190 CATALYZING INQUIRY
Box 5.19
Modeling the In Vivo Dynamics of HIV-1 Infection
Mathematical models of HIV infection and treatment have provided quantitative insights into the major bio-
logical processes that underlie HIV pathogenesis and helped establish the treatment of patients with combina-
tion therapy. This in turn has changed HIV from a fatal disease to a treatable one. The models successfully
describe the changes in viral load in patients under therapy and have yielded estimates of how rapidly HIV is
produced and cleared in vivo, how long HIV-infected cells survive while producing HIV, and how fast HIV
mutates and evolves drug resistance. They have also provided clues into the process of T-cell depletion that
characterizes AIDS. The models have also provided means to rapidly screen antiviral drug candidates for
potency in vivo, thus hastening the introduction of new antiretroviral therapies.
On average, HIV takes about 10 years to advance from initial infection to immune dysfunction (or AIDS).
During this period the amount of virus measured in a person’s blood hardly changes. Because of this slow
progression and the unchanging level of virus it was initially thought that this infection was slow and it was
unclear whether treating this disease early, when symptoms were not apparent, was worthwhile.
Recognizing that constant levels of virus meant only that the rates of viral production and clearance were in
balance, but not necessarily slow, Perelson and David Ho from Rockefeller University used experimental drug
therapy to “perturb” the viral steady state. Mathematically modeling the response to this perturbation using a
system of ordinary differential equations that kept track of the concentrations of infected cells and HIV, and
fitting the experimental data to the model, revealed a plethora of new features of HIV infection.
Figure 5.19.1 shows that after therapy is initiated at time 0, levels of HIV RNA (a surrogate for virus) fall ten-
to a hundredfold in the first week or two of therapy. This suggested that HIV has a half-life (t1/2) of 1-2 days,
and thus maintaining the pre-therapy constant level of virus requires enormous virus production—in fact, the
amount of virus in the body must double every 1-2 days.
Detailed analysis showed that this viral decay was governed by two processes, clearance of free virus particles
(t1/2 < 6 hours) and loss of productively infected cells (t1/2 < 1.6 days). From this rapid clearance of virus one
could compute that at steady state, ~10^10 virions are produced daily and given the mutation rate of HIV, that
each single and most double mutations of the HIV genome are produced daily. Thus, effective drug therapy
FIGURE 5.19.1 Model predictions (lines) of the biphasic decay of HIV viral load compared with typical patient data
(symbols). SOURCE: Courtesy of A.S. Perelson, Los Alamos National Laboratory.
continued
Days
HIV RNA Copies (per ml)
104
103
105
106
Days
HIV RNA Copies (per ml)
104
103
105
106
102
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