The number of possible viral variants

milky-wayIf you have been following our discussion of quasispecies here on virology blog, you might be wondering exactly how many possible variants there are for a viral genome. The answer is quite simple: for a genome N nucleotides in length, there are 4N possible variants, because there are 4 different nucleotides. This is a huge number, even for small viral genomes. For example, there are 10180 different variants for a genome that is only 300 nucleotides in length. The HIV-1 genome, which is about 10,000 nucleotides in length, can exist as 106020 different sequences. To put this number in perspective, there are 1011 stars in the Milky Way galaxy and 1080 protons in the universe.

How many different viral genomes are present at any given time? Here is an interesting calculation in Virus Dynamics by Martin A. Nowak and Robert McCredie May (Oxford University Press):

Suppose that the average virus load in an (untreated) HIV infected person is 1010 particles and that this amout of virus particles is produced every day. Thus in 10 years, an HIV infected individual could generate about 1013 virus particles. All HIV infected people in the world could generate up to 1020 virus particles in the course of 10 years. If we assume that only 1% of the nucleotides in the HIV genome are variable (which is a gross underestimation), then there would be about 1060 HIV mutants that coincide in 99% of their genetic sequences. Thus the worldwide pandemic would only produce a fraction 10-40 of all such variants during 10 years. While HIV is extremely variable, at any one time only a minute fraction of all possible variants is present worldwide.

Most of the HIV virions produced in an infected individual appear to be nonviable, suggesting that the population exists at its error threshold. What would happen if we could push replicating genomes over the error threshold?

6 thoughts on “The number of possible viral variants”

  1. Actually, I think you are underestimating the number of possible viral mutants by leaving out deletion and insertion of nucleotides out of your calculations.

  2. I think you meant the question as rhetorical, but I'd like to try out my own informal reasoning.

    I think the key is the observation that “Most of the HIV virions produced in an infected individual appear to be nonviable”. As your error rate increases, you are contributing more non-viable virions to the final population than viable ones. Increase the error rate enough and you might drop below the threshold of viable virions needed to sustain an infection (I'm assuming viable means ABLE to infect, not that it will successfully infect, and also that below a certain number, the immune system will eradicate them – I don't really know that this is the case, but seems the reasonable to me). At least, I suspect, you will lower the probability of the infection taking root or sustaining itself.

    My rather simple minded probability model for my argument would be:
    P(v'e) = P(v'|e) P(e)
    P(v'e) = Probability of virion being a mutant copy AND the copy being inviable [this is the resulting distribution of non-viable virions]
    P(v'|e) = Probability of the virion being inviable given that it is a mutant copy [this is the 'Most' observation, i.e. > .50]
    P(e) = Probability of the virion being a mutant copy [this is the factor we're pushing upward]

    I know this is rather simple minded, but is it in the right direction?

  3. According to me,this is merely underestimation.HIV virus is very rapidly growing and is highly nfectous at the same time.

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