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A computational clonal analysis of the developing mouse limb bud.

Marcon L, Arqués CG, Torres MS, Sharpe J - PLoS Comput. Biol. (2011)

Bottom Line: However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward.Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time.The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis.

View Article: PubMed Central - PubMed

Affiliation: EMBL-CRG Systems Biology Research Unit, Center for Genomic Regulation (CRG), Universitat Pompeu Fabra, Barcelona, Spain. luciano.marcon@crg.es

ABSTRACT
A comprehensive spatio-temporal description of the tissue movements underlying organogenesis would be an extremely useful resource to developmental biology. Clonal analysis and fate mappings are popular experiments to study tissue movement during morphogenesis. Such experiments allow cell populations to be labeled at an early stage of development and to follow their spatial evolution over time. However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward. To overcome this problem, we develop a novel computational method that combines accurate quantification of 2D limb bud morphologies and growth modeling to analyze mouse clonal data of early limb development. Firstly, we explore various tissue movements that match experimental limb bud shape changes. Secondly, by comparing computational clones with newly generated mouse clonal data we are able to choose and characterize the tissue movement map that better matches experimental data. Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time. The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis. Lastly, we show that this comprehensive description can be used to reassess spatio-temporal gene regulations taking tissue movement into account and to investigate PD patterning hypothesis.

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Related in: MedlinePlus

From morphologies to velocity vector fields.(A) A sequence of limb photos at different developmental stages. (B)The chronological sequence of limb morphologies derived from [28] (blue color) is overlaid by the boundary control splines (black lines). Intersection points between control splines and limb morphologies (green dots) define a set of control vectors that are interpolated using radial basis functions (RBF) onto the boundary mesh points. In this way a series of velocity vector fields is obtained (red arrows) which define how to displace the boundary mesh points to match the following mesh in the sequence. (C) Starting from the boundary displacement, a velocity vector field that displaces internal mesh points (red arrows) is calculated by using an edge spring analogy. (D) An example of deformation obtained with an edge spring analogy. 1) A deformation is applied to the boundary points of the mesh (red points) and the displacements of mesh points of the left-most boundary are fixed to zero (green points). 2) Edge springs of the triangles close to the deformation exercise tension forces to the neighboring triangles. 3) Relaxation of the forces to reach equilibrium provides a smooth deformation of the mesh. (E) A mesh (blue mesh) is deformed to match the next mesh in the sequence (green mesh). A triangle (red triangle) of the deformed mesh is split into the overlapping triangles of the next mesh by considering the respective areas of overlap (seven red segments on the right). (F) An example of virtual fate map. A triangular element is labeled with a green dye (probability equal to one) at early stages of development and its fate is simulated using the sequence of deformations and interpolations.
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pcbi-1001071-g002: From morphologies to velocity vector fields.(A) A sequence of limb photos at different developmental stages. (B)The chronological sequence of limb morphologies derived from [28] (blue color) is overlaid by the boundary control splines (black lines). Intersection points between control splines and limb morphologies (green dots) define a set of control vectors that are interpolated using radial basis functions (RBF) onto the boundary mesh points. In this way a series of velocity vector fields is obtained (red arrows) which define how to displace the boundary mesh points to match the following mesh in the sequence. (C) Starting from the boundary displacement, a velocity vector field that displaces internal mesh points (red arrows) is calculated by using an edge spring analogy. (D) An example of deformation obtained with an edge spring analogy. 1) A deformation is applied to the boundary points of the mesh (red points) and the displacements of mesh points of the left-most boundary are fixed to zero (green points). 2) Edge springs of the triangles close to the deformation exercise tension forces to the neighboring triangles. 3) Relaxation of the forces to reach equilibrium provides a smooth deformation of the mesh. (E) A mesh (blue mesh) is deformed to match the next mesh in the sequence (green mesh). A triangle (red triangle) of the deformed mesh is split into the overlapping triangles of the next mesh by considering the respective areas of overlap (seven red segments on the right). (F) An example of virtual fate map. A triangular element is labeled with a green dye (probability equal to one) at early stages of development and its fate is simulated using the sequence of deformations and interpolations.

Mentions: For this study we had to develop software that would allow the exploration of a set of possible velocity vector fields that can each reproduce the same observed boundary changes. In particular, different tissue movement maps are equivalent to considering the 2D limb shape as a rubber sheet or mesh, with different distributions of elastic deformation (e.g.. the various mesh deformations shown in Figure 1B–E). To cover the whole temporal sequence of development, a single complete map would include a sequence of slightly changing hour-by-hour deformations across all 72 shapes. We thus spatially discretized each of the limb bud shapes using an unstructured triangular grid. An example of the type of grid generated is given in Figure 2C. We then sought a convenient approach to parameterize the variety of possible mesh deformations across time, and devised a two-step method – the first step dealing with boundary, and the second with the internal tissue movements.


A computational clonal analysis of the developing mouse limb bud.

Marcon L, Arqués CG, Torres MS, Sharpe J - PLoS Comput. Biol. (2011)

From morphologies to velocity vector fields.(A) A sequence of limb photos at different developmental stages. (B)The chronological sequence of limb morphologies derived from [28] (blue color) is overlaid by the boundary control splines (black lines). Intersection points between control splines and limb morphologies (green dots) define a set of control vectors that are interpolated using radial basis functions (RBF) onto the boundary mesh points. In this way a series of velocity vector fields is obtained (red arrows) which define how to displace the boundary mesh points to match the following mesh in the sequence. (C) Starting from the boundary displacement, a velocity vector field that displaces internal mesh points (red arrows) is calculated by using an edge spring analogy. (D) An example of deformation obtained with an edge spring analogy. 1) A deformation is applied to the boundary points of the mesh (red points) and the displacements of mesh points of the left-most boundary are fixed to zero (green points). 2) Edge springs of the triangles close to the deformation exercise tension forces to the neighboring triangles. 3) Relaxation of the forces to reach equilibrium provides a smooth deformation of the mesh. (E) A mesh (blue mesh) is deformed to match the next mesh in the sequence (green mesh). A triangle (red triangle) of the deformed mesh is split into the overlapping triangles of the next mesh by considering the respective areas of overlap (seven red segments on the right). (F) An example of virtual fate map. A triangular element is labeled with a green dye (probability equal to one) at early stages of development and its fate is simulated using the sequence of deformations and interpolations.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3037386&req=5

pcbi-1001071-g002: From morphologies to velocity vector fields.(A) A sequence of limb photos at different developmental stages. (B)The chronological sequence of limb morphologies derived from [28] (blue color) is overlaid by the boundary control splines (black lines). Intersection points between control splines and limb morphologies (green dots) define a set of control vectors that are interpolated using radial basis functions (RBF) onto the boundary mesh points. In this way a series of velocity vector fields is obtained (red arrows) which define how to displace the boundary mesh points to match the following mesh in the sequence. (C) Starting from the boundary displacement, a velocity vector field that displaces internal mesh points (red arrows) is calculated by using an edge spring analogy. (D) An example of deformation obtained with an edge spring analogy. 1) A deformation is applied to the boundary points of the mesh (red points) and the displacements of mesh points of the left-most boundary are fixed to zero (green points). 2) Edge springs of the triangles close to the deformation exercise tension forces to the neighboring triangles. 3) Relaxation of the forces to reach equilibrium provides a smooth deformation of the mesh. (E) A mesh (blue mesh) is deformed to match the next mesh in the sequence (green mesh). A triangle (red triangle) of the deformed mesh is split into the overlapping triangles of the next mesh by considering the respective areas of overlap (seven red segments on the right). (F) An example of virtual fate map. A triangular element is labeled with a green dye (probability equal to one) at early stages of development and its fate is simulated using the sequence of deformations and interpolations.
Mentions: For this study we had to develop software that would allow the exploration of a set of possible velocity vector fields that can each reproduce the same observed boundary changes. In particular, different tissue movement maps are equivalent to considering the 2D limb shape as a rubber sheet or mesh, with different distributions of elastic deformation (e.g.. the various mesh deformations shown in Figure 1B–E). To cover the whole temporal sequence of development, a single complete map would include a sequence of slightly changing hour-by-hour deformations across all 72 shapes. We thus spatially discretized each of the limb bud shapes using an unstructured triangular grid. An example of the type of grid generated is given in Figure 2C. We then sought a convenient approach to parameterize the variety of possible mesh deformations across time, and devised a two-step method – the first step dealing with boundary, and the second with the internal tissue movements.

Bottom Line: However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward.Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time.The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis.

View Article: PubMed Central - PubMed

Affiliation: EMBL-CRG Systems Biology Research Unit, Center for Genomic Regulation (CRG), Universitat Pompeu Fabra, Barcelona, Spain. luciano.marcon@crg.es

ABSTRACT
A comprehensive spatio-temporal description of the tissue movements underlying organogenesis would be an extremely useful resource to developmental biology. Clonal analysis and fate mappings are popular experiments to study tissue movement during morphogenesis. Such experiments allow cell populations to be labeled at an early stage of development and to follow their spatial evolution over time. However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward. To overcome this problem, we develop a novel computational method that combines accurate quantification of 2D limb bud morphologies and growth modeling to analyze mouse clonal data of early limb development. Firstly, we explore various tissue movements that match experimental limb bud shape changes. Secondly, by comparing computational clones with newly generated mouse clonal data we are able to choose and characterize the tissue movement map that better matches experimental data. Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time. The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis. Lastly, we show that this comprehensive description can be used to reassess spatio-temporal gene regulations taking tissue movement into account and to investigate PD patterning hypothesis.

Show MeSH
Related in: MedlinePlus