Holistic View on the Structure of Immune Response: Petri Net Model

Abstract

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell–cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Group Theory of Messenger RNA Metabolism and Disease

“…Another consensus poly(A) sequence takes the form rel2 = UGUAA, which corresponds to a three-generator group of the form f p 〈A, U, G|rel2〉. The card seq of such a group is found to be [1,3,7,26,97,624,4,163,•••]. Intriguingly, the free group F 2 = 〈A, U, G|AUG〉, of rank 2, has the same card seq as the f p group with relation rel2, despite both groups not being isomorphic.…”

“…Genome-scale metabolic pathways, genome-environment interactions, the immune response, post-transcriptional regulatory mechanisms, and oncohistones represent aspects of a research field connecting the heritable genetic code to other biological codes. [1][2][3][4][5][6] The aforementioned genetic code is defined precisely as a noninjective map from the 64 codons to the 20 amino acids. Both finite groups and quantum groups have leading roles in modeling this code.…”

Group Theory of Messenger RNA Metabolism and Disease

“…Genome-scale metabolic pathways [1,2], genome-environment interactions [3], the immune response [4], post-transcriptional regulatory mechanisms [5] and oncohistones [6] represent aspects of a research field connecting the heritable genetic code to other biological codes.…”

Multidimensionale Charakterisierung reaktiver und neoplastischer menschlicher Lymphknoten unter Anwendung von Methoden aus dem Bereich Bioinformatik, digitale Pathologie, Datenanalyse und Graphentheorie

“…So kann zukünftig die Reintegration medizinischer Fachgebiete gefördert werden, um schließlich eine ganzheitliche Betrachtung des Patienten zu ermöglichen [136]. [144,145,136,146]. Bis dies jedoch möglich ist, ist noch ein weiter Weg in der Vereinheitlichung immunhistologischer Präprozessierungsprozesse, der Digitalisierung der klinischen Routinen und einer fortschreitenden Robustheit digital-pathologischer Methoden zu gehen [136,147,148].…”