The series of cooperative transitions that lead to [d(TG4)4.(K+)m] quadruplex assembly upon rapid addition of KCl to d(TG4) strands were studied. Quadruplex samples were dialyzed against KCl then Li-EDTA and found to retain between three and five strongly bound potassiums with affinities >10(6) M-2. Absorbance thermal denaturation (melt) and circular dichroism (CD) equilibrium binding data were obtained. The latter were analyzed using two classes of binding models to simulate the effects of the assumed intermolecular interactions on the binding curves (isotherms). The melt experiments yielded equilibrium dissociation constants (Kd) ranging from 10(-11) to 10(-12) M3 at the melting temperatures. Extrapolating these values to 23 degrees C predicts Kd values in the 10(-28) M3 range if the heat capacity (Cp) is not strongly dependent upon temperature changes over this range. Assuming Ka is equal to 1/Kd (from melting analyses), very large association free energies stabilize the quadruplex at 23 degrees C in 100 mM KCl (DeltaGa = -43 kcal mol-1). Plots of the differential melt curve peak half-widths, a measure of cooperativity, versus d(TG4) concentration showed that quadruplex dissociation is much more cooperative at 400 mM KCl than at 100 mM KCl. Forty-eight hour quadruplex assembly time courses were monitored by CD at 264 nm. Equilibrium quadruplex accumulation generally required over 10 h, and net reaction extents were in the 10-85% range. Hill plots of the data show that initial steps in the multistep pathway are positively cooperative, presumably due to strong strand-cation and strand-strand binding interactions in duplex and triplex assembly reactions, then negatively cooperative in quadruplex formation. Models were developed to rationalize the experimental observations in terms of consecutive cooperative allosteric transitions from cation-deficient relaxed (R) strand-aggregates to cation-containing tense (T) structures, driven by the allosteric effector K+. Quantitative mappings of positive and then negative cooperativity were obtained by fitting the results as a function of strand number incorporated during quadruplex assembly. Surprisingly, models for reactions involving incorporation of five and six strands fit the data better than models involving only four strands. The 5-step "induced fit" model fits the data as well as or better than 3- and 4-step models and better than all of the strand aggregation models that were devised and investigated. Net association free energies (summation operatori=1,n) ranged from -20 to -26 kcal mol-1, approximately half the magnitude of the apparent stabilities measured by absorbance melts. Likely explanations for this discrepancy involve hysteresis and errors due to inadequate equilibration in the melt experiments. Hysteresis is thought to be produced by irreversibility due to different predominant mechanisms in absorbance (dissociation) and CD (association) experiments. The kinetic block to quadruplex assembly can be unambiguously attributed to quadruplex formation and not intermediate steps in the assembly mechanism. On the basis of these results we propose that, in addition to the more conventional assembly mechanisms involving duplex dimerization and stepwise strand addition, quadruplex formation can also proceed by triplex-triplex disproportionation. Interaction statistics arguments that support the energetic feasibility of the disproportionation pathway are presented. The allosteric quadruplex assembly model provides a mechanism which could be used by the cell to simultaneously modulate DNA structure and activity within telomeres, transcriptional promoters, recombination-prone chromatin, and other G-rich DNAs. As a result of this allosterism, cation and strand availability and strand-pairing capabilities could profoundly influence the functional capacity of a particular strand over a relatively narrow range of effector concentration changes. (ABSTRACT TRUNCATED)