| Abstract: | In this paper we put forward improved mathematical methods for detecting synthesis parameters in connection with analyzing crude products of chemically synthesized oligonucleotides. The crude products experimentally sampled are separated by high-performance capillary electrophoresis and ion-exchange high-performance liquid chromatography. The measured separation profiles of experimental syntheses can be expressed as target and nontarget yields; they are characterized by a few parameters. These parameters account for nonlinear synthesis equations that are solvable by employing iteration procedures. We provide here a theoretical as well as computational analysis based upon specific models for stepwise chain growth. Under nonconstant (nonuniform) conditions we use here an exponential form of growth, with different expressions for calculating the fractal dimension of the biochemical process under study. Step lengths of parameter variations in an interval of finite length have to be adjusted properly to find convergent solutions in a mathematical, regularly four-dimensional parameter space. It is conceivable to have most, if not all, of the calculating and plotting carefully done by a computer. This analysis represents the experimental situation up to 65-mer target oligonucleotides analyzed so far. We thus obtain the dynamics of the polymerization process limited in number by fractal models. The advantage, calculating these new methods as compared to qualitatively judged experimental methods, lies in the satisfactory evaluation of crude products, also of large amounts, of syntheses of these biopolymers. © 1998 John Wiley & Sons, Inc. Biopoly 45: 361–379, 1998 |
