Modelling viral infection of cells

[Mathematician]

Here's a question with a short version and a long version.

Short version: what are your favourite mathematical or computer models of viral infections of cells? References, please

Longer version:

Supposing I want either

a) a program that simulates what happens when a cell is infected by a virus (I'm interested in flu viruses, of course, but models of any viral infection would be somewhat interesting), or

b) enough information to let me write one.

Where do I find it? At a minimum, I want to be able to run the intracellular model (whether or not I wrote it) and find out things like how many virions are emitted from a cell, how long after initial infection, in what kinds of groupings. If I'm looking at an actual model, I want it to incorporate probability appropriately, i.e. if run many times the outcomes should be justifiably similar in distribution to actual outcomes, rather than, say, modelling one possible outcome only. If I'm looking at an information source, I want it to give me that kind of information. In an ideal world, someone would point me at a model which incorporates everything currently known about flu virus infections, simulating it all in the model and providing easy ways to plug in different hypotheses where there's no consensus...

What I have already is plenty of textbook and textbook-style step by step descriptions of what happens, but without the kind of quantitative information I need for a model (how long does this process take? what is the probability that it completes as described? what influences either of those answers?) I also have a paper by Sidorenko and Reichl, "Structured model of influenza virus replication in MDCK cells" which is closer to what I want, but ideally I'd like something that talks about what happens to individual molecules rather than differential equations describing what happens to quantities of them.

(The background is that I'm new to this kind of modelling, but am working with people who know a lot about it. However, if I want to convince them that flu is a good case study - and I do - it's not enough for me to be the one who knows about flu, we need real papers, better still real people, to validate the modelling choices we make. Otherwise, we risk developing a model of flu infection which is great from the modelling interest point of view but biologically ridiculous, and that will not be useful, nor get published. The interest of the modelling work is providing a generic platform into which one can easily plug information to get both an intra- and an inter-cellular model, so if a fully-worked-out intracellular model of influenza virus infection turne up, what I'd do next would be to try to work out how to plug it into the prototype platform to give an integrated model, as demonstration that one can plug in existing models. Ultimately, of course, one would want to be able to use the integrated model to do in silico experiments concerning, for example, the emergence of Tamiflu resistant or otherwise mutated strains, etc. etc....)

What I'd *ideally* like of course is a "tame" virologist, or similar, who'd be happy to talk to have me bounce ideas off them, look at my early modelling attempts and point out the obvious problems, etc., either just casually or as the beginning of a serious collaboration. But that's probably too much to hope...

Please either reply here or mail me as emathematician at googlemail dot com. (I'll be happy to go to real names, of course, but prefer not to on here.)

 

[gsgs]

Re: Modelling viral infection of cells

very good ! Will the program be available ?
Seems, that you just need some few parameters for
probabilities or such. But these can be kept variable
and improved/assigned later, so in principle you can
start right now ...

I have been wondering about these numbers myself some time ago,
even emailed to Barry, he had some numbers on page 105 in "the
great influenza", refering to Fields,Holland, which I couldn't believe.
I'll search the thread...

Get all flu-sequences from genbank, for each of the 13500/3
positions compute a probability that codon x mutates to codon y
from the frequencies in the database.

Well, basically each nucleotide mutates from x to y independent
of position,x,y I assume. But most mutations are not viable/infectious.
The probabilities must be approximated...

The final parameters can be found experimentally by checking the
#of mutations in practise.
You might also consider reassortment,recombination but we can't
know how viable and infectious a new hypothetical mutated virus is.

 

[gsgs]

Re: Modelling viral infection of cells

posted last year, maybe meanwhile I know a bit more ?!

can synonymous mutations be deleterious ?

I keep reading, that influenza mutates very quickly and that there
are myriard of influenza viruses produced by faulty replication
in an individual, most of which are deleterious.
http://www.sciencemag.org/cgi/content/full/312/5772/394
(page 397, top of medium column)
John Barry, the great influenza, page 105

But then, I'm wondering why we usually only see 1-5
nucleotide-mutations in a host. See e.g. the recently published
sequences from the Karo-cluster.

Most mutations (about 80%?) are synonymous, they don't affect the
amino-acid sequence. As I read and understood, these viruses should have
the same properties as the original virus and thus should be viable
and not deleterious. Still, we don't observe viruses with many
synonymous mutations in one host, as I would expect
when there are myriards of deleterious mutations.

Can someone explain this or has an idea where I can find an explanation ?


-------------------------------------

most mutations _which we observe_ are synonymous.
Most of the non-synonymous ones might have died before we see them.
I'm still in conflict with the numbers from Barry's book, who gives:
* 10h per reproduction cycle, so about 10 virus-generations per
human infection.
* 1e5-1e6 fold replication per cycle
* 99% of these are too defective and will die
* trillions of viruses in a host
* the swarm as a whole will routinely contain almost every possible
permutation of its genetic code
[the last one is clearly nonsense]

-------------------------------------

with Barry's (referring to Holland,Fields) numbers and
assuming that 99% of viruses are defective, assuming that
synonymous mutations can't produce defective viruses, assuming
that all mutations are changes of a single nucleotide (no deletion
of nucleotides or such), assuming that all positions and replacements
are equally likely, then this seems to imply that there are
>3 mutations in average per cycle. Else we would expect more than
1% synonymous-only-mutated viruses.
With 10 replication cycles per infection this gives more than 30
mutations per human host. That's not what we observe.

------------------------------------

same assumptions as above.
Then there is a 25% chance that a mutation is synonymous and a chance
of about 10% that a non-synonymous mutation is viable.
The human body has about 1e13 cells, so even with Barry's smaller
reproduction rate of 1000 per cycle , there will be no more healthy
cells after 2 days. So most viruses die because of lack of healthy cells
to infect, not because of defectiveness.
I calculate a mutation-probability of about 1e-5 per nucleotide-position
and 85% of viruses would survive (and maybe will early in the desease ?)-
if only they could find new cells.

 

[Mathematician]

Re: Modelling viral infection of cells

very good ! Will the program be available ?

Anything I write myself or in which I'm prime mover, almost certainly yes - I believe in free software (which goes well with being a stickler for copyright and precise licensing conditions, see another place However, there is software involved from my collaborators and that I think is not OS - they have a different approach.

Seems, that you just need some few parameters for
probabilities or such. But these can be kept variable
and improved/assigned later, so in principle you can
start right now ...

that's what I've done Still, of course the devil is in the details. Knowing which numbers one really needs is half the battle. And nobody will take any notice unless there is a virologist, or at the very least a definitive virology paper, involved.

Get all flu-sequences from genbank, for each of the 13500/3
positions compute a probability that codon x mutates to codon y
from the frequencies in the database.

Well, basically each nucleotide mutates from x to y independent
of position,x,y I assume. But most mutations are not viable/infectious.
The probabilities must be approximated...

The final parameters can be found experimentally by checking the
#of mutations in practise.
You might also consider reassortment,recombination but we can't
know how viable and infectious a new hypothetical mutated virus is.

That's one idea FWIW, not clear that the probabilities are independent of x,y. At any rate, at the amino acid level, some changes are very much more likely than others, and this is a standard ingredient of bioinformatics.

 

[gsgs]

Re: Modelling viral infection of cells

http://www.cs.unm.edu/~cbeau/docs/these.pdf

7 variable , 11 parameter model of influenza infection
as cellular automaton (chapter 5 , page 68 )
references 11,87

 

[Mathematician]

Re: Modelling viral infection of cells

http://www.cs.unm.edu/~cbeau/docs/these.pdf

7 variable , 11 parameter model of influenza infection
as cellular automaton (chapter 5 , page 68 )
references 11,87

(I followed this up in the PFI version, but I suppose there's some point in repeating the comment here in case anyone else ever reads this here only.)

Thanks, but that's not really what I'm looking for - I want an intra-cellular model, but that is an inter-cellular model.