Multiplicity of Infection/Multiplicity of Confusion
Authors: Paul Shabram, Estuardo Aguilar-Cordova
Journal: Molecular Therapy (2000)

C'est magnifique, mais ne c'est pas science. This is the phrase that most comes to mind when multiplicity of infection (m.o.i.) is used as a descriptive measurement in scientific presentations. Multiplicity of infection is commonly defined as the ratio of infectious virions to cells in a culture. On the surface, the concept is simple, easy to calculate, and easy to use in speech and written reports. Nevertheless, m.o.i. is an overly simplistic depiction of a complex setting. Yes, it is an easy concept that gives the impression of quantitative preciseness. However, it would be more precise to refer to m.o.i. as a qualitative term used to conjure an image of a reality that may not truly resemble the experimental conditions. m.o.i. is a term ingrained in the virology community's lexicon since its original use by Max Delbruck and colleagues about 60 years ago (1Ellis E.L. Delbruck M. The growth of bacteriophage.J. Gen. Physiol. 1939; 22: 365-384Crossref PubMed Scopus (372) Google Scholar). At that time, m.o.i. was used as a convenient term to describe the ratio of T4 phages and bacteria in an agitated suspension in order to calculate the average number of virions infecting each cell. The purpose was to define the relative concentration of virus and bacteria that would lead to a controlled number of infections per bacterium. This assumed that all virions were infectious and that all cells were susceptible. Assuming that the number of phage infecting each bacterium was a random distribution, the number of phage infecting each bacterium could be calculated from the Poisson equation P(n) = (mn × e-m)/n!, where P(n) is the probability that a cell will be infected with exactly n phage and m is the average number of phage per cell (i.e., the m.o.i.). With the assumptions and conditions used for those experiments, multiplicity of infection (m) could be used to define the average number of virus particles that infect a cell. In most virus infections, there are uninfected cells (P[0] = e–m), cells infected with a single virus particle (P[1] = me–m), and cells infected with multiple virus particles (P[>1] = 1 – (e–m(m + 1))). Thus, m.o.i. (m) can be calculated from the equation above as m = –ln P[0], where ln is natural log and P[0] is the proportion of uninfected cells. Consequently, if no infectious events are detected, one may calculate an m.o.i. of zero, i.e., no virus. This would clearly be the wrong conclusion if the true explanation were that the target cells were not susceptible to the virus or if the experimental conditions were such that the virus and cells never came in contact. It is this ambiguity and lack of precision, inherent in such a descriptive term, that is the impetus to discourage the use of m.o.i. as a sole description of scientific conditions. Further, m.o.i. is misleading because it implies a homogeneous infected cell population. Yet, as explained above, it is a statistical probability with a Poisson distribution. When a particle collides and infects a cell it is a discrete event. The same cell may become infected a second, third, fourth, etc., time. These cell populations may be different and may demonstrate different behavior, but an m.o.i. of 5, for example, implies that each cell can become infected five times. Conclusions about the activity of a transgene can miss the mark if this is not taken into account. One could argue that m.o.i. is a useful descriptor within a given laboratory. Much like "the dark car," it may be useful to help identify a vehicle in your own two-car garage. However, it would not be very useful in the 1000-car city parking lot. Likewise, the adjective m.o.i. is not sufficient in the context of a scientific community, and research is a community activity. Research reports should be explicit to allow other scientists to interpret and duplicate the results and to serve as an archival record for future generations. m.o.i. is a remnant of bacterial genetics, a way to measure phage as a function of their infectivity and, subsequently, to estimate the number of infectious events to expect per bacterium. Today it is often used as a descriptor of experimental conditions. In itself it cannot serve this function. A physical explanation for this conclusion can be as follows. A viral solution is a sol, a colloidal suspension of solid particles in a liquid. One everyday example of a sol is paint, where there is a suspension of minute solid pigment particles in a liquid vehicle. In these suspensions the solid particles are so small that the incessant bombardment from the molecules of the liquid medium is sufficient to keep the solid particles in suspension. The random motions of particles under these conditions are called Brownian motion. The molecules of the liquid can "push" the solid particles up, down, or sideways, the net movement being negligible. Therefore, just like under practical time frames, where pigment does not settle to the bottom of a paint can, virions do not settle to the bottom of a culture dish. Therefore, for practical purposes, the only virions with a possibility of coming in contact with target cells are those immediately above the cells. Adding volume (depth) to the culture would alter the m.o.i., add many more virions with regard to the number of cells in the well, but not change the number of potential infectious events. Once emptied, the bottom of the paint can would be the same color if it had held just enough paint to cover the surface as if it had had a full gallon of paint. If, however, the force of gravity is greatly increased, like in a centrifuge, the suspension of a sol can be broken and the particles made to settle. The lack of sensitivity in tittering assays has furthered the concept of particle-to-infectious unit ratio, or PIU. With adenoviral vectors, this concept is based on the supposition that "most adenoviral particles are not infective." However, we are not aware of any objective experimental data to support this supposition. In fact, the contrary is true. Experiments using a model derived from Fick's Law of Diffusion and centrifugation demonstrated that most, if not all, adenoviral particles are indeed infective (2Nyberg-Hoffman C. Shabram P. Li W. Giroux A. Aguilar-Cordova E. Sensitivity and reproducibility in adenoviral infectious titer determination.Nat. Med. 1997; 3: 808-811Crossref PubMed Scopus (176) Google Scholar). That work, and others, demonstrates the role of diffusion in the mechanics of virus binding and the dependence of infectious titer determination on experimental conditions. Concurrently, it underscores the weakness in the meaning of m.o.i. For example, if an experiment describes the effects of an m.o.i. of 10 relative to an m.o.i. of 50, one can make some conclusions on the effects of increasing the viral concentration by five. However, no specific information on what those viral concentrations might be can be defined. Therefore, without additional information the experiment would be unreproducible and, under most peer-review criteria, unpublishable. To avoid these confusions all of the significant variables of an infectious protocol most be described. These include virus concentration, infection time duration, and target surface area. The first important bit of information is the titer of the original virus. Interpretation of the infectious titer also requires a full description of all the infection set-up conditions. Alternatively, one could use a unit like normalized adjusted standard (NAS) (2Nyberg-Hoffman C. Shabram P. Li W. Giroux A. Aguilar-Cordova E. Sensitivity and reproducibility in adenoviral infectious titer determination.Nat. Med. 1997; 3: 808-811Crossref PubMed Scopus (176) Google Scholar) titer that accounts for all these variables. In the older animal virus literature the tittering methodology used for measuring infectious titer was simple. Lay as thin a layer of a viral preparation as possible over the target cells for as long as practical. It was intuitively understood that infections were diffusion limited and this methodology would help to mitigate underrepresenting the titer. Done properly, these assays would only underestimate by 10- to 20-fold. However, many cell cultures can not be maintained with very low media levels. Mitigating the sensitivity of the cells to culture conditions by adding more media can lead to results that underestimate titers by two to three logs. Thus, it is no surprise that when we sent the exact same adenoviral preparation to different commercial labs for tittering we got back titers that fell in a two-log range. The explanation for lower infectious titers, given quantitative particle titers, has been accepted by nearly everyone by employing the age-old "most of the particles must not be infective" argument. The PIU misconception stems from the differences found between particle quantitation assays and infectious titer assays. However, the proportion of cells that come in contact with adenoviral particles in a given assay is dependent on the concentration of the adenovirus and the time of exposure. What had not been accounted for is that an adenoviral particle (or any particle of similar size) diffuses very slowly in solution. Therefore, most of the added particles in a titer assay never come in contact with the target cell. In a typical titer assay the cells will die or overgrow before most virions can come in contact with them. Changes in assay conditions such as particle concentration or exposure time can have a dramatic effect. Changes in m.o.i. may have no effect at all. The practice of using m.o.i. to describe experimental conditions, now standard, becomes even more problematic when one wishes to make claims about gene-specific effects or recommend doses for clinical studies. Translational research, the process by which scientific discovery is converted into clinically applicable products, brings an enormous array of obstacles. One key set of obstacles is proving whether or not a candidate product is safe and efficacious. The first question is whether it is active in vitro, then whether it is safe and efficacious in animals, and finally whether it is safe and efficacious in humans. Without close scrutiny of preclinical data, a human clinical trail is difficult to justify, especially when the difference between efficacious and toxic dose may be small. It is impossible to interpret and compare dose-escalation studies without a solid understanding of the units used to describe the doses. A two-log variability in titer "estimation" is unacceptable when dose-escalation cohorts may be in half-log increments. Such impreciseness is perpetuated by the use of descriptive terms like m.o.i. as quantitative units. Thus, even though as a community we have used the term for many decades, it is time we reconsider its context and discontinue its use as a quantitative term. As Ralph Waldo Emerson said, "a foolish consistency is the hobgoblin of little minds."