COMPUTATIONAL MODELING AND SIMULATION AS ENABLERS FOR BIOLOGICAL DISCOVERY 191
takes a very long time, and individuals who have not progressed to full-blown AIDS are asymptomatic.
As Box 5.19 suggests, computational models have been able to shed considerable light on this phenom-
enology, and these insights have altered the view of AIDS from a static picture in which the virus is
essentially dormant and does not do very much for a long time to a much more dynamic picture of a rough
balance between the virus and the immune system, both working very hard, for that period of time. These
findings have had tangible impact, because they have affected drug treatment regimes considerably.
More specifically, the average rate of HIV production in the human body is on the order of 10^10
copies per day as noted in Box 5.19. Empirical data indicate that errors in HIV replication occur at a rate
on the order of 10–4 to 10–5 per base per generation, and since the HIV genome is 10,000 base pairs long,
the likelihood that a replicated genome will contain at least one error is 10 percent to nearly unity (and
the vast majority of these errors are errors in a single base). Because there are only four possible bases in
DNA (and hence each base can change into only one of three other bases), there are only 30,000 possible
single-base mutations of a given genome. An error rate of 10–4 to 10–5 per base per generation distrib-
uted among 10^10 copies each with 10^4 bases means that each generation produces 10^9 to 10^10 mutations,
which are distributed over the set of 30,000 possible mutations. Put differently, every new day brings to
life on the order of 10^5 instances of every possible single-base variant of HIV.
Thus, a drug known to bind to a particular sequence of amino acids at a certain location in a protein
today will face 10^5 to 10^6 new variants tomorrow against which its effectiveness will be questionable.
This fact suggests that drug treatment regimes must target multiple binding sites, and hence combina-
tion drug therapy is likely to be more effective because drug-resistant variants must then be the result of
multiple errors in the replication process (which occur much less frequently). This in fact reflects recent
experience with combination drug regimes.^107
5.4.7 Epidemiology
Epidemiology is the study of the dynamics of disease in a population of individuals. Of particular
interest is the epidemiology of infectious diseases, which arise from contact between an environmental
Box 5.19 Continuedwould require drug combinations that can sustain at least three mutations before resistance arises, and this
engendered the idea of triple combination therapy. Other analyses showed that the slope of viral decay was
proportional to the drug combinations’ antiviral efficacy, providing a means of comparing therapies.Following the rapid 1-2 week “first phase” loss, the rate of HIV RNA decline slows. Models of this “second
phase” of decline, when fitted to the kinetic data, suggested that a small fraction of infected cells might live a
period of weeks while infected (t1/2 ~ 14 days).Following upon the success of these joint modeling and experimental efforts, many similar studies were
undertaken and revealed a fourth, much longer time-scale for the decay of latently infected cells of 6-44
months. Latently infected cells, which harbor the HIV genome but do not produce virus, can hide from the
immune system and reignite infection when the cells are stimulated into proliferation. Clearing latently infect-
ed cells is one of the last remaining obstacles to eradicating HIV from the body.(^107) For further discussion, see A.G. Rodrigo, “HIV Evolutionary Genetics,” Proceedings of the National Academy of Sciences
96(19):10559-10561, 1999; B.A. Cipra, “Will Viruses Succumb to Mathematical Models?” SIAM News 32(2), 1999, available at
http://www.siam.org/siamnews/03-99/viruses.pdf.