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Fractal dimension of error sequence dynamics in quantitative modeling of syntheses of short oligonucleotide and single-stranded DNA sequences.

Oligonucleotides are becoming more and more important in molecular biomedicine; for example, they are used as defined primers in polymerase chain reaction and as antisense oligonucleotides in gene therapy. In this paper, we model the dynamics of polymer-supported oligonucleotide synthesis to an inverse power law of driven multi-cycle synthesis on fixed starting sites. The mathematical model is employed by presenting the accompanying view of error sequences dynamics. This model is a practical one, and is applicable beyond oligonucleotide synthesis to dynamics of biological diversity. Computer simulations show that the polymer support synthesis of oligonucleotides and single-stranded DNA sequences in iterated cyclic format can be assumed as scale-invariant. This synthesis is quantitatively described by nonlinear equations. From these the fractal dimension Da (N,d) is derived as the growth term (N = number of target nucleotides, d = coupling probability function). Da(N,d) is directly measurable from oligonucleotide yields via high-performance liquid chromatography or capillary electrophoresis, and quantitative gel electrophoresis. Different oligonucleotide syntheses, including those with large-scale products can be directly compared with regard to error sequences dynamics. In addition, for short sequences the fractal dimension Da (N,d) is characteristic for the efficiency with which a polymer support of a given load allows oligonucleotide chain growth. We analyze the results of separations of crude oligonucleotide product from the synthesis of a 30 mer. Preliminary analysis of a 238 mer single-stranded DNA sequence is consistent with a simulated estimate of crude synthesis product, although the target sequence itself is not detectable. We characterize the oligonucleotide support syntheses by simulated and experimentally determined values of the fractal dimension Da (N,d0) within limitations (d0 = constant (average) coupling probability).