FRACTAL DIMENSION OF ERROR SEQUENCE DYNAMICS IN QUANTITATIVE MODELINGOF SYNTHESES OF SHORT OLIGONUCLEOTIDE AND SINGLE-STRANDED-DNA SEQUENCES

Oligonucleotides are becoming more and more important in molecular bio medicine; for example, they are used as defined primers in polymerase chain reaction and as antisense oligonucleotides in gene therapy. In t his paper, we model the dynamics of polymer-supported oligonucleotide synthesis to an inverse power law of driven multi-cycle synthesis on f ixed starting sites. The mathematical model is employed by presenting the accompanying view of error sequences dynamics. This model is a pra ctical one, and is applicable beyond oligonucleotide synthesis to dyna mics of biological diversity. Computer simulations show that the polym er support synthesis of oligonucleotides and single-stranded DNA seque nces in iterated cyclic format can be assumed as scale-invariant. This synthesis is quantitatively described by nonlinear equations. From th ese the fractal dimension D-u (N, d) is derived as the growth term (N = number of target nucleotides, d = coupling probability function). D- u (N, d) is directly measurable from oligonucleotide yields via high-p erformance liquid chromatography or capillary electrophoresis, and qua ntitative gel electrophoresis. Different oligonucleotide syntheses, in cluding those with large-scale products can be directly compared with regard to error sequences dynamics. In addition, for short sequences t he fractal dimension D-u (N, d) is characteristic for the efficiency w ith which a polymer support of a given load allows oligonucleotide cha in growth. We analyze the results of separations of crude oligonucleot ide product from the synthesis of a 30 mer. Preliminary analysis of a 238 mer single-stranded DNA sequence is consistent with a simulated es timate of crude synthesis product, although the target sequence itself is not detectable. We characterize the oligonucleotide support synthe ses by simulated and experimentally determined values of the fractal d imension D-u (N, d(o)) within imitations (d(o) = constant (average) co upling probability).