🔬 One-Step Growth Calculator

The Phage One-Step Growth Calculator accepts titer time-point data entered by the user, assigns each point to its OSG phase (pre-lysis, rise, post-rise, or unadsorbed), and then computes the two canonical outputs of an OSG experiment — the minimum latent period (constant period) and the average burst size — along with a normalized, plotted OSG curve. Each step of the computation is described below.

Each time-point row entered by the user is assigned to one of four phases:

• Pre-lysis — post-adsorption, pre-lysis infective center counts. These should be stable over time. They form the denominator of the burst size calculation and the normalization baseline for the plotted curve.
• Rise — time points taken during active lysis, when titers are increasing. These are used solely to visualize the lysis event and to identify the start of the rise for latent period estimation. Rise-phase points are not included in burst size numerator or denominator calculations.
• Post-rise — time points taken after lysis is complete and titers have plateaued. These form the numerator of the burst size calculation. They must be genuinely stable; a continuing upward trend in post-rise titers is flagged as a potential sign of multi-step growth.
• Unadsorbed — a titer of free, unadsorbed virions remaining after the adsorption step, measured from a separate sub-volume (e.g., by centrifugation to pellet bacteria, then titering the supernatant; or by chloroform treatment during the eclipse). This value is subtracted from both the pre-lysis and post-rise means before burst size is computed.

Rows flagged by the user as outliers (⚠) are excluded from all calculations but remain visible in the data table. This implements the recommendation of Adams (1959) to disregard anomalously high titer counts near the expected time of lysis, which likely result from a phage-infected bacterium lysing during the plating process itself.

Rows with missing or non-numeric time or titer values are silently skipped. All remaining active rows are sorted by time within each phase before any calculations are performed.

For both the pre-lysis and post-rise phases, the calculator computes four aggregate statistics from the set of active (non-outlier) titer values in that phase. All four are reported in the results table to allow comparison:

• Arithmetic mean — the standard average: Σ(x_i) / n. Most commonly used, but sensitive to outliers.
• Median — the middle value when data are sorted. Discussed in detail by Abedon and Katsaounis (2021) and recommended by Abedon (2025) as the most robust estimator for OSG titer data, because it is entirely unaffected by a single anomalously high or low value provided n ≥ 3. For even n, the median is the mean of the two central values.
• 25% Trimmed mean — the arithmetic mean after removing the highest and lowest 25% of values (TRIMMEAN in Excel). This offers a balance between robustness and use of all central data, and is discussed by Abedon (2025) as a preferred alternative to the simple mean.
• Geometric mean — exp(mean of ln(x_i)). Applied to positive titer values only. Reduces the disproportionate influence of high outliers relative to the arithmetic mean, and is appropriate when titer data are expected to be log-normally distributed.

Standard deviation and coefficient of variation (CV = SD/mean × 100%) are also computed for the arithmetic mean, as a measure of within-phase consistency. High CV values in the pre-lysis phase may indicate ongoing adsorption, premature lysis during plating, or sampling error, and warrant investigation before accepting the burst size calculation. For detailed statistical guidance on plaque-based titer data, see Abedon and Katsaounis (2021).

The unadsorbed virion titer, if provided, is computed as the arithmetic mean of all unadsorbed-phase rows. Separate mean and median values are shown. This value represents free phages that were not adsorbed during the adsorption step and therefore should not be counted among phage-infected bacteria in the pre-lysis denominator.

Burst size is the ratio of the number of free phages present after lysis is complete (the post-rise titer) to the number of phage-infected bacteria present before lysis began (the pre-lysis titer). The fundamental formula is:

When T_free = 0 (no unadsorbed-phase data entered), the formula simplifies to T_post / T_pre. This is the standard calculation as described by Adams (1959), Ellis and Delbrück (1939), and Hyman and Abedon (2009).

The calculator applies this formula four times, once for each aggregate method (arithmetic mean, median, 25% trimmed mean, geometric mean), producing four independent burst size estimates. These are displayed side-by-side so the user can assess consistency. Large discrepancies between the mean-based and median-based estimates are a warning sign that one or more outlier time points may be distorting the mean.

Why subtract unadsorbed virions? If a fraction of added phages failed to adsorb during the adsorption step, those free virions will contribute plaques to pre-lysis plates, inflating the denominator and causing burst size to be underestimated. For example, if 10% of phages remained unadsorbed, the true burst size will be underestimated by approximately 10%. At the same time, those same unadsorbed virions also contribute to the post-rise numerator. Subtracting T_free from both corrects for this bias. Even small levels of unadsorbed phages (e.g., 1–2%) have negligible effect on results, but levels of 10% or more are meaningful and should always be corrected for.

Note on incorrect burst size formulas: Burst size is the ratio of post-rise to pre-lysis titers, not the difference divided by the pre-lysis titer. The latter formulation — sometimes encountered in the literature — subtracts 1 from the true burst size, an error that becomes biologically meaningful for small burst sizes. For example, a true burst size of 5 would be reported as 4.

The minimum latent period — also called the constant period — is defined as the time from the start of phage adsorption to the first lysis event across the infected bacterial population, observable as the first detected rise in titer above the pre-lysis baseline. The calculator estimates this in two stages:

1. Rise detection threshold: The calculator scans rise-phase time points in chronological order for the first point whose titer exceeds 110% of the pre-lysis arithmetic mean (i.e., more than 10% above baseline). This threshold guards against flagging routine pre-lysis titer variation as the start of lysis.
2. Bounding interval: The latent period is reported as a bounding interval — "between t_last-pre and t_first-rise" — rather than a single point estimate. This correctly reflects that the true end of the constant period is known only to lie within that interval, and avoids false precision. Precision can only be improved by taking more time points around the expected start of lysis, as recommended by Adams (1959) and Abedon (2025).

If all rise-phase points fall within 110% of the pre-lysis mean — for instance if the rise was only partially captured and the data end before lysis is well established — the first rise-phase time point is used as a lower bound estimate and flagged as such. If no rise-phase data are entered at all, the latent period cannot be estimated and is reported as unavailable.

Important caveat on precision: The minimum latent period can only be stated with a precision equal to the interval between time points taken around the start of lysis. If time points are 5 minutes apart, the latent period can only be resolved to within a 5-minute window. Shorter intervals around the expected rise, as few as 1–2 minutes, substantially improve resolution. This calculator reports the bounding interval explicitly so that the user does not inadvertently claim greater precision than the data support.

The OSG curve is plotted as an interactive Chart.js scatter plot with connected line segments within each phase. Two display modes are available and can be toggled at any time:

• Normalized y-axis (default): All titer values are divided by the pre-lysis arithmetic mean. This places the pre-lysis baseline at y = 1, so that the post-rise plateau reads directly as the burst size. A dashed reference line at y = 1 is drawn across the full time range. Normalization is recommended by Abedon (2025) because it makes burst sizes immediately readable by eye and allows biological replicates starting at different absolute titers to be overlaid on the same graph.
• Absolute y-axis: Titers are plotted in the original units as entered. Useful when the user wishes to inspect raw plaque counts or compare absolute values across experiments.

The y-axis scale can be toggled between logarithmic (base-10, default) and linear. Log scale is strongly preferred for OSG data for two reasons: first, it makes pre-lysis variation visible — on a linear scale, small fluctuations around the low pre-lysis titer are compressed and invisible relative to the large post-rise plateau; second, the linear portion of the rise on a log scale can be used to draw a best-fit line whose intersection with the pre-lysis baseline provides an alternative, regression-based estimate of the minimum latent period (Adams, 1959).

Data points are color-coded by phase: blue = pre-lysis, orange = rise, green = post-rise, purple triangles = unadsorbed. Outlier-flagged points are excluded from the plot entirely, consistent with their exclusion from calculations.

The calculator automatically checks for a set of common OSG quality issues and displays warnings at the top of the results panel when they are detected:

• Fewer than 3 or 5 pre-lysis time points — the denominator is imprecisely determined. At n < 3 the median loses its outlier-robustness properties entirely.
• Fewer than 3 or 5 post-rise time points — the numerator is imprecisely determined, and it cannot be confirmed that the rise has truly ended and titers have stabilized.
• No unadsorbed virion titer entered — burst size may be underestimated if adsorption was incomplete. Flagged as an informational notice rather than an error.
• Post-rise titers still increasing — the slope of the post-rise time series is compared to the mean post-rise titer. If the net upward drift exceeds 15% of the mean per unit time, a warning is issued. This pattern is the primary diagnostic indicator of multi-step rather than one-step growth, almost always caused by insufficient dilution of the experimental culture following the adsorption step.
• Burst size > 200 — warrants verification by independent means (e.g., single-burst experiment).
• Burst size > 500 — flagged in red as a strong indicator of potential multi-step growth, possible lysis inhibition, or experimental error. Burst sizes above a few hundred are uncommon for most phage-host systems and should not be accepted without additional rigorous testing.
• Fewer than 3 rise time points — insufficient data to characterize the lysis event or estimate latent period reliably.

These checks implement the core quality-control recommendations of Abedon (2025) and Adams (1959). They do not prevent the calculator from returning results — the user retains full discretion — but they ensure that potential problems are made explicit rather than hidden.

The Experiment Designer tab performs prospective calculations to help users plan their OSG protocol before conducting it. Given user-supplied starting parameters, it computes:

• Input MOI — phages per bacterium in the adsorption mixture, computed as (phage titer × phage volume / total adsorption volume) / bacterial concentration. Compared against the recommended threshold of ≤ 0.1. For further discussion of adsorption rates see adsorption.phage.org.
• Infected bacteria/mL after dilution — (phage titer in adsorption mixture × adsorption efficiency) / post-adsorption dilution fold. This is the expected concentration of phage-infected bacteria in the main working tube (Tube B) from which pre-lysis platings are made.
• Expected pre-lysis plaques per plate — infected bacteria/mL × plating volume (converted to mL). The target is approximately 100 plaques per plate, which gives a theoretical minimum counting error of ~10% (equal to the square root of the mean, per Adams, 1959).
• Expected post-rise plaques per plate — as above but multiplied by the user-supplied expected burst size, reflecting the increase in titer after lysis. If this exceeds ~500 plaques, an additional dilution tube is recommended for post-rise platings.
• Unadsorbed virions/mL — (phage titer × (1 − adsorption efficiency)) / dilution. Expressed also as a percentage of the pre-lysis titer.
• Remaining bacteria/mL after dilution — used to assess whether released phages post-lysis could encounter sufficient bacteria to cause secondary adsorption and multi-step growth.

The Poisson MOI checker computes the expected distribution of phage adsorptions over bacteria using the Poisson probability mass function P(k) = e^−λλ^k/k!, where λ is the MOI. It reports the fraction of bacteria that are uninfected (k = 0), singly infected (k = 1), and the fraction of infected bacteria that carry more than one phage (k ≥ 2 | k ≥ 1). At MOI = 0.1, only ~5% of infected bacteria are multiply infected; at MOI = 1, this rises to ~42%.

This calculator performs computations on data as entered by the user. It does not validate the underlying experimental design, correct for errors in dilution or plating, or replace the need for careful laboratory practice. In particular:

• The flatness check will not flag multi-step growth if the experiment was terminated shortly after lysis — a post-rise that looks flat because too few time points were taken cannot be distinguished computationally from a genuinely stable plateau. The user must inspect the curve and consider whether the rise has truly ended and titers have stabilized.
• The latent period estimate depends entirely on the density of time points the user took around the rise. No computation can recover precision lost due to infrequent sampling.
• The burst size calculation assumes that all pre-lysis infective centers are phage-infected bacteria and that all post-rise PFUs are free phages. If experimental culture dilution was inadequate, post-rise PFUs may include contributions from a second round of lysis, inflating the burst size estimate.
• The unadsorbed virion correction assumes that T_free was measured under conditions where phage-infected bacteria were excluded (e.g., by centrifugation or chloroform treatment during the eclipse). Errors in this measurement propagate directly into burst size calculations.

For full guidance on avoiding these and other common pitfalls, see Abedon (2025) and Hyman and Abedon (2009).

One-step growth (OSG) experiments — also called single-step growth — are the foundational assay for determining two key bacteriophage life-history characteristics: the latent period (minimum: the constant period) and the burst size. First systematized by Ellis and Delbrück (1939), OSG consists of following phage infective centers (plaque-forming units, PFUs) through three successive phases:

1. Pre-lysis (constant period): Post-adsorption, pre-lysis titers of phage-infected bacteria. These should be stable (flat) and represent the denominator in burst size calculations.
2. Rise: Increasing titers as phage-infected bacteria lyse and release virions. The start of the rise defines the end of the minimum (constant) latent period.
3. Post-rise (plateau): Stable free-phage titers after lysis is complete. These represent the numerator in burst size calculations.

Burst size = (mean post-rise titer − unadsorbed virion titer) ÷ (mean pre-lysis titer − unadsorbed virion titer)

Minimum latent period (constant period) = time from start of adsorption to the first detected rise in titer.