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UNWINDING THE DOUBLE HELIX: USING DIFFERENTIAL MECHANICS TO PROBE CONFORMATIONAL CHANGES IN 192 DNA approximate equilibrium value corrected for the estimated effects of all neglected, high-energy states: (7.16) Examples of correctable parameters include the population-averaged values of the total numbers of separated base pairs, runs of transition, and separated A·T pairs. The only important quantities that cannot be refined in this way are the transition and destabilization profiles, because their calculation involves positional information. However, their accuracy can be estimated by comparing the corrected ensemble average number of separated base pairs with its (uncorrected) value that is computed as the sum of the probabilities of separation for all base pairs in the sequence. In this way the accuracy of the profiles calculated with any specified threshold can be assessed. This allows the threshold to be chosen to give any required degree of accuracy. In practice accuracies exceeding 99 percent are feasible at physiological temperatures, even for highly supercoiled molecules. Evaluation of Free-Energy Parameters Before these techniques can yield quantitatively precise calculations, accurate values must be known for the energy parameters. Only the separation energetics bAT and bGC have been accurately measured under a wide range of environmental conditions (Marmur and Doty, 1962; Schildkraut and Lifson, 1968). The other parameters (the quadratic coefficient K governing residual linking, the cooperativity free energy a, and the coefficient C governing interstrand twisting of strand-separated DNA) are known only for a restricted range of molecules and environmental conditions. The theoretical methods described above can be used to determine the best fitting values of the unknown parameters based on the analysis of experimental data on superhelical strand separation. Allowing the parameters
UNWINDING THE DOUBLE HELIX: USING DIFFERENTIAL MECHANICS TO PROBE CONFORMATIONAL CHANGES IN 193 DNA to vary within reasonable ranges, the analyses are repeated, and the set of values is found for which the computed transition properties best fit the experimental data (Benham, 1992). Application of this method to data on strand separation in pBR322 DNA at [Na+] = 0.01 M, T = 310 K finds a unique optimum fit when K = 2350 ± 80 RT/N, a = 10.84 ± 0.2 kcal, and C= 2.5 ± 0.3 à 10â13erg-nt/rad2. Extensive sample calculations of strand separations in superhelical DNA have been performed using these energy parameters (Benham, 1992). As described above, substantial amounts of free energy are required to drive strand separation. In consequence, this transition is favored only when the DNA is significantly supercoiled. This is shown in Figure 7.2, where the solid line depicts the probability of strand separation in pBR322 DNA (N = 4,363 base pairs) as a function of imposed negative superhelicity under low-salt conditions. The dashed line gives the ensemble average number of strand-separated base pairs as a function of âα. Separation occurs only when the linking difference satisfies α ⤠â18 turns and is confined to the terminator (3,200 to 3,300) and promoter (4,100 to 4,200) regions of one particular gene, as shown in Figure 7.1 above. These results are in precise agreement with experiment (Kowalski et al., 1988). Figure 7.2 The onset of strand separation in pBR322 DNA.
