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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.


Behaviors of topologies under simulated mutant conditions of AC signaling.(A) Robustness (Q value) of topologies under varying AC signal conditions; left: representative topologies for three strategies, from Fig 4; middle: top topologies with “AND” rule, from Fig 3; right: top topologies with “AND & Additive” rule, from Fig 3. (B) Pie charts show the number and percentage of robust topologies that reproduce expected mutant patterns reported in Ref. [26] with “AND” rule (top) and “Combined AND & Additive” rule (bottom). (C, D) Average frequency of expected mutant patterns produced by different types of topologies in 1,000 runs of simulation with functional parameters under AC ablation (C) and EGF overexpression (D). The expected mutant patterns are from Ref. [26]. Results of simulation in “Combined AND & Additive” rule are shown. (E) Expected mutant patterns reproduced by representative topologies for three strategies under AC ablation and EGF overexpression. The top two most-frequent patterns along with corresponding occurrences from total 1,000 runs of simulation are shown. Simulation was modeled with “Combined AND & Additive” rule.
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pone.0131397.g007: Behaviors of topologies under simulated mutant conditions of AC signaling.(A) Robustness (Q value) of topologies under varying AC signal conditions; left: representative topologies for three strategies, from Fig 4; middle: top topologies with “AND” rule, from Fig 3; right: top topologies with “AND & Additive” rule, from Fig 3. (B) Pie charts show the number and percentage of robust topologies that reproduce expected mutant patterns reported in Ref. [26] with “AND” rule (top) and “Combined AND & Additive” rule (bottom). (C, D) Average frequency of expected mutant patterns produced by different types of topologies in 1,000 runs of simulation with functional parameters under AC ablation (C) and EGF overexpression (D). The expected mutant patterns are from Ref. [26]. Results of simulation in “Combined AND & Additive” rule are shown. (E) Expected mutant patterns reproduced by representative topologies for three strategies under AC ablation and EGF overexpression. The top two most-frequent patterns along with corresponding occurrences from total 1,000 runs of simulation are shown. Simulation was modeled with “Combined AND & Additive” rule.

Mentions: Previous experiments have shown that perturbations of LIN-3/EGF signaling or Notch signaling may result in error cell fate patterns in VPC system [26,27]. Herein we sought to investigate how identified robust topologies perform under the variations of source signaling and lateral signaling in our model. We first altered the AC signal strength and see how robustness changes. We simulated the AC signal level from low to high by varying S1, S2, and S3 from 0 to 1, while keeping S1 > S2 > S3 (Fig 7A). As expected, from low to high AC signal, all three strategies and the identified top topologies show a similar pattern of change in robustness: first increases and then decreases, with the peak robustness at different places (low AC signal for sequential induction, medium for morphogen gradient induction and high for lateral antagonism strategy) (Fig 7A, S9 and S10 Tables). We also investigated the Q values of topologies with three strategies under the conditions of varying S1 and S2 concordantly (S5 Fig). Results show that increasing both S1 and S2 concordantly leads to similar results as obtained by fixing S1 = 1 and only increasing S2 level (S5A Fig). On the other hand, slightly decreasing S1 and S2 concordantly to a half (0.5×) does not change Q values much, while decreasing S1 and S2 to one tenth (0.1×) decreases the Q values (S5B Fig), which is consistent with the results under the conditions of decreasing AC signal above (Fig 7A).


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

Ping X, Tang C - PLoS ONE (2015)

Behaviors of topologies under simulated mutant conditions of AC signaling.(A) Robustness (Q value) of topologies under varying AC signal conditions; left: representative topologies for three strategies, from Fig 4; middle: top topologies with “AND” rule, from Fig 3; right: top topologies with “AND & Additive” rule, from Fig 3. (B) Pie charts show the number and percentage of robust topologies that reproduce expected mutant patterns reported in Ref. [26] with “AND” rule (top) and “Combined AND & Additive” rule (bottom). (C, D) Average frequency of expected mutant patterns produced by different types of topologies in 1,000 runs of simulation with functional parameters under AC ablation (C) and EGF overexpression (D). The expected mutant patterns are from Ref. [26]. Results of simulation in “Combined AND & Additive” rule are shown. (E) Expected mutant patterns reproduced by representative topologies for three strategies under AC ablation and EGF overexpression. The top two most-frequent patterns along with corresponding occurrences from total 1,000 runs of simulation are shown. Simulation was modeled with “Combined AND & Additive” rule.
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getmorefigures.php?uid=PMC4482679&req=5

pone.0131397.g007: Behaviors of topologies under simulated mutant conditions of AC signaling.(A) Robustness (Q value) of topologies under varying AC signal conditions; left: representative topologies for three strategies, from Fig 4; middle: top topologies with “AND” rule, from Fig 3; right: top topologies with “AND & Additive” rule, from Fig 3. (B) Pie charts show the number and percentage of robust topologies that reproduce expected mutant patterns reported in Ref. [26] with “AND” rule (top) and “Combined AND & Additive” rule (bottom). (C, D) Average frequency of expected mutant patterns produced by different types of topologies in 1,000 runs of simulation with functional parameters under AC ablation (C) and EGF overexpression (D). The expected mutant patterns are from Ref. [26]. Results of simulation in “Combined AND & Additive” rule are shown. (E) Expected mutant patterns reproduced by representative topologies for three strategies under AC ablation and EGF overexpression. The top two most-frequent patterns along with corresponding occurrences from total 1,000 runs of simulation are shown. Simulation was modeled with “Combined AND & Additive” rule.
Mentions: Previous experiments have shown that perturbations of LIN-3/EGF signaling or Notch signaling may result in error cell fate patterns in VPC system [26,27]. Herein we sought to investigate how identified robust topologies perform under the variations of source signaling and lateral signaling in our model. We first altered the AC signal strength and see how robustness changes. We simulated the AC signal level from low to high by varying S1, S2, and S3 from 0 to 1, while keeping S1 > S2 > S3 (Fig 7A). As expected, from low to high AC signal, all three strategies and the identified top topologies show a similar pattern of change in robustness: first increases and then decreases, with the peak robustness at different places (low AC signal for sequential induction, medium for morphogen gradient induction and high for lateral antagonism strategy) (Fig 7A, S9 and S10 Tables). We also investigated the Q values of topologies with three strategies under the conditions of varying S1 and S2 concordantly (S5 Fig). Results show that increasing both S1 and S2 concordantly leads to similar results as obtained by fixing S1 = 1 and only increasing S2 level (S5A Fig). On the other hand, slightly decreasing S1 and S2 concordantly to a half (0.5×) does not change Q values much, while decreasing S1 and S2 to one tenth (0.1×) decreases the Q values (S5B Fig), which is consistent with the results under the conditions of decreasing AC signal above (Fig 7A).

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.