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Bioassay-guided fractionation separates a mixture repeatedly while using a bioassay to decide which separated portions retain the biological response of interest. The physical separation may use chromatography; the selection criterion is biological activity, rather than the largest chemical peak. The goal is to connect a reproducible response to particular material while tracking what is recovered and what is lost.

A historically important example is the separation of tumour-derived angiogenic material by Judah Folkman, Ezio Merler, Charles Abernathy and Gretchen Williams. Their 1971 study combined size-exclusion chromatography with biological testing of separated fractions in a rat dorsal air sac assay.^[ref] Following activity through a separation is evidence about where the activity resides; it is not by itself proof of a chemically pure molecule.

An original bookkeeping example assumes that the assay has been converted to calibrated, additive activity units over the concentration range used. An initial $100\mathrm{mg}$ mixture contains 1000 units, or 10 units per milligram. Fraction A contains $10\mathrm{mg}$ and 600 units, while fraction B contains $90\mathrm{mg}$ and 100 units. Thus A hasThe combined recovery is 70 percent even though the recovered mass is 100 percent. Loss of activity could reflect degradation or removal of a required interacting component. Conversely, removal of an inhibitor could increase measured activity. Neither mass conservation nor a larger response per milligram settles the molecular explanation.

The additive-unit assumption matters. A visual grade or a percentage response at a single test concentration cannot automatically be added across fractions. Fractions should be compared with controlled solvent exposure and an appropriate range of concentrations, using matched negative controls. Recombining separated portions can test whether the original response required their joint presence. Independent chemical characterization then tests composition; a positive bioassay alone does not determine molecular identity or clinical effectiveness.

Ezio Merler coauthored the 1971 study of angiogenic activity isolated from tumours, alongside Judah Folkman, Charles Abernathy and Gretchen Williams.^[ref] The investigators coupled biochemical separation with a biological response, asking whether separated material could induce new capillaries.

This is the logic of bioassay-guided fractionation: a fraction is interesting because a reproducible biological effect follows it through the separation procedure. An active fraction need not be a single pure molecule. The historical preparation should therefore not be identified retrospectively with vascular endothelial growth factor merely because both concern angiogenesis.

An original example distinguishes recovery from enrichment. Suppose a starting extract contains 100 arbitrary units of angiogenic activity in 20 milligrams of protein. Its activity per milligram is $100/20=5$. A later fraction contains 40 units in 2 milligrams, giving $40/2=20$ units per milligram. The process has achieved fourfold enrichment with 40 percent activity recovery. Neither number establishes chemical purity. Here the activity units are assumed additive for illustration; an ordinal visual score cannot automatically be treated as an additive biochemical quantity.