phase of rapid filament elongation during which subunits are added quickly to the ends of the nucleated filaments (Figure 16–13A). Finally, as the concentration of actin monomers declines, the system approaches a steady state at which the rate of addition of new subunits to the filament ends exactly balances the rate of subunit dissociation. The concentration of free subunits left in solution at this point is called the critical concentration, Cc. As explained in Panel 16–2, the value of the critical concentration is equal to the rate constant for subunit loss divided by the rate constant for subunit addition—that is, Cc = koff/kon, which is equal to the dissociation constant, Kd, and the inverse of the equilibrium constant, K (see Figure 3–44). In a test tube, the Cc for actin polymerization—that is, the free actin monomer concentration at which the fraction of actin in the polymer stops increasing—is about 0.2 μM. Inside the cell, the concentration of unpolymerized actin is much higher than this, and the cell has evolved mechanisms to prevent most of its monomeric actin from assembling into filaments, as we discuss later.
The lag phase in filament growth is eliminated if preexisting seeds (such as fragments of actin filaments that have been chemically cross-linked) are added to the solution at the beginning of the polymerization reaction (Figure 16–13B). The cell takes great advantage of this nucleation requirement: it uses special proteins to catalyze filament nucleation at specific sites, thereby determining the location at which new actin filaments are assembled.
Due to the uniform orientation of asymmetric actin subunits in the filament, the structures at its two ends are different. This orientation makes the two ends of each polymer different in ways that have a profound effect on filament growth rates. The kinetic rate constants for actin subunit association and dissociation— kon and koff, respectively—are much greater at the plus end than the minus end. This can be seen when an excess of purified actin monomers is allowed to assemble onto polarity-marked filaments—the plus end of the filament elongates up to ten times faster (see Figure 16–12). If filaments are rapidly diluted so that the free subunit concentration drops below the critical concentration, the plus end also depolymerizes faster.
It is important to note, however, that the two ends of an actin filament have the same net affinity for actin subunits, if all of the subunits are in the same nucleotide state. Addition of a subunit to either end of a filament of n subunits results in a filament of n + 1 subunits. Thus, the free-energy difference, and therefore the equilibrium constant (and the critical concentration), must be the same for addition of subunits at either end of the polymer. In this case, the ratio of the rate constants, koff/kon, must be identical at the two ends, even though the absolute values of these rate constants are very different at each end (see Panel 16–2).
The cell takes advantage of actin filament dynamics and polarity to do mechanical work. Filament elongation proceeds spontaneously when the free-energy change (∆G) for addition of the soluble subunit is less than zero. This is the case when the concentration of subunits in solution exceeds the critical concentration. A cell can couple an energetically unfavorable process to this spontaneous process; thus, the cell can use free energy released during spontaneous filament polymerization to move an attached load. For example, by orienting the fast-growing plus ends of actin filaments toward its leading edge, a motile cell can push its plasma membrane forward, as we discuss later.
ATP Hydrolysis Within Actin Filaments Leads to Treadmilling at Steady State