Video-microscopy-based automated trajectory determination.

We present a method for tracking densely clustered, high-velocity, indistinguishable objects being spawned at a high rate and moving in a directed force field using only object centroids as inputs and no other image information. The algorithm places minimal restrictions on the velocities or accelerations of the objects being tracked and uses a methodology based on a scoring function and a backtracking refinement process. This combination leads to successful tracking of hundreds of particles in challenging environments even when the displacement of the individual objects at successive times approaches the separation between neighboring objects in any one frame. We note that these cases can be particularly difficult to handle by existing methods. The performance of the algorithm is methodically examined by comparison to simulated trajectories, which vary the temporal and spatial densities, velocities, and accelerations of the objects in motion, as well as the signal/noise ratio. Also, we demonstrate its capability by analyzing data from experiments with superparamagnetic microspheres moving in an inhomogeneous magnetic field in aqueous buffer at room temperature. Our method should be widely applicable since trajectory determination problems are ubiquitous in video microscopy applications in biology, materials science, physics, and engineering.

Horizontal magnetic tweezers and its applications in single molecule micromanipulation experiments.

Magnetic tweezers (MTs) have become indispensable tools for gaining mechanistic insights into the behavior of DNA-processing enzymes and acquiring detailed, high-resolution data on the mechanical properties of DNA. Currently, MTs have two distinct designs: vertical and horizontal (or transverse) configurations. While the vertical design and its applications have been extensively documented, there is a noticeable gap in comprehensive information pertaining to the design details, experimental procedures, and types of studies conducted with horizontal MTs. This article aims to address this gap by providing a concise overview of the fundamental principles underlying transverse MTs. It will explore the multifaceted applications of this technique as an exceptional instrument for scrutinizing DNA and its interactions with DNA-binding proteins at the single-molecule level.

Micromechanical Study of Hyperacetylated Nucleosomes Using Single Molecule Transverse Magnetic Tweezers.

Nucleosomes are stable complexes of DNA and histone proteins that are essential for the proper functioning of the genome. These structures must be unwrapped and disassembled for processes such as gene expression, replication, and repair. Histone post-translational modifications (PTMs) are known to play a significant role in regulating the structural changes of nucleosomes. However, the underlying mechanisms by which these modifications function remain unclear. In this study, we report the results of single molecule micromanipulation experiments on DNA-protein complexes composed of hyperacetylated histone proteins using transverse magnetic tweezers. The experiments were conducted by pre-extending λ-DNA with a force less than 4 pN before introducing hyperacetylated histones into the sample chamber. The DNA shortened as the histones formed complexes with it and the nucleosome arrays were then exposed to increasing tension, resulting in quantized changes in the DNA's extension with step sizes of (integral multiples of) ~50 nm. We also compared results of experiments using PTM histones and native histones with data collected for both types of histones for the same force ranges (2-80 pN) and loading rates. Our data show that hyperacetylated nucleosomes require an unbinding force of around ~2.5 pN, which is similar to that required for native histones. Moreover, we identified clear differences between the step-size distributions of native and hyperacetylated histones and found that in contrast to tethers reconstituted with native histones, the majority of nucleosomes in tethers compacted with hyperacetylated histones underwent disassembly at forces significantly lower than 6 pN.

Magnetic tweezers: development and use in single-molecule research.

The use of magnetic tweezers for single-molecule micromanipulation has evolved rapidly since its introduction approximately 30 years ago. Magnetic tweezers have provided important insights into the dynamic activity of DNA-processing enzymes, as well as detailed, high-resolution information on the mechanical properties of DNA. These successes have been enabled by major advancements in the hardware and software components of these devices. These developments now allow for a much richer mechanistic understanding of the functions and mechanisms of DNA-binding enzymes. In this review, the authors briefly discuss the fundamental principles of magnetic tweezers and describe the advancements that have made it a superlative tool for investigating, at the single-molecule level, DNA and its interactions with DNA-binding proteins.

Dataset of Bessel function J n maxima and minima to 600 orders and 10000 extrema.

Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function J . To do this, we employ an adaptive root solver bounded by the roots of the Bessel function and solve to an accuracy of 10 - 19 . We compare with the existing literature (to 30 orders and 5 maxima and minima) and the results match exactly. It is hoped that these data provide values needed for orthogonal function expansions and numerical expressions including the calculation of geometric correction factors in the measurement of resistivity of materials, as is done in the original paper using these data.

A Horizontal Magnetic Tweezers for Studying Single DNA Molecules and DNA-Binding Proteins.

We report data from single molecule studies on the interaction between single DNA molecules and core histones using custom-designed horizontal magnetic tweezers. The DNA-core histone complexes were formed using λ-DNA tethers, core histones, and NAP1 and were exposed to forces ranging from ~2 pN to ~74 pN. During the assembly events, we observed the length of the DNA decrease in approximate integer multiples of ~50 nm, suggesting the binding of the histone octamers to the DNA tether. During the mechanically induced disassembly events, we observed disruption lengths in approximate integer multiples of ~50 nm, suggesting the unbinding of one or more octamers from the DNA tether. We also observed histone octamer unbinding events at forces as low as ~2 pN. Our horizontal magnetic tweezers yielded high-resolution, low-noise data on force-mediated DNA-core histone assembly and disassembly processes.

Weak localization and small anomalous Hall conductivity in ferromagnetic Weyl semimetal Co2TiGe.

Several cobalt-based Heusler alloys have been predicted to exhibit Weyl Semimetal behavior due to time reversal symmetry breaking. Co2TiGe is one of the predicted ferromagnetic Weyl semimetals. In this work, we report weak localization and small anomalous Hall conductivity in half-metallic Co2TiGe thin films grown by molecular beam epitaxy. The longitudinal resistivity shows semimetallic behavior. Elaborate analysis of longitudinal magnetoconductance shows the presence of a weak localization quantum correction present even up to room temperature and reduction in dephasing length at lower temperature. Negative longitudinal magnetoresistance is observed from 5 to 300 K, but at 300 K magnetoresistance becomes positive above 0.5 T magnetic field. The anomalous Hall effect has been investigated in these thin films. The measured anomalous Hall conductivity decreases with increasing temperature, and a small anomalous Hall conductivity has been measured at various temperatures which may be arising due to both intrinsic and extrinsic mechanisms.

A Horizontal Magnetic Tweezers and Its Use for Studying Single DNA Molecules.

We report the development of a magnetic tweezers that can be used to micromanipulate single DNA molecules by applying picoNewton (pN)-scale forces in the horizontal plane. The resulting force⁻extension data from our experiments show high-resolution detection of changes in the DNA tether's extension: ~0.5 pN in the force and <10 nm change in extension. We calibrate our instrument using multiple orthogonal techniques including the well-characterized DNA overstretching transition. We also quantify the repeatability of force and extension measurements, and present data on the behavior of the overstretching transition under varying salt conditions. The design and experimental protocols are described in detail, which should enable straightforward reproduction of the tweezers.

Coarse Graining, Nonmaximal Entropy, and Power Laws.

We show that coarse graining produces significant and predictable effects on the entropy of states of equilibrium when the scale of coarse graining becomes comparable to that of density fluctuations. We demonstrate that a coarse-grained entropy typically evolves toward a state of effective equilibrium with a lower value than that of the state of maximum entropy theoretically possible. The finer the coarse graining, the greater the drop in effective entropy, and the more relevant the fluctuations around that. Fundamental considerations allow us to derive a remarkable power law that relates coarse graining to the effective entropy gap. Another power law is found that precisely relates the noise range of effective entropy fluctuations to coarse graining. We test both power laws with numerical simulations based on a well-studied two-dimensional lattice gas model. As expected, the effects of these power laws diminish as our description approaches a macroscopic level, eventually disappearing in the thermodynamic limit, where the maximum entropy principle is reasserted.

Density of States for Warped Energy Bands.

Warping of energy bands can affect the density of states (DOS) in ways that can be large or subtle. Despite their potential for significant practical impacts on materials properties, these effects have not been rigorously demonstrated previously. Here we rectify this using an angular effective mass formalism that we have developed. To clarify the often confusing terminology in this field, "band warping" is precisely defined as pertaining to any multivariate energy function E(k) that does not admit a second-order differential at an isolated critical point in k-space, which we clearly distinguish from band non-parabolicity. We further describe band "corrugation" as a qualitative form of band warping that increasingly deviates from being twice differentiable at an isolated critical point. These features affect the density-of-states and other parameters ascribed to band warping in various ways. We demonstrate these effects, providing explicit calculations of DOS and their effective masses for warped energy dispersions originally derived by Kittel and others. Other physical and mathematical examples are provided to demonstrate fundamental distinctions that must be drawn between DOS contributions that originate from band warping and contributions that derive from band non-parabolicity. For some non-degenerate bands in thermoelectric materials, this may have profound consequences of practical interest.

Simple horizontal magnetic tweezers for micromanipulation of single DNA molecules and DNA-protein complexes.

We report the development of a simple-to-implement magnetic force transducer that can apply a wide range of piconewton (pN) scale forces on single DNA molecules and DNA-protein complexes in the horizontal plane. The resulting low-noise force-extension data enable very high-resolution detection of changes in the DNA tether's extension: ~0.05 pN in force and <10 nm change in extension. We have also verified that we can manipulate DNA in near equilibrium conditions through the wide range of forces by ramping the force from low to high and back again, and observing minimal hysteresis in the molecule's force response. Using a calibration technique based on Stokes' drag law, we have confirmed our force measurements from DNA force-extension experiments obtained using the fluctuation-dissipation theorem applied to transverse fluctuations of the magnetic microsphere. We present data on the force-distance characteristics of a DNA molecule complexed with histones. The results illustrate how the tweezers can be used to study DNA binding proteins at the single molecule level.

Behavior of technetium in nuclear waste vitrification processes.

Nearly 100 tests were performed with prototypical melters and off-gas system components to investigate the extents to which technetium is incorporated into the glass melt, partitioned to the off-gas stream, and captured by the off-gas treatment system components during waste vitrification. The tests employed several simulants, spiked with 99mTc and Re (a potential surrogate), of the low activity waste separated from nuclear wastes in storage in the Hanford tanks, which is planned for immobilization in borosilicate glass. Single-pass technetium retention averaged about 35 % and increased significantly with recycle of the off-gas treatment fluids. The fraction escaping the recycle loop was very small.

DuraLith geopolymer waste form for Hanford secondary waste: correlating setting behavior to hydration heat evolution.

The binary furnace slag-metakaolin DuraLith geopolymer waste form, which has been considered as one of the candidate waste forms for immobilization of certain Hanford secondary wastes (HSW) from the vitrification of nuclear wastes at the Hanford Site, Washington, was extended to a ternary fly ash-furnace slag-metakaolin system to improve workability, reduce hydration heat, and evaluate high HSW waste loading. A concentrated HSW simulant, consisting of more than 20 chemicals with a sodium concentration of 5 mol/L, was employed to prepare the alkaline activating solution. Fly ash was incorporated at up to 60 wt% into the binder materials, whereas metakaolin was kept constant at 26 wt%. The fresh waste form pastes were subjected to isothermal calorimetry and setting time measurement, and the cured samples were further characterized by compressive strength and TCLP leach tests. This study has firstly established quantitative linear relationships between both initial and final setting times and hydration heat, which were never discovered in scientific literature for any cementitious waste form or geopolymeric material. The successful establishment of the correlations between setting times and hydration heat may make it possible to efficiently design and optimize cementitious waste forms and industrial wastes based geopolymers using limited testing results.

Mechanically unzipping dsDNA with built-in sequence inhomogeneities and bound proteins.

We theoretically analyze the force signal expected during unzipping through a single double-stranded DNA (dsDNA) molecule with designed subsequences or inhomogeneities with large stability differentials compared to the rest of the molecule. Our calculations describe experiments where the extension between the unzipped ends is fixed--the so-called fixed-extension ensemble--and the equilibrium force is measured. Two different types of force traces are obtained depending on the inhomogeneity length and strength. For short inhomogeneities, a "sawtooth" force trace is obtained, with a force jump corresponding to release of the entire inhomogeneity at once, as observed in unzipping of natural-sequence DNA (Bockelmann et al., Biophy. J. 82, 1537 (2002)). For longer inhomogeneities, traces with force plateaus are obtained, corresponding to a gradual unpeeling of the strongly bound region. We find that inhomogeneities are disrupted in sequence giving rise to a succession of force spikes superposed on the baseline unzipping force of 15pN. The height of the force pulses diminishes as regions further down the molecule are unzipped, and asymptotically the force response approaches that of DNA without large stability-enhanced islands. Our model also allows us to describe the transition between intact and disrupted binding zones by thermally activated kinetics. We then analyze the related situation where multiple proteins are bound at specific points on the DNA with or without cooperative interactions between proteins, and where the removal of each protein is required for unzipping to proceed further along the DNA. The proteins bind stably to dsDNA and also to single-stranded DNA (ssDNA) but with a lower binding enthalpy. The force jumps correspond to the extra mechanical work that has to be done to overcome the large protein binding enthalpy to either dsDNA or ssDNA. Each force jump leads to the dissociation of a corresponding protein, but we do not find simultaneous release of cooperatively stabilized proteins under the range of interactions strengths considered here. Our model is then used to describe recent experiments where the stability of nucleosome and nucleosome-analogues was assayed by mechanically unzipping the DNA template. Using physiological values of model parameters we find good agreement with the data.

High temperature thermal conductivity of platinum microwire by 3ω method.

The 3ω method for thermal conductivity measurement has emerged as an effective technique applicable to micro/nanowires and thin films. This paper describes the adaptation of the method to temperatures as high as 725 K enabling reliable thermal conductivity measurements on such samples for which previously published methods have been found inadequate. In the technique, a sample wire is heated by applying a sinusoidal current at an angular frequency ω, which causes a temperature and resistance variation at an angular frequency, 2ω, leading to a voltage signal at 3ω. The sample is connected as a four-terminal resistor to a digital lock-in amplifier, which is used to detect the in-phase and out-of-phase 3ω voltages resulting from the applied 1ω current. The data are fitted by varying the values of the thermal resistance and diffusion time, both of which are functions of thermal conductivity. Measurements are made at steady state temperatures between 300 and 725 K. Meaningful measurements at elevated temperatures require that thermal losses be understood and minimized. Conduction losses are prevented by suspending the sample above the mounting substrate. Convection losses are minimized by maintaining a vacuum of ~10(-5) torr inside the sample chamber. To minimize radiation losses, an appropriately sized sample is shrouded with a double heat-shield, with the inner shield temperature near that of the sample. Using the 3ω method, the thermal conductivity of platinum was determined to vary between 71.8 and 80.7 Wm(-1) K(-1) over the temperature range of 300 to 725 K, in agreement with published values measured for bulk samples.

Tc and Re behavior in borosilicate waste glass vapor hydration tests.

Technetium, found in some nuclear wastes (such as those generated from spent fuel reprocessing), is of particular concern with regard to long-term waste storage because of its long half-life (2.13 x 10(5) years) and high mobility in the environment. One method of stabilization of such waste is through vitrification to produce a durable borosilicate glass matrix. The fate of Tc under hydrothermal conditions in the vapor hydration test (VHT) was studied to assess and possibly predict the long-term rate of release of Tc from borosilicate waste glass. For comparison, the fate of rhenium, the preferred nonradioactive surrogate for Tc, was similarly studied. X-ray absorption spectroscopy (XAS) and scanning electron microscopy (SEM) measurements were made on each original borosilicate glass and the corresponding sample after the VHT. Tc K-edge XAS indicates that, despite starting with different Tc(IV) and Tc(VII) distributions in each glass, both corresponding VHT samples contain 100% Tc(IV). The Tc reduction within the VHT samples may be driven by the low-oxygen atmosphere compounded by oxygen depletion from corrosion of the surrounding stainless steel vessel. From SEM analyses, both of the Tc-containing VHT samples show complete alteration of the original glass, significant Tc enrichment near the sample surface, and nearly complete depletion of Tc toward the sample center. XAS indicates Tc(IV)O6 octahedra, possibly within gel-like amorphous silicates in both VHT samples, where Tc-Tc correlations are observed in the higher Tc-content VHT sample. Re L(II)-edge XAS and SEM indicate quite different behavior for Re under VHT conditions. The Re oxidation state appears to be invariant with respect to the VHT treatment, where perrhenate (Re(VII)) species are dominant in all Re-containing samples investigated; Re2O7 concentrations are low near the sample surface and increase to approach that of the unreacted glass toward the sample center.