Branching Processes Applied to Cell Surface Aggregation Phenomena

By Catherine A. MacKen

Aggregation processes are studied within a number of different fields--c- loid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation pro ces ses involve monomer units (e. g. , biological cells, liquid or colloidal droplets, latex beads, molecules, or even stars) that join together to form polymers or aggregates. A quantitative theory of aggre- tion was first formulated in 1916 by Smoluchowski who proposed that the time e- lution of the aggregate size distribution is governed by the infinite system of differential equations: (1) K . . c. c. - c k = 1, 2, . . . k 1. J 1. J L ~ i+j=k j=l where c is the concentration of k-mers, and aggregates are assumed to form by ir? k reversible condensation reactions [i-mer + j-mer -+ (i+j)-mer]. When the kernel K . . can be represented by A + B(i+j) + Cij, with A, B, and C constant; and the in- 1. J itial condition is chosen to correspond to a monodisperse solution (i. e. , c (0) = 1 0, k > 1), then the Smoluchowski equation can be co' a constant; and ck(O) solved exactly (Trubnikov, 1971; Drake, 1972; Ernst, Hendriks, and Ziff, 1982; Dongen and Ernst, 1983; Spouge, 1983; Ziff, 1984). For arbitrary K , the solution ij is not known and in some ca ses may not even exist.

• Format: Paperback
• Language: English
• ISBN: 3540156569
• ISBN13: 9783540156567
• Release Date: July 1985
• Publisher: Springer
• Length: 124 Pages
• Weight: 0.76 lbs.
• Dimensions: 0.3" x 8.3" x 11.7"