 Charles Abernathy

Charles Abernathy coauthored the 1971 experimental study of a tumour-derived angiogenic fraction with Judah Folkman, Ezio Merler and Gretchen Williams.^[ref] An important aspect of the experimental argument was spatial separation: blood vessels could respond outside filter chambers containing tumour cells.^[ref]

A barrier experiment tests whether direct cellular contact is necessary. Its interpretation depends on membrane permeability: passage of a dissolved substance differs from passage of an intact cell. Exclusion of cells with persistence of a vascular response supports a diffusible signal, but does not uniquely identify the signal's molecular structure.

An original dimensional estimate shows why distance and time belong in the interpretation. A characteristic diffusion time over a distance $L$ is $t\sim L^2/D$, where $D$ is a diffusion coefficient. Taking stipulated values $L=0.5\mathrm{mm}$ and $D=10^{-10}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ gives about $2500\mathrm{s}$, or 42 minutes. Doubling the distance multiplies that estimate by four. Binding, degradation and geometry can alter the actual response; the calculation is not a reconstruction of the experiment.