Model-free 3D localization with precision estimates for brightfield-imaged particles

Three-dimensional close-to-substrate trajectories of magnetic microparticles in dynamically changing magnetic field landscapes

The transport of magnetic particles (MPs) by dynamic magnetic field landscapes (MFLs) using magnetically patterned substrates is promising for the development of Lab-on-a-chip (LOC) systems. The inherent close-to-substrate MP motion is sensitive to changing particle-substrate interactions. Thus, the detection of a modified particle-substrate separation distance caused by surface binding of an analyte is expected to be a promising probe in analytics and diagnostics. Here, we present an essential prerequisite for such an application, namely the label-free quantitative experimental determination of the three-dimensional trajectories of superparamagnetic particles (SPPs) transported by a dynamically changing MFL. The evaluation of defocused SPP images from optical bright-field microscopy revealed a "hopping"-like motion of the magnetic particles, previously predicted by theory, additionally allowing a quantification of maximum jump heights. As our findings pave the way towards precise determination of particle-substrate separations, they bear deep implications for future LOC detection schemes using only optical microscopy.

Tracking Janus microswimmers in 3D with machine learning

Advancements in artificial active matter systems heavily rely on our ability to characterise their motion. Yet, the most widely used tool to analyse the latter is standard wide-field microscopy, which is largely limited to the study of two-dimensional motion. In contrast, real-world applications often require the navigation of complex three-dimensional environments. Here, we present a Machine Learning (ML) approach to track Janus microswimmers in three dimensions, using Z-stacks as labelled training data. We demonstrate several examples of ML algorithms using freely available and well-documented software, and find that an ensemble Decision Tree-based model (Extremely Randomised Decision Trees) performs the best at tracking the particles over a volume spanning more than 40 μm. With this model, we are able to localise Janus particles with a significant optical asymmetry from standard wide-field microscopy images, bypassing the need for specialised equipment and expertise such as that required for digital holographic microscopy. We expect that ML algorithms will become increasingly prevalent by necessity in the study of active matter systems, and encourage experimentalists to take advantage of this powerful tool to address the various challenges within the field.

Positive supercoiling favors transcription elongation through lac repressor-mediated DNA loops

Some proteins, like the lac repressor (LacI), mediate long-range loops that alter DNA topology and create torsional barriers. During transcription, RNA polymerase generates supercoiling that may facilitate passage through such barriers. We monitored E. coli RNA polymerase progress along templates in conditions that prevented, or favored, 400 bp LacI-mediated DNA looping. Tethered particle motion measurements revealed that RNA polymerase paused longer at unlooped LacI obstacles or those barring entry to a loop than those barring exit from the loop. Enhanced dissociation of a LacI roadblock by the positive supercoiling generated ahead of a transcribing RNA polymerase within a torsion-constrained DNA loop may be responsible for this reduction in pause time. In support of this idea, RNA polymerase transcribed 6-fold more slowly through looped DNA and paused at LacI obstacles for 66% less time on positively supercoiled compared to relaxed templates, especially under increased tension (torque). Positive supercoiling propagating ahead of polymerase facilitated elongation along topologically complex, protein-coated templates.

Modification to axial tracking for mobile magnetic microspheres

Three-dimensional particle tracking is a routine experimental procedure for various biophysical applications including magnetic tweezers. A common method for tracking the axial position of particles involves the analysis of diffraction rings whose pattern depends sensitively on the axial position of the bead relative to the focal plane. To infer the axial position, the observed rings are compared with reference images of a bead at known axial positions. Often the precision or accuracy of these algorithms is measured on immobilized beads over a limited axial range, while many experiments are performed using freely mobile beads. This inconsistency raises the possibility of incorrect estimates of experimental uncertainty. By manipulating magnetic beads in a bidirectional magnetic tweezer setup, we evaluated the error associated with tracking mobile magnetic beads and found that the error of tracking a moving magnetic bead increases by almost an order of magnitude compared to the error of tracking a stationary bead. We found that this additional error can be ameliorated by excluding the center-most region of the diffraction ring pattern from tracking analysis. Evaluation of the limitations of a tracking algorithm is essential for understanding the error associated with a measurement. These findings promise to bring increased resolution to three-dimensional bead tracking of magnetic microspheres.

Force spectroscopy with electromagnetic tweezers

Force spectroscopy using magnetic tweezers (MTs) is a powerful method to probe the physical characteristics of single polymers. Typically, molecules are functionalized for specific attachment to a glass surface at one end and a micrometer-scale paramagnetic bead at the other end. By applying an external magnetic field, multiple molecules can be stretched and twisted simultaneously without exposure to potentially damaging radiation. The majority of MTs utilize mobile, permanent magnets to produce forces on the beads (and the molecule under test). However, translating and rotating the permanent magnets may require expensive precision actuators, limit the rate at which force can be changed, and may induce vibrations that disturb tether dynamics and bead tracking. Alternatively, the magnetic field can be produced with an electromagnet, which allows fast force modulation and eliminates motor-associated vibration. Here, we describe a low-cost quadrapolar electromagnetic tweezer design capable of manipulating DNA-tethered MyOne paramagnetic beads with forces as high as 15 pN. The solid-state nature of the generated B-field modulated along two axes is convenient for accessing the range of forces and torques relevant for studying the activity of DNA motor enzymes like polymerases and helicases. Our design specifically leverages technology available at an increasing number of university maker spaces and student-run machine shops. Thus, it is an accessible tool for undergraduate education that is applicable to a wide range of biophysical research questions.

Precision single-particle localization using radial variance transform

We introduce an image transform designed to highlight features with high degree of radial symmetry for identification and subpixel localization of particles in microscopy images. The transform is based on analyzing pixel value variations in radial and angular directions. We compare the subpixel localization performance of this algorithm to other common methods based on radial or mirror symmetry (such as fast radial symmetry transform, orientation alignment transform, XCorr, and quadrant interpolation), using both synthetic and experimentally obtained data. We find that in all cases it achieves the same or lower localization error, frequently reaching the theoretical limit.