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Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model.

Benítez M, Espinosa-Soto C, Padilla-Longoria P, Alvarez-Buylla ER - BMC Syst Biol (2008)

Bottom Line: The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible.A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.

View Article: PubMed Central - HTML - PubMed

Affiliation: Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad Universitaria 3er Circuito Exterior, Junto Jardín Botánico Exterior, Coyoacán 04510, DF, Mexico. marianabk@gmail.com

ABSTRACT

Background: Dynamical models are instrumental for exploring the way information required to generate robust developmental patterns arises from complex interactions among genetic and non-genetic factors. We address this fundamental issue of developmental biology studying the leaf and root epidermis of Arabidopsis. We propose an experimentally-grounded model of gene regulatory networks (GRNs) that are coupled by protein diffusion and comprise a meta-GRN implemented on cellularised domains.

Results: Steady states of the meta-GRN model correspond to gene expression profiles typical of hair and non-hair epidermal cells. The simulations also render spatial patterns that match the cellular arrangements observed in root and leaf epidermis. As in actual plants, such patterns are robust in the face of diverse perturbations. We validated the model by checking that it also reproduced the patterns of reported mutants. The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.

Conclusion: The spatial meta-GRN model integrates available experimental data and contributes to further understanding of the Arabidopsis epidermal system. It also provides a systems biology framework to explore the interplay among sub-networks of a GRN, cell-to-cell communication, cell shape and domain traits, which could help understanding of general aspects of patterning processes. For instance, our model suggests that the information needed for cell fate determination emerges from dynamic processes that depend upon molecular components inside and outside differentiating cells, suggesting that the classical distinction of lineage versus positional cell differentiation may be instrumental but rather artificial. It also suggests that interlinkage of nonlinear and redundant sub-networks in larger networks is important for pattern robustness. Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible. A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.

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Diagrammatic representation of the model structure. In every time-step, the nodes' states are updated according to logical rules [see Additional file 1], then the mobile elements are allowed to diffuse and, finally, diffusion is considered to recalculate the states of mobile elements. These new values are entered into the logical rules in the next iteration. The state of non-mobile elements is only determined by the logical rules applied every time-step.
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Figure 2: Diagrammatic representation of the model structure. In every time-step, the nodes' states are updated according to logical rules [see Additional file 1], then the mobile elements are allowed to diffuse and, finally, diffusion is considered to recalculate the states of mobile elements. These new values are entered into the logical rules in the next iteration. The state of non-mobile elements is only determined by the logical rules applied every time-step.

Mentions: According to experimental data, some proteins codified by elements of the network move to neighbouring cells and affect gene expression in a non-cell-autonomous fashion (TRY, CPC and TTG1 in the leaf epidermis and CPC, GL3 and EGL3 in the root epidermis), giving rise to a network of coupled networks (herein meta-GRN). Although empirical evidence supporting cell-to-cell motion rather than aplopastic transport only exists for CPC and TTG1, all available data are congruent with the assumption that all mobile elements of the GRN move in a cell-to-cell manner. In the spatial model we therefore allowed for certain elements to move among neighbouring cells (Figures 1C, 1D and 2) following the equation:


Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model.

Benítez M, Espinosa-Soto C, Padilla-Longoria P, Alvarez-Buylla ER - BMC Syst Biol (2008)

Diagrammatic representation of the model structure. In every time-step, the nodes' states are updated according to logical rules [see Additional file 1], then the mobile elements are allowed to diffuse and, finally, diffusion is considered to recalculate the states of mobile elements. These new values are entered into the logical rules in the next iteration. The state of non-mobile elements is only determined by the logical rules applied every time-step.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2600786&req=5

Figure 2: Diagrammatic representation of the model structure. In every time-step, the nodes' states are updated according to logical rules [see Additional file 1], then the mobile elements are allowed to diffuse and, finally, diffusion is considered to recalculate the states of mobile elements. These new values are entered into the logical rules in the next iteration. The state of non-mobile elements is only determined by the logical rules applied every time-step.
Mentions: According to experimental data, some proteins codified by elements of the network move to neighbouring cells and affect gene expression in a non-cell-autonomous fashion (TRY, CPC and TTG1 in the leaf epidermis and CPC, GL3 and EGL3 in the root epidermis), giving rise to a network of coupled networks (herein meta-GRN). Although empirical evidence supporting cell-to-cell motion rather than aplopastic transport only exists for CPC and TTG1, all available data are congruent with the assumption that all mobile elements of the GRN move in a cell-to-cell manner. In the spatial model we therefore allowed for certain elements to move among neighbouring cells (Figures 1C, 1D and 2) following the equation:

Bottom Line: The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible.A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.

View Article: PubMed Central - HTML - PubMed

Affiliation: Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad Universitaria 3er Circuito Exterior, Junto Jardín Botánico Exterior, Coyoacán 04510, DF, Mexico. marianabk@gmail.com

ABSTRACT

Background: Dynamical models are instrumental for exploring the way information required to generate robust developmental patterns arises from complex interactions among genetic and non-genetic factors. We address this fundamental issue of developmental biology studying the leaf and root epidermis of Arabidopsis. We propose an experimentally-grounded model of gene regulatory networks (GRNs) that are coupled by protein diffusion and comprise a meta-GRN implemented on cellularised domains.

Results: Steady states of the meta-GRN model correspond to gene expression profiles typical of hair and non-hair epidermal cells. The simulations also render spatial patterns that match the cellular arrangements observed in root and leaf epidermis. As in actual plants, such patterns are robust in the face of diverse perturbations. We validated the model by checking that it also reproduced the patterns of reported mutants. The meta-GRN model shows that interlinked sub-networks contribute redundantly to the formation of robust hair patterns and permits to advance novel and testable predictions regarding the effect of cell shape, signalling pathways and additional gene interactions affecting spatial cell-patterning.

Conclusion: The spatial meta-GRN model integrates available experimental data and contributes to further understanding of the Arabidopsis epidermal system. It also provides a systems biology framework to explore the interplay among sub-networks of a GRN, cell-to-cell communication, cell shape and domain traits, which could help understanding of general aspects of patterning processes. For instance, our model suggests that the information needed for cell fate determination emerges from dynamic processes that depend upon molecular components inside and outside differentiating cells, suggesting that the classical distinction of lineage versus positional cell differentiation may be instrumental but rather artificial. It also suggests that interlinkage of nonlinear and redundant sub-networks in larger networks is important for pattern robustness. Pursuing dynamic analyses of larger (genomic) coupled networks is still not possible. A repertoire of well-characterised regulatory modules, like the one presented here, will, however, help to uncover general principles of the patterning-associated networks, as well as the peculiarities that originate diversity.

Show MeSH