💊 Phage Adsorptions Calculator

What This Calculator Computes

Phage adsorption follows mass-action kinetics: the rate at which free phage adsorptions occur depends on the adsorption rate constant k, the bacterial concentration N, and the phage concentration P:

Note that the per-phage rate at which a given free phage adsorption occurs is a function of only N and k, not of P. This is the fundamental assumption underlying both models in this calculator. Nonetheless, to arrive at total phage adsorptions one must multiply by the number of phages present — giving the P dependence seen in the equations below.

Two scenarios are calculated:

1. Without phage replacement (exponential — more realistic). As phages adsorb they are removed from the free pool, so the free-phage concentration declines exponentially. The fraction of phages that adsorb over time t is 1 − e^−kNt, giving:

Note: when phage numbers are declining over time without replacement, the instantaneous adsorption rate per bacterium likewise declines. "Average adsorptions per bacterium per min" is therefore a time-averaged figure — the instantaneous rate at time zero is k · P₀ and falls continuously toward zero as P(t) → 0.

2. With phage replacement (linear — simpler, less realistic). If the free-phage pool is assumed constant (phages replaced as they adsorb), the adsorption rate per bacterium is constant and total adsorptions accumulate linearly:

The two approaches converge when kNt is very small (few phages adsorb in total). At higher bacterial densities or longer durations the exponential model predicts fewer cumulative adsorptions, because the depleting free-phage pool slows the absolute rate of phage loss to adsorption (though not the rate relative to the number of free phages still present).

MOI_actual vs. MOI_input

The nominal or input MOI (MOI_input = P₀/N) describes how many phages are present per bacterium at time zero, without regard to whether adsorption actually occurs or will occur. The MOI_actual is the mean number of phage-bacterium adsorption events per bacterium — the biologically relevant quantity for infection outcomes. This calculator outputs MOI_actual.

Adsorption Rate Constant k

The default value of k = 2.5 × 10⁻⁹ mL min⁻¹ comes from Stent (1963) and is a widely cited representative value for many double-stranded DNA phages infecting Escherichia coli. Real values vary considerably across phage-host pairs, temperature, ionic conditions, and bacterial surface properties — roughly 10⁻¹⁰ to 10⁻⁸ mL min⁻¹ in most experimental systems, with exceptional cases outside that range.

To determine k from experimentally determined free-phage decline data, use the companion tool: adsorption.phage.org — Adsorption Rate Calculator (regression-based, with file upload and unit converter).

Cite This Calculator

See also the companion tool: Abedon, S.T. (2026). Adsorption Rate Calculator. adsorption.phage.org

Key References

• Stent, G.S. (1963). Molecular Biology of Bacterial Viruses. W.H. Freeman, San Francisco. [Source of the default k = 2.5 × 10⁻⁹ mL/min.]
• Abedon, S.T. (2011). Advances in Applied Microbiology 77:1–40. 10.1016/B978-0-12-387044-5.00001-0
• Abedon, S.T. (2023). Antibiotics 12:723. 10.3390/antibiotics12040723

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