Nucleic Acids Research, 2005, Vol. 33, No. 13 4215 Table 1. Calculated binding energies and component contributions Binding step Dimer formation RD + DNA CBFb + RD Trimer formation RD–DNA + CBFb RD–CBFb + DNA Trimer total D Trimer–dimer DGsolvation 2403.1 262.0 201.0 2342.1 2604.1 61.0 DEstrain 109.0 104.7 75.5 289.2 184.5 180.2 DEIE 2513.4 238.7 363.0 2637.7 2876.4 124.4 DGbinda 0.2 81.0 87.0 6.3 87.3 6.0 DTSMM 49.4 48.5 52.0 52.9 101.4 3.5 DGbind,TSb 49.2 32.5 35.0 46.6 14.1 2.5 Energies in kcal/mol calculated using Equations 1–4 from the data reported in Supplementary Table S4. aFree energy of binding based on the differences in the free energy of each monomer or complex, G, in Supplementary Table S4. It should be noted that the sum of the terms DGsolvation, DEstrain and DEIE are not exactly equivalent to DGbind due to rounding errors. Based on the sums, free energies of binding of 1.3, 81.4, 86.5, 6.4, 87.8 and 5.2 kcal/mol were obtained for the RD + DNA, CBFb + RD, RD–DNA + CBFb, RD–CBFb + DNA, trimer total and D trimer–dimer, respectively. bFree energy of binding including the molecular mechanical entropic contribution, DTSMM. Figure 2. Overall binding pathways RD–DNA, RD–CBFb and RD–CBFb– DNA. Free energies before and after the/represent DGbind and DGbind,TS, as reported in Table 1. the potential energy function and the force ﬁeld (44) along with possible limitations in the sampling of conformational space. For example, underestimation of the protein–DNA interaction energies in the force ﬁeld by <4% would account for the prediction that binding of RD to CBFb is more favor- able than RD binding to DNA. With respect to the TSMM, the use of gas phase minimized structures may be problematic, especially in the case of the polyanionic DNA where the electrostatic screening due to the 4r dielectric is expected to be insufﬁcient when compared with the proteins. However, when the two types of binding free energy are compared, the trends are similar. Moreover, in both scenarios, the binding of DNA to the RD–CBFb dimer to form the trimer is more favorable than the binding of RD and DNA to form the RD–DNA dimer, consistent with the experimental data (16,18). Thus, it appears that the present results, although not in quantitative agreement with experiment due to assu- mptions and limitations in the theoretical models, are repres- entative of the experimental regimen, allowing for atomic details of events driving binding to be elucidated. In addition, the emphasis in this work on differences in energies and struc- tures between the systems rather than absolute energies should allow for increased conﬁdence in the observations and the conclusions based on those observations. Concerning the con- vergence of the present results, the energies calculated from the two independent DNA simulations are within the estimated errors (Supplementary Table S4), suggesting that the present calculations have adequately converged. Analysis of the thermodynamic cycle in Figure 2 predicts that binding of both CBFb and DNA are cooperative. These results are consistent with previous studies showing the bind- ing of DNA to RD to be enhanced by the binding of CBFb as well as the binding of CBFb to RD to be enhanced by DNA based on electrophoretic mobility shift assay (10,16,18). As discussed, such cooperativity may be important for maintain- ing binding of RD to DNA via stabilization of the ternary complex to insure adequate transcriptional activation. Tighter protein–protein interactions due to DNA binding have been observed in other types of transcription factors (45). Contributions from solvation, strain and interaction energies to the calculated binding energies are shown in Table 1. As expected, the solvation energies are all unfavorable upon bind- ing, with the unfavorable contributions being signiﬁcantly larger for the interactions involving the highly solvated poly- anionic DNA. The strain energies are all also unfavorable with the exception of formation of the CBFb–RD dimer. Typically, it would be expected that the protein–protein or protein–DNA interactions would lead to an unfavorable strain contribution upon binding (23). Ongoing studies in our laboratory are investigating the unusual behavior in the CBFb–RD dimer interaction. Countering the unfavorable solvation and strain contributions are favorable interaction energies for all cases. Clearly, the free energies of binding are driven by the large, opposing forces of solvation and, typically, strain energies versus interaction energies between the macromolecules in the complexes. Data at the bottom of Table 1 addresses the contributions to the calculated gain in binding energy associated with cooper- ativity upon going from the dimers to the trimer. Contributing to the cooperativity is a decrease in the unfavorable solvation that occurs upon binding, evidenced by the Dtrimer–dimer value for DGsolvation being 61 kcal/mol. In addition, the inter- action energies become more favorable by 124 kcal/mol. The more favorable change in interaction energy occurred with both the RD–DNA and the RD–CBFb interactions in the trimer (Table 1); details of the contributions of different regions of the proteins to this will be discussed below. Coun- tering these contributions are unfavorable increases in the strain energy, consistent with gains in interaction energies, as discussed above. Thus, the cooperativity of DNA and CBFb binding to RD is predicted to be dominated by gains in the favorable interactions between the macromolecules and with lowering of the solvation penalty to complex formation.