UC Riverside

This thesis addresses the dynamics of HIV latently infected clones by integrating concepts from physics and mathematical modeling. With the prevalence of HIV and the absence of a cure, understanding the underlying dynamics becomes crucial. The fundamental concept of Brownian motion, rooted in physics, serves as a cornerstone for understanding the continuous random fluctuations observed in biological systems. Leveraging this notion, the Wiener process, also known as the mathematical foundation for Brownian motion, enables the incorporation of stochasticity into the modeling of biological phenomena. By adopting the Wiener process as a key component, the dynamics of HIV-infected clones can be described in a probabilistic manner, enhancing our comprehension of their behavior. Furthermore, the model of an overdamped spring in a thermal bath provides a valuable analogy for characterizing the fluctuating antigen interactions within HIV clones. Drawing inspiration from this physics-based concept, we can simulate the dynamic variations in antigenic stimulation that influence the persistence and reactivation of the latent HIV reservoir. By explicitly considering these thermal fluctuations, our model captures the complex dynamics of HIV-infected clones in a more realistic and nuanced manner. Taking the heterogeneity of the reservoir and doing an ensemble approach on top of that typical of statistical mechanics allows us to understand the phenomena observed in clinical data. By integrating physics-inspired modeling techniques, this research unravels the dynamics of HIV-infected clones, contributing to a deeper understanding of HIV pathogenesis and informing potential therapeutic interventions. The introduction emphasizes the gravity of HIV infection and the urgent need for physics-inspired modeling approaches. Chapter 2 delves into HIV dynamics and existing mathematical models. Chapter 3 includes our research into characterizing whether proviruses found in lymph nodes are systematically similar or different than the ones found in peripheral blood, an essential piece of knowledge based on which modeling decisions are taken. Chapter 4, the centerpiece of this thesis, explores clonal heterogeneity and antigenic stimulation's impact on the persistence of the latent HIV reservoir, proposing a mathematical model and rigorous comparison with clinical data. By bridging disciplines, this research aims to contribute significantly to HIV research and support global efforts in combating this persistent health crisis.