Positional information from oscillatory phase shifts : insights from in silico evolution

Signaling oscillations in embryonic development

Tight spatiotemporal control of cellular behavior and cell fate decisions is paramount to the formation of multicellular organisms during embryonic development. Intercellular communication via signaling pathways mediates this control. Interestingly, these signaling pathways are not static, but dynamic and change in activity over time. Signaling oscillations as a specific type of dynamics are found in various signaling pathways and model systems. Functions of oscillations include the regulation of periodic events or the transmission of information by encoding signals in the dynamic properties of a signaling pathway. For instance, signaling oscillations in neural or pancreatic progenitor cells modulate their proliferation and differentiation. Oscillations between neighboring cells can also be synchronized, leading to the emergence of waves traveling through the tissue. Such population-wide signaling oscillations regulate for example the consecutive segmentation of vertebrate embryos, a process called somitogenesis. Here, we outline our current understanding of signaling oscillations in embryonic development, how signaling oscillations are generated, how they are studied and how they contribute to the regulation of embryonic development.

Molecular and Mechanical Cues for Somite Periodicity

Somitogenesis refers to the segmentation of the paraxial mesoderm, a tissue located on the back of the embryo, into regularly spaced and sized pieces, i.e., the somites. This periodicity is important to assure, for example, the formation of a functional vertebral column. Prevailing models of somitogenesis are based on the existence of a gene regulatory network capable of generating a striped pattern of gene expression, which is subsequently translated into periodic tissue boundaries. An alternative view is that the pre-pattern that guides somitogenesis is not chemical, but of a mechanical origin. A striped pattern of mechanical strain can be formed in physically connected tissues expanding at different rates, as it occurs in the embryo. Here we argue that both molecular and mechanical cues could drive somite periodicity and suggest how they could be integrated.

Positional information encoded in the dynamic differences between neighboring oscillators during vertebrate segmentation

A central problem in developmental biology is to understand how cells interpret their positional information to give rise to spatial patterns, such as the process of periodic segmentation of the vertebrate embryo into somites. For decades, somite formation has been interpreted according to the clock-and-wavefront model. In this conceptual framework, molecular oscillators set the frequency of somite formation while the positional information is encoded in signaling gradients. Recent experiments using ex vivo explants have challenged this interpretation, suggesting that positional information is encoded in the properties of the oscillators, independent of long-range modulations such as signaling gradients. Here, we propose that positional information is encoded in the difference in the levels of neighboring oscillators. The differences gradually increase because both the amplitude and the period of the oscillators increase with time. When this difference exceeds a certain threshold, the segmentation program starts. Using this framework, we quantitatively fit experimental data from in vivo and ex vivo mouse segmentation, and propose mechanisms of somite scaling. Our results suggest a novel mechanism of spatial pattern formation based on the local interactions between dynamic molecular oscillators.

Towards a physical understanding of developmental patterning

The temporal coordination of events at cellular and tissue scales is essential for the proper development of organisms, and involves cell-intrinsic processes that can be coupled by local cellular signalling and instructed by global signalling, thereby creating spatial patterns of cellular states that change over time. The timing and structure of these patterns determine how an organism develops. Traditional developmental genetic methods have revealed the complex molecular circuits regulating these processes but are limited in their ability to predict and understand the emergent spatio-temporal dynamics. Increasingly, approaches from physics are now being used to help capture the dynamics of the system by providing simplified, generic descriptions. Combined with advances in imaging and computational power, such approaches aim to provide insight into timing and patterning in developing systems.

Geometric models for robust encoding of dynamical information into embryonic patterns

During development, cells gradually assume specialized fates via changes of transcriptional dynamics, sometimes even within the same developmental stage. For anterior-posterior (AP) patterning in metazoans, it has been suggested that the gradual transition from a dynamic genetic regime to a static one is encoded by different transcriptional modules. In that case, the static regime has an essential role in pattern formation in addition to its maintenance function. In this work, we introduce a geometric approach to study such transition. We exhibit two types of genetic regime transitions arising through local or global bifurcations, respectively. We find that the global bifurcation type is more generic, more robust, and better preserves dynamical information. This could parsimoniously explain common features of metazoan segmentation, such as changes of periods leading to waves of gene expressions, ‘speed/frequency-gradient’ dynamics, and changes of wave patterns. Geometric approaches appear as possible alternatives to gene regulatory networks to understand development.

Patterning via local cell-cell interactions in developing systems

Spatial patterning during embryonic development emerges from the differentiation of progenitor cells that share the same genetic program. One of the main challenges in systems biology is to understand the relationship between gene network and patterning, especially how the cells communicate to coordinate their differentiation. This review aims to describe the principles of pattern formation from local cell-cell interactions mediated by the Notch signalling pathway. Notch mediates signalling via direct cell-cell contact and regulates cell fate decisions in many tissues during embryonic development. Here, I will describe the patterning mechanisms via different Notch ligands and the critical role of Notch oscillations during the segmentation of the vertebrate body, brain development, and blood vessel formation.

Sustained Oscillations of Epithelial Cell Sheets

Morphological changes during development, tissue repair, and disease largely rely on coordinated cell movements and are controlled by the tissue environment. Epithelial cell sheets are often subjected to large-scale deformation during tissue formation. The active mechanical environment in which epithelial cells operate have the ability to promote collective oscillations, but how these cellular movements are generated and relate to collective migration remains unclear. Here, combining in vitro experiments and computational modeling, we describe a form of collective oscillations in confined epithelial tissues in which the oscillatory motion is the dominant contribution to the cellular movements. We show that epithelial cells exhibit large-scale coherent oscillations when constrained within micropatterns of varying shapes and sizes and that their period and amplitude are set by the smallest confinement dimension. Using molecular perturbations, we then demonstrate that force transmission at cell-cell junctions and its coupling to cell polarity are pivotal for the generation of these collective movements. We find that the resulting tissue deformations are sufficient to trigger osillatory mechanotransduction of YAP within cells, potentially affecting a wide range of cellular processes.

Modulation of Phase Shift between Wnt and Notch Signaling Oscillations Controls Mesoderm Segmentation

How signaling dynamics encode information is a central question in biology. During vertebrate development, dynamic Notch signaling oscillations control segmentation of the presomitic mesoderm (PSM). In mouse embryos, this molecular clock comprises signaling oscillations of several pathways, i.e., Notch, Wnt, and FGF signaling. Here, we directly address the role of the relative timing between Wnt and Notch signaling oscillations during PSM patterning. To this end, we developed a new experimental strategy using microfluidics-based entrainment that enables specific control of the rhythm of segmentation clock oscillations. Using this approach, we find that Wnt and Notch signaling are coupled at the level of their oscillation dynamics. Furthermore, we provide functional evidence that the oscillation phase shift between Wnt and Notch signaling is critical for PSM segmentation. Our work hence reveals that dynamic signaling, i.e., the relative timing between oscillatory signals, encodes essential information during multicellular development.

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Wnt and Notch signaling wave dynamics differ within segmenting mouse mesoderm

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Entraining oscillations by microfluidics allows external control of the dynamics

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Oscillatory Wnt and Notch signaling networks are coupled at the level of dynamics

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Relative timing of Wnt and Notch signaling oscillations is critical for segmentation

Around the clock: gradient shape and noise impact the evolution of oscillatory segmentation dynamics

BACKGROUND

Segmentation, the subdivision of the major body axis into repeated elements, is considered one of the major evolutionary innovations in bilaterian animals. In all three segmented animal clades, the predominant segmentation mechanism is sequential segmentation, where segments are generated one by one in anterior-posterior order from a posterior undifferentiated zone. In vertebrates and arthropods, sequential segmentation is thought to arise from a clock-and-wavefront-type mechanism, where oscillations in the posterior growth zone are transformed into a segmental prepattern in the anterior by a receding wavefront. Previous evo-devo simulation studies have demonstrated that this segmentation type repeatedly arises, supporting the idea of parallel evolutionary origins in these animal clades. Sequential segmentation has been studied most extensively in vertebrates, where travelling waves have been observed that reflect the slowing down of oscillations prior to their cessation and where these oscillations involve a highly complex regulatory network. It is currently unclear under which conditions this oscillator complexity and slowing should be expected to evolve, how they are related and to what extent similar properties should be expected for sequential segmentation in other animal species.

RESULTS

To investigate these questions, we extend a previously developed computational model for the evolution of segmentation. We vary the slope of the posterior morphogen gradient and the strength of gene expression noise. We find that compared to a shallow gradient, a steep morphogen gradient allows for faster evolution and evolved oscillator networks are simpler. Furthermore, under steep gradients, damped oscillators often evolve, whereas shallow gradients appear to require persistent oscillators which are regularly accompanied by travelling waves, indicative of a frequency gradient. We show that gene expression noise increases the likelihood of evolving persistent oscillators under steep gradients and of evolving frequency gradients under shallow gradients. Surprisingly, we find that the evolutions of oscillator complexity and travelling waves are not correlated, suggesting that these properties may have evolved separately.

CONCLUSIONS

Based on our findings, we suggest that travelling waves may have evolved in response to shallow morphogen gradients and gene expression noise. These two factors may thus also be responsible for the observed differences between different species within both the arthropod and chordate phyla.

Electrical Programming of Soft Matter: Using Temporally Varying Electrical Inputs To Spatially Control Self Assembly

The growing importance of hydrogels in translational medicine has stimulated the development of top-down fabrication methods, yet often these methods lack the capabilities to generate the complex matrix architectures observed in biology. Here we show that temporally varying electrical signals can cue a self-assembling polysaccharide to controllably form a hydrogel with complex internal patterns. Evidence from theory and experiment indicate that internal structure emerges through a subtle interplay between the electrical current that triggers self-assembly and the electrical potential (or electric field) that recruits and appears to orient the polysaccharide chains at the growing gel front. These studies demonstrate that short sequences (minutes) of low-power (∼1 V) electrical inputs can provide the program to guide self-assembly that yields hydrogels with stable, complex, and spatially varying structure and properties.

Modelling asymmetric somitogenesis: Deciphering the mechanisms behind species differences

Somitogenesis is one of the major hallmarks of bilateral symmetry in vertebrates. This symmetry is lost when retinoic acid (RA) signalling is inhibited, allowing the left-right determination pathway to influence somitogenesis. In all three studied vertebrate model species, zebrafish, chicken and mouse, the frequency of somite formation becomes asymmetric, with slower gene expression oscillations driving somitogenesis on the right side. Still, intriguingly, the resulting left-right asymmetric phenotypes differ significantly between these model species. While somitogenesis is generally considered as functionally equivalent among different vertebrates, substantial differences exist in the subset of oscillating genes between different vertebrate species. Variation also appears to exist in the way oscillations cease and somite boundaries become patterned. In addition, in absence of RA, the FGF8 gradient thought to constitute the determination wavefront becomes asymmetric in zebrafish and mouse, extending more anteriorly to the right, while remaining symmetric in chicken. Here we use a computational modelling approach to decipher the causes underlying species differences in asymmetric somitogenesis. Specifically, we investigate to what extent differences can be explained from observed differences in FGF asymmetry and whether differences in somite determination dynamics may also be involved. We demonstrate that a simple clock-and-wavefront model incorporating the observed left-right differences in somitogenesis frequency readily reproduces asymmetric somitogenesis in chicken. However, incorporating asymmetry in FGF signalling was insufficient to robustly reproduce mouse or zebrafish asymmetry phenotypes. In order to explain these phenoptypes we needed to extend the basic model, incorporating species-specific details of the somitogenesis determination mechanism. Our results thus demonstrate that a combination of differences in FGF dynamics and somite determination cause species differences in asymmetric somitogenesis. In addition,they highlight the power of using computational models as well as studying left-right asymmetry to obtain more insight in somitogenesis.