Assembly of a homomeric three-membered ring. (*A*) In this graph, we consider the percentage of monomers in the various association states (monomer, dimer, and trimer) as a function of time. The affinities are uniformly very strong (*K*_{d} = 10^{-12} M). The data are plotted on a logarithmic timescale because a linear scale obscures the existence of the plateau phase. The on-rate *α* = 2.53 × 10^{6} M^{-1} s^{-1} and total subunit concentration *X*_{T} = 400 nM. (*B*) Variation in assembly time (measured by *T*_{99} as described in the text) with affinity (*K*_{d}) for various initial monomer concentrations *X*_{T}. All concentrations exhibit a distinct minimum in *T*_{99}; the *K*_{d} at which this minimum occurs is proportional to the total monomer concentration (see *SI Appendix*, Fig. S9). α as in *A*. (*C*) Steady-state yield (defined as the fraction of monomers in the full ring) as a function of affinity when subunit synthesis and degradation are taken into account according to model A (see *SI Appendix*, Sections 2.4 and 4.2). The synthesis and degradation parameters were chosen to yield the average concentration and half-life of proteins in *Saccharomyces cerevisiae* (, ), approximately 480 nM and 42 min, respectively. The solid curve represents an analytical solution of the steady-state yield and the circles represent steady-state results from the numerical integration of model A (see *SI Appendix*, Sections 2.4.1 and 3.2.1). The parameters in this case are α as in *A*, monomer synthesis rate *Q* = 1.31 × 10^{-10} M s^{-1}, degradation rate *δ* = 2.75 × 10^{-4} s^{-1}, and *X*_{T} = *Q*/*δ* = 477 nM.

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