MOIinput (Multiplicity of Addition) vs. MOIactual (Multiplicity of Adsorption)
by Stephen T. Abedon Ph.D. (abedon.1@osu.edu)
phage.org | phage-therapy.org | biologyaspoetry.org | abedon.phage.org | google scholar
Jump to: 🔬 Calculator | 📈 Explore | 📖 Methodology | 📚 Background | 🧮 More Calculators
moi.phage.org · Abedon’s Books · DOI: 10.5281/zenodo.21115786
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Enter values either as plain numbers (e.g. 10000000) or in scientific notation
(e.g. 1e7 = 1 × 107). Keep your units consistent —
concentrations as per mL, time and k both per minute.
This plot uses the P0, B, and k values from the Calculator tab and traces predicted multiplicity of adsorption (MOA) as the adsorption period lengthens. The non-depleting curve assumes free phage stays fixed at P0; the depleting curve lets free phage fall as it is consumed. They track together early, then separate once an appreciable fraction of the phage pool has adsorbed.
In the calculator, set P0 = 1e7 /mL, B = 1e4 /mL, and t = 120 min (with default k). The input "MOI" is 1000, yet the actual MOI (MOA) is only about 3 — barely 0.3% of the added phages have found a host. Now raise the phage titer to P0 = 1e8 /mL: the ratio of MOA to MOIinput is unchanged, but MOA itself climbs from roughly 3 to about 30.
That tenfold jump is the practical argument behind a long-standing recommendation: for phage therapy, aim for titers on the order of 108 /mL in the vicinity of the target bacteria, whether reached by dosing alone or through phage population growth in situ. At low host densities, adding more phages does little unless their concentration is high enough to make adsorption efficient within a useful window of time. For more on phage therapy, see phage-therapy.org.
The simplest and most commonly reported quantity is just the ratio of phages added to bacteria present:
It is time-independent and says nothing about whether adsorption has actually occurred. Because it can badly overstate the number of phages reaching each cell — particularly at low bacterial densities — it is more accurately described as a multiplicity of addition than a multiplicity of infection.
Phage adsorption to bacteria follows first-order kinetics with rate constant k. Free phage decline as P(t) = P0 e−kBt, so the fraction of phages predicted to have adsorbed by time t is 1 − e−kBt. The average number of phages adsorbed per bacterium — the MOA, equivalently MOIactual — can be framed two ways:
The non-depleting form treats each bacterium as drawing from an inexhaustible phage pool, so adsorptions accumulate linearly in time. The depleting form conserves phages: the total adsorbed across the population, P0(1 − e−kBt) per mL, divided among B bacteria per mL. When little of the pool has been consumed (small kBt) the two coincide, because 1 − e−kBt ≈ kBt; as consumption grows, the non-depleting form sits above the depleting one. Real values may also exceed both once phages replicate in situ, which is why the term multiplicity of adsorption (MOA) — counting adsorption events rather than presumed adsorption or infections — is the more careful description.
If adsorptions are distributed randomly (Poisson) across bacteria with mean MOA, the predicted fraction of bacteria that adsorb at least one phage is:
For finer control over the full Poisson distribution — the fractions adsorbing exactly 0, 1, 2, … phages — see the Poisson Frequencies calculator.
There are a number of issues tied to the definition of multiplicity of infection, ones that, in my opinion, have a hampering effect on certain aspects of phage research. The biggest problem appears to be confusion over the actual definition of MOI, together with how one should calculate MOI in its various guises.
This calculator allows not only the calculation of "actual" multiplicity of infection — MOIactual, the historically accurate definition — but also comparison with the truly problematic "input" multiplicity, MOIinput, which is better described as a multiplicity of addition.
I prefer the term MOA — multiplicity of adsorption — as a more accurate way of thinking about MOIactual. What we can measure and predict are adsorption events; whether each adsorption goes on to produce a productive infection is a separate question. The Explore tab walks through a worked example showing how MOIinput of 1000 can correspond to a MOA of only about 3, and why raising phage titer tenfold raises the MOA proportionally.
MOA is reported here in two ways, each shown only when t > 0: (i) assuming free phage concentration stays constant, and (ii) allowing free phage to decline as a consequence of adsorption to bacteria. In the latter case the number of adsorbable bacteria is not assumed to decline, only the virions. Because phage populations can also grow in situ, actual multiplicities of adsorption may eventually be found somewhere between these two approximations — or, ultimately, could be greater than either.
For phage therapy and other biocontrol purposes it is desirable not to rely solely on MOI to describe what phage quantities have been applied. Bacterial densities can change between bacterial challenge and phage application, may not be easily determined immediately beforehand, and target populations may not be homogeneous in terms of phage access. Dosing is better described in terms of phage titers, volumes applied, and absolute numbers of phages delivered. The worked example makes the underlying reason concrete: at low host density, what determines whether phages reach their targets is their concentration, not the phage-to-bacterium ratio.
For discussion of multiplicity-related terminology, see multiplicity.phage.org. For phage adsorption theory and estimation of k, see adsorption.phage.org. For the underlying Poisson distribution of adsorptions across bacteria, see poisson.phage.org.