Microscopic description of DNA thermal denaturation

摘要

We propose a microscopic model describing the process of DNA thermal denaturation. The process consists of the splitting of DNA base pairs, or nucleotides, resulting in the separation of two complementary DNA strands. In contrast to the previous modelling attempts we take into account the states of all base pairs of DNA which in fact imposes the microscopic nature of the approach. The model is a linear integro-differential non-autonomous equation describing the dynamics of probability density which characterizes the distances between the bases within individual base pairs. The non autonomous structure of the equation comes from the dependence on temperature that may be in the general case a (given) function of time. To our knowledge it is the first model taking into account not only the strength of double and triple hydrogen bonds between the complementary bases but also the stacking interactions between neighborhood base pairs. In the present paper the basic preliminary properties of the model including the existence, uniqueness and stability results in various cases are discussed. Moreover the symmetrized version of the model is considered and the “macroscopic limit” is studied. The performed numerical simulations reproduce the sigmoid shape of DNA melting curves and reveal the appearance of experimentally observed denaturation bubbles.