The Relationship The Relationship Between T-Cells and HIV Between T-Cells and HIV

ProgressionProgression

Kiran Dhillon and Kelly NuibeKiran Dhillon and Kelly Nuibe

Courtesy of http://webs.wichita.edu/mschneegurt/biol103/lecture15/hiv_cellbinding.gif

HIV: Human Immunodeficiency Virus

T Cell

Biological Variables and Biological Variables and ParametersParameters

V = virus particles

I = productively infected cells

P = rate per cell

C = clearance rate

Predator-Prey ModelsPredator-Prey Models

Target T-Cell Limitation:

Logistic Model

Activated T Cell Model

Immune Control Model

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The Logistic ModelThe Logistic Model(as seen in class)(as seen in class)

Target T Cell Limitation: Logistic ModelTarget T Cell Limitation: Logistic Model

T = target cells

I = productively infected cells

V = equation 1

β = true infection rate (cells per particle per day)

δ1 = 0.5 day-1, turnover rate of productively infected T cells

γ = combines all other virus induced depletion of the CD4 T cells

α = 0.1 day-1 rate of increase; the max rate of T cell renewal

Tmax = 1000 cells µ L-1, non-infected steady state CD4 count

Ttot = T+I

Target T Cell Limitation: Activated T Cell ModelTarget T Cell Limitation: Activated T Cell Model

T = activated CD4 cells

αQ = rate at which quiescent T cells are activated

δQ = rate they die at

β = rate at which activated CD4 cells are infected by virus

r = rate at which activated CD4 cells revert back to the quiescent state

2rT/(1+Ttot/Tmax) = defines a density dependent regulation of the proliferation rate

Ttot = Q+T+I

Immune Control ModelImmune Control Model

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VIRUS

Immune Response

(CD8 Cells, aka “Killer Cells”)

Immune Control (continued)Immune Control (continued)

When V is at an equilibrium state

Ē = pβ/cK, E: cytotoxic effector T cells

T-Cell Count and HIV ProgressionT-Cell Count and HIV Progression