# 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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##### References:
 [1] Wei Li, Hengming Zhao, Rongcun Qin, Dianhua Wu. Constructions of optimal balanced $(m, n, \{4, 5\}, 1)$-OOSPCs. Advances in Mathematics of Communications, 2019, 13 (2) : 329-341. doi: 10.3934/amc.2019022 [2] Carlos Gutierrez, Víctor Guíñez. Simple umbilic points on surfaces immersed in $\R^4$. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 877-900. doi: 10.3934/dcds.2003.9.877 [3] Liancheng Wang, Sean Ellermeyer. HIV infection and CD4+ T cell dynamics. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1417-1430. doi: 10.3934/dcdsb.2006.6.1417 [4] Masoud Sabzevari, Joël Merker, Samuel Pocchiola. Canonical Cartan connections on maximally minimal generic submanifolds $\mathbf{M^5 \subset \mathbb{C}^4}$. Electronic Research Announcements, 2014, 21: 153-166. doi: 10.3934/era.2014.21.153 [5] Jianying Fang. 5-SEEDs from the lifted Golay code of length 24 over Z4. Advances in Mathematics of Communications, 2017, 11 (1) : 259-266. doi: 10.3934/amc.2017017 [6] Huangsheng Yu, Feifei Xie, Dianhua Wu, Hengming Zhao. Further results on optimal $(n, \{3, 4, 5\}, \Lambda_a, 1, Q)$-OOCs. Advances in Mathematics of Communications, 2019, 13 (2) : 297-312. doi: 10.3934/amc.2019020 [7] Dan Liu, Shigui Ruan, Deming Zhu. Nongeneric bifurcations near heterodimensional cycles with inclination flip in $\mathbb{R}^4$. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1511-1532. doi: 10.3934/dcdss.2011.4.1511 [8] Viktor L. Ginzburg and Basak Z. Gurel. On the construction of a $C^2$-counterexample to the Hamiltonian Seifert Conjecture in $\mathbb{R}^4$. Electronic Research Announcements, 2002, 8: 11-19. [9] Federica Sani. A biharmonic equation in $\mathbb{R}^4$ involving nonlinearities with critical exponential growth. Communications on Pure & Applied Analysis, 2013, 12 (1) : 405-428. doi: 10.3934/cpaa.2013.12.405 [10] Dwayne Chambers, Erica Flapan, John D. O'Brien. Topological symmetry groups of $K_{4r+3}$. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1401-1411. doi: 10.3934/dcdss.2011.4.1401 [11] Matías Navarro, Federico Sánchez-Bringas. Dynamics of principal configurations near umbilics for surfaces in $mathbb(R)^4$. Conference Publications, 2003, 2003 (Special) : 664-671. doi: 10.3934/proc.2003.2003.664 [12] Jaume Llibre, Y. Paulina Martínez, Claudio Vidal. Phase portraits of linear type centers of polynomial Hamiltonian systems with Hamiltonian function of degree 5 of the form $H = H_1(x)+H_2(y)$. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 75-113. doi: 10.3934/dcds.2019004 [13] Alonso Sepúlveda, Guilherme Tizziotti. Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$. Advances in Mathematics of Communications, 2014, 8 (1) : 67-72. doi: 10.3934/amc.2014.8.67 [14] Robert M. Strain, Keya Zhu. Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$. Kinetic & Related Models, 2012, 5 (2) : 383-415. doi: 10.3934/krm.2012.5.383 [15] Sami Aouaoui. On some semilinear equation in $R^4$ containing a Laplacian term and involving nonlinearity with exponential growth. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2185-2201. doi: 10.3934/cpaa.2015.14.2185 [16] John D. Nagy, Dieter Armbruster. Evolution of uncontrolled proliferation and the angiogenic switch in cancer. Mathematical Biosciences & Engineering, 2012, 9 (4) : 843-876. doi: 10.3934/mbe.2012.9.843 [17] Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 [18] Koya Nishimura. Global existence for the Boltzmann equation in $L^r_v L^\infty_t L^\infty_x$ spaces. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1769-1782. doi: 10.3934/cpaa.2019083 [19] Somkid Intep, Desmond J. Higham. Zero, one and two-switch models of gene regulation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 495-513. doi: 10.3934/dcdsb.2010.14.495 [20] David Ginzburg and Joseph Hundley. The adjoint $L$-function for $GL_5$. Electronic Research Announcements, 2008, 15: 24-32. doi: 10.3934/era.2008.15.24

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