparse data from literature, we find, in contrast to other statements in literature, that there is not much evidence for synergistic binding in the regulatory region of Hes1, and that the Hill coefficient is about three. As a model for the negative feedback loop, we use a Goodwin system and find sustained oscillations for systems with a large enough number of linear differential equations. By a suitable variation of the number of equations, we provide a rational lower bound for the Hill coefficient for such a system. Our results suggest that there exist additional nonlinear processes outside of the regulatory region of Hes1.

Cycling of CRYPTOCHROME Proteins Is Not Necessary for Circadian-Clock Function in Mammalian Fibroblasts

An interlocked transcriptional-translational feedback loop (TTFL) is thought to generate the mammalian circadian clockwork in both the central pacemaker residing in the hypothalamic suprachiasmatic nuclei and in peripheral tissues. The core circadian genes, including Period1 and Period2 (Per1 and Per2), Cryptochrome1 and Cryptochrome2 (Cry1 and Cry2), Bmal1, and Clock are indispensable components of this biological clockwork. The cycling of the PER and CRY clock proteins has been thought to be necessary to keep the mammalian clock ticking. We provide a novel cell-permeant protein approach for manipulating cryptochrome protein levels to evaluate the current transcription and translation feedback model of the circadian clockwork. Cell-permeant cryptochrome proteins appear to be functional on the basis of several criteria, including the abilities to (1) rescue circadian properties in Cry1(-/-)Cry2(-/-) mouse fibroblasts, (2) act as transcriptional repressors, and (3) phase shift the circadian oscillator in Rat-1 fibroblasts. By using cell-permeant cryptochrome proteins, we demonstrate that cycling of CRY1, CRY2, and BMAL1 is not necessary for circadian-clock function in fibroblasts. These results are not supportive of the current version of the transcription and translation feedback-loop model of the mammalian clock mechanism, in which cycling of the essential clock proteins CRY1 and CRY2 is thought to be necessary.

Dynamics of a Minimal Model of Interlocked Positive and Negative Feedback Loops of Transcriptional Regulation by cAMP-Response Element Binding Proteins

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.