Mathematical Models of HIV-1 Dynamics, Transcription, and Latency
<p>The basic viral dynamics model. (<b>A</b>) Cell population processes that are simulated in the mathematical model (Equation (<a href="#FD1-viruses-15-02119" class="html-disp-formula">1</a>)). (<b>B</b>,<b>C</b>) Example trajectory of viral load (V) and uninfected target cells (CD4 T cells, T) when <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </mrow> </semantics></math> (red) and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </semantics></math> (blue). Graphs were generated by numerically integrating Equation (<a href="#FD1-viruses-15-02119" class="html-disp-formula">1</a>) with parameters <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> cells/µL, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math> or 0/day/(virus/mL), <math display="inline"><semantics> <mrow> <mi>k</mi> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> <mn>150</mn> </mrow> </semantics></math> virus/cell, <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>T</mi> </msub> <mo>=</mo> <mn>0.05</mn> <mo>/</mo> </mrow> </semantics></math>day, <math display="inline"><semantics> <mrow> <msub> <mi>d</mi> <mi>I</mi> </msub> <mo>=</mo> <mn>0.7</mn> <mo>/</mo> </mrow> </semantics></math>day, <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>1.7</mn> </mrow> </semantics></math>/day using JSim v2.21 with standard integration parameters [<a href="#B32-viruses-15-02119" class="html-bibr">32</a>]. (Figure adapted from Hill [<a href="#B18-viruses-15-02119" class="html-bibr">18</a>] and created by part (<b>A</b>) with <a href="http://BioRender.com" target="_blank">BioRender.com</a>).</p> "> Figure 2
<p>Schematic of a viral dynamics model involving multiple populations of infected cells. (<b>A</b>) A flow diagram between two populations of uninfected cells (T, T<math display="inline"><semantics> <msub> <mrow/> <mn>2</mn> </msub> </semantics></math>), virus infected cells (I, I<math display="inline"><semantics> <msub> <mrow/> <mn>2</mn> </msub> </semantics></math>), a latently infected cell population (L) and free HIV-1 (V) according to the ODE shown in Equation (<a href="#FD4-viruses-15-02119" class="html-disp-formula">4</a>). Red X’es indicate the complete interruption of viral infection during fully effective therapy. (<b>B</b>) The decay of the viral load in multiple stages is shown. (<b>C</b>) The decay of distinct host-cell populations, as predicted by the model, are depicted. Time-series were integrated using JSim v2.21 with standard integration parameters [<a href="#B32-viruses-15-02119" class="html-bibr">32</a>]. (Figure adapted from Hill [<a href="#B18-viruses-15-02119" class="html-bibr">18</a>] and created by part (<b>A</b>) with <a href="http://BioRender.com" target="_blank">BioRender.com</a>).</p> "> Figure 3
<p>Schematic of latent reservoir dynamics. The latent reservoir involves long-lived resting memory CD4 cells, with potentially integrated HIV-1 provirus. At subcritical viral replication rate (<math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </semantics></math>), the persistence of virus represents the maintenance of the latent reservoir. Infected host cells within this reservoir may occasionally die (marked by skull and bones), proliferate, or reactivate. A large proliferation rate leads to a decrease in viral diversity within the latent reservoir. New infections (bursts) are either completely blocked (Reactivation blocked) or may occasionally occur by stochastic processes. But continuous chains of replication are inhibited in the <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </semantics></math> regime (Infection controlled). After treatment interruption (<math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </mrow> </semantics></math>), reactivated cells can produce virus that infects other host cells yielding to exponential growth in viral load (see <a href="#sec4-viruses-15-02119" class="html-sec">Section 4</a>, in particular Figure 4C). (Figure adapted from Hill [<a href="#B18-viruses-15-02119" class="html-bibr">18</a>] and created with <a href="http://BioRender.com" target="_blank">BioRender.com</a>).</p> "> Figure 4
<p>Mathematical model of the host and viral phases of the HIV-1 transcriptional program [<a href="#B121-viruses-15-02119" class="html-bibr">121</a>]. (<b>A</b>) Simplified model of the host and viral phases of the HIV-1 transcriptional program. (<b>B</b>) Experimental data and fitted stochastic computer simulation of a host cell infected by HIV-1 in the host phase without feedback by Tat. (<b>C</b>) Experimental data and fitted stochastic computer simulation of a host cell infected by HIV-1 in the viral phase with feedback by Tat.</p> "> Figure 5
<p>Positive feedback on the RNAPII pause release rate (PPRR) activation does not influence bimodality of the mRNA and protein distributions in the three-state transcriptional cycling model [<a href="#B109-viruses-15-02119" class="html-bibr">109</a>]. Updated three-state promoter system with HIV-1 nucleosome remodeling, RelA recruitment, and Tat-mediated transcript elongation, which is amplified via positive feedback. Positive feedback is modeled as a saturating function with an amplitude, <span class="html-italic">A</span>, and half-max, <span class="html-italic">K</span>.</p> ">
Abstract
:1. Introduction
2. History of Mathematical Models of HIV-1
2.1. Viral Dynamics Model
2.1.1. The Basic Viral Dynamics Model
2.1.2. Models of ART
2.2. Mechanisms of Latent Reservoir Persistence
3. Molecular Features Contributing to HIV-1 Latency and Reactivation
3.1. Integration Site
3.2. Chromatin
3.3. Transcription Machinery
4. Transcriptional Bursting and Mathematical Modeling
4.1. Transcriptional Bursting and Gene Expression Noise
4.2. A Stochastic Model to Describe the HIV-1 Transcriptional Circuit
4.3. Incorporating Host and Viral Phases to Model the HIV-1 Transcriptional Circuit
4.4. Two-State HIV-1 Transcriptional Model
4.5. Three-State HIV-1 Transcriptional Model
5. Discussion and Future Perspective
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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D’Orso, I.; Forst, C.V. Mathematical Models of HIV-1 Dynamics, Transcription, and Latency. Viruses 2023, 15, 2119. https://doi.org/10.3390/v15102119
D’Orso I, Forst CV. Mathematical Models of HIV-1 Dynamics, Transcription, and Latency. Viruses. 2023; 15(10):2119. https://doi.org/10.3390/v15102119
Chicago/Turabian StyleD’Orso, Iván, and Christian V. Forst. 2023. "Mathematical Models of HIV-1 Dynamics, Transcription, and Latency" Viruses 15, no. 10: 2119. https://doi.org/10.3390/v15102119