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In this work the statistical properties of quasi-periodic structures disturbed by thermal fluctuations are investigated. A chain of DNA as an example of such structure is under consideration. This chain interacts with some chemical elements and creates grate variety of stable nanostructures. The process is called DNA-origami. The problem of interaction of DNA-molecule with periodic flat surface is solved by using a semi-phenomenological model. The places of DNA attachments to the surface correspond to a quasi-periodic sequence of random points. The model allows determinate the optimal frequency of chemical periodical patterning on a substrate.