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Modeling Intracellular Dynamics of HIV Infection and Treatment

Samira Khalili and Antonios Armaou. Chemical Engineering, The Pennsylvania State University, University Park, PA 16802

Human Immunodeficiency Virus, the causative agent of acquired immunodeficiency syndrome (AIDS), has been classified in retrovirus family, and specifically in lentivirus group. Retroviruses are enveloped RNA viruses with specific characteristics and their replication cycle includes some uncommon features. The unusual morphological characteristics (cylindrical or cone-shape nuclei), several genes with regulatory function, and a biphasic course of gene expression distinguish lentiviruses form other retroviruses. HIV distinctively encodes six auxiliary genes (Tat, Rev, Nef, Vpr, Vif, and Vpu) with specific roles in infection cycle, leading to a complicated yet robust sequence of events that eventually leads to the creation of new virus particles and the lysis of the infected T-cell.

Like other biological systems, dynamics of HIV infection is very complicated. There are several mathematical models in the open literature that describe different aspects of the infection [1, 2, 3]; however most of them focus on the extracellular components of the infection. The interaction dynamics of intracellular components are extremely complicated and on the other hand, quantitative information from experimental studies does not include all parts of the cycle. These obstacles make developing intracellular mathematical models of HIV very difficult. In [4], a model for the entire infection cycle is proposed. However, some stages don't have the necessary level of detail. In other works [5, 6] precise models have been proposed, yet for a specific part of the cycle.

In this work we propose an intracellular model which covers the complete infection cycle yet is detailed enough that can provide a good insight into the HIV infection cycle. The current model includes feedback loops to capture the regulatory effects of important proteins such as Tat and Rev. Furthermore, this detailed model provides information about dynamics of viral components which can improve drug administration scheduling. For instance, Reverse Transcriptase Inhibitor (RTI) is most effective before the production of double stranded DNA from viral RNA. Decision about drug dosage and administration can be made with the knowledge of components trajectories over the time provided by this model. Ultimately, this model can be linked to a previously developed extracellular model [3] by coarsening the intracellular events and generate a multiscale model of HIV infection which considers dynamics of viral RNA and proteins production at the intracellular level, yet captures the disease progression at the animal level.

[1] A. S. Perelson and P. W. Nelson. Mathematical analysis of HIV-1 dynamics in vivo. SIAM review, 41(1): 3-44, 1999.

[2] J. M. Heffernan and L. M. Wahl. Natural variation in HIV-1 infection: Monte carlo estimates that include CD8 effector cells. J. Theor. Biol., 243: 191-204, 2006.

[3] S. Khalili and A. Armaou. Sensitivity analysis of HIV infection response to treatment via stochastic modeling. Chemical Engineering Science, 63(5):1330-1341, 2008.

[4] B. Reddy and J. Yin. Quantitative intracellular kinetics of HIV type 1. AIDS Res. Hum. Retroviruses. 15:273-283, 1999.

[5] K. Lim and J. Yin. Dynamic tradeoffs in the raft-mediated entry of Human Immunodeficiency Virus type 1 into cells. Biothech. & Bioeng. 93(2): 246-257, 2006.

[6] H. Kim and J. Yin. Robust growth of Human Immunodeficiency Virus Type. Biophysical Journal, 89: 2210-2221, 2005.