title: Fractals for multicyclic synthesis conditions of biopolymers. Examples of oligonucleotide synthesis measured by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography.
abstract: We have developed models of patterns for nucleotide chain growth. These patterns are measurable by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography in crude products of solid-phase synthesized 30mer and 65mer oligodeoxyribonucleotide target sequences N. We introduce mathematical methods for finding characteristic values d(o) and p(o) for constant chemical modes of growth as well as d and p for non-constant chemical modes of growth (d = probability of propagation, p = probability of termination). These methods are employed by presenting the accompanying computer software developed by us in C code, Mathematica R languages, and Fortran. Characteristic values of the parameters d, p, and the target nucleotide length N describe the complete composition of the crude product. From this we have developed the relation 2 - [N/(N - 1)]/Da, measurable(N,d) as a universal quantitative measure for multicyclic synthesis conditions (D, fractal dimension and similarity exponent, respectively). We use this mathematical treatment to compare the efficiency of oligodeoxyribonucleotide syntheses of different target length N on polymer support materials. Further, we analyze selected syntheses of short and long oligodeoxyribonucleotides as well as single-stranded DNA sequences by well-known empirical autocorrelation, fast Fourier transformation, and embedding dimension techniques.
authors.affiliation: Sektion Polymere, Universität Ulm, Germany.
authors.forename: Z
authors.initials: Z
authors.lastname: Földes-Papp
authors.forename: E
authors.initials: E
authors.lastname: Birch-Hirschfeld
authors.forename: H
authors.initials: H
authors.lastname: Eickhoff
authors.forename: G
authors.initials: G
authors.lastname: Baumann
authors.forename: W G
authors.initials: WG
authors.lastname: Peng
authors.forename: T
authors.initials: T
authors.lastname: Biber
authors.forename: R
authors.initials: R
authors.lastname: Seydel
authors.forename: A K
authors.initials: AK
authors.lastname: Kleinschmidt
authors.forename: H
authors.initials: H
authors.lastname: Seliger
mesh_terms: D001483:Base Sequence; D002851:Chromatography, High Pressure Liquid / Q000379:methods* / Q000706:statistics & numerical data; D002852:Chromatography, Ion Exchange / Q000379:methods / Q000706:statistics & numerical data; D019075:Electrophoresis, Capillary / Q000379:methods* / Q000706:statistics & numerical data; D017709:Fractals; D008433:Mathematics; D008956:Models, Chemical; D008969:Molecular Sequence Data; D009841:Oligonucleotides / Q000138:chemical synthesis* / Q000737:chemistry; D012984:Software
chemical_list: D009841:Oligonucleotides