Multiplicity of infection

Multiplicity of infection (MOI) is a frequently used term in virology which refers to the number of virions that are added per cell during infection. If one million virions are added to one million cells, the MOI is one. If ten million virions are added, the MOI is ten. Add 100,000 virions, and the MOI is 0.1. The concept is straightforward.

But here is the tricky part. If you infect cells at a MOI of one, does that mean that each cell in the cutlure receives one virion?

The answer is no.

Here is another way to look at this problem: imagine a room containing 100 buckets. If you threw 100 tennis balls into that room – all at the same time – would each bucket get one ball? Most likely not.

How many tennis balls end up in each bucket, or the number of virions that each cell receives at different MOI, is described by the Poisson distribution:

P(k) = e-mmk/k!

In this equation, P(k) is the fraction of cells infected by k virus particles, and m is the MOI. The equation can be simplified to calculate the fraction of uninfected cells (k=0), cells with a single infection (k=1), and cells with multiple infection (k>1):

P(0) = e-m

P(1) = me-m

P(>1) = 1-e-m(m+1)*

*this value is obtained by subtracting from unity (the sum of all probabilities for any value of k) the probabilities P(0) and P(1)

Here are some examples of how these equations can be used. If we have a million cells in a culture dish and infect them at a MOI of 10, how many cells receive 0, 1, and more than one virion? The fraction of uninfected cells – those which receive 0 particles – is

P(0) = e-10

= 4.5 x 10-5

In a culture of one million cells this is 45 uninfected cells. That’s why an MOI of 10 is used in many virology experiments – it assures that essentially every cell is infected.

At the same MOI of 10, the number of cells that receive 1 particle is calculated by

P(1) = 10e-10

= 10 x 4.5 x 10-5

= 4.5 x 10-4

In a culture of one million cells, 450 cells receive 1 particle.

How many cells receive more than one particle is calculated by

P(>1) = 1-e-10(10+1)


In a culture of one million cells, 999,500 cells receive more than one particle.

Using the same formulas, we can determine the fraction of cells receiving 0, 1, and more than one virus particle if we infect one million cells at a MOI of 1:

P(0) = e-1 = 0.37 = 37% of cells are uninfected

P(1) = 1 x e-1 = 37% of cells receive one virion

P(>1) = 1 – e-1(1+1) = 26% of cells are multiply infected

An assumption inherent in these calculations is that all cells in a culture are identical in their ability to be infected. In a clonal cell culture (such as HeLa cells) the deviations in size and surface properties are small enough to be negligible. However, in a multicellular animal there are substantial differences in cell types that affect susceptibility to infection. Under these conditions, it is experimentally difficult to determine how many virions infect different cells.

High MOI is used when the experiment requires that every cell in the culture is infected. By contrast, low MOI is used when multiple cycles of infection are required. However, it is not possible to calculate the MOI unless the virus titer can be determined – for example by plaque assay or any other method of quantifying infectivity.

Now playing: Viral plaque formation

viral_plaquesOne of the most important procedures in virology is measuring the virus titer – the concentration of viruses in a sample. A widely used approach for determining the quantity of infectious virus is the plaque assay. In this technique, the spread of progeny viruses released by individually infected cells is restricted to neighboring cells by a semisolid medium. Consequently, each infectious particle produces a circular zone of infected cells called a plaque. By imagining live, virus-infected cells using a microscope, beautiful movies have been made which show how a plaque develops in real time.

To produce the movies, cells were infected with vaccinia virus, covered with a semi-solid medium, and placed in an incubator. The monolayers were examined periodically until a small plaque became visible. The infected cells were then placed on an inverted microscope fitted with a camera. Images of the plaque were taken every hour for 12-19 hours and assembled into a movie.

The first movie shows plaque formation on monkey cells infected with vaccinia virus. The virus infection begins at a small focus in the center, then spreads radially outwards. As the infection spreads, the cells undergo changes know as cytopathic effect. The large circle of dead cells would appear as a plaque if the monolayer were stained.

The second movie, made at higher magnification, shows spread at the edge of a viral plaque. The vaccinia virus used for this experiment carries the gene encoding enhanced green fluorescent protein (EGFP). Hence the infected cells fluoresce green as viral replication proceeds.

By showing very clearly how a viral plaque develops, these movies will be an invaluable teaching resource for years to come. I am grateful to the authors of this study for providing an up-close view of a technique that animal virologists have been using since 1952.

Doceul, V., Hollinshead, M., van der Linden, L., & Smith, G. (2010). Repulsion of Superinfecting Virions: A Mechanism for Rapid Virus Spread Science DOI: 10.1126/science.1183173

Rhinovirus and zinc part 5: Magnesium is not the culprit

If you have been following the results of my experiments on inhibition of rhinovirus replication by ZnCl2, you know that I’ve been trying to determine why concentrations of the salt higher than 0.1 mM are toxic to HeLa cells. I have found that 0.1 mM ZnCl2 does inhibit rhinovirus plaque formation but not sufficiently to be able to select resistant mutants. In today’s set of experiments I asked whether the presence of MgCl2 in the agar overlay potentiates zinc toxicity.

We always include MgCl2 (40 mM) in the agar overlay when assaying rhinoviruses, because it significantly improves plaque size. The following monolayers of HeLa cells were inoculated with 200 plaque-forming units of rhinovirus type 1a, then incubated at 32°C for 5 days. The effect of MgCl2 is remarkable.


The use of MgCl2 to improve plaque formation of certain picornaviruses dates to the 1962 observation that the salt increases susceptibility of cells to poliovirus infection. It was later shown to enhance plaque formation of rhinoviruses.

Unfortunately, omission of MgCl2 from the agar overlay has no effect on zinc toxicity. As shown below, cell viability was still poor in the presence of 0.2 mM ZnCl2.


What’s next? One reader suggested that I try selecting HeLa cells in successively higher concentrations of ZnCl2 to obtain cells resistant to the toxic effects of the salt. This approach is under way. I will also attempt to propagate rhinovirus in cells covered with liquid growth medium rather than under agar. If 0.1 mM ZnCl2 is included in the culture medium, a good fraction of the viruses produced might be resistant to the salt. The virus produced in these infected cells will be used to infect fresh cells, also in culture medium with ZnCl2. After 5-10 passages in this manner the majority of the viral population should be resistant to ZnCl2. This is a more time consuming approach that the plaque assay, but might yield zinc resistant rhinovirus mutants.

Wallis, C., & Melnick, J. (1962). Magnesium chloride enhancement of cell susceptibility to poliovirus. Virology, 16 (2), 122-132 DOI: 10.1016/0042-6822(62)90287-8

Fiala M, & Kenny GE (1966). Enhancement of rhinovirus plaque formation in human heteroploid cell cultures by magnesium and calcium. Journal of bacteriology, 92 (6), 1710-5 PMID: 4289358

Zinc and rhinovirus replication

hrv1a_zincRecently I began experiments to understand how zinc inhibits rhinovirus replication, and I promised to document my findings on the pages of this blog. Here are the results of the second plaque assay.

In the last experiment I confirmed the finding that 0.1 mM ZnCl2 inhibits plaque formation by rhinovirus type 1A. Based on the results of that plaque assay, shown in the figure at left, I’ve decided that this concentration of zinc isn’t sufficient to completely inhibit viral replication. Although 0.1 mM ZnCl2 blocked plaque formation when 20 or 200 pfu were inoculated on cells, many plaques arose on plates inoculated with 2000 pfu. These cannot be viral mutants resistant to zinc – there are too many of them. If there are 2000 plaques on the untreated plate, and 200 on the plate with zinc, that would mean that resistance to zinc arises at a frequence of 200/2000 = 0.1 or one in ten viruses. I would expect a mutation rate for an RNA virus to be more in the range of 1/1000 – 1/10,000.

I decided to repeat the plaque assay with higher levels of zinc in the agar overlay – 0.2, 0.3, and 0.4 mM. The results of that experiment are shown below.


Unfortunately, the cells did not like the higher concentrations of ZnCl2! All the plates with zinc had very lightly staining monolayers – compare with the original experiment shown above – and no plaques were visible.

I was surprised that slight increases in the concentration of ZnCl2 would have such a dramatic effect on cell viability. The cells I used are HeLa cells, which are quite sturdy. Two other variables were changed in this experiment. I made a new stock of ZnCl2 – I took the 1 M stock I made for the first experiment and diluted it to 0.1 M. I doubt this made any difference. Second, the cell monolayers were less confluent than in the first experiment – about 70% of the surface of the cell culture dish was covered with cells. In the previous experiment, the monolayers were 100% confluent.

I repeated the experiment with HeLa cell monolayers that are 100% confluent. The results will be posted here in a few days.

Zinc inhibits rhinovirus replication

hrv1a_zincThe title of this post should not come as a surprise to readers of virology blog – it was shown in 1974 that zinc could interfere with replication of rhinoviruses (see “Zinc and the common cold“). I am referring to the result of my first experiment to study the mechanism of zinc inhibition – something I promised I would document on these pages.

I am interested in understanding how zinc inhibits rhinovirus replication. Answering this question could lead to new ways to prevent common colds caused by these viruses. The first step was to reproduce the effect of zinc in my laboratory with my stocks of rhinovirus. I selected rhinovirus type 1a for my initial experiments because we’ve worked with this serotype in the past: we know the genome sequence and how the virus behaves in a mouse model. I started by doing a plaque assay with and without zinc in the medium. I prepared tenfold dilutions of virus and inoculated separate monolayers of HeLa cells with 2000, 200, and 20 plaque forming units. After allowing the virus to attach to cells for 45 minutes, I added an agar overlay to the cells with or without zinc chloride (ZnCl2). I selected 0.1 millimolar ZnCl2 because that is the concentration which had been reported to effectively inhibit plaque formation by rhinovirus type 1a. The plates were incubated for four days at 32°C and then stained. The results are shown in the photo. Plaque assays are typically done in duplicate but for simplicity only one plate of each dilution is shown.

Twenty plaques were observed on the highest dilution of virus plated in the absence of ZnCl2. Ten-fold lower dilutions produced increases in plaque number, although the plaques are too numerous to count. In the presence of ZnCl2, no plaques were observed on cells inoculated with 20 PFU. A few plaques are observed on the intermediate dilution and many more on the lowest dilution. Plaques observed in the presence of ZnCl2 are smaller than those observed in the absence of the metal.

What do you think is going on here, and what should I do next? If you’ve kept up with virology 101 you have all the tools to answer these questions. Please post your thoughts in the comments section.

KORANT, B., KAUER, J., & BUTTERWORTH, B. (1974). Zinc ions inhibit replication of rhinoviruses Nature, 248 (5449), 588-590 DOI: 10.1038/248588a0

How many viruses are needed to form a plaque?

The plaque assay is an essential tool for determining virus titers. The concept is simple: virus infection is restricted to neighboring cells by a semisolid overlay. By counting the number of plaques, the virus titer can be calculated in PFU per ml. A key question is: how many viruses are needed to form a single plaque?

For most animal viruses, one infectious particle is sufficient to initiate infection. This conclusion can be reached by studying the relationship between the number of infectious virus particles and the plaque count. A linear relationship means that one infectious particle can form a plaque. In this case the virus is said to infect cells with one-hit kinetics. This concept is illustrated below. In this figure, the number of plaques produced by a virus with one-hit kinetics or two-hit kinetics is plotted versus the relative concentration of the virus.


There are some examples of viruses with two-hit kinetics: in other words, two different types of viral particles must infect a cell to initiate the infectious cycle. Examples include the genomes of some (+) strand RNA viruses of plants, which consists of two RNA molecules that are packaged in different particles. The dose-response curve of such viruses is parabolic rather than linear.

When a single virus particle can form a plaque, the viral progeny within the plaque are clones. Virus stocks prepared from a single plaque are called plaque purified virus stocks. To prepare such virus stocks, the tip of a small pipette is inserted into the agar overlay above the plaque. The plug of agar is removed and placed in buffer. The viruses within the agar plug move into the buffer, which can then be used to infect cultured cells. To ensure purity, this process is usually repeated at least one more time. Plaque purification is used extensively in virology to establish clonal virus stocks. The ability to prepare clonal virus stocks was an essential development that permitted genetic analysis of viruses.

Detecting viruses: the plaque assay

One of the most important procedures in virology is measuring the virus titer – the concentration of viruses in a sample. A widely used approach for determining the quantity of infectious virus is the plaque assay. This technique was first developed to calculate the titers of bacteriophage stocks. Renato Dulbecco modified this procedure in 1952 for use in animal virology, and it has since been used for reliable determination of the titers of many different viruses.

polio-plaquesTo perform a plaque assay, 10-fold dilutions of a virus stock are prepared, and 0.1 ml aliquots are inoculated onto susceptible cell monolayers. After an incubation period, to allow virus to attach to cells, the monolayers are covered with a nutrient medium containing a substance, usually agar, that causes the formation of a gel. When the plates are incubated, the original infected cells release viral progeny. The spread of the new viruses is restricted to neighboring cells by the gel. Consequently, each infectious particle produces a circular zone of infected cells called a plaque. Eventually the plaque becomes large enough to be visible to the naked eye. Dyes that stain living cells are often used to enhance the contrast between the living cells and the plaques. Only viruses that cause visible damage of cells can be assayed in this way. An example of plaques formed by poliovirus on a monolayer of HeLa cells is shown at left. In this image, the cells have been stained with crystal violet, and the plaques are readily visible where the cells have been destroyed by viral infection.

The titer of a virus stock can be calculated in plaque-forming units (PFU) per milliliter. To determine the virus titer, the plaques are counted. To minimize error, only plates containing between 10 and 100 plaques are counted, depending on the size of the cell culture plate that is used. Statistical principles dictate that when 100 plaques are counted, the sample titer will vary by plus or minus 10%. Each dilution is plated in duplicate to enhance accuracy. In the example shown below, there are 17 plaques on the plate made from the 10-6 dilution. The titer of the virus stock is therefore 1.7 x 108 PFU/ml.


Next we’ll consider how the plaque assay can be used to prepare clonal virus stocks, a step that is essential for studying viral genetics.

Dulbecco, R., & Vogt, M. (1953). Some problems of animal virology as studied by the plaque technique. Cold Spring Harbor Symp. Quant. Biol., 18, 273-279