Accurate modeling of DNA conformational flexibility by a multivariate Ising model

The sequence-dependent structure and deformability of DNA play a major role for binding of proteins and regulation of gene expression. So far, most efforts to model DNA flexibility are based on unimodal harmonic stiffness models at base-pair resolution. However, multimodal behavior due to distinct conformational substates also contributes significantly to the conformational flexibility of DNA. Moreover, these local substates are correlated to their nearest-neighbor substates. A description for DNA elasticity which includes both multimodality and nearest-neighbor coupling has remained a challenge, which we solve by combining our multivariate harmonic approximation with an Ising model for the substates. In a series of applications to DNA fluctuations and protein–DNA complexes, we demonstrate substantial improvements over the unimodal stiffness model. Furthermore, our multivariate Ising model reveals a mechanical destabilization for adenine (A)-tracts to undergo nucleosome formation. Our approach offers a wide range of applications to determine sequence-dependent deformation energies of DNA and to investigate indirect readout contributions to protein–DNA recognition.

Determining Trap Compliances, Microsphere Size Variations, and Response Linearities in Single DNA Molecule Elasticity Measurements with Optical Tweezers

We previously introduced the use of DNA molecules for calibration of biophysical force and displacement measurements with optical tweezers. Force and length scale factors can be determined from measurements of DNA stretching. Trap compliance can be determined by fitting the data to a nonlinear DNA elasticity model, however, noise/drift/offsets in the measurement can affect the reliability of this determination. Here we demonstrate a more robust method that uses a linear approximation for DNA elasticity applied to high force range (25–45 pN) data. We show that this method can be used to assess how small variations in microsphere sizes affect DNA length measurements and demonstrate methods for correcting for these errors. We further show that these measurements can be used to check assumed linearities of system responses. Finally, we demonstrate methods combining microsphere imaging and DNA stretching to check the compliance and positioning of individual traps.

Statics of DNA Deformations

DNA is a deformable molecule. The term “deformable” implies phenomena rooted in the collective behavior of many atoms, and a description based on concepts of continuum and statistical mechanics. Long DNA molecules are an excellent experimental system to study the equilibrium conformations and dynamics of long, flexible molecules. This chapter discusses the following: DNA melting, the zipper model, experimental melting curves, base pairing and base stacking as separate, Hamiltonian formulation of the zipper model, 2 × 2 model, nearest neighbor model, connection to nonlinear dynamics, linear and nonlinear elasticity of DNA, bending modulus and persistence length, measurements of DNA elasticity (short and long molecules), the Euler instability, and the DNA yield transition.