Size distribution of linear and helical polymers in actin solution analyzed by photon counting histogram

Actin is a ubiquitous protein that is a major component of the cytoskeleton, playing an important role in muscle contraction and cell motility. At steady state, actin monomers and filaments (F-actin) coexist, and actin subunits continuously attach and detach at the filament ends. However, the size distribution of actin oligomers in F-actin solution has never been clarified. In this study, we investigated the size distribution of actin oligomers using photon-counting histograms. For this purpose, actin was labeled with a fluorescent dye, and the emitted photons were detected by confocal optics (the detection volume was of femtoliter (fL) order). Photon-counting histograms were analyzed to obtain the number distribution of actin oligomers in the detection area from their brightness, assuming that the brightness of an oligomer was proportional to the number of protomers. We found that the major populations at physiological ionic strength were 1-5mers. For data analysis, we successfully applied the theory of linear and helical aggregations of macromolecules. The model postulates three states of actin, i.e., monomers, linear polymers, and helical polymers. Here we obtained three parameters: the equilibrium constants for polymerization of linear polymers, K_l = (5.2 ± 1.1) × 10⁶ M^-1, and helical polymers, K_h = (1.6 ± 0.5) × 10⁷ M^-1; and the ratio of helical to linear trimers, γ = (3.6 ± 2.3) × 10^-2. The excess free energy of transforming a linear trimer to a helical trimer, which is assumed to be a nucleus for helical polymers, was calculated to be 2.0 kcal/mol. These analyses demonstrate that the oligomeric phase at steady state is predominantly composed of linear 1-5mers, and the transition from linear to helical polymers occurs on the level of 5-7mers.