## What is it about?

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.

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## Why is it important?

Theory on individual molecules in chemically solid-phase synthesized oligonucleotides and DNA sequences. EACH INDIVIDUAL MOLECULE DURING MUTICYCLIC SYNTHESIS ON A SOLID SUPPORT WAS THEORETICALLY CAPTURED: THUS, IT IS A SINGLE-MOLECULE STUDY. Any mathematical formulation of chemical oligonucleotide synthesis on solid support is based on the following prerequisites (briefly described here, see also [4]): It is a driven growth process starting from 3' to 5' direction, or vice versa. The growing oligonucleotide or single stranded DNA is covalently bound to the support. We assume average constant conditions of fully tritylated nucleoside loading of the support. The cyclic repetition of coupling and capping steps during the growth process is considered as a linear undisturbed flow in first approximation. Error sequences are shorter than the target sequence, ending with a nucleoside; they can be separated according to their length. The error sequences are some how truncated versions of a target sequence. The system described above acts as a variation generator. «1» represents an arbitrary (A, G, T, C) nucleotide/nucleoside in a sequence of oligonucleotides. As a coupling step either succeeds or fails, we use a second symbol for such missing nucleotides: symbol «0». Furthermore, we use a symbol for the capping group: symbol «2». Capping can only be done after a failed coupling step. Hence, symbol «2» is located only after symbol «0» as the last element of a sequence. It is convenient to formulate the problem as follows: We consider the variation V with repetition w of two elements (m = 2) «1» and «0» to (N - l)th power. N is the integer number of nucleotides/nucleoside of the target sequence. N - 1 gives us the integer number of the last reaction cycle. Keywords Fractal Dimension Integer Number Error Sequence Reaction Cycle Iterate Function System. Individual molecule calculation

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This page is a summary of: Error Propagation Theory of Chemically Solid Phase Synthesized Oligonucleotides and DNA Sequences for Biomedical Application, January 1994, Springer Science + Business Media, DOI: 10.1007/978-3-0348-8501-0_13.

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