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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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Spatial root-like pattern is stabilised by differential diffusion in the x and y axes. The pattern generated by the coupled GRN model gives rise to a striped pattern with some 'errors' that would correspond to ectopic hairs (A). A similar pattern but with fewer or no errors is obtained when diffusion rate in the x axis is larger than that in the y axis (Dy-axis = 0) and the same random seed is taken (B). The parameter spaces for each case are presented below their typical cell arrangements (C), (D). The colour scale indicates the logarithm of the average number of ectopic cell-types for every combination of parameters. Note that, overall, the parameter space obtained for differential diffusion exhibits fewer ectopic trichoblasts.
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Figure 5: Spatial root-like pattern is stabilised by differential diffusion in the x and y axes. The pattern generated by the coupled GRN model gives rise to a striped pattern with some 'errors' that would correspond to ectopic hairs (A). A similar pattern but with fewer or no errors is obtained when diffusion rate in the x axis is larger than that in the y axis (Dy-axis = 0) and the same random seed is taken (B). The parameter spaces for each case are presented below their typical cell arrangements (C), (D). The colour scale indicates the logarithm of the average number of ectopic cell-types for every combination of parameters. Note that, overall, the parameter space obtained for differential diffusion exhibits fewer ectopic trichoblasts.

Mentions: The simulated spatial cellular pattern of hair and non-hair young cells is very similar to that observed in Arabidopsis roots. It is characterised by bands of trichoblasts (black cells in Figure 4) in the H position, where the positional cue is simulated, and bands of atrichoblasts (white cells in Figure 3) in the NH position. This pattern is recovered within a wide range of parameter values (Figure 5). In most of the parameter space generated by varying the diffusion values DCPC and DbHLH from 0 to 0.25 (step size 0.1), the percentage of errors (cells in the NH position without activator complex) is approximately 0.16% (Figure 5). Such positional errors would correspond to ectopic hairs in the root and are smaller than those reported in actual wild-type Arabidopsis roots (Col) [41].


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)

Spatial root-like pattern is stabilised by differential diffusion in the x and y axes. The pattern generated by the coupled GRN model gives rise to a striped pattern with some 'errors' that would correspond to ectopic hairs (A). A similar pattern but with fewer or no errors is obtained when diffusion rate in the x axis is larger than that in the y axis (Dy-axis = 0) and the same random seed is taken (B). The parameter spaces for each case are presented below their typical cell arrangements (C), (D). The colour scale indicates the logarithm of the average number of ectopic cell-types for every combination of parameters. Note that, overall, the parameter space obtained for differential diffusion exhibits fewer ectopic trichoblasts.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Spatial root-like pattern is stabilised by differential diffusion in the x and y axes. The pattern generated by the coupled GRN model gives rise to a striped pattern with some 'errors' that would correspond to ectopic hairs (A). A similar pattern but with fewer or no errors is obtained when diffusion rate in the x axis is larger than that in the y axis (Dy-axis = 0) and the same random seed is taken (B). The parameter spaces for each case are presented below their typical cell arrangements (C), (D). The colour scale indicates the logarithm of the average number of ectopic cell-types for every combination of parameters. Note that, overall, the parameter space obtained for differential diffusion exhibits fewer ectopic trichoblasts.
Mentions: The simulated spatial cellular pattern of hair and non-hair young cells is very similar to that observed in Arabidopsis roots. It is characterised by bands of trichoblasts (black cells in Figure 4) in the H position, where the positional cue is simulated, and bands of atrichoblasts (white cells in Figure 3) in the NH position. This pattern is recovered within a wide range of parameter values (Figure 5). In most of the parameter space generated by varying the diffusion values DCPC and DbHLH from 0 to 0.25 (step size 0.1), the percentage of errors (cells in the NH position without activator complex) is approximately 0.16% (Figure 5). Such positional errors would correspond to ectopic hairs in the root and are smaller than those reported in actual wild-type Arabidopsis roots (Col) [41].

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
Related in: MedlinePlus