Host Normalized Adsorption Fit

Fit a host-density-normalized adsorption constant from free-virus decay, assuming negligible replication and independent loss.

Description

Infer a host-density-normalized adsorption constant from two positive free-virus titers under a constant-density exponential-loss model.

Adsorption describes virus attachment to host cells. Measuring free-virus titer before and after a defined interval can summarize the loss from the unbound population. Classical phage growth work distinguishes adsorption from the later production and release of progeny.^[1]

In a simple model with constant host density H, free titer follows V(t) = V0 exp(−kHt). The fitted k is normalized by both elapsed time and host cells per milliliter. Assigning all observed loss to adsorption requires other causes of titer decline to be negligible.

Host Normalized Adsorption Fit returns k in mL per cell per hour and the fraction of free titer lost. It uses two observations and does not fit a full time course.

When to check a two-point adsorption-only model

Use the tool for compatible free-virus measurements with a positive host density and known elapsed hours. The model is useful for an arithmetic check when constant density and negligible progeny production are reasonable assumptions.

Normalize free-virus loss by host-cell density.
Compare two-point calculations under matched assay conditions.
Separate a loss fraction from the kinetic constant.

How to enter titers and infer an adsorption constant

Enter positive Initial free titer and Final free titer in the same assay units and volume basis.
Ensure final titer is no greater than initial titer.
Enter positive Elapsed hours and Host cells per ml.
Run the calculation and read Adsorption constant ml per cell hour and Free virus loss fraction.

k = [ln(initialFreeTiter) − ln(finalFreeTiter)]/(elapsedHours×hostCellsPerMl); loss = 1 − finalFreeTiter/initialFreeTiter

The implementation subtracts natural logarithms and divides by elapsed time and host density. It applies no independent-decay correction.

json

{
  "input": {
    "initialFreeTiter": 100,
    "finalFreeTiter": 50,
    "elapsedHours": 1,
    "hostCellsPerMl": 1000000
  },
  "output": {
    "adsorptionConstantMlPerCellHour": 6.931471805599452e-7,
    "freeVirusLossFraction": 0.5
  }
}

Unchanged titer gives zero k and zero loss. Zero final titer is rejected because its logarithm is undefined. Increasing titer, nonpositive inputs, or nonfinite values produce errors; host density may be fractional because it is a concentration.

Limitations and interpretation

The calculation assigns all free-titer decline to adsorption. Inactivation, sampling loss, or assay changes require separate consideration.
No replication, desorption, changing host density, multiple observations, residual analysis, or uncertainty interval is modeled.
The supplied titers must describe free virus rather than an unseparated mixture of bound and free material.
A two-point constant does not independently establish the attachment mechanism or later infection success.

Alternative or Complementary methods

Record adsorption completion separately when calculating experimental eclipse and release delays. Inoculum-MOI arithmetic uses a supplied infectious stock and target multiplicity rather than estimating attachment kinetics.

References

The Growth of Bacteriophage — Journal of General Physiology; E. L. Ellis and M. Delbrück (1939)

Similar or alternative tools

Eclipse Latent Period Timeline
Calculate assay-event delays relative to a supplied adsorption-completion time.
Cells For Inoculum MOI
Calculate a target cell count from infectious stock, volume, dilution, and supplied MOI.