Theory of DNA melting curves

Abstract Exact algorithms for the calculation of melting curves of heterogeneous DNA with N base pairs apparently require computer time proportional to N 2 . However, it is shown that a decomposition of the loop entropy factor into a sum of I exponential functions (1) gives an extremely accurate approximation to the loop entropy factor for small values of I and (2) makes the computer time for the exact algorithms proportional to I · N . In effect, exact results for melting curves and lengths of helix or coil stretches are obtained with computer time comparable to that required for the Frank‐Kamenetskii approximation. The remarkable accuracy of the latter for the fraction of helical content (errors of 0.01–0.05) is confirmed, but appreciably larger errors are found for the lengths of helix or coil stretches (typical errors of 30–100%).