The RNA polymerase II C-terminal domain (CTD), which serves as a scaffold to recruit machinery involved in transcription, is modified post-translationally. Although the O-GlcNAc modification of RNA polymerase II CTD was documented in 1993, its functional significance remained obscure. We show that O-GlcNAc transferase (OGT) modified CTD serine residues 5 and 7. Drug inhibition of OGT and OGA (N-acetylglucosaminidase) blocked transcription during preinitiation complex assembly. Polymerase II and OGT co-immunoprecipitated, and OGT is a component of the preinitiation complex. OGT shRNA experiments showed that reduction of OGT causes a reduction in transcription and RNA polymerase II occupancy at several B-cell promoters. These data suggest that the cycling of O-GlcNAc on and off of polymerase II occurs during assembly of the preinitiation complex. Our results define unexpected roles for both the CTD and O-GlcNAc in the regulation of transcription initiation in higher eukaryotes.

Leprosy is characterized by complex biological and cellular interactions, driven primarily by the interplay between Th₁ and Th₂ cells. In this study, we develop a deterministic mathematical model to investigate the interactions among healthy and infected Schwann cells, M. leprae bacteria, and Th₁–Th₂ immune responses. The positivity and boundedness of the proposed five-dimensional system are established, and the disease persistence condition is characterized in terms of the basic reproduction number (${\mathcal{R}}_0$). The existence conditions for the endemic equilibrium are derived, while the global asymptotic stability of the endemic state is established through the construction of an appropriate Lyapunov function. To evaluate the robustness of the proposed model, parameter sensitivity with respect to ${\mathcal{R}}_0$ is investigated using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient sensitivity analysis. Furthermore, Monte Carlo uncertainty analysis (UA) is incorporated to account for the inherent uncertainty in the system, whereas a Sobol-based global sensitivity analysis quantifies the contribution of individual model parameters to the overall uncertainty. To further validate the dynamical behavior of the proposed system numerically, Lyapunov exponents are computed using the Benettin (renormalization) algorithm. The impact of combined multidrug therapy (MDT) and IL-10 inhibitor therapy is subsequently investigated within an optimal control framework, and the corresponding optimal treatment strategies are derived using Pontryagin’s maximum principle. Numerical simulations demonstrate that suppressing the Th₂-mediated weakening of the host immune response through IL-10 inhibitor therapy provides superior long-term control of leprosy. The proposed treatment strategy therefore identifies IL-10 inhibitor therapy as a promising adjunct immunomodulatory intervention alongside MDT for enhancing protective cellular immunity against M. leprae in a cost-effective manner.

In this study, a delay-induced mathematical model for biodiesel production is proposed by introducing a discrete time delay into a reaction kinetic framework. The delay represents the intrinsic lag associated with intermediate biochemical processes during biodiesel synthesis. An optimal control strategy based on ultrasound-assisted production is further incorporated to regulate biodiesel yield while minimizing control cost. The resulting delayed optimal control system is analyzed using Pontryagin’s Maximum Principle. To efficiently simulate the delayed dynamics, a fixed-step RK4 solver for delay differential equations is developed and validated against the ddeint method. Numerical simulations demonstrate that delay significantly affects transient biodiesel dynamics and may induce oscillatory behavior. Sensitivity and uncertainty analyses identify key kinetic parameters governing oscillation amplitude and system robustness. The results highlight the potential of ultrasound-assisted control strategies for enhancing biodiesel production.

Cervical cancer is strongly associated with persistent infection by high-risk human papillomavirus (HPV) and continues to pose a major global health burden in recent times. Oncolytic virotherapy has emerged as a promising targeted strategy that selectively eliminates cancer cells while simultaneously activating host immune responses. In this study, a deterministic mathematical model is developed to investigate the dynamics of HPV-induced cervical cancer under oncolytic virotherapy, both as a standalone intervention and in combination with chemotherapy. The model captures the interactions among HPV-infected epithelial cells, cancer cells, oncolytic virus–infected cancer cells, free viral particles, and virus-specific cytotoxic T-lymphocytes. Fundamental qualitative properties of the system are established, and threshold conditions governing oncolytic virus persistence are identified. To elucidate the relative influence of biological and therapeutic parameters, a comprehensive global sensitivity analysis is performed using the extended Fourier amplitude sensitivity test (eFAST) and partial rank correlation coefficients. This analysis reveals key mechanisms regulating cancer cell dynamics and highlights parameters that critically shape treatment outcomes. An optimal control framework is further employed to assess time-dependent therapeutic strategies, providing insight into effective scheduling of virotherapy and chemotherapy while balancing treatment cost. Furthermore, numerical simulation-based evidences justify the analytical findings obtained in the study and demonstrate the comparative advantages of the combined strategy.