Topology and dynamics of the zebrafish segmentation clock core circuit

Faster embryonic segmentation through elevated Delta-Notch signalling

An important step in understanding biological rhythms is the control of period. A multicellular, rhythmic patterning system termed the segmentation clock is thought to govern the sequential production of the vertebrate embryo's body segments, the somites. Several genetic loss-of-function conditions, including the Delta-Notch intercellular signalling mutants, result in slower segmentation. Here, we generate DeltaD transgenic zebrafish lines with a range of copy numbers and correspondingly increased signalling levels, and observe faster segmentation. The highest-expressing line shows an altered oscillating gene expression wave pattern and shortened segmentation period, producing embryos with more, shorter body segments. Our results reveal surprising differences in how Notch signalling strength is quantitatively interpreted in different organ systems, and suggest a role for intercellular communication in regulating the output period of the segmentation clock by altering its spatial pattern.

Rhythmic patterning governs the formation of somites in vertebrates, but how the period of such rhythms can be changed is unclear. Here, the authors generate a genetic model in zebrafish to increase DeltaD expression, which increases the range of Delta-Notch signalling, causing faster segmentation.

Formation and maintenance of nitrogen-fixing cell patterns in filamentous cyanobacteria

Cyanobacteria forming one-dimensional filaments are paradigmatic model organisms of the transition between unicellular and multicellular living forms. Under nitrogen-limiting conditions, in filaments of the genus Anabaena, some cells differentiate into heterocysts, which lose the possibility to divide but are able to fix environmental nitrogen for the colony. These heterocysts form a quasiregular pattern in the filament, representing a prototype of patterning and morphogenesis in prokaryotes. Recent years have seen advances in the identification of the molecular mechanism regulating this pattern. We use these data to build a theory on heterocyst pattern formation, for which both genetic regulation and the effects of cell division and filament growth are key components. The theory is based on the interplay of three generic mechanisms: local autoactivation, early long-range inhibition, and late long-range inhibition. These mechanisms can be identified with the dynamics of hetR, patS, and hetN expression. Our theory reproduces quantitatively the experimental dynamics of pattern formation and maintenance for wild type and mutants. We find that hetN alone is not enough to play the role as the late inhibitory mechanism: a second mechanism, hypothetically the products of nitrogen fixation supplied by heterocysts, must also play a role in late long-range inhibition. The preponderance of even intervals between heterocysts arises naturally as a result of the interplay between the timescales of genetic regulation and cell division. We also find that a purely stochastic initiation of the pattern, without a two-stage process, is enough to reproduce experimental observations.

Persistence, period and precision of autonomous cellular oscillators from the zebrafish segmentation clock

In vertebrate development, the sequential and rhythmic segmentation of the body axis is regulated by a “segmentation clock”. This clock is comprised of a population of coordinated oscillating cells that together produce rhythmic gene expression patterns in the embryo. Whether individual cells autonomously maintain oscillations, or whether oscillations depend on signals from neighboring cells is unknown. Using a transgenic zebrafish reporter line for the cyclic transcription factor Her1, we recorded single tailbud cells in vitro. We demonstrate that individual cells can behave as autonomous cellular oscillators. We described the observed variability in cell behavior using a theory of generic oscillators with correlated noise. Single cells have longer periods and lower precision than the tissue, highlighting the role of collective processes in the segmentation clock. Our work reveals a population of cells from the zebrafish segmentation clock that behave as self-sustained, autonomous oscillators with distinctive noisy dynamics.

DOI:http://dx.doi.org/10.7554/eLife.08438.001

The timing and pattern of gene activity in cells can be very important. For example, precise gene activity patterns in 24-hour circadian clocks help to set daily cycles of rest and activity in organisms. In such scenarios, cells often communicate with each other to coordinate the activity of their genes. To fully understand how the behavior of the population emerges, scientists must first understand the gene activity patterns in individual cells.

Rhythmic gene activity is essential for the spinal column to form in fish and other vertebrate embryos. A group of cells that switch genes on/off in a coordinated pattern act like a clock to regulate the timing of the various steps in the process of backbone formation. However, it is not clear if each cell is able to maintain a rhythm of gene expression on their own, or whether they rely on messages from neighboring cells to achieve it.

Now, Webb et al. use time-lapse videos of individual cells isolated from the tail of zebrafish embryos to show that each cell can maintain a pattern of rhythmic activity in a gene called Her1. In the experiments, individual cells were removed from zebrafish and placed under a microscope to record and track the activity of Her1 over time using fluorescent proteins. These experiments show that each cell is able to maintain a rhythmic pattern of Her1 expression on its own.

Webb et al. then compared the Her1 activity patterns in individual cells with the Her1 patterns present in a larger piece of zebrafish tissue. The experiments showed that the rhythms in the individual cells are slower and less precise in their timing than in the tissue. This suggests that groups of cells must work together to create the synchronized rhythms of gene expression with the right precision and timing needed for the spinal column to be patterned correctly.

In the future, further experiment with these cells will allow researchers to investigate the genetic basis of the rhythms in single cells, and find out how individual cells work together with their neighbors to allow tissues to work properly.

DOI:http://dx.doi.org/10.7554/eLife.08438.002

Timing by rhythms: Daily clocks and developmental rulers

Biological rhythms are widespread, allowing organisms to temporally organize their behavior and metabolism in advantageous ways. Such proper timing of molecular and cellular events is critical to their development and health. This is best understood in the case of the circadian clock that orchestrates the daily sleep/wake cycle of organisms. Temporal rhythms can also be used for spatial organization, if information from an oscillating system can be recorded within the tissue in a manner that leaves a permanent periodic pattern. One example of this is the "segmentation clock" used by the vertebrate embryo to rhythmically and sequentially subdivide its elongating body axis. The segmentation clock moves with the elongation of the embryo, such that its period sets the segment length as the tissue grows outward. Although the study of this system is still relatively young compared to the circadian clock, outlines of molecular, cellular, and tissue-level regulatory mechanisms of timing have emerged. The question remains, however, is it truly a clock? Here we seek to introduce the segmentation clock to a wider audience of chronobiologists, focusing on the role and control of timing in the system. We compare and contrast the segmentation clock with the circadian clock, and propose that the segmentation clock is actually an oscillatory ruler, with a primary function to measure embryonic space.

Molecular mechanism for cyclic generation of somites: Lessons from mice and zebrafish

The somite is the most prominent metameric structure observed during vertebrate embryogenesis, and its metamerism preserves the characteristic structures of the vertebrae and muscles in the adult body. During vertebrate somitogenesis, sequential formation of epithelialized cell boundaries generates the somites. According to the "clock and wavefront model," the periodical and sequential generation of somites is achieved by the integration of spatiotemporal information provided by the segmentation clock and wavefront. In the anterior region of the presomitic mesoderm, which is the somite precursor, the orchestration between the segmentation clock and the wavefront achieves morphogenesis of somites through multiple processes such as determination of somite boundary position, generation of morophological boundary, and establishment of the rostrocaudal polarity within a somite. Recently, numerous studies using various model animals including mouse, zebrafish, and chick have gradually revealed the molecular aspect of the "clock and wavefront" model and the molecular mechanism connecting the segmentation clock and the wavefront to the multiple processes of somite morphogenesis. In this review, we first summarize the current knowledge about the molecular mechanisms underlying the clock and the wavefront and then describe those of the three processes of somite morphogenesis. Especially, we will discuss the conservation and diversification in the molecular network of the somitigenesis among vertebrates, focusing on two typical model animals used for genetic analyses, i.e., the mouse and zebrafish. In this review, we described molecular mechanism for the generation of somites based on the spatiotemporal information provided by "segmentation clock" and "wavefront" focusing on the evidences obtained from mouse and zebrafish.

Stochastic Regulation of her1/7 Gene Expression Is the Source of Noise in the Zebrafish Somite Clock Counteracted by Notch Signalling

The somite segmentation clock is a robust oscillator used to generate regularly-sized segments during early vertebrate embryogenesis. It has been proposed that the clocks of neighbouring cells are synchronised via inter-cellular Notch signalling, in order to overcome the effects of noisy gene expression. When Notch-dependent communication between cells fails, the clocks of individual cells operate erratically and lose synchrony over a period of about 5 to 8 segmentation clock cycles (2-3 hours in the zebrafish). Here, we quantitatively investigate the effects of stochasticity on cell synchrony, using mathematical modelling, to investigate the likely source of such noise. We find that variations in the transcription, translation and degradation rate of key Notch signalling regulators do not explain the in vivo kinetics of desynchronisation. Rather, the analysis predicts that clock desynchronisation, in the absence of Notch signalling, is due to the stochastic dissociation of Her1/7 repressor proteins from the oscillating her1/7 autorepressed target genes. Using in situ hybridisation to visualise sites of active her1 transcription, we measure an average delay of approximately three minutes between the times of activation of the two her1 alleles in a cell. Our model shows that such a delay is sufficient to explain the in vivo rate of clock desynchronisation in Notch pathway mutant embryos and also that Notch-mediated synchronisation is sufficient to overcome this stochastic variation. This suggests that the stochastic nature of repressor/DNA dissociation is the major source of noise in the segmentation clock.

Continuum theory of gene expression waves during vertebrate segmentation

The segmentation of the vertebrate body plan during embryonic development is a rhythmic and sequential process governed by genetic oscillations. These genetic oscillations give rise to traveling waves of gene expression in the segmenting tissue. Here we present a minimal continuum theory of vertebrate segmentation that captures the key principles governing the dynamic patterns of gene expression including the effects of shortening of the oscillating tissue. We show that our theory can quantitatively account for the key features of segmentation observed in zebrafish, in particular the shape of the wave patterns, the period of segmentation and the segment length as a function of time.

An Optimal Free Energy Dissipation Strategy of the MinCDE Oscillator in Regulating Symmetric Bacterial Cell Division

Sustained molecular oscillations are ubiquitous in biology. The obtained oscillatory patterns provide vital functions as timekeepers, pacemakers and spacemarkers. Models based on control theory have been introduced to explain how specific oscillatory behaviors stem from protein interaction feedbacks, whereas the energy dissipation through the oscillating processes and its role in the regulatory function remain unexplored. Here we developed a general framework to assess an oscillator’s regulation performance at different dissipation levels. Using the Escherichia coli MinCDE oscillator as a model system, we showed that a sufficient amount of energy dissipation is needed to switch on the oscillation, which is tightly coupled to the system’s regulatory performance. Once the dissipation level is beyond this threshold, unlike stationary regulators’ monotonic performance-to-cost relation, excess dissipation at certain steps in the oscillating process damages the oscillator’s regulatory performance. We further discovered that the chemical free energy from ATP hydrolysis has to be strategically assigned to the MinE-aided MinD release and the MinD immobilization steps for optimal performance, and a higher energy budget improves the robustness of the oscillator. These results unfold a novel mode by which living systems trade energy for regulatory function.

This paper presents a unique dissipation mode of converting biochemical free energy in ATP to regulatory function through the MinCDE bio-oscillator that marks the mid-cell position for symmetric bacterial cell division. Through assessing the oscillator’s performance-to-cost relation, we demonstrate that some dissipation threshold needs to be satisfied to switch on the oscillation, but the oscillator’s performance can be damaged by excess free energy dissipation, which is distinct from the known monotonic tradeoff relation of stationary regulators. An optimal dissipation strategy has been unveiled: the ATP free energy must be precisely allocated to specific reaction steps for accurate mid-cell recognition, which also coincides with the dynamic requirements for robust oscillation to occur. These discoveries identify an optimizable operation scheme of free energy consumption in biological systems and provide deep insights into the evolution of dynamic regulatory networks.

Collective cell movement promotes synchronization of coupled genetic oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.

Multiple roles of timing in somite formation

During development, vertebrate embryos produce serially repeated elements, the somites, on each side of the midline. These generate the vertebral column, skeletal musculature and dermis. They form sequentially, one pair at a time, from mesenchymal tissue near the tail. Somite development is a complex process. The embryo must control the number, size, and timing of somite formation, their subdivision into functional regions along three axes, regional identity such that somites develop in a region-specific way, and interactions with neighbouring tissues that coordinate them with nearby structures. Here we discuss many timing-related mechanisms that contribute to set up the spatial pattern.

Mechanically Induced Trapping of Molecular Interactions and Its Applications

Measuring binding affinities and association/dissociation rates of molecular interactions is important for a quantitative understanding of cellular mechanisms. Many low-throughput methods have been developed throughout the years to obtain these parameters. Acquiring data with higher accuracy and throughput is, however, necessary to characterize complex biological networks. Here, we provide an overview of a high-throughput microfluidic method based on mechanically induced trapping of molecular interactions (MITOMI). MITOMI can be used to obtain affinity constants and kinetic rates of hundreds of protein-ligand interactions in parallel. It has been used in dozens of studies to measure binding affinities of transcription factors, map protein interaction networks, identify pharmacological inhibitors, and perform high-throughput, low-cost molecular diagnostics. This article covers the technological aspects of MITOMI and its applications.

Dynamic properties of the segmentation clock mediated by microRNA

Somites are embryonic precursors that give rise to the axial skeleton and skeletal muscles and form the segmental vertebrate body plan. Somitogenesis is controlled by the "segmentation clock", which contains multiple oscillator genes that must be tightly regulated at both the transcriptional and post-transcriptional levels for proper clock function. However, how the segmentation clock governs the formation of the somites at post-transcriptional level, remains unclear. In this work, we develop an integrated model with three modules for the segmentation clock and explore the mechanism for somite segmentation based on the dynamics of the network. By numerical simulations, we find that the amplitude and period of the somite segmentation clock are sensitive to Notch activity, which is fine-tuned by Lunatic fringe (Lfng) and microRNA (miRNA), and Lfng and miRNA are essential for forming the proper segmentation during somitogenesis. Moreover, miRNA is found to have a crucial role in minimizing the fluctuation period and amplitude to maintain coherent oscillation. Introduction of stochasticity in the model enables us to explain the available experimental data with dampening of oscillations. These findings uncover a fresh mechanism for regulation of the segmentation clock at a post-transcriptional level and provide important insights into how the relatively subtle effects of miRNAs on target genes can have broad effects in developmental situations that have critical requirements for tight posttranscriptional regulation.

Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves

The vertebrate segmentation clock is a gene expression oscillator controlling rhythmic segmentation of the vertebral column during embryonic development. The period of oscillations becomes longer as cells are displaced along the posterior to anterior axis, which results in traveling waves of clock gene expression sweeping in the unsegmented tissue. Although various hypotheses necessitating the inclusion of additional regulatory genes into the core clock network at different spatial locations have been proposed, the mechanism underlying traveling waves has remained elusive. Here, we combined molecular-level computational modeling and quantitative experimentation to solve this puzzle. Our model predicts the existence of an increasing gradient of gene expression time delays along the posterior to anterior direction to recapitulate spatiotemporal profiles of the traveling segmentation clock waves in different genetic backgrounds in zebrafish. We validated this prediction by measuring an increased time delay of oscillatory Her1 protein production along the unsegmented tissue. Our results refuted the need for spatial expansion of the core feedback loop to explain the occurrence of traveling waves. Spatial regulation of gene expression time delays is a novel way of creating dynamic patterns; this is the first report demonstrating such a control mechanism in any tissue and future investigations will explore the presence of analogous examples in other biological systems.

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.

Networks of coupled circuits: from a versatile toggle switch to collective coherent behavior

We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits are coupled with mutual repression, the system can function as a toggle switch. The variety of its states can be controlled by two parameters as we demonstrate by a detailed bifurcation analysis. In the bistable regimes, switches between the coexisting attractors can be induced by noise. When we couple larger sets of these units, we numerically observe collective coherent modes of individual fixed-point and limit-cycle behavior. It is there that the monotonic change of a single bifurcation parameter allows one to control the onset and arrest of the synchronized oscillations. This mechanism may play a role in biological applications, in particular, in connection with the segmentation clock. While tuning the bifurcation parameter, also a variety of transient patterns emerges upon approaching the stationary states, in particular, a self-organized pacemaker in a completely uniformly equipped ensemble, so that the symmetry breaking happens dynamically.

Chevron formation of the zebrafish muscle segments

The muscle segments of fish have a folded shape, termed a chevron, which is thought to be optimal for the undulating body movements of swimming. However, the mechanism shaping the chevron during embryogenesis is not understood. Here, we used time-lapse microscopy of developing zebrafish embryos spanning the entire somitogenesis period to quantify the dynamics of chevron shape development. By comparing such time courses with the start of movements in wildtype zebrafish and analysing immobile mutants, we show that the previously implicated body movements do not play a role in chevron formation. Further, the monotonic increase of chevron angle along the anteroposterior axis revealed by our data constrains or rules out possible contributions by previously proposed mechanisms. In particular, we found that muscle pioneers are not required for chevron formation. We put forward a tension-and-resistance mechanism involving interactions between intra-segmental tension and segment boundaries. To evaluate this mechanism, we derived and analysed a mechanical model of a chain of contractile and resisting elements. The predictions of this model were verified by comparison with experimental data. Altogether, our results support the notion that a simple physical mechanism suffices to self-organize the observed spatiotemporal pattern in chevron formation.

Caudal regulates the spatiotemporal dynamics of pair-rule waves in Tribolium

In the short-germ beetle Tribolium castaneum, waves of pair-rule gene expression propagate from the posterior end of the embryo towards the anterior and eventually freeze into stable stripes, partitioning the anterior-posterior axis into segments. Similar waves in vertebrates are assumed to arise due to the modulation of a molecular clock by a posterior-to-anterior frequency gradient. However, neither a molecular candidate nor a functional role has been identified to date for such a frequency gradient, either in vertebrates or elsewhere. Here we provide evidence that the posterior gradient of Tc-caudal expression regulates the oscillation frequency of pair-rule gene expression in Tribolium. We show this by analyzing the spatiotemporal dynamics of Tc-even-skipped expression in strong and mild knockdown of Tc-caudal, and by correlating the extension, level and slope of the Tc-caudal expression gradient to the spatiotemporal dynamics of Tc-even-skipped expression in wild type as well as in different RNAi knockdowns of Tc-caudal regulators. Further, we show that besides its absolute importance for stripe generation in the static phase of the Tribolium blastoderm, a frequency gradient might serve as a buffer against noise during axis elongation phase in Tribolium as well as vertebrates. Our results highlight the role of frequency gradients in pattern formation.

One of the most popular problems in development is how the anterior-posterior axis of vertebrates, arthropods and annelids is partitioned into segments. In vertebrates, and recently shown in the beetle Tribolium castaneum, segments are demarcated by means of gene expression waves that propagate from posterior to anterior as the embryo elongates. These waves are assumed to arise due to the regulation of a molecular clock by a frequency gradient. However, to date, neither a candidate nor a functional role has been identified for such a frequency gradient. Here we provide evidence that a static expression gradient of caudal regulates pair-rule oscillations during blastoderm stage in Tribolium. In such a static setup, a frequency gradient is essential to convert clock oscillations into a striped pattern. We further show that a frequency gradient might be essential even in the presence of axis elongation as a buffer against noise. Our work also provides the best evidence to date that Caudal acts as a type of morphogen gradient in the blastoderm of short-germ arthropods; however, Caudal seems to convey positional information through frequency regulation of pair-rule oscillations, rather than through threshold concentration levels in the gradient.

Circadian genes, xBmal1 and xNocturnin, modulate the timing and differentiation of somites in Xenopus laevis

We have been investigating whether xBmal1 and xNocturnin play a role in somitogenesis, a cyclic developmental process with an ultradian period. Previous work from our lab shows that circadian genes (xPeriod1, xPeriod2, xBmal1, and xNocturnin) are expressed in developing somites. Somites eventually form the vertebrae, muscles of the back, and dermis. In Xenopus, a pair of somites is formed about every 50 minutes from anterior to posterior. We were intrigued by the co-localization of circadian genes in an embryonic tissue known to be regulated by an ultradian clock. Cyclic expression of genes involved in Notch signaling has been implicated in the somite clock. Disruption of Notch signaling in humans has been linked to skeletal defects in the vertebral column. We found that both depletion (morpholino) and overexpression (mRNA) of xBMAL1 protein (bHLH transcription factor) or xNOCTURNIN protein (deadenylase) on one side of the developing embryo led to a significant decrease in somite number with respect to the untreated side (p<0.001). These manipulations also significantly affect expression of a somite clock component (xESR9; p<0.05). We observed opposing effects on somite size. Depletion of xBMAL1 or xNOCTURNIN caused a statistically significant decrease in somite area (quantified using NIH ImageJ; p<0.002), while overexpression of these proteins caused a significant dose dependent increase in somite area (p<0.02; p<0.001, respectively). We speculate that circadian genes may play two separate roles during somitogenesis. Depletion and overexpression of xBMAL1 and NOCTURNIN both decrease somite number and influence expression of a somite clock component, suggesting that these proteins may modulate the timing of the somite clock in the undifferentiated presomitic mesoderm. The dosage dependent effects on somite area suggest that xBMAL1 and xNOCTURNIN may also act during somite differentiation to promote myogenesis.

Rbm24a and Rbm24b are required for normal somitogenesis

We recently demonstrated that the gene encoding the RNA binding motif protein 24 (RBM24) is expressed during mouse cardiogenesis, and determined the developmental requirement for its zebrafish homologs Rbm24a and Rbm24b during cardiac development. We demonstrate here that both Rbm24a and Rbm24b are also required for normal somite and craniofacial development. Diminution of rbm24a or rbm24b gene products by morpholino knockdown resulted in significant disruption of somite formation. Detailed in situ hybridization-based analyses of a spectrum of somitogenesis-associated transcripts revealed reduced expression of the cyclic muscle pattering genes dlc and dld encoding Notch ligands, as well as their respective target genes her7, her1. By contrast expression of the Notch receptors notch1a and notch3 appears unchanged. Some RBM-family members have been implicated in pre-mRNA processing. Analysis of affected Notch-pathway mRNAs in rbm24a and rbm24b morpholino-injected embryos revealed aberrant transcript fragments of dlc and dld, but not her1 or her7, suggesting the reduction in transcription levels of Notch pathway components may result from aberrant processing of its ligands. These data imply a previously unknown requirement for Rbm24a and Rbm24b in somite and craniofacial development. Although we anticipate the influence of disrupting RBM24 homologs likely extends beyond the Notch pathway, our results suggest their perturbation may directly, or indirectly, compromise post-transcriptional processing, exemplified by imprecise processing of dlc and dld.

It is not the parts, but how they interact that determines the behaviour of circadian rhythms across scales and organisms

Biological rhythms, generated by feedback loops containing interacting genes, proteins and/or cells, time physiological processes in many organisms. While many of the components of the systems that generate biological rhythms have been identified, much less is known about the details of their interactions. Using examples from the circadian (daily) clock in three organisms, Neurospora, Drosophila and mouse, we show, with mathematical models of varying complexity, how interactions among (i) promoter sites, (ii) proteins forming complexes, and (iii) cells can have a drastic effect on timekeeping. Inspired by the identification of many transcription factors, for example as involved in the Neurospora circadian clock, that can both activate and repress, we show how these multiple actions can cause complex oscillatory patterns in a transcription–translation feedback loop (TTFL). Inspired by the timekeeping complex formed by the NMO–PER–TIM–SGG complex that regulates the negative TTFL in the Drosophila circadian clock, we show how the mechanism of complex formation can determine the prevalence of oscillations in a TTFL. Finally, we note that most mathematical models of intracellular clocks model a single cell, but compare with experimental data from collections of cells. We find that refitting the most detailed model of the mammalian circadian clock, so that the coupling between cells matches experimental data, yields different dynamics and makes an interesting prediction that also matches experimental data: individual cells are bistable, and network coupling removes this bistability and causes the network to be more robust to external perturbations. Taken together, we propose that the interactions between components in biological timekeeping systems are carefully tuned towards proper function. We also show how timekeeping can be controlled by novel mechanisms at different levels of organization.

Pulses of Notch activation synchronise oscillating somite cells and entrain the zebrafish segmentation clock

Formation of somites, the rudiments of vertebrate body segments, is an oscillatory process governed by a gene-expression oscillator, the segmentation clock. This operates in each cell of the presomitic mesoderm (PSM), but the individual cells drift out of synchrony when Delta/Notch signalling fails, causing gross anatomical defects. We and others have suggested that this is because synchrony is maintained by pulses of Notch activation, delivered cyclically by each cell to its neighbours, that serve to adjust or reset the phase of the intracellular oscillator. This, however, has never been proved. Here, we provide direct experimental evidence, using zebrafish containing a heat-shock-driven transgene that lets us deliver artificial pulses of expression of the Notch ligand DeltaC. In DeltaC-defective embryos, in which endogenous Notch signalling fails, the artificial pulses restore synchrony, thereby rescuing somite formation. The spacing of segment boundaries produced by repetitive heat-shocking varies according to the time interval between one heat-shock and the next. The induced synchrony is manifest both morphologically and at the level of the oscillations of her1, a core component of the intracellular oscillator. Thus, entrainment of intracellular clocks by periodic activation of the Notch pathway is indeed the mechanism maintaining cell synchrony during somitogenesis.

Latent phenotypes pervade gene regulatory circuits

BACKGROUND

Latent phenotypes are non-adaptive byproducts of adaptive phenotypes. They exist in biological systems as different as promiscuous enzymes and genome-scale metabolic reaction networks, and can give rise to evolutionary adaptations and innovations. We know little about their prevalence in the gene expression phenotypes of regulatory circuits, important sources of evolutionary innovations.

RESULTS

Here, we study a space of more than sixteen million three-gene model regulatory circuits, where each circuit is represented by a genotype, and has one or more functions embodied in one or more gene expression phenotypes. We find that the majority of circuits with single functions have latent expression phenotypes. Moreover, the set of circuits with a given spectrum of functions has a repertoire of latent phenotypes that is much larger than that of any one circuit. Most of this latent repertoire can be easily accessed through a series of small genetic changes that preserve a circuit's main functions. Both circuits and gene expression phenotypes that are robust to genetic change are associated with a greater number of latent phenotypes.

CONCLUSIONS

Our observations suggest that latent phenotypes are pervasive in regulatory circuits, and may thus be an important source of evolutionary adaptations and innovations involving gene regulation.

The roles and mechanism of ultradian oscillatory expression of the mouse Hes genes

Somites, metameric structures, give rise to the vertebral column, ribs, skeletal muscles and subcutaneous tissues. In mouse embryos, a pair of somites is formed every 2h by segmentation of the anterior parts of the presomitic mesoderm. This periodic event is regulated by a biological clock called the segmentation clock, which involves cyclic expression of the basic helix-loop-helix gene Hes7. Hes7 oscillation is regulated by negative feedback with a delayed timing. This process has been mathematically simulated by differential-delay equations, which predict that negative feedback with shorter delays would abolish oscillations or produce dampened but more rapid oscillations. We found that reducing the number of introns within the Hes7 gene shortens the delay and abolishes Hes7 oscillation or results in a more rapid tempo of Hes7 oscillation, increasing the number of somites and vertebrae in the cervical and upper thoracic region. We also found that Hes1, a Hes7-related gene, is expressed in an oscillatory manner by many cell types, including fibroblasts and neural stem cells. In these cells, Hes1 expression oscillates with a period of about 2-3h, and this oscillation is important for cell cycle progression. Furthermore, in neural stem cells, Hes1 oscillation drives cyclic expression of the proneural genes Ascl1 and Neurogenin2 and regulates multipotency. Hes1 expression oscillates more slowly in embryonic stem cells, and Hes1 oscillation regulates their fate preferences. Taken together, these results suggest that oscillatory expression with short periods (ultradian oscillation) is important for many biological events.

Stochastic simulation of notch signaling reveals novel factors that mediate the differentiation of neural stem cells

Notch signaling controls cell fate decisions and regulates multiple biological processes, such as cell proliferation, differentiation, and apoptosis. Computational modeling of the deterministic simulation of Notch signaling has provided important insight into the possible molecular mechanisms that underlie the switch from the undifferentiated stem cell to the differentiated cell. Here, we constructed a stochastic model of a Notch signaling model containing Hes1, Notch1, RBP-Jk, Mash1, Hes6, and Delta. mRNA and protein were represented as a discrete state, and 334 reactions were employed for each biochemical reaction using a graphics processing unit-accelerated Gillespie scheme. We employed the tuning of 40 molecular mechanisms and revealed several potential mediators capable of enabling the switch from cell stemness to differentiation. These effective mediators encompass different aspects of cellular regulations, including the nuclear transport of Hes1, the degradation of mRNA (Hes1 and Notch1) and protein (Notch1), the association between RBP-Jk and Notch intracellular domain (NICD), and the cleavage efficiency of the NICD. These mechanisms overlap with many modifiers that have only recently been discovered to modulate the Notch signaling output, including microRNA action, ubiquitin-mediated proteolysis, and the competitive binding of the RBP-Jk-DNA complex. Moreover, we identified the degradation of Hes1 mRNA and nuclear transport of Hes1 as the dominant mechanisms that were capable of abolishing the cell state transition induced by other molecular mechanisms.

Models in biology: 'accurate descriptions of our pathetic thinking'

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as 'predictive', in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders.

Modeling the zebrafish segmentation clock's gene regulatory network constrained by expression data suggests evolutionary transitions between oscillating and nonoscillating transcription

During segmentation of vertebrate embryos, somites form in accordance with a periodic pattern established by the segmentation clock. In the zebrafish (Danio rerio), the segmentation clock includes six hairy/enhancer of split-related (her/hes) genes, five of which oscillate due to negative autofeedback. The nonoscillating gene hes6 forms the hub of a network of 10 Her/Hes protein dimers, which includes 7 DNA-binding dimers and 4 weak or non-DNA-binding dimers. The balance of dimer species is critical for segmentation clock function, and loss-of-function studies suggest that the her genes have both unique and redundant functions within the clock. However, the precise regulatory interactions underlying the negative feedback loop are unknown. Here, we combine quantitative experimental data, in silico modeling, and a global optimization algorithm to identify a gene regulatory network (GRN) designed to fit measured transcriptional responses to gene knockdown. Surprisingly, we find that hes6, the clock gene that does not oscillate, responds to negative feedback. Consistent with prior in silico analyses, we find that variation in transcription, translation, and degradation rates can mediate the gain and loss of oscillatory behavior for genes regulated by negative feedback. Extending our study, we found that transcription of the nonoscillating Fgf pathway gene sef responds to her/hes perturbation similarly to oscillating her genes. These observations suggest a more extensive underlying regulatory similarity between the zebrafish segmentation clock and the mouse and chick segmentation clocks, which exhibit oscillations of her/hes genes as well as numerous other Notch, Fgf, and Wnt pathway genes.

An anterior limit of FGF/Erk signal activity marks the earliest future somite boundary in zebrafish

Vertebrate segments called somites are generated by periodic segmentation of the anterior extremity of the presomitic mesoderm (PSM). During somite segmentation in zebrafish, mesp-b determines a future somite boundary at position B-2 within the PSM. Heat-shock experiments, however, suggest that an earlier future somite boundary exists at B-5, but the molecular signature of this boundary remains unidentified. Here, we characterized fibroblast growth factor (FGF) signal activity within the PSM, and demonstrated that an anterior limit of downstream Erk activity corresponds to the future B-5 somite boundary. Moreover, the segmentation clock is required for a stepwise posterior shift of the Erk activity boundary during each segmentation. Our results provide the first molecular evidence of the future somite boundary at B-5, and we propose that clock-dependent cyclic inhibition of the FGF/Erk signal is a key mechanism in the generation of perfect repetitive structures in zebrafish development.

Mathematical modeling of regenerative processes

In many animals, regenerative processes can replace lost body parts. Organ and tissue regeneration consequently also hold great medical promise. The regulation of regenerative processes is achieved through concerted actions of multiple organizational levels of the organism, from diffusing molecules and cellular gene expression patterns up to tissue mechanics. Our intuition is usually not adapted well to this degree of complexity and the quantitative aspects of the regulation of regenerative processes remain poorly understood. One way out of this dilemma lies in the combination of experimentation and mathematical modeling within an iterative process of model development/refinement, model predictions for novel experimental conditions, quantitative experiments testing these predictions, and subsequent model refinement. This interdisciplinary approach has already provided key insights into smaller scale processes during embryonic development and a so-far limited number of more complex regeneration processes. This review discusses selected theoretical and interdisciplinary studies and is structured along the three phases of regeneration: (1) initiation of a regeneration response, (2) tissue patterning during regenerate growth, (3) arresting the regeneration response. Moreover, we highlight the opportunities provided by extensions of mathematical models from developmental processes toward the study of related regenerative processes.

Modeling Notch signaling: a practical tutorial

Theoretical and computational approaches for understanding different aspects of Notch signaling and Notch dependent patterning are gaining popularity in recent years. These in silico methodologies can provide dynamic insights that are often not intuitive and may help guide experiments aimed at elucidating these processes. This chapter is an introductory tutorial intended to allow someone with basic mathematical and computational knowledge to explore new mathematical models of Notch-mediated processes and perform numerical simulations of these models. In particular, we explain how to define and simulate models of lateral inhibition patterning processes. We provide a Matlab code for simulating various lateral inhibition models in a simple and intuitive manner, and show how to present the results from the computational models. This code can be used as a starting point for exploring more specific models that include additional aspects of the Notch pathway and its regulation.

Deadpan contributes to the robustness of the notch response

Notch signaling regulates many fundamental events including lateral inhibition and boundary formation to generate very reproducible patterns in developing tissues. Its targets include genes of the bHLH hairy and Enhancer of split [E(spl)] family, which contribute to many of these developmental decisions. One member of this family in Drosophila, deadpan (dpn), was originally found to have functions independent of Notch in promoting neural development. Employing genome-wide chromatin-immunoprecipitation we have identified several Notch responsive enhancers in dpn, demonstrating its direct regulation by Notch in a range of contexts including the Drosophila wing and eye. dpn expression largely overlaps that of several E(spl) genes and the combined knock-down leads to more severe phenotypes than either alone. In addition, Dpn contributes to the establishment of Cut expression at the wing dorsal-ventral (D/V) boundary; in its absence Cut expression is delayed. Furthermore, over-expression of Dpn inhibits expression from E(spl) gene enhancers, but not vice versa, suggesting that dpn contributes to a feed-back mechanism that limits E(spl) gene expression following Notch activation. Thus the combined actions of dpn and E(spl) appear to provide a mechanism that confers an initial rapid output from Notch activity which becomes self-limited via feedback between the targets.

Short-lived Her proteins drive robust synchronized oscillations in the zebrafish segmentation clock

Oscillations are prevalent in natural systems. A gene expression oscillator, called the segmentation clock, controls segmentation of precursors of the vertebral column. Genes belonging to the Hes/her family encode the only conserved oscillating genes in all analyzed vertebrate species. Hes/Her proteins form dimers and negatively autoregulate their own transcription. Here, we developed a stochastic two-dimensional multicellular computational model to elucidate how the dynamics, i.e. period, amplitude and synchronization, of the segmentation clock are regulated. We performed parameter searches to demonstrate that autoregulatory negative-feedback loops of the redundant repressor Her dimers can generate synchronized gene expression oscillations in wild-type embryos and reproduce the dynamics of the segmentation oscillator in different mutant conditions. Our model also predicts that synchronized oscillations can be robustly generated as long as the half-lives of the repressor dimers are shorter than 6 minutes. We validated this prediction by measuring, for the first time, the half-life of Her7 protein as 3.5 minutes. These results demonstrate the importance of building biologically realistic stochastic models to test biological models more stringently and make predictions for future experimental studies.

Modeling gene expression in time and space

Cell populations rarely exhibit gene-expression profiles that are homogeneous in time and space. In the temporal domain, dynamical behaviors such as oscillations and pulses of protein production pervade cell biology, underlying phenomena as diverse as circadian rhythmicity, cell cycle control, stress and damage responses, and stem-cell pluripotency. In multicellular populations, spatial heterogeneities are crucial for decision making and development, among many other functions. Cells need to exquisitely coordinate this temporal and spatial variation to survive. Although the spatiotemporal character of gene expression is challenging to quantify experimentally at the level of individual cells, it is beneficial from the modeling viewpoint, because it provides strong constraints that can be probed by theoretically analyzing mathematical models of candidate gene and protein circuits. Here, we review recent examples of temporal dynamics and spatial patterning in gene expression to show how modeling such phenomenology can help us unravel the molecular mechanisms of cellular function.

Formation and segmentation of the vertebrate body axis

Body axis elongation and segmentation are major morphogenetic events that take place concomitantly during vertebrate embryonic development. Establishment of the final body plan requires tight coordination between these two key processes. In this review, we detail the cellular and molecular as well as the physical processes underlying body axis formation and patterning. We discuss how formation of the anterior region of the body axis differs from that of the posterior region. We describe the developmental mechanism of segmentation and the regulation of body length and segment numbers. We focus mainly on the chicken embryo as a model system. Its accessibility and relatively flat structure allow high-quality time-lapse imaging experiments, which makes it one of the reference models used to study morphogenesis. Additionally, we illustrate conservation and divergence of specific developmental mechanisms by discussing findings in other major embryonic model systems, such as mice, frogs, and zebrafish.

The elongation rate of RNA polymerase II in zebrafish and its significance in the somite segmentation clock

A gene expression oscillator called the segmentation clock controls somite segmentation in the vertebrate embryo. In zebrafish, the oscillatory transcriptional repressor genes her1 and her7 are crucial for genesis of the oscillations, which are thought to arise from negative autoregulation of these genes. The period of oscillation is predicted to depend on delays in the negative-feedback loop, including, most importantly, the transcriptional delay - the time taken to make each molecule of her1 or her7 mRNA. her1 and her7 operate in parallel. Loss of both gene functions, or mutation of her1 combined with knockdown of Hes6, which we show to be a binding partner of Her7, disrupts segmentation drastically. However, mutants in which only her1 or her7 is functional show only mild segmentation defects and their oscillations have almost identical periods. This is unexpected because the her1 and her7 genes differ greatly in length. We use transgenic zebrafish to measure the RNA polymerase II elongation rate, for the first time, in the intact embryo. This rate is unexpectedly rapid, at 4.8 kb/minute at 28.5°C, implying that, for both genes, the time taken for transcript elongation is insignificant compared with other sources of delay, explaining why the mutants have similar clock periods. Our computational model shows how loss of her1 or her7 can allow oscillations to continue with unchanged period but with reduced amplitude and impaired synchrony, as manifested in the in situ hybridisation patterns of the single mutants.

Single-cell-resolution imaging of the impact of Notch signaling and mitosis on segmentation clock dynamics

Vertebrate body segmentation is controlled by the segmentation clock, a molecular oscillator involving transcriptional oscillations of cyclic genes in presomitic mesoderm cells. The rapid and highly dynamic nature of this oscillating system has proved challenging for study at the single-cell level. We achieved visualization of clock activity with a cellular level of resolution in living embryos, allowing direct comparison of oscillations in neighbor cells. We provide direct evidence that presomitic mesoderm cells oscillate asynchronously in zebrafish Notch pathway mutants. By tracking oscillations in mitotic cells, we reveal that a robust cell-autonomous, Notch-independent mechanism resumes oscillations after mitosis. Finally, we find that cells preferentially divide at a certain oscillation phase, likely reducing the noise generated by cell division in cell synchrony and suggesting an intriguing relationship between the mitotic cycle and clock oscillation.

iSLIM: a comprehensive approach to mapping and characterizing gene regulatory networks

Mapping gene regulatory networks is a significant challenge in systems biology, yet only a few methods are currently capable of systems-level identification of transcription factors (TFs) that bind a specific regulatory element. We developed a microfluidic method for integrated systems-level interaction mapping of TF-DNA interactions, generating and interrogating an array of 423 full-length Drosophila TFs. With integrated systems-level interaction mapping, it is now possible to rapidly and quantitatively map gene regulatory networks of higher eukaryotes.