Characterization of Stable Regulatory Attractors in Malaria Parasite Gene Networks: Asynchronous Boolean Update Method

Plasmodium falciparum, the most virulent human malaria parasite, possesses a highly regulated genome that supports survival, adaptation, virulence, drug resistance, developmental switching, and stress responses within the human host. This study characterizes stable regulatory attractors in a malaria-parasite gene regulatory network using an asynchronous Boolean update method. The network is formulated as a Boolean dynamical system with nine biological components: \(X_1=\mathrm{PfEMP1}\), \(X_2=\mathrm{PfCRT}\), \(X_3=\mathrm{PfMDR1}\), \(X_4=\mathrm{PfDHFR}\), \(X_5=\mathrm{AP2\text{-}G}\), \(X_6=\mathrm{PfSIR2A}\), \(X_7=\mathrm{PfK13}\), \(X_8=\mathrm{HP1}\), and \(X_9=\mathrm{H3K9me3}\), representing regulators associated with virulence, drug resistance, developmental regulation, stress response, and epigenetic control. External pressure is represented by a general stress signal \(\omega\) together with selectors for chloroquine \((\lambda)\), antifolate pressure \((\alpha)\), artemisinin pressure \((\beta)\), and partner-drug pressure \((\rho)\). Fixed points are states satisfying \(F(X)=X\); such states are invariant under either synchronous or asynchronous updating. Under the all-stress-OFF condition, the model yields three fixed points, whereas the all-stress-ON condition yields four fixed points. The attractors show how stress-dependent logical regulation can shift the network between distinct stable expression patterns and provide a mathematical framework for exploring regulatory states associated with parasite adaptation and antimalarial pressure.