insight - Computational Biology - # Axial patterning in multicellular systems

Efficient Local Signaling Strategies for Robust and Tunable Axial Patterning in Multicellular Systems

Q: How could the patterning strategies identified in this work be extended to two-dimensional systems, and what additional challenges or capabilities might emerge

The patterning strategies identified in this study could be extended to two-dimensional systems by considering interactions between cells in a grid-like arrangement. In a two-dimensional system, cells would communicate with their neighboring cells in a more complex manner, potentially involving diagonal interactions as well. This would require updating the rules to account for the additional dimensions and the different configurations that can arise in a two-dimensional grid. One challenge that might emerge in two-dimensional systems is the coordination of patterning across different axes. While the strategies identified for one-dimensional patterning can be extended to two dimensions, ensuring the proper alignment and coordination of patterns along multiple axes could be more challenging. Additionally, the diffusion of signaling molecules or the propagation of patterning signals may behave differently in two-dimensional space, requiring adjustments to the rules to account for these differences. On the other hand, two-dimensional systems offer the capability of forming more intricate and spatially diverse patterns. The interactions between cells in a two-dimensional grid can lead to the emergence of complex patterns with different shapes, sizes, and orientations. This increased complexity can provide a richer landscape for studying pattern formation and could potentially lead to the discovery of novel patterning mechanisms that are unique to two-dimensional systems.

Q: What biological mechanisms or constraints might favor the implementation of a pure sorting strategy versus a bulldozer-based strategy for axial patterning in natural systems

Biological mechanisms or constraints that might favor the implementation of a pure sorting strategy over a bulldozer-based strategy for axial patterning in natural systems could be related to the specific requirements of the patterning process. A pure sorting strategy, where cells are systematically rearranged into distinct regions based on their initial states, could be advantageous in scenarios where precise spatial organization is crucial. For example, in developmental processes where specific cell types need to be positioned in a precise order along an axis, a sorting strategy ensures accurate placement without the need for extensive reorganization or erasure of existing patterns. This can be particularly important in cases where the final pattern needs to be maintained over time without significant changes. On the other hand, a bulldozer-based strategy, which involves erasing and reconstructing the pattern through the movement of specific cell states, might be favored in situations where dynamic changes in the pattern are required. This strategy allows for more flexibility in reshaping the pattern and can accommodate alterations in the spatial arrangement of cell types over time. In scenarios where the patterning process needs to adapt to changing environmental cues or developmental signals, a bulldozer-based strategy could provide the necessary plasticity and responsiveness. The choice between these strategies could also be influenced by the underlying biological context, such as the signaling mechanisms available, the robustness required in the patterning process, and the specific spatial constraints of the system being patterned.

Q: Could the principles of modular patterning identified here be applied to the formation of more complex, multi-regional patterns beyond the French flag problem

The principles of modular patterning identified in this work could be applied to the formation of more complex, multi-regional patterns beyond the French flag problem by combining and reconfiguring the identified patterning modules to create diverse spatial arrangements. By breaking down the patterning process into modular components, each responsible for specific aspects of pattern formation, it becomes possible to mix and match these modules to generate a wide range of patterns with varying regions and structures. For example, by combining sorting modules with bulldozer modules in different configurations, it may be possible to create patterns with multiple stripes, checkerboard patterns, or even intricate motifs with distinct regions of different cell types. Additionally, the concept of consensus rules and multiple alignment can help in identifying common patterning principles that can be generalized and applied to different patterning problems. By understanding the fundamental building blocks of patterning mechanisms, researchers can design synthetic systems or interpret biological processes in a more systematic and modular way. Overall, the modular approach to patterning identified in this study provides a framework for designing and understanding complex spatial patterns in biological systems, offering a versatile and adaptable strategy for engineering diverse multicellular patterns.

Core Concepts

Cellular automata models with local cell-cell signaling can generate robust and tunable axial patterning patterns, such as the French flag, without requiring global signaling mechanisms.

Abstract

The content explores alternative mechanisms for axial patterning in multicellular systems, focusing on strategies that rely only on local cell-cell signaling, rather than global signaling.

Key highlights:

The authors use cellular automata (CA) models to investigate patterning strategies that can form axial patterns, such as the French flag pattern, using only local signaling between neighboring cells.
An evolutionary algorithm is used to identify high-fitness CA rules that can generate the French flag pattern from random initial conditions. A consensus rule is then extracted through a multiple alignment procedure, revealing two key patterning modules: a sorting module and a bulldozer module.
Expanding the rule space to 4 states enables the discovery of additional patterning strategies, including a pure sorting strategy and a full erase-and-reconstruct strategy, in addition to the mixed strategy of the 3-state consensus rule.
The different patterning strategies are analyzed and compared in terms of their accuracy, speed, robustness to noise and growth, and tunability of the resulting patterns.
The authors show that the patterning strategies based on local signaling can generate accurate axial patterns that scale with system size, while exhibiting different trade-offs between properties like robustness and patterning speed.
The regulatory logic underlying the identified patterning modules could serve as a basis for the design of synthetic patterning systems and as a conceptual framework for interpreting biological patterning mechanisms.

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Quotes

"Cellular automata (CA) as a minimal model of pattern formation via local cell-cell signaling."
"The regulatory logic underlying these modules could therefore serve as the basis for the design of synthetic patterning systems, and as a conceptual framework for the interpretation of biological mechanisms."
"Mechanisms based on short-range signaling, between cells and their neighbors, are particularly promising in this context."

Key Insights Distilled From

The French flag problem revisited: Creating robust and tunable axial patterns without global signaling

by Kremser,S., ... at www.biorxiv.org 12-30-2023

https://www.biorxiv.org/content/10.1101/2023.12.29.573602v1

Deeper Inquiries

How could the patterning strategies identified in this work be extended to two-dimensional systems, and what additional challenges or capabilities might emerge

The patterning strategies identified in this study could be extended to two-dimensional systems by considering interactions between cells in a grid-like arrangement. In a two-dimensional system, cells would communicate with their neighboring cells in a more complex manner, potentially involving diagonal interactions as well. This would require updating the rules to account for the additional dimensions and the different configurations that can arise in a two-dimensional grid.
One challenge that might emerge in two-dimensional systems is the coordination of patterning across different axes. While the strategies identified for one-dimensional patterning can be extended to two dimensions, ensuring the proper alignment and coordination of patterns along multiple axes could be more challenging. Additionally, the diffusion of signaling molecules or the propagation of patterning signals may behave differently in two-dimensional space, requiring adjustments to the rules to account for these differences.
On the other hand, two-dimensional systems offer the capability of forming more intricate and spatially diverse patterns. The interactions between cells in a two-dimensional grid can lead to the emergence of complex patterns with different shapes, sizes, and orientations. This increased complexity can provide a richer landscape for studying pattern formation and could potentially lead to the discovery of novel patterning mechanisms that are unique to two-dimensional systems.

What biological mechanisms or constraints might favor the implementation of a pure sorting strategy versus a bulldozer-based strategy for axial patterning in natural systems

Biological mechanisms or constraints that might favor the implementation of a pure sorting strategy over a bulldozer-based strategy for axial patterning in natural systems could be related to the specific requirements of the patterning process.
A pure sorting strategy, where cells are systematically rearranged into distinct regions based on their initial states, could be advantageous in scenarios where precise spatial organization is crucial. For example, in developmental processes where specific cell types need to be positioned in a precise order along an axis, a sorting strategy ensures accurate placement without the need for extensive reorganization or erasure of existing patterns. This can be particularly important in cases where the final pattern needs to be maintained over time without significant changes.
On the other hand, a bulldozer-based strategy, which involves erasing and reconstructing the pattern through the movement of specific cell states, might be favored in situations where dynamic changes in the pattern are required. This strategy allows for more flexibility in reshaping the pattern and can accommodate alterations in the spatial arrangement of cell types over time. In scenarios where the patterning process needs to adapt to changing environmental cues or developmental signals, a bulldozer-based strategy could provide the necessary plasticity and responsiveness.
The choice between these strategies could also be influenced by the underlying biological context, such as the signaling mechanisms available, the robustness required in the patterning process, and the specific spatial constraints of the system being patterned.

Could the principles of modular patterning identified here be applied to the formation of more complex, multi-regional patterns beyond the French flag problem

The principles of modular patterning identified in this work could be applied to the formation of more complex, multi-regional patterns beyond the French flag problem by combining and reconfiguring the identified patterning modules to create diverse spatial arrangements.
By breaking down the patterning process into modular components, each responsible for specific aspects of pattern formation, it becomes possible to mix and match these modules to generate a wide range of patterns with varying regions and structures. For example, by combining sorting modules with bulldozer modules in different configurations, it may be possible to create patterns with multiple stripes, checkerboard patterns, or even intricate motifs with distinct regions of different cell types.
Additionally, the concept of consensus rules and multiple alignment can help in identifying common patterning principles that can be generalized and applied to different patterning problems. By understanding the fundamental building blocks of patterning mechanisms, researchers can design synthetic systems or interpret biological processes in a more systematic and modular way.
Overall, the modular approach to patterning identified in this study provides a framework for designing and understanding complex spatial patterns in biological systems, offering a versatile and adaptable strategy for engineering diverse multicellular patterns.