Number of active transcription factor binding sites is essential for the Hes7 oscillator

The role of cooperativity in a p53-miR34 dynamical mathematical model

The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.

Novel structural features drive DNA binding properties of Cmr, a CRP family protein in TB complex mycobacteria

Mycobacterium tuberculosis (Mtb) encodes two CRP/FNR family transcription factors (TF) that contribute to virulence, Cmr (Rv1675c) and CRP_Mt (Rv3676). Prior studies identified distinct chromosomal binding profiles for each TF despite their recognizing overlapping DNA motifs. The present study shows that Cmr binding specificity is determined by discriminator nucleotides at motif positions 4 and 13. X-ray crystallography and targeted mutational analyses identified an arginine-rich loop that expands Cmr’s DNA interactions beyond the classical helix-turn-helix contacts common to all CRP/FNR family members and facilitates binding to imperfect DNA sequences. Cmr binding to DNA results in a pronounced asymmetric bending of the DNA and its high level of cooperativity is consistent with DNA-facilitated dimerization. A unique N-terminal extension inserts between the DNA binding and dimerization domains, partially occluding the site where the canonical cAMP binding pocket is found. However, an unstructured region of this N-terminus may help modulate Cmr activity in response to cellular signals. Cmr’s multiple levels of DNA interaction likely enhance its ability to integrate diverse gene regulatory signals, while its novel structural features establish Cmr as an atypical CRP/FNR family member.

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.

Fast synchronization of ultradian oscillators controlled by delta-notch signaling with cis-inhibition

While it is known that a large fraction of vertebrate genes are under the control of a gene regulatory network (GRN) forming a clock with circadian periodicity, shorter period oscillatory genes like the Hairy-enhancer-of split (Hes) genes are discussed mostly in connection with the embryonic process of somitogenesis. They form the core of the somitogenesis-clock, which orchestrates the periodic separation of somites from the presomitic mesoderm (PSM). The formation of sharp boundaries between the blocks of many cells works only when the oscillators in the cells forming the boundary are synchronized. It has been shown experimentally that Delta-Notch (D/N) signaling is responsible for this synchronization. This process has to happen rather fast as a cell experiences at most five oscillations from its 'birth' to its incorporation into a somite. Computer simulations describing synchronized oscillators with classical modes of D/N-interaction have difficulties to achieve synchronization in an appropriate time. One approach to solving this problem of modeling fast synchronization in the PSM was the consideration of cell movements. Here we show that fast synchronization of Hes-type oscillators can be achieved without cell movements by including D/N cis-inhibition, wherein the mutual interaction of DELTA and NOTCH in the same cell leads to a titration of ligand against receptor so that only one sort of molecule prevails. Consequently, the symmetry between sender and receiver is partially broken and one cell becomes preferentially sender or receiver at a given moment, which leads to faster entrainment of oscillators. Although not yet confirmed by experiment, the proposed mechanism of enhanced synchronization of mesenchymal cells in the PSM would be a new distinct developmental mechanism employing D/N cis-inhibition. Consequently, the way in which Delta-Notch signaling was modeled so far should be carefully reconsidered.

GATA4 represses an ileal program of gene expression in the proximal small intestine by inhibiting the acetylation of histone H3, lysine 27

GATA4 is expressed in the proximal 85% of small intestine where it promotes a proximal intestinal ('jejunal') identity while repressing a distal intestinal ('ileal') identity, but its molecular mechanisms are unclear. Here, we tested the hypothesis that GATA4 promotes a jejunal versus ileal identity in mouse intestine by directly activating and repressing specific subsets of absorptive enterocyte genes by modulating the acetylation of histone H3, lysine 27 (H3K27), a mark of active chromatin, at sites of GATA4 occupancy. Global analysis of mouse jejunal epithelium showed a statistically significant association of GATA4 occupancy with GATA4-regulated genes. Occupancy was equally distributed between down- and up-regulated targets, and occupancy sites showed a dichotomy of unique motif over-representation at down- versus up-regulated genes. H3K27ac enrichment at GATA4-binding loci that mapped to down-regulated genes (activation targets) was elevated, changed little upon conditional Gata4 deletion, and was similar to control ileum, whereas H3K27ac enrichment at GATA4-binding loci that mapped to up-regulated genes (repression targets) was depleted, increased upon conditional Gata4 deletion, and approached H3K27ac enrichment in wild-type control ileum. These data support the hypothesis that GATA4 both activates and represses intestinal genes, and show that GATA4 represses an ileal program of gene expression in the proximal small intestine by inhibiting the acetylation of H3K27.

Delay-managed tradeoff in the molecular dynamics of the segmentation clock

The molecular segmentation clock is a complex regulatory network that governs the periodic somite segmentation in vertebrate embryos. Underlying the rhythm of the segmentation clock is a single-cell level pace-making circuit, where inevitable molecular noise and time delay impose normal operating constraints to the pace-making. However, how the molecular mechanisms of the core circuit of the segmentation clock coordinate the operating constraints and maintain the rhythmic nature of the developmental process remains poorly understood. To address this question, we construct two biologically-motivated mathematical models with multiple clock protein transcription binding sites, with differential or rate-limited decay rates for protein monomers and dimers. We demonstrate that the rate-limited decay significantly enlarges the parameter space of noise-induced and delay-induced oscillations. Interestingly, focusing on the stochastic characters of noise-induced and delay-induced oscillations in terms of phase coherence and phase averaged amplitude noise in the polar coordinate, we find that there is a delay-managed tradeoff between phase coherence and phase averaged amplitude noise. In particular, the model with both multiple binding sites and rate-limited decay can show regular tunability as the delay increases. Our results indicate that transcriptional and post-translational mechanisms constrain the combined effects of noise and delay on the molecular dynamics of the segmentation clock.

Topology and dynamics of the zebrafish segmentation clock core circuit

By combining biochemical, embryological, and mathematical approaches, this work uncovers an important role for protein-protein interactions in determining the dynamics of the somite-forming segmentation clock in vertebrates.

During vertebrate embryogenesis, the rhythmic and sequential segmentation of the body axis is regulated by an oscillating genetic network termed the segmentation clock. We describe a new dynamic model for the core pace-making circuit of the zebrafish segmentation clock based on a systematic biochemical investigation of the network's topology and precise measurements of somitogenesis dynamics in novel genetic mutants. We show that the core pace-making circuit consists of two distinct negative feedback loops, one with Her1 homodimers and the other with Her7:Hes6 heterodimers, operating in parallel. To explain the observed single and double mutant phenotypes of her1, her7, and hes6 mutant embryos in our dynamic model, we postulate that the availability and effective stability of the dimers with DNA binding activity is controlled in a “dimer cloud” that contains all possible dimeric combinations between the three factors. This feature of our model predicts that Hes6 protein levels should oscillate despite constant hes6 mRNA production, which we confirm experimentally using novel Hes6 antibodies. The control of the circuit's dynamics by a population of dimers with and without DNA binding activity is a new principle for the segmentation clock and may be relevant to other biological clocks and transcriptional regulatory networks.

The segmented pattern of the vertebral column, one of the defining features of the vertebrate body, is established during embryogenesis. The embryo's segments, called somites, form sequentially and rhythmically from head to tail. The periodicity of somite formation is regulated by the segmentation clock, a genetic oscillator that ticks in the posterior-most embryonic tissue: for each tick of the clock, one new bilateral pair of segments is made. The period of the clock appears to determine the number and the length of segments, but what controls this periodicity? In this article, we have investigated the interactions of three transcription factors that form the core of the clock's regulatory circuit, and have measured how the period of segmentation changes when these factors are mutated alone or in combination. We find that these three factors contribute to a “dimer cloud” that contains all possible dimeric combinations; however, only two dimers in this cloud can bind DNA, which allows them to directly regulate the oscillatory gene expression that underpins the periodicity of segment formation. Nevertheless, a mathematical model of the clock's dynamics based on our experimental findings indicates that the non-DNA-binding dimers also influence the stability, and hence the function, of the two DNA-binding dimers controlling the segmentation clock's period. Such involvement of non-DNA-binding dimers is a novel regulatory principle for the segmentation clock, which might also be a general mechanism that operates in other biological clocks.

From dynamic expression patterns to boundary formation in the presomitic mesoderm

The segmentation of the vertebrate body is laid down during early embryogenesis. The formation of signaling gradients, the periodic expression of genes of the Notch-, Fgf- and Wnt-pathways and their interplay in the unsegmented presomitic mesoderm (PSM) precedes the rhythmic budding of nascent somites at its anterior end, which later develops into epithelialized structures, the somites. Although many in silico models describing partial aspects of somitogenesis already exist, simulations of a complete causal chain from gene expression in the growth zone via the interaction of multiple cells to segmentation are rare. Here, we present an enhanced gene regulatory network (GRN) for mice in a simulation program that models the growing PSM by many virtual cells and integrates WNT3A and FGF8 gradient formation, periodic gene expression and Delta/Notch signaling. Assuming Hes7 as core of the somitogenesis clock and LFNG as modulator, we postulate a negative feedback of HES7 on Dll1 leading to an oscillating Dll1 expression as seen in vivo. Furthermore, we are able to simulate the experimentally observed wave of activated NOTCH (NICD) as a result of the interactions in the GRN. We esteem our model as robust for a wide range of parameter values with the Hes7 mRNA and protein decays exerting a strong influence on the core oscillator. Moreover, our model predicts interference between Hes1 and HES7 oscillators when their intrinsic frequencies differ. In conclusion, we have built a comprehensive model of somitogenesis with HES7 as core oscillator that is able to reproduce many experimentally observed data in mice.

MiR-206-mediated dynamic mechanism of the mammalian circadian clock

BACKGROUND

As a group of highly conserved small non-coding RNAs with a length of 21~23 nucleotides, microRNAs (miRNAs) regulate the gene expression post-transcriptionally by base pairing with the partial or full complementary sequences in target mRNAs, thus resulting in the repression of mRNA translation and the acceleration of mRNA degradation. Recent work has revealed that miRNAs are essential for the development and functioning of the skeletal muscles where they are. In particular, miR-206 has not only been identified as the only miRNA expressed in skeletal muscles, but also exhibited crucial roles in regulation of the muscle development. Although miRNAs are known to regulate various biological processes ranging from development to cancer, much less is known about their role in the dynamic regulation of the mammalian circadian clock.

RESULTS

A detailed dynamic model of miR-206-mediated mammalian circadian clock system was developed presently by using Hill-type terms, Michaelis-Menten type and mass action kinetics. Based on a system-theoretic approach, the model accurately predicts both the periodicity and the entrainment of the circadian clock. It also explores the dynamics properties of the oscillations mediated by miR-206 by means of sensitivity analysis and alterations of parameters. Our results show that miR-206 is an important regulator of the circadian clock in skeletal muscle, and thus by study of miR-206 the main features of its mediation on the clock may be captured. Simulations of these processes display that the amplitude and frequency of the oscillation can be significantly altered through the miR-206-mediated control.

CONCLUSIONS

MiR-206 has a profound effect on the dynamic mechanism of the mammalian circadian clock, both by control of the amplitude and control or alteration of the frequency to affect the level of the gene expression and to interfere with the temporal sequence of the gene production or delivery. This undoubtedly uncovers a new mechanism for regulation of the circadian clock at a post-transcriptional level and provides important insights into the normal development as well as the pathological conditions of skeletal muscles, such as the aging, chronic disease and cancer.

Integrated genome-scale prediction of detrimental mutations in transcription networks

A central challenge in genetics is to understand when and why mutations alter the phenotype of an organism. The consequences of gene inhibition have been systematically studied and can be predicted reasonably well across a genome. However, many sequence variants important for disease and evolution may alter gene regulation rather than gene function. The consequences of altering a regulatory interaction (or “edge”) rather than a gene (or “node”) in a network have not been as extensively studied. Here we use an integrative analysis and evolutionary conservation to identify features that predict when the loss of a regulatory interaction is detrimental in the extensively mapped transcription network of budding yeast. Properties such as the strength of an interaction, location and context in a promoter, regulator and target gene importance, and the potential for compensation (redundancy) associate to some extent with interaction importance. Combined, however, these features predict quite well whether the loss of a regulatory interaction is detrimental across many promoters and for many different transcription factors. Thus, despite the potential for regulatory diversity, common principles can be used to understand and predict when changes in regulation are most harmful to an organism.

The genomes of individuals differ in sequence at thousands of base pairs. Some of these polymorphisms affect the sequence of proteins, but many are likely to alter how genes are regulated. When are changes in gene regulation detrimental to an organism? We have used an integrative analysis of transcription factor binding site conservation in budding yeast to address the extent to which different features predict when potential changes in gene regulation are detrimental. We found that, despite the diversity of transcription factors and regulatory regions in a genome, a few simple properties can be used to predict and understand when changes in regulation are most harmful.

Dynamics of coupled repressilators: the role of mRNA kinetics and transcription cooperativity

Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network. Phase-attractive (synchronizing) and phase-repulsive coupling structures were distinguished for regulatory oscillators. In this paper, we question this separation. We study an example of two interacting repressilators (artificial regulatory oscillators based on cyclic repression). We show that changing the cooperativity of transcription repression (Hill coefficient) and reaction timescales dramatically alter synchronization properties. The network becomes birhythmic-it chooses between the in-phase and antiphase synchronization. Thus, the type of synchronization is not characteristic for the network structure. However, we conclude that the specific scenario of emergence and stabilization of synchronous solutions is much more characteristic.

A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics

In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explicitly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

Stoichiometry of STAT3 and mitochondrial proteins: Implications for the regulation of oxidative phosphorylation by protein-protein interactions

The signal transducer and activator of transcription 3 (STAT3) is a transcription factor and downstream product of cytokine and growth factor pathways. Among members of the STAT family, STAT3 has garnered particular interest due to its role in cancer and development. Recently, it was proposed that STAT3 regulates cardiac ATP generation in vivo through protein interaction with the mitochondrial complexes of oxidative phosphorylation, specifically Complexes I/II. For this mechanism to work effectively, the cellular ratio of Complexes I/II and STAT3 must approach one. However, using three different proteomic approaches in cardiac tissue, we determined the ratio of Complexes I/II and STAT3 to be ∼10⁵. This finding suggests that direct protein interaction between Complexes I/II and STAT3 cannot be required for optimal ATP production, nor can it dramatically modulate oxidative phosphorylation in vivo. Thus, STAT3 is likely altering mitochondrial function via transcriptional regulation or indirect signaling pathways that warrant further investigation.

Somitogenesis clock-wave initiation requires differential decay and multiple binding sites for clock protein

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms.

The vertebral column is a characteristic structure of all vertebrates. Individual vertebrae, together with ribs and attached muscles, develop from repeated embryonic structures called somites. The somite pattern forms in the embryo during somitogenesis. We know that this process uses periodic gene expression (a biomolecular “clock”) to generate the pattern, but we do not know precisely how this expression is controlled within the cell and coordinated across multiple cells. We propose a mathematical model that incorporates experimentally confirmed features of somitogenesis. We then test four different mechanisms that may control the clock and ask if the comparison between model simulations and experimental observation can select the best model and thus suggest how the clock is controlled. We find that the model scenario with both multiple DNA binding sites and differential protein decay rates is best able to reproduce experimental observations. Because these findings can be tested experimentally, our results should help guide future experiments.

Expression of the oscillating gene her1 is directly regulated by Hairy/Enhancer of Split, T-box, and Suppressor of Hairless proteins in the zebrafish segmentation clock

Somites are segmental units of the mesoderm in vertebrate embryos that give rise to the axial skeleton, muscle, and dermis. Somitogenesis occurs in a periodic manner and is governed by a segmentation clock that causes cells to undergo repeated oscillations of gene expression. Here, we present a detailed analysis of cis-regulatory elements that control oscillating expression of the zebrafish her1 gene in the anterior presomitic mesoderm. We identify binding sites for Her proteins and demonstrate that they are necessary for transcriptional repression. This result confirms that direct negative autoregulation of her gene expression constitutes part of the oscillator mechanism. We also characterize binding sites for fused somites/Tbx24 and Suppressor of Hairless proteins and show that they are required for activation of her1 expression. These data provide the foundation for a precise description of the regulatory grammar that defines oscillating gene expression in the zebrafish segmentation clock.

Computational models of the Notch network elucidate mechanisms of context-dependent signaling

The Notch signaling pathway controls numerous cell fate decisions during development and adulthood through diverse mechanisms. Thus, whereas it functions as an oscillator during somitogenesis, it can mediate an all-or-none cell fate switch to influence pattern formation in various tissues during development. Furthermore, while in some contexts continuous Notch signaling is required, in others a transient Notch signal is sufficient to influence cell fate decisions. However, the signaling mechanisms that underlie these diverse behaviors in different cellular contexts have not been understood. Notch1 along with two downstream transcription factors hes1 and RBP-Jk forms an intricate network of positive and negative feedback loops, and we have implemented a systems biology approach to computationally study this gene regulation network. Our results indicate that the system exhibits bistability and is capable of switching states at a critical level of Notch signaling initiated by its ligand Delta in a particular range of parameter values. In this mode, transient activation of Delta is also capable of inducing prolonged high expression of Hes1, mimicking the “ON” state depending on the intensity and duration of the signal. Furthermore, this system is highly sensitive to certain model parameters and can transition from functioning as a bistable switch to an oscillator by tuning a single parameter value. This parameter, the transcriptional repression constant of hes1, can thus qualitatively govern the behavior of the signaling network. In addition, we find that the system is able to dampen and reduce the effects of biological noise that arise from stochastic effects in gene expression for systems that respond quickly to Notch signaling.

This work thus helps our understanding of an important cell fate control system and begins to elucidate how this context dependent signaling system can be modulated in different cellular settings to exhibit entirely different behaviors.

The Notch signaling pathway is an evolutionarily conserved signaling system that is involved in various cell fate decisions, both during development of an organism and during adulthood. While the same core circuit functions in various different cellular contexts, it has experimentally been shown to elicit varied behaviors and responses. On the one hand, it functions as a cellular oscillator critical for somitogenesis, whereas in other situations, it can function as a cell fate switch to pattern developing tissue, for example in the Drosophila eye. Furthermore, malfunctioning of Notch signaling is implicated in various cancers. To better understand the underlying mechanisms that allow the network to function distinctly in different contexts, we have mathematically modeled the behavior of the Notch network, encompassing the Notch gene along with two of its downstream effector transcription factors, which together form a network of positive and negative feedback loops. Our results indicate that the qualitative and quantitative behavior of the system can readily be tuned based on key parameters to reflect its multiple roles. Furthermore, our results provide insights into alterations in the signaling system that lead to malfunction and hence disease, which could be used to identify potential drug targets for therapy.

Oscillatory expression of Hes family transcription factors: insights from mathematical modelling

Oscillatory expression of the Hes family of transcription factors plays a central role in the segmentation of the vertebrate body during embryonic development. Analogous oscillations in cultured cells suggest that Hes oscillations may be important in other developmental processes, and provide an excellent opportunity to explore the origin of these oscillations in a relatively simple setting. Mathematical and computational modelling have been used in combination with quantitative mRNA and protein expression data to analyse the origin and properties of Hes oscillations, and have highlighted the important roles played by time delays in negative feedback circuits. In this chapter, we review recent theoretical and experimental results, and discuss how analysis of existing models suggests potential avenues for further study of delayed feedback oscillators.

Understanding the somitogenesis clock: what's missing?

The segmentation of vertebrate embryos depends on a complex genetic network that generates highly dynamic gene expression. Many of the elements of the network have been identified, but their interaction and their influence on segmentation remain poorly understood. A few mathematical models have been proposed to explain the dynamics of subsets of the network, but the mechanistic bases remain controversial. This review focuses on outstanding problems with the generation of somitogenesis clock oscillations, and the ways they could regulate segmentation. Proposals that oscillations are generated by a negative feedback loop formed by Lunatic fringe and Notch signaling are weighed against a model based on positive feedback, and the experimental basis for models of simple negative feedback involving Her/Hes genes or Wnt targets is evaluated. Differences are then made explicit between the many 'clock and wavefront' model variants that have been proposed to explain how the clock regulates segmentation. An understanding of the somitogenesis clock will require addressing experimentally the many questions that arise from the study of simple models.

Practical lessons from theoretical models about the somitogenesis

Vertebrae and other mammalian repetitive structures are formed from embryonic organs called somites. Somites arise sequentially from the unsegmented presomitic mesoderm (PSM). In mice, a new bilateral pair of somites arise every two hours from the rostral PSM. On the other hand, cells are added to the caudal side of the PSM due to cell proliferation of the tail bud. Somite formation correlates with cycles of cell-autonomous expression in the PSM of genes like Hes7. Because the somitogenesis is a highly dynamic and coordinated process, this event has been subjected to extensive theoretical modeling. Here, we describe the current understanding about the somitogenesis in mouse embryos with an emphasis on insights gained from computer simulations. It is worth noting that the combination of experiments and computer simulations has uncovered dynamical properties of the somitogenesis clock such as the transcription/translation delays, the half-life and the synchronization mechanism across the PSM. Theoretical models have also been useful to provide predictions and rigorous hypothesis about poorly understood processes such as the mechanisms by which the temporal PSM oscillations are arrested and converted into an spatial pattern. We aim at reviewing this theoretical literature in such a way that experimentalists might appreciate the resulting conclusions.

The role of microRNA in the delayed negative feedback regulation of gene expression

Oscillatory gene expression plays an important role in somite segmentation during the early developmental stages of vertebrates. Recent experimental studies have shown that microRNA can regulate gene expression by stimulating degradation of mRNA and/or repression of translation. In this communication, we incorporate miRNA into a previous mathematical model of gene expression with delayed negative feedback and demonstrate how this modified model can elucidate the possible effect of miRNA on the oscillatory gene expression. Our finding suggests that miRNA maybe a destabilizing or stabilizing factor in the dynamics of gene expression depending on the severity of its effect on mRNA degradation. Our finding provides testable hypothesis for experimental biologists to further investigate miRNA's increasing functional roles in regulating cellular processes and development.

Intracellular delay limits cyclic changes in gene expression

Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kappaB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays introduces a transition from a stable steady state to limit cycle oscillations and then a second transition back to a stable steady state which has not been observed in previously published models. We demonstrate our approach for two models. The first model describes Hes1 autorepression with equations for Hes1 mRNA production and Hes1 protein translation. The second model describes Hes1 repression by the protein complex Gro/TLE1/Hes1, where Gro/TLE1 is activated by Hes1 phosphorylation. Finally, we discuss our analytical and numerical results in relation to experimental data.

Practical Lessons from Theoretical Models about the Somitogenesis

Vertebrae and other mammalian repetitive structures are formed from embryonic organs called somites. Somites arise sequentially from the unsegmented presomitic mesoderm (PSM). In mice, a new bilateral pair of somites arise every two hours from the rostral PSM. On the other hand, cells are added to the caudal side of the PSM due to cell proliferation of the tail bud. Somite formation correlates with cycles of cell-autonomous expression in the PSM of genes like Hes7. Because the somitogenesis is a highly dynamic and coordinated process, this event has been subjected to extensive theoretical modeling. Here, we describe the current understanding about the somitogenesis in mouse embryos with an emphasis on insights gained from computer simulations. It is worth noting that the combination of experiments and computer simulations has uncovered dynamical properties of the somitogenesis clock such as the transcription/translation delays, the half-life and the synchronization mechanism across the PSM. Theoretical models have also been useful to provide predictions and rigorous hypothesis about poorly understood processes such as the mechanisms by which the temporal PSM oscillations are arrested and converted into an spatial pattern. We aim at reviewing this theoretical literature in such a way that experimentalists might appreciate the resulting conclusions.