We study the effect of the composition of the genetic sequence on the melting temperature ofdouble stranded DNA, using some simple analytically solvable models proposed in the framework of thewetting problem. We review previous work on disordered versions of these models and solve them whenthere were not preexistent solutions. We check the solutions with Monte Carlo simulations and transfermatrix numerical calculations. We present numerical evidence that suggests that the logarithmic correctionsto the critical temperature due to disorder, previously found in RSOS models, apply more generally toASOS and continuous models. The agreement between the theoretical models and experimental data showsthat, in this context, disorder should be the crucial ingredient of any model while other aspects may be keptvery simple, an approach that can be useful for a wider class of problems. Our work has also implicationsfor the existence of correlations in DNA sequences.
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