A Wnt oscillator model for somitogenesis

Cell Fate Dynamics Reconstruction Identifies TPT1 and PTPRZ1 Feedback Loops as Master Regulators of Differentiation in Pediatric Glioblastoma-Immune Cell Networks

Pediatric glioblastoma is a complex dynamical disease that is difficult to treat due to its multiple adaptive behaviors driven largely by phenotypic plasticity. Integrated data science and network theory pipelines offer novel approaches to studying glioblastoma cell fate dynamics, particularly phenotypic transitions over time. Here we used various single-cell trajectory inference algorithms to infer signaling dynamics regulating pediatric glioblastoma-immune cell networks. We identified GATA2, PTPRZ1, TPT1, MTRNR2L1/2, OLIG1/2, SOX11, FXYD6, SEZ6L, PDGFRA, EGFR, S100B, WNT, TNF α , and NF-kB as critical transition genes or signals regulating glioblastoma-immune network dynamics, revealing potential clinically relevant targets. Further, we reconstructed glioblastoma cell fate attractors and found complex bifurcation dynamics within glioblastoma phenotypic transitions, suggesting that a causal pattern may be driving glioblastoma evolution and cell fate decision-making. Together, our findings have implications for developing targeted therapies against glioblastoma, and the continued integration of quantitative approaches and artificial intelligence (AI) to understand pediatric glioblastoma tumor-immune interactions.

Information geometry for multiparameter models: new perspectives on the origin of simplicity

Complex models in physics, biology, economics, and engineering are oftensloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce themodel manifoldof predictions, whose coordinates are the model parameters. Itshyperribbonstructure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold-emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed 'intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.

Regulatory role of RNA N6-methyladenosine modifications during skeletal muscle development

Functional cells in embryonic myogenesis and postnatal muscle development undergo multiple stages of proliferation and differentiation, which are strict procedural regulation processes. N⁶-methyladenosine (m⁶A) is the most abundant RNA modification that regulates gene expression in specific cell types in eukaryotes and regulates various biological activities, such as RNA processing and metabolism. Recent studies have shown that m⁶A modification-mediated transcriptional and post-transcriptional regulation plays an essential role in myogenesis. This review outlines embryonic and postnatal myogenic differentiation and summarizes the important roles played by functional cells in each developmental period. Furthermore, the key roles of m⁶A modifications and their regulators in myogenesis were highlighted, and the synergistic regulation of m⁶A modifications with myogenic transcription factors was emphasized to characterize the cascade of transcriptional and post-transcriptional regulation during myogenesis. This review also discusses the crosstalk between m⁶A modifications and non-coding RNAs, proposing a novel mechanism for post-transcriptional regulation during skeletal muscle development. In summary, the transcriptional and post-transcriptional regulatory mechanisms mediated by m⁶A and their regulators may help develop new strategies to maintain muscle homeostasis, which are expected to become targets for animal muscle-specific trait breeding and treatment of muscle metabolic diseases.

Dissecting cell fate dynamics in pediatric glioblastoma through the lens of complex systems and cellular cybernetics

Cancers are complex dynamic ecosystems. Reductionist approaches to science are inadequate in characterizing their self-organized patterns and collective emergent behaviors. Since current approaches to single-cell analysis in cancer systems rely primarily on single time-point multiomics, many of the temporal features and causal adaptive behaviors in cancer dynamics are vastly ignored. As such, tools and concepts from the interdisciplinary paradigm of complex systems theory are introduced herein to decode the cellular cybernetics of cancer differentiation dynamics and behavioral patterns. An intuition for the attractors and complex networks underlying cancer processes such as cell fate decision-making, multiscale pattern formation systems, and epigenetic state-transitions is developed. The applications of complex systems physics in paving targeted therapies and causal pattern discovery in precision oncology are discussed. Pediatric high-grade gliomas are discussed as a model-system to demonstrate that cancers are complex adaptive systems, in which the emergence and selection of heterogeneous cellular states and phenotypic plasticity are driven by complex multiscale network dynamics. In specific, pediatric glioblastoma (GBM) is used as a proof-of-concept model to illustrate the applications of the complex systems framework in understanding GBM cell fate decisions and decoding their adaptive cellular dynamics. The scope of these tools in forecasting cancer cell fate dynamics in the emerging field of computational oncology and patient-centered systems medicine is highlighted.

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems medicine. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems, and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

DVL1 and DVL3 require nuclear localisation to regulate proliferation in human myoblasts

WNT signalling is essential for regulating a diverse range of cellular processes. In skeletal muscle, the WNT pathway plays crucial roles in maintenance of the stem cell pool and myogenic differentiation. Focus is usually directed at examining the function of central components of the WNT pathway, including β-CATENIN and the GSK3β complex and TCF/LEF transcription factors, in tissue homeostasis and cancer. Other core components of the WNT pathway though, are three dishevelled (DVL) proteins: membrane associated proteins that propagate WNT signalling from membrane to nucleus. Here we examined DVL function in human myogenesis and the muscle-related cancer alveolar rhabdomyosarcoma. We demonstrate that DVL1 and DVL3 are necessary for efficient proliferation in human myoblasts and are important for timely myogenic differentiation. DVL1 and DVL3 also contribute to regulation of proliferation in rhabdomyosarcoma. DVL1 or DVL3 must be present in the nucleus to regulate proliferation, but they operate through different protein domains: DVL3 requires the DIX and PDZ domains, while DVL1 does not. Importantly, DVL1 and DVL3 activity is independent of markedly increased translocation of β-CATENIN to the nucleus, normally a hallmark of active canonical WNT signalling.

Signalling dynamics in embryonic development

In multicellular organisms, cellular behaviour is tightly regulated to allow proper embryonic development and maintenance of adult tissue. A critical component in this control is the communication between cells via signalling pathways, as errors in intercellular communication can induce developmental defects or diseases such as cancer. It has become clear over the last years that signalling is not static but varies in activity over time. Feedback mechanisms present in every signalling pathway lead to diverse dynamic phenotypes, such as transient activation, signal ramping or oscillations, occurring in a cell type- and stage-dependent manner. In cells, such dynamics can exert various functions that allow organisms to develop in a robust and reproducible way. Here, we focus on Erk, Wnt and Notch signalling pathways, which are dynamic in several tissue types and organisms, including the periodic segmentation of vertebrate embryos, and are often dysregulated in cancer. We will discuss how biochemical processes influence their dynamics and how these impact on cellular behaviour within multicellular systems.

Relating simulation studies by provenance-Developing a family of Wnt signaling models

For many biological systems, a variety of simulation models exist. A new simulation model is rarely developed from scratch, but rather revises and extends an existing one. A key challenge, however, is to decide which model might be an appropriate starting point for a particular problem and why. To answer this question, we need to identify entities and activities that contributed to the development of a simulation model. Therefore, we exploit the provenance data model, PROV-DM, of the World Wide Web Consortium and, building on previous work, continue developing a PROV ontology for simulation studies. Based on a case study of 19 Wnt/β-catenin signaling models, we identify crucial entities and activities as well as useful metadata to both capture the provenance information from individual simulation studies and relate these forming a family of models. The approach is implemented in WebProv, a web application for inserting and querying provenance information. Our specialization of PROV-DM contains the entities Research Question, Assumption, Requirement, Qualitative Model, Simulation Model, Simulation Experiment, Simulation Data, and Wet-lab Data as well as activities referring to building, calibrating, validating, and analyzing a simulation model. We show that most Wnt simulation models are connected to other Wnt models by using (parts of) these models. However, the overlap, especially regarding the Wet-lab Data used for calibration or validation of the models is small. Making these aspects of developing a model explicit and queryable is an important step for assessing and reusing simulation models more effectively. Exposing this information helps to integrate a new simulation model within a family of existing ones and may lead to the development of more robust and valid simulation models. We hope that our approach becomes part of a standardization effort and that modelers adopt the benefits of provenance when considering or creating simulation models.

We revise a provenance ontology for simulation studies of cellular biochemical models. Provenance information is useful for understanding the creation of a simulation model because it not only contains information about the entities and activities that have led to a simulation model but also their relations, all of which can be visualized. It provides additional structure by explicitly recording research questions, assumptions, and requirements and relating them along with data, qualitative models, simulation models, and simulation experiments through a small set of predefined but extensible activities.

We have applied our concept to a family of 19 Wnt signaling models and implemented a web-based tool (WebProv) to store the provenance information from these studies. The resulting provenance graph visualizes the story line of simulation studies and demonstrates the creation and calibration of simulation models, the successive attempts of validation and extension, and shows, beyond an individual simulation study, how the Wnt models are related. Thereby, the steps and sources that contributed to a simulation model are made explicit.

Our approach complements other approaches aimed at facilitating the reuse and assessment of simulation products in systems biology such as model repositories as well as annotation and documentation guidelines.

Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans

Gene expression oscillators can structure biological events temporally and spatially. Different biological functions benefit from distinct oscillator properties. Thus, finite developmental processes rely on oscillators that start and stop at specific times, a poorly understood behavior. Here, we have characterized a massive gene expression oscillator comprising > 3,700 genes in Caenorhabditis elegans larvae. We report that oscillations initiate in embryos, arrest transiently after hatching and in response to perturbation, and cease in adults. Experimental observation of the transitions between oscillatory and non-oscillatory states at high temporal resolution reveals an oscillator operating near a Saddle Node on Invariant Cycle (SNIC) bifurcation. These findings constrain the architecture and mathematical models that can represent this oscillator. They also reveal that oscillator arrests occur reproducibly in a specific phase. Since we find oscillations to be coupled to developmental processes, including molting, this characteristic of SNIC bifurcations endows the oscillator with the potential to halt larval development at defined intervals, and thereby execute a developmental checkpoint function.

Intrinsic noise, Delta-Notch signalling and delayed reactions promote sustained, coherent, synchronized oscillations in the presomitic mesoderm

Using a stochastic individual-based modelling approach, we examine the role that Delta-Notch signalling plays in the regulation of a robust and reliable somite segmentation clock. We find that not only can Delta-Notch signalling synchronize noisy cycles of gene expression in adjacent cells in the presomitic mesoderm (as is known), but it can also amplify and increase the coherence of these cycles. We examine some of the shortcomings of deterministic approaches to modelling these cycles and demonstrate how intrinsic noise can play an active role in promoting sustained oscillations, giving rise to noise-induced quasi-cycles. Finally, we explore how translational/transcriptional delays can result in the cycles in neighbouring cells oscillating in anti-phase and we study how this effect relates to the propagation of noise-induced stochastic waves.

Constraints on somite formation in developing embryos

Segment formation in vertebrate embryos is a stunning example of biological self-organization. Here, we present an idealized framework, in which we treat the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the framework to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our analysis makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

Unwinding the model manifold: Choosing similarity measures to remove local minima in sloppy dynamical systems

In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases, models are sloppy, that is, exhibit an exponential hierarchy of parameter sensitivities. We propose a parameter classification scheme based on how the sensitivities scale at long observation times. We show that for oscillatory models, either with a limit cycle or a strange attractor, sensitivities can become arbitrarily large, which implies a high effective dimensionality on the model manifold. Sloppy models with a single fixed point have model manifolds with low effective dimensionality, previously described as a "hyper-ribbon." In contrast, models with high effective dimensionality translate into multimodal fitting problems. We define a measure of curvature on the model manifold which we call the winding frequency that estimates the density of local minima in the model's parameter space. We then show how alternative choices of fitting metrics can "unwind" the model manifold and give low winding frequencies. This prescription translates the model manifold from one of high effective dimensionality into the hyper-ribbon structures observed elsewhere. This translation opens the door for applications of sloppy model analysis and model reduction methods developed for models with low effective dimensionality.

Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes

Background

Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/ β-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/ β-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells.

Results

Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/ β-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength.

Conclusions

Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter- and intracellular processes, such as Dkk feedback, diffusion and Wnt/ β-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0470-9) contains supplementary material, which is available to authorized users.

How likely are oscillations in a genetic feedback loop with delay?

Some genetic control networks display temporal oscillations as a result of delays in their homeostatic control. A relevant question about these systems is whether the oscillating regime is a rare feature, or it corresponds to a sizeable volume of the space of parameters. The answer is not trivial mainly due to the large number of parameters controlling the rate equations which describe the network. We have developed an efficient sampling scheme of the parameter space, based on a Monte Carlo algorithm, and applied it to a two-node system with delay, characterised by a 8-dimension parameter space. The result is that the volume fraction of the parameter space associated with oscillations is small but not negligible, and it is weakly dependent on the duration of the delay. The most critical parameter to control oscillations is the coupling production rates, which must have opposite sign, giving rise to a negative feedback loop. The oscillating regions are connected except along the equilibrium constants between the two species, not allowing neutral evolution along this parameter.

Dynamical states, possibilities and propagation of stress signal

The stress driven dynamics of Notch-Wnt-p53 cross-talk is subjected to a few possible dynamical states governed by simple fractal rules, and allowed to decide its own fate by choosing one of these states which are contributed from long range correlation with varied fluctuations due to active molecular interaction. The topological properties of the networks corresponding to these dynamical states have hierarchical features with assortive structure. The stress signal driven by nutlin and modulated by mediator GSK3 acts as anti-apoptotic signal in this system, whereas, the stress signal driven by Axin and modulated by GSK3 behaves as anti-apoptotic for a certain range of Axin and GSK3 interaction, and beyond which the signal acts as favor-apoptotic signal. However, this stress system prefers to stay in an active dynamical state whose counterpart complex network is closest to hierarchical topology with exhibited roles of few interacting hubs. During the propagation of stress signal, the system allows the propagator pathway to inherit all possible properties of the state to the receiver pathway/pathways with slight modifications, indicating efficient information processing and democratic sharing of responsibilities in the system via cross-talk. The increase in the number of cross-talk pathways in the system favors to establish self-organization.

Dynamics of p53 and Wnt cross talk

We present the mechanism of interaction of Wnt network module, which is responsible for periodic somitogenesis, with p53 regulatory network, which is one of the main regulators of various cellular functions, and switching of various oscillating states by investigating p53-Wnt model. The variation in Nutlin concentration in p53 regulating network drives the Wnt network module to different states, stabilized, damped and sustain oscillation states, and even to cycle arrest. Similarly, the change in Axin2 concentration in Wnt could able to modulate the p53 dynamics at these states. We then solve the set of coupled ordinary differential equations of the model using quasi steady state approximation. We, further, demonstrate the change of p53 and GSK3 interaction rate, due to hypothetical catalytic reaction or external stimuli, can able to regulate the dynamics of the two network modules, and even can control their dynamics to protect the system from cycle arrest (apoptosis).

Modelling coupled oscillations in the Notch, Wnt, and FGF signaling pathways during somitogenesis: a comprehensive mathematical model

Somite formation in the early stage of vertebrate embryonic development is controlled by a complicated gene network named segmentation clock, which is defined by the periodic expression of genes related to the Notch, Wnt, and the fibroblast growth factor (FGF) pathways. Although in recent years some findings about crosstalk among the Notch, Wnt, and FGF pathways in somitogenesis have been reported, the investigation of their crosstalk mechanisms from a systematic point of view is still lacking. In this study, a more comprehensive mathematical model was proposed to simulate the dynamics of the Notch, Wnt, and FGF pathways in the segmentation clock. Simulations and bifurcation analyses of this model suggested that the concentration gradients of both Wnt, and FGF signals along the presomitic mesoderm (PSM) are corresponding to the whole process from start to stop of the segmentation clock. A number of highly sensitive parameters to the segmentation clock's oscillatory pattern were identified. By further bifurcation analyses for these sensitive parameters, and several complementary mechanisms in respect of the maintenance of the stable oscillation of the segmentation clock were revealed.

Barx2 and Pax7 have antagonistic functions in regulation of wnt signaling and satellite cell differentiation

The canonical Wnt signaling pathway is critical for myogenesis and can induce muscle progenitors to switch from proliferation to differentiation; how Wnt signals integrate with muscle-specific regulatory factors in this process is poorly understood. We previously demonstrated that the Barx2 homeobox protein promotes differentiation in cooperation with the muscle regulatory factor (MRF) MyoD. Pax7, another important muscle homeobox factor, represses differentiation. We now identify Barx2, MyoD, and Pax7 as novel components of the Wnt effector complex, providing a new molecular pathway for regulation of muscle progenitor differentiation. Canonical Wnt signaling induces Barx2 expression in muscle progenitors and perturbation of Barx2 leads to misregulation of Wnt target genes. Barx2 activates two endogenous Wnt target promoters as well as the Wnt reporter gene TOPflash, the latter synergistically with MyoD. Moreover, Barx2 interacts with the core Wnt effectors β-catenin and T cell-factor 4 (TCF4), is recruited to TCF/lymphoid enhancer factor sites, and promotes recruitment of β-catenin. In contrast, Pax7 represses the Wnt reporter gene and antagonizes the activating effect of Barx2. Pax7 also binds β-catenin suggesting that Barx2 and Pax7 may compete for interaction with the core Wnt effector complex. Overall, the data show for the first time that Barx2, Pax7, and MRFs can act as direct transcriptional effectors of Wnt signals in myoblasts and that Barx2 and Wnt signaling participate in a regulatory loop. We propose that antagonism between Barx2 and Pax7 in regulation of Wnt signaling may help mediate the switch from myoblast proliferation to differentiation.

Mathematical model of the Tat-Rev regulation of HIV-1 replication in an activated cell predicts the existence of oscillatory dynamics in the synthesis of viral components

Background

The life cycle of human immunodeficiency virus type-1 (HIV-1) makes possible the realization of regulatory strategies that can lead to complex dynamical behavior of the system. We analyze the strategy which is based on two feedback mechanisms, one mediating a positive regulation of the virus replication by Tat protein via the antitermination of the genomic RNAs transcription on TAR (transactivation responsive) element of the proviral DNA and the second mechanism providing a negative regulation of the splicing of the full-length (9 kb) RNAs and incompletely spliced (4 kb) RNAs via their transport from the nucleus to the cytoplasm. Although the existence of these two regulatory feedback loops has been considered in other mathematical models, none of them examined the conditions for the emergence of complex oscillatory patterns in the intracellular dynamics of viral components.

Results

We developed a mechanistic mathematical model for the Tat-Rev mediated regulation of HIV-1 replication, which considers the activation of proviral DNA transcription, the Tat-specific antitermination of transcription on TAR-element, resulting in the synthesis of the full-length 9 kb RNA, the splicing of the 9 kb RNA down to the 4 kb RNA and the 4 kb RNA to 2 kb RNA, the transport of 2 kb mRNAs from the nucleus to the cytoplasm by the intracellular mechanisms, the multiple binding of the Rev protein to RRE (Rev Response Element) sites on 9 kb and 4 kb RNA resulting in their export to the cytoplasm and the synthesis of Tat and Rev proteins in the cytoplasm followed by their transport into the nucleus. The degradation of all viral proteins and RNAs both in the cytoplasm and the nucleus is described. The model parameters values were derived from the published literature data. The model was used to examine the dynamics of the synthesis of the viral proteins Tat and Rev, the mRNAs under the intracellular conditions specific for activated HIV-1 infected macrophages. In addition, we analyzed alternative hypotheses for the re-cycling of the Rev proteins both in the cytoplasm and the nuclear pore complex.

Conclusions

The quantitative mathematical model of the Tat-Rev regulation of HIV-1 replication predicts the existence of oscillatory dynamics which depends on the efficacy of the Tat and TAR interaction as well as on the Rev-mediated transport processes. The biological relevance of the oscillatory regimes for the HIV-1 life cycle is discussed.

β-Catenin induces T-cell transformation by promoting genomic instability

Deregulated activation of β-catenin in cancer has been correlated with genomic instability. During thymocyte development, β-catenin activates transcription in partnership with T-cell-specific transcription factor 1 (Tcf-1). We previously reported that targeted activation of β-catenin in thymocytes (CAT mice) induces lymphomas that depend on recombination activating gene (RAG) and myelocytomatosis oncogene (Myc) activities. Here we show that these lymphomas have recurring Tcra/Myc translocations that resulted from illegitimate RAG recombination events and resembled oncogenic translocations previously described in human T-ALL. We therefore used the CAT animal model to obtain mechanistic insights into the transformation process. ChIP-seq analysis uncovered a link between Tcf-1 and RAG2 showing that the two proteins shared binding sites marked by trimethylated histone-3 lysine-4 (H3K4me3) throughout the genome, including near the translocation sites. Pretransformed CAT thymocytes had increased DNA damage at the translocating loci and showed altered repair of RAG-induced DNA double strand breaks. These cells were able to survive despite DNA damage because activated β-catenin promoted an antiapoptosis gene expression profile. Thus, activated β-catenin promotes genomic instability that leads to T-cell lymphomas as a consequence of altered double strand break repair and increased survival of thymocytes with damaged DNA.

From Drosophila development to adult: clues to Notch function in long-term memory

Notch is a cell surface receptor that is well known to mediate inter-cellular communication during animal development. Data in the field indicate that it is also involved in the formation of long-term memory (LTM) in the fully developed adults and in memory loss upon neurodegeneration. Our studies in the model organism Drosophila reveal that a non-canonical Notch-protein kinase C activity that plays critical roles in embryonic development also regulates cyclic-AMP response element binding protein during LTM formation in adults. Here we present a perspective on how the various known features of Notch function relate to LTM formation and how they might interface with elements of Wingless/Wnt signaling in this process.

The dynamics of genetic control in the cell: the good and bad of being late

The expression of genes in the cell is controlled by a complex interaction network involving proteins, RNA and DNA. The molecular events associated with the nodes of such a network take place on a variety of time scales, and thus cannot be regarded as instantaneous. In many cases, the cell is robust with respect to the delay in gene expression control, behaving as if it were instantaneous. However, there are specific cases in which delay gives rise to temporal oscillations. This is the case, for example, of the expression of tumour-suppressor protein p53, of protein Hes1, involved in the differentiation of stem cells, of NFkB and Wnt, in which case delay arises implicitly from the structure of the associated network. By means of delay rate equations, we study the kinetics of small regulatory networks, emphasizing the role of delay in an evolutionary context. These models suggest that oscillations are a typical outcome of the dynamics of regulatory networks, and evolution has to work to avoid them when not required (and not vice versa).

Mathematical models for the Notch and Wnt signaling pathways and the crosstalk between them during somitogenesis

Background

Somitogenesis is a fundamental characteristic feature of development in various animal embryos. Molecular evidence has proved that the Notch and Wnt pathways play important roles in regulating the process of somitogenesis and there is crosstalk between these two pathways. However, it is difficult to investigate the detailed mechanism of these two pathways and their interactions in somitogenesis through biological experiments. In recent years some mathematical models have been proposed for the purpose of studying the dynamics of the Notch and Wnt pathways in somitogenesis. Unfortunately, only a few of these models have explored the interactions between them.

Results

In this study, we have proposed three mathematical models for the Notch signalling pathway alone, the Wnt signalling pathway alone, and the interactions between them. These models can simulate the dynamics of the Notch and Wnt pathways in somitogenesis, and are capable of reproducing the observations derived from wet experiments. They were used to investigate the molecular mechanisms of the Notch and Wnt pathways and their crosstalk in somitogenesis through the model simulations.

Conclusions

Three mathematical models are proposed for the Notch and Wnt pathways and their interaction during somitogenesis. The simulations demonstrate that the extracellular Notch and Wnt signals are essential for the oscillating expressions of both Notch and Wnt target genes. Moreover, the internal negative feedback loops and the three levels of crosstalk between these pathways play important but distinct roles in maintaining the system oscillation. In addition, the results of the parameter sensitivity analysis of the models indicate that the Notch pathway is more sensitive to perturbation in somitogenesis.

Modeling Wnt/β-Catenin Target Gene Expression in APC and Wnt Gradients Under Wild Type and Mutant Conditions

The Wnt/β-catenin pathway is involved in the regulation of a multitude of physiological processes by controlling the differential expression of target genes. In certain tissues such as the adult liver, the Wnt/β-catenin pathway can attain different levels of activity due to gradients of Wnt ligands and/or intracellular pathway components like APC. How graded pathway activity is converted into regionally distinct patterns of Wnt/β-catenin target gene expression is largely unknown. Here, we apply a mathematical modeling approach to investigate the impact of different regulatory mechanisms on target gene expression within Wnt or APC concentration gradients. We develop a minimal model of Wnt/β-catenin signal transduction and combine it with various mechanisms of target gene regulation. In particular, the effects of activation, inhibition, and an incoherent feedforward loop (iFFL) are compared. To specify activation kinetics, we analyze experimental data that quantify the response of β-catenin/TCF reporter constructs to different Wnt concentrations, and demonstrate that the induction of these constructs occurs in a cooperative manner with Hill coefficients between 2 and 5. In summary, our study shows that the combination of specific gene regulatory mechanisms with a time-independent gradient of Wnt or APC is sufficient to generate distinct target gene expression patterns as have been experimentally observed in liver. We find that cooperative gene activation in combination with a TCF feedback can establish sharp borders of target gene expression in Wnt or APC gradients. In contrast, the iFFL renders gene expression independent of gradients of the upstream signaling components. Our subsequent analysis of carcinogenic pathway mutations reveals that their impact on gene expression is determined by the gene regulatory mechanism and the APC concentration of the cell in which the mutation occurs.

Diffusion- and convection-based activation of Wnt/β-catenin signaling in a gradient generating microfluidic chip

Stem cells and developing tissues respond to long-range signaling molecules (morphogens), by starting different nuclear programs that decide about the cell fate. Cells sense the local morphogen concentration and the shape of the gradient. We developed a two-chambered microfluidic chip to reproduce the in vivo situation under shear stress free conditions. The gradient is generated in the lower part of our device and recognized by cells grown in the upper part in the microchamber. We tested our device by activating the Wnt/β-catenin signaling pathway in HeLa cells as proven by nuclear β-catenin accumulation in response to the Wnt pathway activator 6-bromoindirubin-3'-oxime (BIO). Applying the same readout system to a recombinant Wnt3a and Dkk-1 bipolar gradient we demonstrate that our microfluidic chip is suitable for morphogens as well as small molecules. More interestingly, our microfluidic device is highly flexible. While the generated gradients are stable for several hours and reproducible, we can change the kind and the shape of the gradient actively on demand. We also can switch from diffusion- to convection-based transport, thus applying the morphogen gradient either in a polarized or non-polarized manner.

Dickkopf1--a new player in modelling the Wnt pathway

The Wnt signaling pathway transducing the stabilization of β-catenin is essential for metazoan embryo development and is misregulated in many diseases such as cancers. In recent years models have been proposed for the Wnt signaling pathway during the segmentation process in developing embryos. Many of these include negative feedback loops where Axin2 plays a key role. However, Axin2 null mice show no segmentation phenotype. We therefore propose a new model where the negative feedback involves Dkk1 rather than Axin2. We show that this model can exhibit the same type of oscillations as the previous models with Axin2 and as observed in experiments. We show that a spatial Wnt gradient can consistently convert this temporal periodicity into the spatial periodicity of somites, provided the oscillations in new cells arising in the presomitic mesoderm are synchronized with the oscillations of older cells. We further investigate the hypothesis that a change in the Wnt level in the tail bud during the later stages of somitogenesis can lengthen the time period of the oscillations and hence the size and separation of the later somites.

A multi-cell, multi-scale model of vertebrate segmentation and somite formation

Somitogenesis, the formation of the body's primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell-adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length.

Modeling oscillatory control in NF-κB, p53 and Wnt signaling

Oscillations are commonly observed in cellular behavior and span a wide range of timescales, from seconds in calcium signaling to 24 hours in circadian rhythms. In between lie oscillations with time periods of 1-5 hours seen in NF-κB, p53 and Wnt signaling, which play key roles in the immune system, cell growth/death and embryo development, respectively. In the first part of this article, we provide a brief overview of simple deterministic models of oscillations. In particular, we explain the mechanism of saturated degradation that has been used to model oscillations in the NF-κB, p53 and Wnt systems. The second part deals with the potential physiological role of oscillations. We use the simple models described earlier to explore whether oscillatory signals can encode more information than steady-state signals. We then discuss a few simple genetic circuits that could decode information stored in the average, amplitude or frequency of oscillations. The presence of frequency-detector circuit downstream of NF-κB or p53 would be a strong clue that oscillations are important for the physiological response of these signaling systems.