IF are made of fibrous subunits. Drug results rule out microfilaments which are made of actin and implicate MT which are made of tubulin. It is likely that different motor molecules, which move in opposite directions, like dynein and kinesin, position the Golgi and ER respectively. MT are usually arrayed in a pattern so that they spread out from a single area, the centrosome or MTOC, near the center of the cell. The MT are all arranged with their minus ends near the centrosome.
Sputum has something in it that speeds up polymerization of added actin.
The more MF's there are in the sputum, the more plus ends there are, and the faster the polymerization goes. C. Gelsolin cuts filaments directly, and then forms a cap on the newly formed plus end so that the newly exposed end cannot grow any more. Gelsolin probably liquifies the sputum faster because it cuts the polymers in the middle, instead of shortening steadily from the ends, and because it acts directly, instead of trapping monomers as they fall off. If you have a tangled web of MF's, it will come apart much faster if you cut the filaments than if you dismantle the individual filaments from the ends, one monomer at a time. If DNase were primarily liquifing sputum by acting as an enzyme, it should act very quickly and at low concentration.