Actin polymerization is coupled to the hydrolysis of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (Pi). Therefore, each protomer within an actin ﬁlament can attain three different nucleotide states corresponding to bound ATP, ADP / Pi, and ADP. These protomer states form spatial patterns on the growing (or shrinking) ﬁlaments. Using Brownian dynamics simulations, the growth behavior of long ﬁlaments is studied, together with the associated protomer patterns, as a function of ATP-actin monomer concentration, CT, within the surrounding solution. For concentrations close to the critical concentration CT = CT,cr, the ﬁlaments undergo treadmilling, i.e., they grow at the barbed and shrink at the pointed end, which leads to directed translational motion of the whole ﬁlament. The corresponding nonequilibrium states are characterized by several global ﬂuxes and by spatial density and ﬂux proﬁles along the ﬁlaments. We focus on a certain set of transition rates as deduced from in vitro experiments and ﬁnd that the associated treadmilling ﰎor turnoverﰏ rate is about 0.08 monomers per second.