# American Institute of Mathematical Sciences

2011, 8(2): 605-626. doi: 10.3934/mbe.2011.8.605

## Persistence and emergence of X4 virus in HIV infection

 1 Graduate Group in Biophysics, University of California, Berkeley, Berkeley, CA 94720, United States 2 Theoretical Biology and Biophysics, MS-K710, Los Alamos National Laboratory, Los Alamos, NM 87545, United States

Received  March 2010 Revised  November 2010 Published  April 2011

Approximately 50% of late-stage HIV patients develop CXCR4-tropic (X4) virus in addition to CCR5-tropic (R5) virus. X4 emergence occurs with a sharp decline in CD4+ T cell counts and accelerated time to AIDS. Why this phenotypic switch to X4 occurs is not well understood. Previously, we used numerical simulations of a mathematical model to show that across much of parameter space a promising new class of antiretroviral treatments, CCR5 inhibitors, can accelerate X4 emergence and immunodeficiency. Here, we show that mathematical model to be a minimal activation-based HIV model that produces a spontaneous switch to X4 virus at a clinically-representative time point, while also matching in vivo data showing X4 and R5 coexisting and competing to infect memory CD4+ T cells. Our analysis shows that X4 avoids competitive exclusion from an initially fitter R5 virus due to X4v unique ability to productively infect nave CD4+ T cells. We further justify the generalized conditions under which this minimal model holds, implying that a phenotypic switch can even occur when the fraction of activated nave CD4+ T cells increases at a slower rate than the fraction of activated memory CD4+ T cells. We find that it is the ratio of the fractions of activated nave and memory CD4+ T cells that must increase above a threshold to produce a switch. This occurs as the concentration of CD4+ T cells drops beneath a threshold. Thus, highly active antiretroviral therapy (HAART), which increases CD4+ T cell counts and decreases cellular activation levels, inhibits X4 viral growth. However, we show here that even in the simplest dual-strain framework, competition between R5 and X4 viruses often results in accelerated X4 emergence in response to CCR5 inhibition, further highlighting the potential danger of anti-CCR5 monotherapy in multi-strain HIV infection.
Citation: Ariel D. Weinberger, Alan S. Perelson. Persistence and emergence of X4 virus in HIV infection. Mathematical Biosciences & Engineering, 2011, 8 (2) : 605-626. doi: 10.3934/mbe.2011.8.605
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