Error Propagation Theory of Chemically Solid Phase Synthesized Oligonucleotides and DNA Sequences for Biomedical Application

Abstract

Our interest was focused on error propagation during the synthesis of single stranded oligonucleotides and DNA sequences. We have modeled the assumed degenerative effects of such 3′→5′-driven syntheses, or vice versa 5′→3′ Quantification in scaling the theoretically synthesized yields provided the rationale for our approaches to error propagation of synthesized oligonucleotides and DNAss sequences. Our homeodynamical model is governed by nonlinear equations; they possess the relevant features of fractal dimensions. This is significant for implication of a new scale-invariant property of oligonucleotide synthesis. An inverse power law of driven multi-cycle synthesis on fixed starting sites is described with a model of growing oligonucleotides in fractal measures. It equates the constant coupling efficiency d ₀ and the constant capping efficiency p ₀ to the length distribution of sequences produced in the preparation set of oligonucleotides. Attractors in the dynamical model are included. Each sequence is produced randomly with the probability coupling function d and/or randomly with the probability capping function p; d and p are independent from one another. For this general problem we construct effective and computable recursive functions of the relation described by the inverse power law of driven multi-cycle synthesis. Nonlinear fractal dimensions D(N) are computed for theoretical deviations from the constant coupling efficiency d ₀. They offer a new access to the growth dependency on the nucleotides A, G, C, T.

In memory of Severo Ochoa 1905–1993