Simulated Annealing Method for the Automated Simulation of DNA Dynamics in the HhaI Protein Binding Site

Abstract

Solid-state deuterium NMR is well suited to the study of the conformational dynamics of DNA. Deuterium quadrupole echo spectra for a particular motional model can be calculated and matched to the experimental spectrum to extract information on the DNA dynamics; however, doing so can be very time-intensive. The two-axis motion used to model the dynamics of either 2″ or 5′/5″ furanose ring deuteron is particularly complex with up to ten independent variables that can be optimized. Here, we present a program which automates both the input script generation and searches the parameter space for the best fit using a simulated annealing algorithm. The parameter, ${\chi }_{\text{red}}^2$ , provides a relative measure of goodness of fit. This method reduces the overall time to determine the best fit of a line shape to a few days, in most cases, when running on a low-power desktop PC. The automated fitting program presented here can be easily modified to generate input scripts for new models, incorporate a weighting factor to the ${\chi }_{\text{red}}^2$ calculation to emphasize key line shape features, or fit nonsymmetrized data. This adaptable program will make simulation of solid-state deuterium spectra accessible to a broader audience.