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Bacterial math

by mastiffcacher
Tags: bacterial, math
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mastiffcacher
#1
May19-13, 03:03 PM
P: 25
Ok, this is a "stupid" question that I probably should really know the answer to. I am researching bacterial invasion and replication within host cells, A. polyphaga to be exact. I grow the amoeba into a monolayer, add a certain number of bacteria to each sample, and allow them to incubate for 2 hours. This is done in duplicate. At two hours, I remove both sets of samples, remove the media from both, and wash the excess bacteria off gently. One set of samples gets media for the amoeba added and incubated for 46 hours (48 hours total). The first set of samples are washed and the amoeba lysed. The bacteria are serially diluted and plated to determine CFUs. The same is also done at 48 hours with the bacteria concentrated from the supernatant and lysed cells. My question is what calculations should be done to interpret what I am seeing. I will have multiple replicates by the end so everything will be averages eventually. I know one way to present this is just avg CFUs shown to indicate the amount of invasion and hopefully an increase with replication. It was also suggested that I divide the CFUs at 2 hours by the initial CFUs to show the percent that invaded...makes sense to me. I had been told that I should calculate the replication by taking the log of the CFUs at 48 hours divided by CFUs at 2 hours. What would that show? I assume they meant the log(CFUs 48/CFUs2). Any thoughts? Any suggestions with why you would recommend a certain way?
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Curious3141
#2
May19-13, 08:33 PM
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Hmm, I'm not sure what the expected level of your approach should be, but your suggestions seem a little simplistic. First of all, you haven't told us exactly what bacteria you're using in the system. I'm assuming it's something simple like E. coli. The problem, as I see it, is that the bacteria themselves have a typical division time (in the presence of a suitable and plentiful organic carbon source) that's less than 2 hours - I've seen a figure of 45 minutes bandied about, so that means that a log phase population of bacteria is going to increase by 16-fold in that period by division). So there are a few processes that are going on throughout the timeframe, even before the 2 hour cutoff.

1) Bacterial division in the extracellular space (outside the Acanthamoebae).

2) Bacterial invasion into the intracellular space (inside the Acanthamoebae) - remember that this is a composite of bacteria invading the cells, as well as the amoebae engulfing the bacteria.

3) (possibly) Bacterial efflux back from the cells into the medium.

4) (likely) Bacterial division within the cells.

5) (possibly) Bacterial death in the medium (depends on carrying capacity of the medium).

6) (possibly) Bacterial death in the cells (depends on "carrying capacity" of the intracellular environment, and how hostile it is to the bacteria - remember, Acanthamoeba cells eat (ingest/digest) bacteria via their phagocytic vacuoles and enzymes).

Personally, I would approach the problem from a mathematical modelling standpoint (using a deterministic, compartment-based approach). I would put in constants for all the possible processes that could happen (as listed above) - it doesn't matter if one of them doesn't actually happen or is negligible, that constant can just be set to zero later. I would probably assume first order kinetics for simplicity, and see where I go from there.

Have you learnt first-order differential equations?
mastiffcacher
#3
May19-13, 09:24 PM
P: 25
I'm not concerned with any increase in CFUs during the first 2 hours. The division time is pretty high. The 2 hour numbers aren't really the problem as I am just measuring the number that have successfully invaded at that time. At 48 hours, I expect an increase in numbers of CFUs. My question is just how would you calculate the data to display it. I think I actually figured this out this afternoon. The invasion data is shown as a percent of what successfully invaded during 2 hours. The replication is shown as the log increase or decrease compared to what invaded. I haven't been too concerned about the replication outside the host since I control that through the media. Limit specific nutrients extracellularly, then division should only take place intracellularly. Also, I'm accounting for host lysis and extracellular bacteria at 48 hours by concentrating the bacteria out of the supernatant and lysate. My experimental design accounts for most of what you mentioned earlier.

Also, I have seen E. coli have a doubling time of as low as 20-25 minutes from several experiments that have been run. I feel sure that it would depend on strain and media but I love E. coli because of that. Makes constructing a growth curve pretty quick instead of 72-96 hours like I'm having to do now.

Curious3141
#4
May20-13, 12:24 AM
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Bacterial math

You did say you wanted to study bacterial invasion (into the amebae). What I'm saying is that the 2 hour colony count does not correlate with invasion alone, but also replication, both extracellularly as well as intracellularly. And bacterial death may also play a role. So there is no way to study invasion per se using your model.

Replication of the cells intracellularly (or at least *net* change in cell number, which is replication minus death) can, of course, be studied by comparing the colony counts at 48 hours and 2 hours.
mastiffcacher
#5
May20-13, 12:44 PM
P: 25
I agree with what you are saying. My bacteria is very specific in its growth requirements and the media selected will not allow for growth. It also has a long generation time, something like 6 hours or so. There probably is some carry over replication as well as some death. I'm only concerned with how many bacteria are invading. I'm discarding the supernatant and washing so extracellular bacteria are not really a concern.


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