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

• Published in: Journal of theoretical biology Vol. 174; no. 4; pp. 391 - 408
• Main Authors: Földes-Papp, Zeno, Peng, Wei-Guo, Seliger, Hartmut, Kleinschmidt, Albrecht K.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 21-06-1995
• Subjects: Animals; Computer Simulation; DNA, Single-Stranded - biosynthesis; Fractals; Mathematics; Models, Genetic; Oligonucleotides - biosynthesis
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1006/jtbi.1995.0107

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
D
a
(
N, d) is derived as the growth term (
N = number of target nucleotides,
d = coupling probability function).
D
a
(
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
D
a
(
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
D
a
(
N, d
0) within limitations (
d
0 = constant (average) coupling probability).