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Network Biology, 2025, 15(4): 123-149
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Article

State space analysis of diphtheria pathogenesis using semi-tensor products and permutation methods

Ugbene Ifeanyichukwu Jeff, Ighovotueko Sophia Ajuremisan
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Nigeria

Received 9 March 2025;Accepted 20 April 2025;Published online 20 May 2025;Published 1 December 2025
IAEES

Abstract
In this study, we analyze the state space of a Boolean network modeling diphtheria pathogenesis, focusing on key genes such as Tox, Rep, INF1/INF2, TLR, AP1, IL6, and TNF. We introduce targeted perturbations to reveal how the network responds and converges to its attractors. Our approach utilizes semi-tensor product techniques and permutation methods to recast the Boolean dynamics into a linear algebraic scheme, enabling efficient identification of transient states, stable attractors, and Garden-of-Eden states. This work fills an important gap by clarifying how specific gene interactions drive the network toward non-pathogenic states. Our results show that altering regulatory relationships, particularly those between Rep, Tox, and interferon signals, significantly influences basin sizes and attractor stability, thereby enhancing our understanding of the network's resilience and informing potential therapeutic strategies.

Keywords Boolean network;state space analysis;perturbation;semi-tensor product;permutation method;diphtheria pathogenesis;attractor stability;Garden-of-Eden states;transient dynamics;gene regulation.


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