Formally exact method to numerically analyze local denaturation in superhelical DNA

We present a numerically exact technique for analyzing where local DNA denaturation (i.e. separation of the two strands comprising the B-form duplex) will occur in circular super-helical DNA molecules of kilo-base lengths and specified base sequences. This approach incorporates both the base sequence dependence of the denaturation energetics and the imposition of superhelical stress on the DNA molecule. Our analytic method consists of an integration over the twist degrees of freedom followed by the introduction of auxiliary variables that decouple the remaining degrees of freedom, allowing use of the transfer matrix method. The algorithm implementing this method requires O(N²) operations and O(N) memory to analyze a DNA domain containing N base pairs. To analyze kilobase length DNA molecules it must be implemented in high precision floating point arithmetic. An accelerated algorithm can be constructed by imposing an upper bound M on the number of base pairs that can simultaneously denature in a state. This accelerated algorithm requires O(MN) operations. Sample calculations show that it achieves high accuracy (greater than 15 decimal digits) with relatively small values of M (M<0.05 N) for kilobase length molecules under physiological conditions. Calculations are performed on the superhelical pBR322 DNA sequence using these methods. With no free parameters in the model, the predicted locations and extents of local denaturation are in quantitatively precise agreement with experimental measurements.