Extending the range for force calibration in magnetic tweezers.

Magnetic tweezers are a wide-spread tool used to study the mechanics and the function of a large variety of biomolecules and biomolecular machines. This tool uses a magnetic particle and a strong magnetic field gradient to apply defined forces to the molecule of interest. Forces are typically quantified by analyzing the lateral fluctuations of the biomolecule-tethered particle in the direction perpendicular to the applied force. Since the magnetic field pins the anisotropy axis of the particle, the lateral fluctuations follow the geometry of a pendulum with a short pendulum length along and a long pendulum length perpendicular to the field lines. Typically, the short pendulum geometry is used for force calibration by power-spectral-density (PSD) analysis, because the movement of the bead in this direction can be approximated by a simple translational motion. Here, we provide a detailed analysis of the fluctuations according to the long pendulum geometry and show that for this direction, both the translational and the rotational motions of the particle have to be considered. We provide analytical formulas for the PSD of this coupled system that agree well with PSDs obtained in experiments and simulations and that finally allow a faithful quantification of the magnetic force for the long pendulum geometry. We furthermore demonstrate that this methodology allows the calibration of much larger forces than the short pendulum geometry in a tether-length-dependent manner. In addition, the accuracy of determination of the absolute force is improved. Our force calibration based on the long pendulum geometry will facilitate high-resolution magnetic-tweezers experiments that rely on short molecules and large forces, as well as highly parallelized measurements that use low frame rates.

Camera-based three-dimensional real-time particle tracking at kHz rates and Ångström accuracy.

Optical and magnetic tweezers are widely employed to probe the mechanics and activity of individual biomolecular complexes. They rely on micrometre-sized particles to detect molecular conformational changes from the particle position. Real-time particle tracking with Ångström accuracy has so far been only achieved using laser detection through photodiodes. Here we demonstrate that camera-based imaging can provide a similar performance for all three dimensions. Particle imaging at kHz rates is combined, with real-time data processing being accelerated by a graphics-processing unit. For particles that are fixed in the sample cell we can detect 3-Å-sized steps that are introduced by cell translations at rates of 10 Hz, while for DNA-tethered particles 5 Å steps at 1 Hz can be resolved. Moreover, 20 particles can be tracked in parallel with comparable accuracy. Our approach provides a simple and robust way for high-resolution tweezer experiments using multiple particles at a time.

A full-automatic sequence design algorithm for branched DNA structures.

Production of various structures by self-assembling single stranded DNA molecules is a widely used technology in the filed of DNA nanotechnology. Base sequences of single strands do predict the shape of the resulting nanostructure. Therefore, sequence design is crucial for the successful structure fabrication. This paper presents a sequence design algorithm based on mismatch minimization that can be applied to every desired DNA structure. With this algorithm, junctions, loops, single as well as double stranded regions, and very large structures up to several thousand base pairs can be handled. Thereby, the algorithm is fast for the most structures. Algorithm is Java-implemented. Its implementation is called Seed and is available publicly. As an example for a successful sequence generation, this paper presents the fabrication of DNA chain molecules consisting of double-crossover (DX) tiles as well.