# Facilitation of DNA loop formation by protein-DNA non-specific interactions

## TL;DR

This study explores how non-specific electrostatic interactions between proteins and DNA influence the formation of DNA loops, revealing different dynamic regimes and optimization strategies through theoretical modeling and simulations.

## Contribution

It introduces a discrete-state stochastic model to analyze the impact of non-specific protein-DNA interactions on DNA loop formation dynamics, extending beyond previous specific interaction-focused studies.

## Key findings

- Three dynamic regimes of loop formation depending on protein sliding length.
- Loop formation time can be optimized by adjusting sliding length, DNA size, and target position.
- Quantitative predictions for experimental validation are provided.

## Abstract

Complex DNA topological structures, including polymer loops, are frequently observed in biological processes when protein molecules simultaneously bind to several distant sites on DNA. However, the molecular mechanisms of formation of these systems remain not well understood. Existing theoretical studies focus only on specific interactions between protein and DNA molecules at target sequences. However, the electrostatic origin of primary protein-DNA interactions suggests that interactions of proteins with all DNA segments should be considered. Here we theoretically investigate the role of non-specific interactions between protein and DNA molecules on the dynamics of loop formation. Our approach is based on analyzing a discrete-state stochastic model via a method of first-passage probabilities supplemented by Monte Carlo computer simulations. It is found that depending on a protein sliding length during the non-specific binding event three different dynamic regimes of the DNA loop formation might be observed. In addition, the loop formation time might be optimized by varying the protein sliding length, the size of the DNA molecule, and the position of the specific target sequences on DNA. Our results demonstrate the importance of non-specific protein-DNA interactions in the dynamics of DNA loop formations. Several quantitative predictions that can be experimentally tested are also presented.