Template-Directed Copolymerization, Random Walks along Disordered Tracks, and Fractals

Area of Science:

• Molecular Biology
• Biophysics
• Systems Biology

Background:

• Template-directed copolymerization is central to DNA, RNA, and protein synthesis.
• Despite decades of research, the kinetics and thermodynamics of genetic information processing remain unclear.
• Polymerase/ribosome motion on disordered DNA/RNA templates and copying errors pose significant challenges.

Purpose of the Study:

• To develop a quantitative framework for understanding information processing in molecular synthesis.
• To address challenges posed by disordered media and copying errors in biological systems.
• To reveal universal aspects of molecular-scale information processing.

Main Methods:

• Development of a theoretical framework based on iterated function systems.
• Analysis of polymerase and ribosome velocities on template sequences.
• Modeling of copying error probabilities and growth dynamics.

Main Results:

• Local velocities of polymerases/ribosomes follow invariant sets of iterated function systems.
• This framework quantitatively explains sequence heterogeneity effects.
• Copying error probabilities are determined by the iterated function system.
• Growth can exhibit sublinear time dependence with a deducible scaling exponent.

Conclusions:

• A unified framework explains information processing in DNA replication, transcription, and translation.
• Iterated function systems provide universal insights into molecular synthesis kinetics and thermodynamics.
• The model quantitatively addresses sequence heterogeneity and error rates in biological polymerizations.