An analytical method to connect open curves for modeling protein-bound DNA minicircles

Area of Science:

• Biophysics
• Computational Biology
• Structural Biology

Background:

• Understanding the three-dimensional structure of DNA minicircles is crucial for studying DNA packaging and protein-DNA interactions.
• Modeling nucleosome-decorated DNA minicircles presents challenges due to the complex helical pathways and the need for smooth closure.

Purpose of the Study:

• To introduce a general analytical method for generating the pathway of closed protein-bound DNA minicircles.
• To model nucleosome-decorated DNA minicircles by smoothly connecting helical DNA pathways.
• To investigate the influence of DNA wrapping, inter-nucleosome orientation, and salt concentration on minicircle stability.

Main Methods:

• Development of an analytical equation to smoothly connect two open curves, specifically helical DNA pathways.
• Application of the derived expressions to form closed models of nucleosome-decorated DNA minicircles.
• Calculation of bending and electrostatic energies for various minicircle configurations under different salt conditions.

Main Results:

• The simplest smooth connector satisfying boundary and length conditions was found to be a quartic function in the xy-plane and linear in the z-direction.
• The method successfully modeled torsionally relaxed, 360-base pair DNA rings with two ideal nucleosomes.
• Predicted stable states of DNA minicircles showed strong resemblance to experimentally reconstituted minicircles under varying salt concentrations.

Conclusions:

• The developed analytical method provides a general framework for connecting open curves and modeling complex biological structures like DNA minicircles.
• The study elucidates the relationship between DNA minicircle configuration, energy landscapes, and salt conditions.
• The findings offer insights into the structural organization and stability of nucleosome-bound DNA.