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Background: Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.
Results: In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.
Conclusions: The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.
Exposure to community violence through witnessing or being directly victimized has been associated with conduct problems in a range of studies. However, the relationship between community violence exposure (CVE) and conduct problems has never been studied separately in healthy individuals and individuals with conduct disorder (CD). Therefore, it is not clear whether the association between CVE and conduct problems is due to confounding factors, because those with high conduct problems also tend to live in more violent neighborhoods, i.e., an ecological fallacy. Hence, the aim of the present study was: (1) to investigate whether the association between recent CVE and current conduct problems holds true for healthy controls as well as adolescents with a diagnosis of CD; (2) to examine whether the association is stable in both groups when including effects of aggression subtypes (proactive/reactive aggression), age, gender, site and socioeconomic status (SES); and (3) to test whether proactive or reactive aggression mediate the link between CVE and conduct problems. Data from 1178 children and adolescents (62% female; 44% CD) aged between 9 years and 18 years from seven European countries were analyzed. Conduct problems were assessed using the Kiddie-Schedule of Affective Disorders and Schizophrenia diagnostic interview. Information about CVE and aggression subtypes was obtained using self-report questionnaires (Social and Health Assessment and Reactive-Proactive aggression Questionnaire (RPQ), respectively). The association between witnessing community violence and conduct problems was significant in both groups (adolescents with CD and healthy controls). The association was also stable after examining the mediating effects of aggression subtypes while including moderating effects of age, gender and SES and controlling for effects of site in both groups. There were no clear differences between the groups in the strength of the association between witnessing violence and conduct problems. However, we found evidence for a ceiling effect, i.e., individuals with very high levels of conduct problems could not show a further increase if exposed to CVE and vice versa. Results indicate that there was no evidence for an ecological fallacy being the primary cause of the association, i.e., CVE must be considered a valid risk factor in the etiology of CD.