Modeling B cell Dysfunction in HIV infection Loan Nguyen * , Tagan Griffin † , Abdessamad Tridane * , Yang Kuang * July 30, 2007 Abstract Progression from infection with the Human Immunodeficiency Virus (HIV) to AIDS is a complex process that remains poorly understood. While mathematical models representing the ongoing battle between HIV and the immune system have been successful, they remain focused on cellular, as opposed to humoral, immunity. This situation remains in spite of the fact that recent evidence has shown the mediators of humoral immunity, the B cells, to represent a significant factor in the progression to AIDS. We propose here a mathematical model of HIV infection, which, in addition to B cells, includes a population of so-called ”dysfunctional B cells.” These cells are improperly activated by HIV and contribute towards the progression to AIDS as they waste valuable immune resources and promote autoimmunity, which often accompanies HIV infection. By including more relevant aspects of the immune system into our model, we intend to suggest useful experiments as well as gain a more comprehensive picture of HIV infection. 1 Introduction Primary infection with the Human Immunodeficiency Virus (HIV) is characterized by a rapid decrease in the number of CD4 + lymphocytes, otherwise known as T helper cells. These cells are responsible for a wide range of functions regulating the responses of other cells in the immune system. The immune system reacts to the initial, or primary, HIV infection by using both CD8 + cytotoxic T lymphocytes and antibodies produced by B cells to eliminate most of the virus and restore CD4 + numbers in the blood. However, the CD4 + lymphocytes never fully recover and the ensuing chronic infection involves a gradual decrease in CD4 + numbers, culminating in a diagnosis of acquired immune deficiency syndrome (AIDS). Without treatment, AIDS invariably results in opportunistic infections and death. It is less well known that the B cells of patients with primary HIV infection are also decreased in number and show a number of phenotypic and functional changes, most of which continue throughout chronic infection [1, 2]. A number of these changes occur even before CD4 + numbers begin to decrease [2, 3]. They include abnormal regulation of activation and differentiation as well as an impaired response to vaccinations with T cell-dependent and T cell-independent antigens [1, 4, 5]. This and other evidence suggests the possibility that HIV may act directly on B cells, contributing to disease progression [6]. We propose here a mathematical model simulating the relationship between HIV and the humoral immune system during HIV infection, the aim of which is to provide a system of equations that would suggest experiments based on the assumptions and predictions of the model. The model is unique in that it considers the dynamic between free virus, T cells, and B cells when one assumes HIV acts on immature B cells resulting in a dysfunctional B cell. Recent evidence suggests such a population of cells exists and is responsible for the majority of the B cell dysfunctions in HIV infection [4, 5]. By introducing the dysfunctional B cell, the model aims to provide evidence supporting a more complex view of the causes behind the progression to AIDS. If the mechanism(s) responsible for such effects upon B cells were discovered, new directions towards the treatment of HIV might be possible. Observations focused on a hormone called B cell activation factor (BAFF) in part inspired the creation of our model. BAFF is a crucial survival factor for many B cells in the body and was found in HIV patients in levels nearly double that of healthy controls [7]. The excess BAFF could be partially responsible for * Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA † Center for Infectious Disease and Vaccinology at The Biodesign Institute and the School of Life Sciences, Arizona State University, Tempe, AZ 85287-5001, USA 1