Fractals for multicyclic synthesis conditions of biopolymers. Examples of oligonucleotide synthesis measured by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography.
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.