Discrete and continuous mathematical models of DNA branch migration

Area of Science:

• Molecular Biology
• Biophysics
• Computational Biology

Background:

• Holliday junctions are key intermediates in genetic recombination.
• Branch migration involves the movement of a branch point along DNA helices.
• Understanding branch migration dynamics is crucial for comprehending DNA repair and recombination.

Purpose of the Study:

• To model DNA branch migration in Holliday junctions using discrete and continuous random walk approaches.
• To analyze the behavior of branch migration on synthetic oligonucleotides.
• To compare discrete and continuous models and assess their applicability to experimental data.

Main Methods:

• Discrete random walk modeling of branch migration between compartments.
• Continuous random walk modeling as a limit of the discrete model.
• Comparison of discrete and continuous model predictions for both unbiased and biased migration.

Main Results:

• Discrete and continuous models exhibit similar behavior, especially with multiple compartments.
• DNA branch migration on oligonucleotides can be effectively treated as a continuous process.
• Differences between discrete and continuous models are small relative to experimental error, even for biased migration.

Conclusions:

• The continuous model provides a robust approximation for DNA branch migration on oligonucleotides.
• The choice of step size is important for determining rate constants in branch migration.
• Experimental measurements of branch migration should account for the small discrepancies between discrete and continuous models.