4214 Nucleic Acids Research, 2005, Vol. 33, No. 13 þ EvdW þ Eelec: where the overall free energy of each complex was described using (24) G ¼ EMM þ GSolvation TSMM: In Equation 2 EMM describes the molecular mechanical energy of the system consisting of all components in the CHARMM potential energy function, as shown in the follow- ing Equation 3: EMM ¼ Ebond þ Eangle þ EUrey Bradley þ Edihedral þ Eimproper For complexes, EMM, can be separated into interaction energy, EIE and strain, Estrain components: EMM‚ complex ¼ EIE þ Estrain‚ where EIE is the sum of the vdW and electrostatic interaction energy between individual molecules in a complex and Estrain is the sum of EMM terms for each molecule in the complex (i.e. all MM energy contributions for each species ignoring contributions from the other molecules in the complex). The Gsolvation term describes the solvation free energy of a system and includes both electrostatic, Gelec and non-polar, Gnp, components. Gsolvation ¼ Gelectrostatic þ Gnp: The electrostatic portion of the solvation free energy was calculated using the Generalized-Born molecular volume (GBMV) method (25,26). The non-polar portion of the solva- tion energy (i.e. due to cavity formation and hydrophobicity) was calculated using the Still equation, Enp ¼ g SA, where g is an empirical atomic solvation parameter, 7.2 cal/s2, and SA is the solvent accessible surface area calculated with a solvent probe radius of 1.4 s (25,41). The ﬁnal term in Equation 2, TSMM, describes the entropic part of the energy as a sum of translational, rotational and vibrational entropy terms calcu- lated via the harmonic approximation (42) for the temperature 300 K. Vibrational analysis was performed on the solute molecules extracted out of the solvent box. The solute struc- ture was minimized using the Conjugate-Gradient method to an RMS gradient of 10 4 kcal/(mol s) with a distance- dependent dielectric of 4r applied to approximate the screen- ing of electrostatic interactions by solvent, where r is the distance between two atoms, as performed previously (22). To better understand the contributions of the various ener- getic terms to complex formation, differences in the energy terms upon formation of the complexes were calculated. This typically involved calculation of the difference between a selected term for the complex and those of the individual molecules comprising the complex. In the case of the inter- action energies their contribution was simply the sum of the contribution between the individual molecules in each complex (i.e. for the CBFb–RD dimer the EIE between CBFb and RD was included). However, in the case of the trimer formation via dimer + monomer complexation the EIE contribution includes those between the monomer being added and the two molecules in the original dimer along with the change in the interaction energy between the molecules in the original dimer upon going to a trimer. For 2 3 4 5 example, EIE,CBFb-RD + DNA ¼ EIE,CBFb-DNA + EIE,RD-DNA DEIE,CBFb-RD(dimer to trimer). This term accounts for gains or losses in the interaction energy of the molecules in a dimer when the third molecule binds to form a trimer. Interaction energies, Einter, and strain energies, Estrain, were calculated for each individual species using an inﬁnite cutoff in order to mimic the long-range electrostatic interactions treated via PME in the MD simulations. Energy calculations were performed on the 900 structures from each simulation system with statistical analysis performed by dividing each 4.5 ns simulation into nine 500 ps time blocks. Statistical analysis was performed by obtaining the averages from each time block, with those averages treated as independent data points, allowing calculation of the overall averages, and stand- ard errors as described previously (43). The entropy calcu- lations were performed on 30 structures extracted from the simulation trajectories at 150 ps time intervals, with the stat- istical analysis derived by dividing the 30 observations into ten 450 ps independent time blocks from which the averages and the standard errors were obtained. Overall RMS differences of all simulated structures versus the crystallographic structure of the trimer are shown in Supplementary Table S3. RESULTS AND DISCUSSION MD simulation studies were undertaken on the RD to under- stand the nature of interactions with the DNA and with the binding partner, CBFb. Average RMS differences for all non- hydrogen atoms with respect to the crystallographic ternary complex structures were 1.62 ± 0.04, 3.56 ± 0.10, 2.15 ± 0.04, 3.23 ± 0.16, 3.63 ± 0.11 and 2.81 ± 0.05 s for the DNA, RD, CBFb, RD–DNA, RD–CBFb and CBFb–RD–DNA struc- tures, respectively, indicating that the overall structures were maintained in the simulations. The structure of the trimer after a 4.5 ns simulation is illustrated in Figure 1. Analysis focused on the overall binding as calculated using Equation 1 followed by investigation of the contributions of different components to the overall binding (Equations 2 and 4). This was followed by identifying contributions of different regions of the proteins and DNA to binding, ultimately analyzing the role of indi- vidual amino acids. Emphasis was placed on using the present results to interpret the body of experimental data avail- able on RD. Free energies of complex formation for the dimers and the trimer were calculated using Equation 1 based on the data presented in Supplementary Table S4. The resulting free ener- gies of binding for the various complexes are presented in Table 1 and are included in the thermodynamic cycle shown in Figure 2. Two free energies of binding are reported, DGbind and DGbind,TS, that exclude and include the conﬁgura- tion entropy, TSmm, respectively. For DGbind the calculated energies are all favorable, although the interactions involving addition of CBFb are extremely exothermic. In contrast, upon inclusion of the entropy the events that involve DNA binding become unfavorable. In addition, the calculations predict that RD–CBFb binding is more favorable than RD–DNA binding, in contrast to experimental observations (16). The presence of these discrepancies is not surprising due to a variety of assumptions in the calculations, including the omission of energetic contributions, such as the solvation and entropic contributions of the added counterions (23), limitations in