Theory of phase segregation in DNA assemblies containing two different base-pair sequence types

Spontaneous pairing of homologous DNA sequences - a challenging subject in molecular biophysics, often referred to as 'homology recognition' - has been observed in vitro for several DNA systems. One of these experiments involved liquid crystalline quasi-columnar phases formed by a mixture of two kinds of double stranded DNA oligomer. Both oligomer types were of the same length and identical stoichiometric base-pair composition, but the base-pairs followed a different order. Phase segregation of the two DNA types was observed in the experiments, with the formation of boundaries between domains rich in molecules of one type (order) of base pair sequence. We formulate here a modified 'X-Y model' for phase segregation in such assemblies, obtain approximate solutions of the model, compare analytical results to Monte Carlo simulations, and rationalise past experimental observations. This study, furthermore, reveals the factors that affect the degree of segregation. Such information could be used in planning new versions of similar segregation experiments, needed for deepening our understanding of forces that might be involved, e.g., in gene-gene recognition.