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. 2014 Oct 7;9(10):e108830.
doi: 10.1371/journal.pone.0108830. eCollection 2014.

Advanced fault diagnosis methods in molecular networks

Iman Habibi  1 , Effat S Emamian  2 , Ali Abdi  3
Affiliations

Advanced fault diagnosis methods in molecular networks

Iman Habibi et al. PLoS One. .

Abstract

Analysis of the failure of cell signaling networks is an important topic in systems biology and has applications in target discovery and drug development. In this paper, some advanced methods for fault diagnosis in signaling networks are developed and then applied to a caspase network and an SHP2 network. The goal is to understand how, and to what extent, the dysfunction of molecules in a network contributes to the failure of the entire network. Network dysfunction (failure) is defined as failure to produce the expected outputs in response to the input signals. Vulnerability level of a molecule is defined as the probability of the network failure, when the molecule is dysfunctional. In this study, a method to calculate the vulnerability level of single molecules for different combinations of input signals is developed. Furthermore, a more complex yet biologically meaningful method for calculating the multi-fault vulnerability levels is suggested, in which two or more molecules are simultaneously dysfunctional. Finally, a method is developed for fault diagnosis of networks based on a ternary logic model, which considers three activity levels for a molecule instead of the previously published binary logic model, and provides equations for the vulnerabilities of molecules in a ternary framework. Multi-fault analysis shows that the pairs of molecules with high vulnerability typically include a highly vulnerable molecule identified by the single fault analysis. The ternary fault analysis for the caspase network shows that predictions obtained using the more complex ternary model are about the same as the predictions of the simpler binary approach. This study suggests that by increasing the number of activity levels the complexity of the model grows; however, the predictive power of the ternary model does not appear to be increased proportionally.

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Conflict of interest statement

Competing Interests: There is a pending patent that is related to the subject matter of fault diagnosis. The title of the patent is “Systems and methods for fault diagnosis in molecular networks.” This does not alter the authors' adherence to PLOS ONE policies on sharing data and materials.

Figures

Figure 1
Figure 1. The caspase3 network.
The three input molecules are insulin, EGF and TNF, which regulate the output molecule, caspase3, via some intermediate molecules.
Figure 2
Figure 2. Vulnerability versus the fault probability p of each molcule in the caspase3 network.
Vulnerability, which is the probability of the network function failure, shows a non-decreasing trend as the fault probability of a molcule increases. Vulnerability is the highest when AKT is faulty (black graph). When EGFR or MEKK1ASK1 is faulty, vulnerability is the same (blue graph), but less than AKT’s vulnerability. Vulnerability is zero (green graph), when each of the rest of the molecules is faulty.
Figure 3
Figure 3. Caspase3 activity in terms of the TNF activity .
In this figure the activity of TNF changes from 0 to 1, whereas the activities of EGF and insulin are the same, formula image both fixed at 0.2 (blue graph), 0.5 (black graph), and 0.8 (green graph). Overall, caspase3 activity increases with TNF activity. However, its activity decreases as EGF and insulin become more active.
Figure 4
Figure 4. Caspase3 activity in terms of the TNF activity , when AKT is faulty.
In this figure the activity of TNF changes from 0 to 1, whereas the activities of EGF and insulin are the same, formula image. As a baseline, the black graph shows the output activity when there is no faulty molecule. When AKT’s fault probability is small, formula image, the output activity slightly increases (blue graph). However, when AKT’s fault probability is large, formula image, the output activity increases significantly (green graph).
Figure 5
Figure 5. Caspase3 activity in terms of the TNF activity , when MEKK1ASK1 is faulty.
In this figure the activity of TNF changes from 0 to 1, whereas the activities of EGF and insulin are the same, formula image. As a baseline, the black graph shows the output activity when there is no faulty molecule. When MEKK1ASK1’s fault probability is small, formula image, the output activity slightly decreases (blue graph). However, when MEKK1ASK1’s fault probability is large, formula image, the output activity decreases significantly (green graph).
Figure 6
Figure 6. Caspase3 activity in terms of the TNF activity , when IKK is faulty.
In this figure the activity of TNF changes from 0 to 1, whereas the activities of EGF and insulin are the same, formula image. We observe that the output activity does not change, whether IKK is faulty or not. This is because IKK’s vulnerability is zero (as shown in Methods).
Figure 7
Figure 7. Vulnerability versus the fault probability p in the caspase3 network, copmuted using a ternary activity model.
Upon considering three levels of activity for each molecule, active, partially active, and inactive, vulnerability of each molecule is graphed in terms of p. We observe that in the caspase3 network molecules are categorized into six groups, according to their vulnerability levels. Vulnerability is still the highest when AKT is faulty (black graph). EGFR vulnerability (blue) is higher than MEKK1ASK1 vulnerability (green). Vulnerabilities of the rest of the molecules are all below 0.1.
Figure 8
Figure 8. Vulnerability versus the fault probability p for all the molecules in the caspase3 network, while TNF activity is low.
Here TNF activity is 0.2, whereas EGF and insulin activities are fixed at 0.5. We observe that the vulnerability of AKT rapidly increases with p, whereas the vulnerability of other molecules are almost zero. This indicates the critical role of AKT in the network.
Figure 9
Figure 9. Vulnerability versus the fault probability p for all the molecules in the caspase3 network, while TNF activity is high.
Here TNF activity is 0.8, whereas EGF and insulin activities are fixed at 0.5. We observe that the vulnerability of AKT rapidly increases with p, whereas the vulnerabilities of other molecules are zero, except for EGFR and MEKK1ASK1. Due to the increased activity of TNF, these two molecules show some level of vulnerability, which was not present when TNF activity was low.
Figure 10
Figure 10. Comparing vulnerabilities in the caspase3 network obtained via binary and ternary network models.
In this figure dashed and solid graphs represent vulnerabilities for binary and ternary activity models, respectively. In both models AKT shows high vulnerability. While in the binary model EGFR and MEKK1ASK1 exhibit the same vulnerablity, the ternary model shows somewhat different yet still low vulnerability for EGFR. Since vulnerablities for the rest of the molcules are very low in both models, they are not shown, to keep the figure easy to read.
Figure 11
Figure 11. The SHP2 network.
(A) The three input molecules are TCRlig, CD4 and CD28, which regulate the output molecule SHP2. (B) Network vulnerabilities for single faults in the SHP2 network. Highly vulnerable molecules are marked in red, blue is used to identify molecules with low vulnerability and molcules with zero vulnerability are shown in black. (C) Network vulnerabilities for all pairs of faulty molecules (the diagonal elements of the table are single fault vulnerabilities). The color code is the same as panel B.
See this image and copyright information in PMC

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