Actin filaments and microtubules are major dynamic components of the cytoskeleton of eukaryotic cells. Assembly of these polymers from monomeric actin or tubulin occurs with expenditure of energy, because ATP (or GTP) tightly bound to actin (or tubulin) is irreversibly hydrolysed during polymerization. Therefore, actin filaments an microtubules are dissipative structures. Our purpose has been to understand how the dissipation of chemical energy perturbs the laws of reversible helical polymerization defined by Oosawa, and affects the dynamics of these polymers. A kinetic study has shown that nucleotide is hydrolysed on the polymer within at least two steps consecutive to the incorporation of the monomer: cleavage of the gamma-phosphoester bond followed by the slower release of Pi; only the second reaction appears reversible. Pi release, and not cleavage of the gamma-phosphate, is linked to the destabilization of protein-protein interactions in the polymer, and therefore plays the role of a conformational switch. The dynamic properties of the polymer in the NTP- and NDP-Pi intermediate states of the assembly process have been investigated using non-hydrolysable analogues of nucleotides and structural analogues of Pi, AlF4- and (BeF3-, H2O). Because nucleotide hydrolysis is uncoupled from polymerization, actin filaments and microtubules grow with a 'cap' of terminal NTP- and NDP-Pi-subunits that interact strongly, and prevent the rapid depolymerization of the unstable core of the polymer formed of NDP-subunits. The fact that the dynamic properties of the polymer are affected by bound nucleotide results in a nonlinear dependence of the rate of elongation on monomer concentration.(ABSTRACT TRUNCATED AT 250 WORDS)