Actin filament (F-actin) assembly kinetics determines the locomotion and shape of crawling eukaryotic cells, but the nature of these kinetics and their determining reactions are unclear. Live BHK21 fibroblasts, mouse melanoma cells, and Dictyostelium amoebae, locomoting on glass and expressing Green Fluorescent Protein-actin fusion proteins, were examined by confocal microscopy. The cells demonstrated three-dimensional bands of F-actin, which propagated throughout the cytoplasm at rates usually ranging between 2 and 5 mum/min in each cell type and produced lamellipodia or pseudopodia at the cell boundary. F-actin's dynamic behavior and supramolecular spatial patterns resembled in detail self-organized chemical waves in dissipative, physico-chemical systems. On this basis, the present observations provide the first evidence of self-organized, and probably autocatalytic, chemical reaction-diffusion waves of reversible actin filament assembly in vertebrate cells and a comprehensive record of wave and locomotory dynamics in vegetative-stage Dictyostelium cells. The intensity and frequency of F-actin wavefronts determine locomotory cell projections and the rotating oscillatory waves, which structure the cell surface. F-actin assembly waves thus provide a fundamental, deterministic, and nonlinear mechanism of cell locomotion and shape, which complements mechanisms based exclusively on stochastic molecular reaction kinetics. (C) 2002 Elsevier Science (USA).