Modeling transposable element dynamics with fragmentation equations.

Area of Science:

• Genomics
• Computational Biology
• Evolutionary Biology

Background:

• Transposable elements (TEs) are DNA segments capable of self-replication, abundant in genomes.
• TEs can have regulatory functions but often exert deleterious effects on hosts.
• Host genomes contain both active (full-length) and inactive (partial-length) TE copies.

Purpose of the Study:

• To develop a novel mathematical formulation for modeling transposable element (TE) dynamics.
• To analyze the time-evolution of TE length distributions, including full and partial elements.
• To quantify TE replication and mutation rates and uncover drivers of genomic variation.

Main Methods:

• Developed mathematical fragmentation equations in discrete and continuous frameworks.
• Modeled TE replication using both constant (exponential) and logistic growth rates.
• Proved existence and uniqueness of solutions for TE length distributions under four proposed models.
• Applied the exponential model to quantify replication-to-mutation rates using genomic data.

Main Results:

• Derived explicit analytical solutions for TE density under exponential replication and implicit solutions under logistic growth.
• Demonstrated initial agreement between exponential and logistic models.
• Quantified TE dynamics by applying the model to TE collections from fruit-flies, birds, and primates.
• Identified quantitative relationships in TE dynamics across diverse species.

Conclusions:

• The novel mathematical framework accurately describes TE length distributions.
• The model effectively quantifies TE replication and mutation rates.
• This approach provides insights into the biological drivers of genomic variation, applicable to numerous species with increasing genomic data availability.