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An Atlas of Network Topologies Reveals Design Principles for Caenorhabditis elegans Vulval Precursor Cell Fate Patterning.

Ping X, Tang C - PLoS ONE (2015)

Bottom Line: We show that the topology derived by mapping currently known biochemical pathways to our model matches one of our identified functional topologies.Furthermore, our robustness analysis predicts a possible missing link related to the lateral antagonism strategy.Overall, we provide a theoretical atlas of all possible functional networks in varying environments, which may guide novel discoveries of the biological interactions in vulval development of Caenorhabditis elegans and related species.

View Article: PubMed Central - PubMed

Affiliation: Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China.

ABSTRACT
The vulval precursor cell (VPC) fate patterning in Caenorhabditis elegans is a classic model experimental system for cell fate determination and patterning in development. Despite its apparent simplicity (six neighboring cells arranged in one dimension) and many experimental and computational efforts, the patterning strategy and mechanism remain controversial due to incomplete knowledge of the complex biology. Here, we carry out a comprehensive computational analysis and obtain a reservoir of all possible network topologies that are capable of VPC fate patterning under the simulation of various biological environments and regulatory rules. We identify three patterning strategies: sequential induction, morphogen gradient and lateral antagonism, depending on the features of the signal secreted from the anchor cell. The strategy of lateral antagonism, which has not been reported in previous studies of VPC patterning, employs a mutual inhibition of the 2° cell fate in neighboring cells. Robust topologies are built upon minimal topologies with basic patterning strategies and have more flexible and redundant implementations of modular functions. By simulated mutation, we find that all three strategies can reproduce experimental error patterns of mutants. We show that the topology derived by mapping currently known biochemical pathways to our model matches one of our identified functional topologies. Furthermore, our robustness analysis predicts a possible missing link related to the lateral antagonism strategy. Overall, we provide a theoretical atlas of all possible functional networks in varying environments, which may guide novel discoveries of the biological interactions in vulval development of Caenorhabditis elegans and related species.

No MeSH data available.


Top topologies for different ratios of diffusible to membrane-bound intercellular regulation.Q values of top topologies for different ratios of diffusible to membrane-bound intercellular regulation are plotted. “Only_M” means only membrane-bound and “Only_D” means only diffusible. “Random” means the ratio is evenly sampled from (0, 1). “D = 0.01M, 0.5M, M, 2M” means the ratios of diffusible to membrane-bound are 0.01, 0.5, 1, and 2, respectively. Four cases of different S2 values (0, 0.01, 0.1 and 0.5) are shown from top panel to bottom panel.
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pone.0131397.g006: Top topologies for different ratios of diffusible to membrane-bound intercellular regulation.Q values of top topologies for different ratios of diffusible to membrane-bound intercellular regulation are plotted. “Only_M” means only membrane-bound and “Only_D” means only diffusible. “Random” means the ratio is evenly sampled from (0, 1). “D = 0.01M, 0.5M, M, 2M” means the ratios of diffusible to membrane-bound are 0.01, 0.5, 1, and 2, respectively. Four cases of different S2 values (0, 0.01, 0.1 and 0.5) are shown from top panel to bottom panel.

Mentions: As both membrane-bound (LAG-2) and diffusible (DSL) signals are found in the intercellular signaling among fate-patterning cells and the two signal-induced regulations act differently in the system (the membrane-bound signal induced regulation acts only on the adhesive cells, but the diffusible signal induced regulation acts not only on these cells but also on the source cell itself) [17], we further asked how different proportions of the two kinds of intercellular regulation affect the robustness of the uncovered topologies. Instead of using a random proportion of the two kinds of regulation, we repeatedly enumerated all the coarse-grained networks by fixing the proportion and estimated the robustness of each topology from 10,000 samples of parameter sets. For simplicity, we used “AND” rule for this simulation. Comparing the robustness of the previously discovered top topologies for different proportions of the two kinds of regulation, we found that with a higher proportion of membrane-bound intercellular signaling, the uncovered topologies, both types of topologies with lower and higher S2 respectively, have higher Q values than those with a lower proportion of membrane-bound regulation (see Fig 6 and S5–S8 Tables). The advantage of membrane-bound regulation for functional robustness is considerable for topologies with 1P-2P for larger S2 values. For example, for S2 = 0.5, the Q value of the topology 1P-2P-3N-4N-6P-10N is 0.80 for membrane-bound regulation only, and 0.04 for diffusible regulation only. This suggests that high robustness of topologies for high S2 requires a very high proportion of membrane-bound ligands. Though the advantages are not as evident as those for topologies with 1P-2P, larger proportion of membrane-bound regulation also facilitates some networks with 1P-5P to become more robust, such as 1P-5P-3N-4N for S2 = 0.01 (Q = 0.54 for membrane-bound regulation only and Q = 0.34 for diffusible regulation only). However, for an extremely low S2 value, such as S2 = 0, the most robust topologies, such as 1P-5P-2N-3N-4N, perform invariantly for varying proportions of the two kinds of intercellular regulation.


An Atlas of Network Topologies Reveals Design Principles for Caenorhabditis elegans Vulval Precursor Cell Fate Patterning.

Ping X, Tang C - PLoS ONE (2015)

Top topologies for different ratios of diffusible to membrane-bound intercellular regulation.Q values of top topologies for different ratios of diffusible to membrane-bound intercellular regulation are plotted. “Only_M” means only membrane-bound and “Only_D” means only diffusible. “Random” means the ratio is evenly sampled from (0, 1). “D = 0.01M, 0.5M, M, 2M” means the ratios of diffusible to membrane-bound are 0.01, 0.5, 1, and 2, respectively. Four cases of different S2 values (0, 0.01, 0.1 and 0.5) are shown from top panel to bottom panel.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482679&req=5

pone.0131397.g006: Top topologies for different ratios of diffusible to membrane-bound intercellular regulation.Q values of top topologies for different ratios of diffusible to membrane-bound intercellular regulation are plotted. “Only_M” means only membrane-bound and “Only_D” means only diffusible. “Random” means the ratio is evenly sampled from (0, 1). “D = 0.01M, 0.5M, M, 2M” means the ratios of diffusible to membrane-bound are 0.01, 0.5, 1, and 2, respectively. Four cases of different S2 values (0, 0.01, 0.1 and 0.5) are shown from top panel to bottom panel.
Mentions: As both membrane-bound (LAG-2) and diffusible (DSL) signals are found in the intercellular signaling among fate-patterning cells and the two signal-induced regulations act differently in the system (the membrane-bound signal induced regulation acts only on the adhesive cells, but the diffusible signal induced regulation acts not only on these cells but also on the source cell itself) [17], we further asked how different proportions of the two kinds of intercellular regulation affect the robustness of the uncovered topologies. Instead of using a random proportion of the two kinds of regulation, we repeatedly enumerated all the coarse-grained networks by fixing the proportion and estimated the robustness of each topology from 10,000 samples of parameter sets. For simplicity, we used “AND” rule for this simulation. Comparing the robustness of the previously discovered top topologies for different proportions of the two kinds of regulation, we found that with a higher proportion of membrane-bound intercellular signaling, the uncovered topologies, both types of topologies with lower and higher S2 respectively, have higher Q values than those with a lower proportion of membrane-bound regulation (see Fig 6 and S5–S8 Tables). The advantage of membrane-bound regulation for functional robustness is considerable for topologies with 1P-2P for larger S2 values. For example, for S2 = 0.5, the Q value of the topology 1P-2P-3N-4N-6P-10N is 0.80 for membrane-bound regulation only, and 0.04 for diffusible regulation only. This suggests that high robustness of topologies for high S2 requires a very high proportion of membrane-bound ligands. Though the advantages are not as evident as those for topologies with 1P-2P, larger proportion of membrane-bound regulation also facilitates some networks with 1P-5P to become more robust, such as 1P-5P-3N-4N for S2 = 0.01 (Q = 0.54 for membrane-bound regulation only and Q = 0.34 for diffusible regulation only). However, for an extremely low S2 value, such as S2 = 0, the most robust topologies, such as 1P-5P-2N-3N-4N, perform invariantly for varying proportions of the two kinds of intercellular regulation.

Bottom Line: We show that the topology derived by mapping currently known biochemical pathways to our model matches one of our identified functional topologies.Furthermore, our robustness analysis predicts a possible missing link related to the lateral antagonism strategy.Overall, we provide a theoretical atlas of all possible functional networks in varying environments, which may guide novel discoveries of the biological interactions in vulval development of Caenorhabditis elegans and related species.

View Article: PubMed Central - PubMed

Affiliation: Center for Quantitative Biology and Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China.

ABSTRACT
The vulval precursor cell (VPC) fate patterning in Caenorhabditis elegans is a classic model experimental system for cell fate determination and patterning in development. Despite its apparent simplicity (six neighboring cells arranged in one dimension) and many experimental and computational efforts, the patterning strategy and mechanism remain controversial due to incomplete knowledge of the complex biology. Here, we carry out a comprehensive computational analysis and obtain a reservoir of all possible network topologies that are capable of VPC fate patterning under the simulation of various biological environments and regulatory rules. We identify three patterning strategies: sequential induction, morphogen gradient and lateral antagonism, depending on the features of the signal secreted from the anchor cell. The strategy of lateral antagonism, which has not been reported in previous studies of VPC patterning, employs a mutual inhibition of the 2° cell fate in neighboring cells. Robust topologies are built upon minimal topologies with basic patterning strategies and have more flexible and redundant implementations of modular functions. By simulated mutation, we find that all three strategies can reproduce experimental error patterns of mutants. We show that the topology derived by mapping currently known biochemical pathways to our model matches one of our identified functional topologies. Furthermore, our robustness analysis predicts a possible missing link related to the lateral antagonism strategy. Overall, we provide a theoretical atlas of all possible functional networks in varying environments, which may guide novel discoveries of the biological interactions in vulval development of Caenorhabditis elegans and related species.

No MeSH data available.