The patterning of somites is coordinated by presomitic mesoderm cells through synchronised oscillations of Notch signalling, creating sequential waves of gene expression that propagate from the posterior to the anterior end of the tissue. In a new study, Klepstad and Marcon propose a new theoretical framework that recapitulates the dynamics of mouse somitogenesis observed in vivo and in vitro. To learn more about the story behind the paper, we caught up with first author Julie Klepstad and corresponding author Luciano Marcon, Principal Investigator at the Andalusian Center for Developmental Biology.

Julie Klepstad (left) and Luciano Marcon (right)

Luciano, can you give us your scientific biography and the questions your lab is trying to answer?

LM: During my undergraduate studies, under the mentorship of Dr James Sharpe, I worked on a key problem in limb development: the mechanisms underlying digit formation. The prevailing idea was that digits were specified by positional information. Through experiments and modelling, however, we were able to show that digits emerged as a self-organizing periodic pattern resembling a Turing diffusion-driven instability. Turing's theoretical hypothesis, dating back to the 1950s, suggested that diffusion-driven instabilities and self-organization could also promote the emergence of the head-to-tail axis during early embryonic development. In my lab, we're using mouse embryoids to investigate Turing's original hypothesis. Specifically, we are studying how initially uniform stem cell aggregates can autonomously self-organize a main embryonic axis. Our goal is to understand how gene regulatory networks can drive self-organizing processes, like those proposed by Turing, resulting in the distinct cell populations that define the body plan of the embryo.

Julie, how did you come to work in the lab and what drives your research today?

JK: While I was studying theoretical physics in Copenhagen (Denmark) and enjoying learning about lasers and quantum mechanics, I discovered the interesting worlds of computer science and biology. Wanting to follow a path that intersected the two fields, I made a decision to explore the most profound question I could think of: how is life created? This led me to work on complex simulations of early zebrafish development in the lab of the sensational Ala Trusina. Soon thereafter, I moved to Seville (Spain) to join the lab of Luciano, where we are dedicated to applying methodologies from maths and computer science to improve our understanding of how life forms. Specifically, we are studying the topic of self-organization in the early stages of mouse development.

What is the background of the field that inspired your work?

LM: The numerous somitogenesis models found in literature seem to suggest that every good theoretical biologist must conceive at least one in their lifetime. Jokes aside, the abundance of models is a recognition of the fascination that any theoretically inclined person experiences when seeing the beautiful oscillations and waves observed during vertebrate somitogenesis. Each model offers insights into different aspects of this process. However, as is often the case in biology, it may be expected that an ideal model should possess a combination of these aspects. Our aim was to capture the well-established principles of the Clock and Wavefront model proposed by Cooke and Zeeman in the 1970s, while also addressing Olivier Pourquié lab's recent observations of excitable behaviour in vitro. Additionally, we seek to explain the self-organizing circular waves observed in mouse tail explants in vitro by Pourquié's and Alexander Aulehla's labs. Together these different aspects motivated us to develop the Clock and Wavefront Self-Organizing model.

Can you give us the key results of the paper in a paragraph?

LM: We developed a new set of reaction-diffusion equations named Sevilletor, suitable for modelling pattern formation during embryonic development via oscillation coupling. We demonstrate that these equations can capture the main qualitative behaviour of previous somitogenesis models with minimal parameter adjustments. Additionally, we showed that the equations exhibit a previously undescribed self-organizing excitable regime capable of generating phase waves from bistability. Exploiting this regime, we devised an extended Clock and Wavefront somitogenesis model featuring an intermediate region where cells self-organize to generate phase waves. This extended model successfully recapitulates the changes in the relative phase of Wnt and Notch oscillations observed during mouse somitogenesis. More importantly, it provides a novel theoretical framework for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Julie, when doing the research, did you have any particular result or eureka moment that has stuck with you?

JK: Although ‘Eureka’ would be a powerful statement, there was a moment when I truly grasped the full potential of the seemingly simple equations we were exploring. It all started with studying a common type of spiral pattern. But as I began the complex systems analyses and simulations, something remarkable unfolded. We realized that the equations, dubbed the Sevilletor equations, had the astonishing ability to generate a great variety of self-organizing patterns. From chess board-like formations to rotating spirals, excitable waves and bistable patterns – I found that by tweaking just one parameter, we could predict the behaviour of the entire system. Moreover, we could dynamically switch between these behaviours within the same simulation by varying the parameter over time. I also explored spatial variations and discovered that we could incorporate multiple behaviours simultaneously by adjusting the parameter along an axis. And thus, the Sevilletor equations were born, giving rise to the Clock and Wavefront Self-Organizing model.

There was a moment when I truly grasped the full potential of the seemingly simple equations we were exploring.

Two-dimensional self-organizing phase wave pattern generated by the Sevilletor equation through excitability from a bistable regime, initiated from random initial conditions.

Two-dimensional self-organizing phase wave pattern generated by the Sevilletor equation through excitability from a bistable regime, initiated from random initial conditions.

And what about the flipside: any moments of frustration or despair?

JK: Being a theoretician surrounded mostly by biologists brings both joy and challenges in terms of interdisciplinary communication. Biology can, at times, seem like a foreign language to a physicist, and vice versa. I soon realized that mastering the art of presenting my work in a way that is comprehensible to everyone is a valuable skill in its own right. Once I was able to bridge the gap, this ability has proven to be incredibly rewarding as it allows us to continue to push the boundaries of our research further.

Why did you choose to submit this paper to Development?

LM: We believed that, although our study was theoretical, the careful reassessment of previous experimental evidence that we performed would appeal to readers interested in development. Additionally, we were impressed by how Development had established itself as a journal accommodating purely theoretical work in recent years. Lastly, the Spanish National Research Council has an agreement with the journal to promote the open-access publication of any paper authored by council-affiliated researchers. Coupled with our trust in the editorial board and the journal's reputation, we were confident that it was the best platform through which to communicate our work.

Julie, what is next for you after this paper?

JK: This year I am finishing my PhD and I will be looking for my next adventure. Ideally, I would love to find something that combines computer science with environmental sustainability and biodiversity here in Spain.

Luciano, where will this story take your lab next?

LM: The development of the Sevilletor equations and the Clock and Wavefront Self-Organizing model has motivated us to expand our current experimental work with embryoids to include somitogenesis. This expansion will enable us to validate some of the model's predictions with our embryoid in vitro system, such as the influence of the heterogeneity of initial phase values on the types of patterns formed by presomitic mesoderm cells, or to further investigate how mechanical stimuli can modulate the excitable behaviour of presomitic mesoderm cells, as previously shown by Olivier Pourquié's lab. However, the most exciting new line of research we are going to follow is to unify, under a common theoretical and experimental framework, our ongoing investigation of anterior-posterior axis formation with axis segmentation to explore more broadly the relationship between these two self-organizing processes.

Finally, let's move outside the lab – what do you like to do in your spare time?

JK: I love spending time with my wonderful partner at the gym, grilling at home or in the sunshine on Seville's charming terraces. Dancing tango and going for a swim at the beach are also among my favourite pastimes. During the holidays I enjoy visiting friends and family that are spread out across the world, especially my dear family in Norway. And of course, I cannot resist a good thrift shop and upcycling home project that brings old treasures to life!

LM: When I leave the lab, I have two other important experiments running at home; one is almost 6 years old, and the other is 2 years old. These are even more ambitious than the projects in the lab, so I have very little time. Nonetheless, I enjoy training in the Brazilian martial art of Capoeira, which I have been practicing for several years now.

Andalusian Center for Developmental Biology (CABD) CSIC-UPO-JA, Carretera de Utrera km 1, 41013 Seville, Spain.

E-mail: [email protected]

The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro