A theoretical model involving tiny Minecraft-like cubes can help us understand dynamic biological processes, such as cell sorting in embryos
A new approach to model the timescale of multicellular dynamics. Researchers can use Poissonian cellular Potts models to simulate how fast cells sort themselves in the inner cell mass of a developing mouse embryo. Credits: Roman Belousov/EMBL, Isabel Romero Calvo/EMBL
Summary
Time matters in embryonic development, and how fast or slow complex multicellular processes take place depends on physical forces, as well as the material properties of cells.
A new theoretical approach by EMBL researchers and collaborators now allows scientists to model timescales of complex multicellular processes in discrete-state systems.
This approach can be used to investigate the collective effects of interactions between different cell types, for example, to study cell sorting in the developing mouse embryo, as shown in this new study.
Cells in tissues often behave like a school of fish or a flock of birds, collectively moving in concert with each other. This type of ‘collective dynamics’ is critical for many biological phenomena, such as tissue formation, embryo development, cell migration, and even cancer.
In a new study, researchers from the Erzberger Group at EMBL Heidelberg and their collaborators came up with a new approach to better understand the dynamics of collective cell behaviour.
“Our group investigates how cells and multicellular tissues control their shape and how their geometry influences cellular and tissue functions,” said Anna Erzberger, Group Leader at EMBL Heidelberg. “For example, cells in developing embryos frequently change their shape and move around to give rise to new tissues. In particular, certain types of cells actively sort themselves into distinct groups that later form various tissues and organs.”
A standard model used in the field to study such processes is the cellular Potts model. First introduced in 1992, cellular Potts models treat cells as collections of volumetric pixels, or voxels – tiny cubes similar to building blocks in the popular video game Minecraft. When arranged in three-dimensional grids, such voxels represent well how cells with irregular shapes stack against each other in tissues. The model then predicts how small changes in cell shape and position lead them to reach an energetically favoured target state.
“These models provide a very flexible framework for representing complex shapes, but they rely on methods developed to study equilibrium states – states that do not change in time. Therefore, they have significant limitations when it comes to studying dynamical processes, and dynamics is key to any biological phenomenon,” explained Erzberger.
Erzberger and her team added a physical timescale to the model, by considering that different materials take different amounts of time to return to their equilibrium states. An extreme illustration of this is the famous pitch drop experiment. This experiment, running for nearly a century at the University of Queensland in Brisbane, Australia, consists of a sample of extremely viscous pitch slowly flowing down a funnel. Each drop takes about 10 years to form and fall, and it will likely take another century before this system reaches its equilibrium configuration.
This simulation shows how two different types of embryonic cells sort themselves to move into their correct positions in the developing mouse embryo. Credit: Roman Belousov/EMBL
Similarly, different cells have different material properties that determine how quickly or slowly they achieve collective configurations. Roman Belousov, Research Scientist in the Erzberger Group, introduced microscopic rates to the cellular Potts model to represent cells’ kinetic properties. These properties determine how quickly a given kind of ‘Minecraft voxel’ can change, and he related these microscopic rates to the mobility of cellular surfaces. The new framework is especially useful for studying the interactions between materials with different properties, such as cellular and extracellular components, or different cell types, allowing researchers to study the collective dynamics of complex multicellular systems.
“Our extension of the cellular Potts models makes their physics sound and interpretable. In the preexisting approach, a lot of information, especially about the dynamics of modelled systems, was very ambiguous or hard to interpret. Now we understand much better what the model tells us about the phenomenon of interest,” said Belousov, first author of the new study.
To develop the model, the team collaborated with Lamberto Rondoni’s team, including co-hosted master’s student Sabrina Savino, at the Department of Mathematical Sciences in Politecnico di Torino, Italy. The Rondoni group specialises in the dynamics of non-equilibrium systems. They also worked with the team of former EMBL Group Leader Takashi Hiiragi and his PhD student Prachiti Moghe, currently at the Hubrecht Institute in the Netherlands and a professor at Kyoto University, to test the model against experimental data.
Cells in the inner cell mass of the developing mouse embryo sort themselves into two distinct layers, as seen in these immunostaining images taken on embryonic day 3.5 (left) and 8 hours later (right). Credit: Prachiti Moghe/Hubrecht Institute
Hiiragi’s team collected detailed imaging data showing the dynamics of cell sorting in the inner cell mass of developing mouse embryos and measured the cell mechanical parameters of the two cell types involved in the process. The new approach then allowed the team to investigate how different processes contribute to the dynamics and robustness of cell sorting in this system. In particular, the researchers analysed the role of kinetic differences between the two cell types and found that cell divisions or active cell surface fluctuations due to cytoskeletal processes facilitated the sorting process.
“Theoretical models like these provide us with a means to not only understand biological systems but also to uncover the universal principles that underlie many such processes, allowing us to apply them to diverse phenomena and systems,” said Erzberger. The team is excited to take this research, published recently inPhysical Review Letters, even further in the coming months and years – to study interactions between active cellular and passive extracellular components, for example.
Theory@EMBL
EMBL’s Theory@EMBL programme promotes theory-guided paths to understanding and conceptualising underlying principles of biological systems. Among other activities is a special theory visitor/sabbatical programme that can provide support to researchers who work on theoretical and mathematical modelling aspects of biology. Learn more here.
