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Published June 2009 | public
Journal Article

First-principles calculation of DNA looping in tethered particle experiments

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. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. 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 TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k_BT, for loops of length around 300 basepairs. More significantly, 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.

Additional Information

© 2009 IOP Publishing Ltd. Received 9 June 2008. Accepted for publication 23 September 2008. Published 1 July 2009. We thank Paul Wiggins for suggesting the general scheme of the calculations, and Kate Craig, Nily Dan, Jeff Gelles, Lin Han, Stephanie Johnson, Mitch Lewis, Ponzy Lu, Davide Normanno, Gasper Tkacik and Elizabeth Villa for many helpful discussions. PN, JB and KT were supported in part by NSF grants DGE-0221664, DMR04-25780 and DMR-0404674. RP acknowledges the support of the Keck Foundation, National Science Foundation grants CMS- 0301657 and CMS-0404031, and the National Institutes of Health Director's Pioneer Award grant DP1 OD000217. HG was supported in part by both the NSF funded NIRT and the NIH Director's Pioneer Award.

Additional details

Created:
August 20, 2023
Modified:
October 19, 2023