Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co-existing rhythms ("splitting"). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co-culturing slices with rhythmic neonatal wild-type SCNs. These co-culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co-culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

MOTIVATION: Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran's I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus. RESULTS: We found that Moran's I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran's I accounts for the spatial organization of any interacting units. Moran's I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran's I and the traditional Kuramoto order parameter R in a complementary fashion. AVAILABILITY AND IMPLEMENTATION: Python 2.7 code of illustrative examples can be found in the Supplementary Material. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Mammals evolved an endogenous timing system to coordinate their physiology and behaviour to the 24h period of the solar day. While it is well accepted that circadian rhythms are generated by intracellular transcriptional feedback loops, it is still debated which network motifs are necessary and sufficient for generating self-sustained oscillations. Here, we systematically explore a data-based circadian oscillator model with multiple negative and positive feedback loops and identify a series of three subsequent inhibitions known as "repressilator" as a core element of the mammalian circadian oscillator. The central role of the repressilator motif is consistent with time-resolved ChIP-seq experiments of circadian clock transcription factors and loss of rhythmicity in core clock gene knockouts.

Robust synchronization is a critical feature of several systems including the mammalian circadian clock. The master circadian clock in mammals consists of about 20000 'sloppy' neuronal oscillators within the hypothalamus that keep robust time by synchronization driven by inter-neuronal coupling. The complete understanding of this synchronization in the mammalian circadian clock and the mechanisms underlying it remain an open question. Experiments and computational studies have shown that coupling individual oscillators can achieve robust synchrony, despite heterogeneity and different network topologies. But, much less is known regarding the mechanisms and circuits involved in achieving this coupling, due to both system complexity and experimental limitations. Here, we computationally study the coupling mediated by the primary coupling neuropeptide, vasoactive intestinal peptide (VIP) and its canonical receptor, VPAC2R, using the transcriptional elements and generic mode of VIP-VPAC2R signaling. We find that synchrony is only possible if VIP (an inducer of Per expression) is released in-phase with activators of Per expression. Moreover, anti-phasic VIP release suppresses coherent rhythms by moving the network into a desynchronous state. Importantly, experimentally observed rhythms in VPAC2R have little effect on network synchronization, but can improve the amplitude of the SCN network rhythms while narrowing the network entrainment range. We further show that these findings are valid across several computational network models. Thus, we identified a general design principle to achieve robust synchronization: An activating coupling agent, such as VIP, must act in-phase with the activity of core-clock promoters. More generally, the phase of coupling is as critical as the strength of coupling from the viewpoint of synchrony and entrainment.

The circadian clock is accountable for the regulation of internal rhythms in most living organisms. It allows the anticipation of environmental changes during the day and a better adaptation of physiological processes. In mammals the main clock is located in the suprachiasmatic nucleus (SCN) and synchronizes secondary clocks throughout the body. Its molecular constituents form an intracellular network which dictates circadian time and regulates clock-controlled genes. These clock-controlled genes are involved in crucial biological processes including metabolism and cell cycle regulation. Its malfunction can lead to disruption of biological rhythms and cause severe damage to the organism. The detailed mechanisms that govern the circadian system are not yet completely understood. Mathematical models can be of great help to exploit the mechanism of the circadian circuitry. We built a mathematical model for the core clock system using available data on phases and amplitudes of clock components obtained from an extensive literature search. This model was used to answer complex questions for example: how does the degradation rate of Per affect the period of the system and what is the role of the ROR/Bmal/REV-ERB (RBR) loop? Our findings indicate that an increase in the RNA degradation rate of the clock gene Period (Per) can contribute to increase or decrease of the period--a consequence of a non-monotonic effect of Per transcript stability on the circadian period identified by our model. Furthermore, we provide theoretical evidence for a potential role of the RBR loop as an independent oscillator. We carried out overexpression experiments on members of the RBR loop which lead to loss of oscillations consistent with our predictions. These findings challenge the role of the RBR loop as a merely auxiliary loop and might change our view of the clock molecular circuitry and of the function of the nuclear receptors (REV-ERB and ROR) as a putative driving force of molecular oscillations.

In host and cancer tissues, drug metabolism and susceptibility to drugs vary in a circadian (24 h) manner. In particular, the efficacy of a cell cycle specific (CCS) cytotoxic agent is affected by the daily modulation of cell cycle activity in the target tissues. Anti-cancer chronotherapy, in which treatments are administered at a particular time each day, aims at exploiting these biological rhythms to reduce toxicity and improve efficacy of the treatment. The circadian status, which is the timing of physiological and behavioral activity relative to daily environmental cues, largely determines the best timing of treatments. However, the influence of variations in tumor kinetics has not been considered in determining appropriate treatment schedules. We used a simple model for cell populations under chronomodulated treatment to identify which biological parameters are important for the successful design of a chronotherapy strategy. We show that the duration of the phase of the cell cycle targeted by the treatment and the cell proliferation rate are crucial in determining the best times to administer CCS drugs. Thus, optimal treatment times depend not only on the circadian status of the patient but also on the cell cycle kinetics of the tumor. Then, we developed a theoretical analysis of treatment outcome (TATO) to relate the circadian status and cell cycle kinetic parameters to the treatment outcomes. We show that the best and the worst CCS drug administration schedules are those with 24 h intervals, implying that 24 h chronomodulated treatments can be ineffective or even harmful if administered at wrong circadian times. We show that for certain tumors, administration times at intervals different from 24 h may reduce these risks without compromising overall efficacy.

Bioluminescence techniques allow accurate monitoring of the circadian clock in single cells. We have analyzed bioluminescence data of Per gene expression in mouse SCN neurons and fibroblasts. From these data, we extracted parameters such as damping rate and noise intensity using two simple mathematical models, one describing a damped oscillator driven by noise, and one describing a self-sustained noisy oscillator. Both models describe the data well and enabled us to quantitatively characterize both wild-type cells and several mutants. It has been suggested that the circadian clock is self-sustained at the single cell level, but we conclude that present data are not sufficient to determine whether the circadian clock of single SCN neurons and fibroblasts is a damped or a self-sustained oscillator. We show how to settle this question, however, by testing the models' predictions of different phases and amplitudes in response to a periodic entrainment signal (zeitgeber).

MOTIVATION: Periodic processes play fundamental roles in organisms. Prominent examples are the cell cycle and the circadian clock. Microarray array technology has enabled us to screen complete sets of transcripts for possible association with such fundamental periodic processes on a system-wide level. Frequently, quite large numbers of genes have been detected as periodically expressed. However, the small overlap between genes identified in different studies has cast some doubts on the reliability of the periodic expression detected. RESULTS: In this study, comparative analysis suggests that the lacking agreement between different cell-cycle studies might be due to inadequate background models for the determination of significance. We demonstrate that the choice of background model has considerable impact on the statistical significance of periodic expression. For illustration, we reanalyzed two microarray studies of the yeast cell cycle. Our evaluation strongly indicates that the results of previous analyses might have been overoptimistic and that the use of more suitable background model promises to give more realistic results. AVAILABILITY: R scripts are available on request from the corresponding author.

MOTIVATION: Large-scale mappings of protein-protein interactions have started to give us new views of the complex molecular mechanisms inside a cell. After initial projects to systematically map protein interactions in model organisms such as yeast, worm and fly, researchers have begun to focus on the mapping of the human interactome. To tackle this enormous challenge, different approaches have been proposed and pursued. While several large-scale human protein interaction maps have recently been published, their quality remains to be critically assessed. RESULTS: We present here a first comparative analysis of eight currently available large-scale maps with a total of over 10,000 unique proteins and 57,000 interactions included. They are based either on literature search, orthology or by yeast-two-hybrid assays. Comparison reveals only a small, but statistically significant overlap. More importantly, our analysis gives clear indications that all interaction maps imply considerable selection and detection biases. These results have to be taken into account for future assembly of the human interactome. AVAILABILITY: An integrated human interaction network called Unified Human Interactome (UniHI) is made publicly accessible at http://www.mdc-berlin.de/unihi. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The suprachiasmatic nuclei (SCN) host a robust, self-sustained circadian pacemaker that coordinates physiological rhythms with the daily changes in the environment. Neuronal clocks within the SCN form a heterogeneous network that must synchronize to maintain timekeeping activity. Coherent circadian output of the SCN tissue is established by intercellular signaling factors, such as vasointestinal polypeptide. It was recently shown that besides coordinating cells, the synchronization factors play a crucial role in the sustenance of intrinsic cellular rhythmicity. Disruption of intercellular signaling abolishes sustained rhythmicity in a majority of neurons and desynchronizes the remaining rhythmic neurons. Based on these observations, the authors propose a model for the synchronization of circadian oscillators that combines intracellular and intercellular dynamics at the single-cell level. The model is a heterogeneous network of circadian neuronal oscillators where individual oscillators are damped rather than self-sustained. The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles. Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated. The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility.

BACKGROUND: Collections of transcription factor binding profiles (Transfac, Jaspar) are essential to identify regulatory elements in DNA sequences. Subsets of highly similar profiles complicate large scale analysis of transcription factor binding sites. RESULTS: We propose to identify and group similar profiles using two independent similarity measures: chi2 distances between position frequency matrices (PFMs) and correlation coefficients between position weight matrices (PWMs) scores. CONCLUSION: We show that these measures complement each other and allow to associate Jaspar and Transfac matrices. Clusters of highly similar matrices are identified and can be used to optimise the search for regulatory elements. Moreover, the application of the measures is illustrated by assigning E-box matrices of a SELEX experiment and of experimentally characterised binding sites of circadian clock genes to the Myc-Max cluster.

Cellular signaling networks are subject to transcriptional and proteolytic regulation under both physiological and pathological conditions. For example, the expression of proteins subject to covalent modification by phosphorylation is known to be altered upon cellular differentiation or during carcinogenesis. However, it is unclear how moderate alterations in protein expression can bring about large changes in signal transmission as, for example, observed in the case of haploinsufficiency, where halving the expression of signaling proteins abrogates cellular function. By modeling a fundamental motif of signal transduction, the phosphorylation-dephosphorylation cycle, we show that minor alterations in the concentration of the protein subject to phosphorylation (or the phosphatase) can affect signal transmission in a highly ultrasensitive fashion. This "ultrasensitization" is strongly favored by substrate sequestration on the catalyzing enzymes, and can be observed with experimentally measured enzymatic rate constants. Furthermore, we show that coordinated transcription of multiple proteins (i.e., synexpression) within a protein kinase cascade results in even more pronounced all-or-none behavior with respect to signal transmission. Finally, we demonstrate that ultrasensitization can account for specificity and modularity in the regulation of cellular signal transduction. Ultrasensitization can result in all-or-none cell-fate decisions and in highly specific cellular regulation. Additionally, switch-like phenomena such as ultrasensitization are known to contribute to bistability, oscillations, noise reduction, and cellular heterogeneity.

UNLABELLED: Homology Gene List (HOMGL) is a web-based tool for comparing gene lists with different accession numbers and identifiers and between different organisms. UniGene, LocusLink, HomoloGene and Ensembl databases are utilized to map between these lists and to retrieve upstream or transcribed sequences for genes in these lists. We illustrate the use of HOMGL with respect to microarray studies and promoter analysis. AVAILABILITY: http://homgl.biologie.hu-berlin.de/

MOTIVATION: Mathematical models of the cell cycle can contribute to an understanding of its basic mechanisms. Modern simulation tools make the analysis of key components and their interactions very effective. This paper focuses on the role of small modules and feedbacks in the gene-protein network governing the G1/S transition in mammalian cells. Mutations in this network may lead to uncontrolled cell proliferation. Bifurcation analysis helps to identify the key components of this extremely complex interaction network. RESULTS: We identify various positive and negative feedback loops in the network controlling the G1/S transition. It is shown that the positive feedback regulation of E2F1 and a double activator-inhibitor module can lead to bistability. Extensions of the core module preserve the essential features such as bistability. The complete model exhibits a transcritical bifurcation in addition to bistability. We relate these bifurcations to the cell cycle checkpoint and the G1/S phase transition point. Thus, core modules can explain major features of the complex G1/S network and have a robust decision taking function.

MOTIVATION: Even though a number of genome projects have been finished on the sequence level, still only a small proportion of DNA regulatory elements have been identified. Growing amounts of gene expression data provide the possibility of finding coregulated genes by clustering methods. By analysis of the promoter regions of those genes, rather weak signals of transcription factor binding sites may be detected. RESULTS: We introduce the new algorithm ITB, an Integrated Tool for Box finding, which combines frequency and positional information to predict transcription factor binding sites in upstream regions of coregulated genes. Motifs are extracted by exhaustive analysis of regular expression-like patterns and by estimating probabilities of positional clusters of motifs. ITB detects consensus sequences of experimentally verified transcription factor binding sites of the yeast Saccharomyces cerevisiae. Moreover, a number of new binding site candidates with significant scores are predicted. Besides applying ITB on yeast upstream regions, the program is run on human promoter sequences. AVAILABILITY: ITB is available upon request.

MOTIVATION: Completely sequenced genomes allow for detection and analysis of the relatively weak periodicities of 10-11 basepairs (bp). Two sources contribute to such signals: correlations in the corresponding protein sequences due to the amphipatic character of alpha-helices and the folding of DNA (nucleosomal patterns, DNA supercoiling). Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state from sequence periodicities. RESULTS: We show that correlations within proteins affect mainly the oscillations at distances below 35 bp. The long-ranging correlations up to 100 bp reflect primarily DNA folding. For the yeast genome these oscillations are consistent in detail with the chromatin structure. For eubacteria and archaea the periods deviate significantly from the 10.55 bp value for free DNA. These deviations suggest that while a period of 11 bp in bacteria reflects negative supercoiling, the significantly different period of thermophilic archaea close to 10 bp corresponds to positive supercoiling of thermophilic archaeal genomes. AVAILABILITY: Protein sets and C programs for the calculation of correlation functions are available on request from the authors (see http://itb.biologie.hu-berlin.de).