The general features of the kinetics of actin polymerization are investigated by mathematical models, with the aim of identifying the kinetically relevant parameters in the process and detecting and interpreting the alterations occurring in actin polymerization under various experimental conditions. Polymerization curves, obtained by following the increase in fluorescence of actin derivatized with N-(1-pyrenyl) iodoacetamide, are fitted using analytical equations derived from biochemical models of the actin polymerization process. Particular attention is given to the evaluation of the effects of the neuronal phosphoprotein synapsin I. The models obtained under various ionic conditions reveal that synapsin I interacts with actin in a very complex fashion, sharing some of the properties of classical nucleating proteins but displaying also actions not described previously for other actin-binding proteins. Synapsin I appears to bind G-actin with a very high stoichiometry (1:2-4), and the complex behaves as an F-actin nucleus, producing actin filaments under conditions where spontaneous polymerization is negligible. These actions of synapsin I are markedly affected by site-specific phosphorylation of the protein. An original transformation of the fluorescence data, which estimates the disappearance rate of actin monomer toward the critical concentration, is presented and shown to be of general usefulness for the study of actin-binding proteins.