First-principles calculation of DNA looping in tethered particle experiments

TL;DR

This study models DNA looping in tethered particle experiments using a parameter-free elasticity model, successfully predicting bead excursion distributions and revealing discrepancies for very short DNA loops, with implications for understanding DNA-protein interactions.

Contribution

The paper introduces a parameter-free, elasticity-based model that accurately predicts DNA looping behavior in TPM experiments, aligning with observed data without requiring adjustable parameters.

Findings

Model reproduces bead excursion distributions including three-peak structure

Qualitatively matches dependence on tether length and LacI concentration

Short DNA loops show more looping than predicted, indicating limitations of harmonic elasticity model

Abstract

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in Tethered Particle Motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. [...] We show how to compute both the "looping J factor" (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on tethered particle motion, and then compare to our model's predictions. [...] Our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical "open" conformation of the LacI tetramer.