598 Nucleic Acids Research, 2006, Vol. 34, No. 2 Figure 4. Dependence of the transition width DF on the protein concentration. Data are for: (A) NCp7, (B) NCp9, (C) NCp15 and (D) Gag. Each data point for the NC proteins is given as the mean ± standard error for seven experiments, and with fewer experiments for Gag. Data are taken in FIM buffer (see Materials and Methods), and room temperature. The solid lines are linear fits to the data in the low concentration limit, as follows: NCp7: dF ¼ (5.02 ± 0.97)·c; NCp9: dF ¼ (4.69 ± 0.58)·c; NCp15: dF ¼ (3.29 ± 0.22)·c; Gag: dF ¼ (7.54 ± 0.93)·c. Here, dF is the difference between DF in the presence of protein and DF in the absence of protein. The parameters obtained when ﬁtting the experimental data for all proteins studied (Figure 4) are shown in Table 1. We see that while the binding constants for the three processed forms of NC protein are indistinguishable, K 1 · 108 M 1, Table 1. Results of force-induced melting experiments in the presence of HIV-1 NCp7, NCp9, NCp15 and Gag Protein DFsata,b (pN) d(dF)/dca,c,d (pN/nM) Ke DGtotala,f (108 M 1) (kBT/bp) DGtotala,f (kcal/mol bp) None 3.66 ± 0.16 — NCp7 48.4 ± 1.9 5.02 ± 0.97 NCp9 40.9 ± 1.1 4.69 ± 0.58 NCp15 39.1 ± 1.6 3.29 ± 0.22 Gag 11.5 ± 2.0 7.54 ± 0.93 — 2.31 ± 0.05 1.36 ± 0.03 1.22 ± 0.25 0.65 ± 0.02 0.38 ± 0.01 1.40 ± 0.19 0.58 ± 0.02 0.34 ± 0.01 1.04 ± 0.09 0.57 ± 0.02 0.33 ± 0.01 9.43 ± 2.6 1.86 ± 0.07 1.08 ± 0.04 aMeasurements were performed in FIM buffer (see Materials and Methods). bDFsat is the measured transition width at 30 nM HIV-1 NC or 3 nM Gag concentration (saturation) as shown in Figure 4. cdF is defined as the difference between DF in the presence of protein and DF in the absence of protein. dd(dF)/dc is the slope of the linear fit to experimental data in the low binding fraction limit (solid lines in Figure 4). eK is calculated using Equation 4. fThe melting transition free energy DGtotal is calculated as the area between the experimental stretching curve for dsDNA without (open circle)/with (closed circle) protein at saturated transition width (30 nM NC or 3 nM Gag) and the experimental stretching curve for the ssDNA without (open triangle)/with (closed triangle) protein bound on it (Figure 3). Data are reported as mean ± standard error, n > 3. Averages were obtained for seven experiments. Errors for the slopes are calculated using the regression formula. The helix-coil transition free energy DG is reported in units of kBT or kcal/mol per base pair (bp), where kB is the Boltzmann constant and T ¼ 293 K is room temperature (1 kBT ¼ 581 cal/mol ¼ 4 · 10 21 J). the saturated value of the transition width increases slightly from NCp15 to NCp7. That is, DFsat ¼ 35, 37 and 45 pN for NCp15, NCp9 and NCp7, respectively. On the other extreme, the Gag protein has higher binding afﬁnity for ssDNA, K 9 · 108 M 1, but the increase in the transition width is much lower, such that DFsat 11 pN. In addition to measuring the binding constant of each protein to DNA, our DNA stretching curves can be used to determine the dsDNA melting free energy, as discussed pre- viously (42,43). In this report we will outline this approach and then use it for all four proteins at saturated binding in order to characterize the maximum effect of these proteins on DNA duplex stability. Brieﬂy, the area of the mechanical cycle in the (F x) plane delimited by the experimental stretching curve and the extrapolated stretching curve for ssDNA, with or with- out protein bound, gives the melting free energy in each case. Note that if the extension is per base pair, then the free energy is also per base pair, averaged over the whole length of polymeric DNA. The mechanical energy required to melt an average base pair, in turn, equals the free energy of the duplex relative to the single-stranded state of a base pair in the absence of applied force. The latter value is a function of solution conditions, including the concentration of DNA- binding protein. This method allows us to measure directly the effect of the protein on the stability of the duplex. Import- antly, this approach does not rely on any model of the protein– DNA interaction or on the details of the DNA melting transition. We note that when the stretching curves are not reversible, the work done by stretching may not represent the equilibrium melting free energy. If that is the case, our results will slightly overestimate the melting free energy. However, this effect should be very small due to the relatively high cooperativity of DNA melting under the conditions studied here as well as the observed rate-independence (at