Elasticity of spheres with buckled surfaces.

The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important to properly understand the elasticity of the spherical core. Here, by exploiting well-known properties of the solid harmonics, we present a simple, direct method for solving the linear elastic problem of spheres and spherical voids with surface deformations, described by a real spherical harmonic. We calculate the corresponding bulk elastic energies, providing closed-form expressions for any values of the spherical harmonic degree (l), Poisson ratio, and shear modulus. We find that the elastic energies are independent of the spherical harmonic index (m). Using these results, we revisit the buckling instability experienced by a core-shell system comprising an elastic sphere, attached within a membrane of fixed area, that occurs when the area of the membrane sufficiently exceeds the area of the unstrained sphere [C. Fogle et al., Phys. Rev. E 88, 052404 (2013)1539-375510.1103/PhysRevE.88.052404]. We determine the phase diagram of the core-shell sphere's shape, specifying what value of l is realized as a function of the area mismatch and the core-shell elasticity. We also determine the shape phase diagram for a spherical void bounded by a fixed-area membrane.

X-ray near-field speckle: implementation and critical analysis.

The newly introduced coherence-based technique of X-ray near-field speckle (XNFS) has been implemented at 8-ID-I at the Advanced Photon Source. In the near-field regime of high-brilliance synchrotron X-rays scattered from a sample of interest, it turns out that, when the scattered radiation and the main beam both impinge upon an X-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. A micrometer-resolution XNFS detector with a high numerical aperture microscope objective has been built and its capability for studying static structures and dynamics at longer length scales than traditional far-field X-ray scattering techniques is demonstrated. Specifically, the dynamics of dilute silica and polystyrene colloidal samples are characterized. This study reveals certain limitations of the XNFS technique, especially in the characterization of static structures, which is discussed.

Dynamics of colloidal particles in ice.

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration.

Small-angle x-ray scattering measurements of the microstructure of liquid helium mixtures adsorbed in aerogel.

Small-angle x-ray scattering (SAXS) was used to measure the microstructure of isotopic mixtures of 3He and 4He adsorbed into silica aerogels as a function of temperature and 3He concentration. The SAXS measurements could be well described by the formation of a nearly pure film of 4He which separates from the bulk mixture onto the aerogel strands and which thickens with decreasing temperature. Previous observations of a superfluid 3He -rich phase are consistent with superfluidity existing within this film phase. Observed differences between different density aerogels are explained in terms of the depletion of 4He from the bulk mixture due to film formation.

A new method for post-translationally labeling proteins in live cells for fluorescence imaging and tracking.

We present a novel method to fluorescently label proteins, post-translationally, within live Saccharomycescerevisiae. The premise underlying this work is that fluorescent protein (FP) tags are less disruptive to normal processing and function when they are attached post-translationally, because target proteins are allowed to fold properly and reach their final subcellular location before being labeled. We accomplish this post-translational labeling by expressing the target protein fused to a short peptide tag (SpyTag), which is then covalently labeled in situ by controlled expression of an open isopeptide domain (SpyoIPD, a more stable derivative of the SpyCatcher protein) fused to an FP. The formation of a covalent bond between SpyTag and SpyoIPD attaches the FP to the target protein. We demonstrate the general applicability of this strategy by labeling several yeast proteins. Importantly, we show that labeling the membrane protein Pma1 in this manner avoids the mislocalization and growth impairment that occur when Pma1 is genetically fused to an FP. We also demonstrate that this strategy enables a novel approach to spatiotemporal tracking in single cells and we develop a Bayesian analysis to determine the protein's turnover time from such data.

Condensation transition and forced unravelling of DNA-histone H1 toroids: a multi-state free energy landscape.

DNA is known to condense with multivalent cations and positively charged proteins. However, the properties and energetics of DNA superstructures, such as chromatin, are poorly understood. As a model system, we investigate histone H1 condensation of DNA with tethered particle motion and force-extension measurements. We show that after the addition of H1 to DNA, a concentration dependent lag time is followed by the DNA spontaneously condensing. The trigger for this condensation phase transition can be modeled as sufficient H1s having bound to the DNA, providing insight into the 30 nm fiber condensation upon H1 binding. Furthermore, optical tweezers force-extension measurements of histone H1 condensed DNA reveals a sequence of state transitions corresponding to the unwinding of superhelical turns. We determine the complete, experimental, multi-state free energy landscape for the complex using Crooks fluctuation theorem. The measured force-versus-extension and free energy landscape are compared to predictions from a simple, theoretical model. This work encourages the theoretical description of DNA/protein structure and energetics and their role in chromatin and other, more complex, systems.

Active drift stabilization in three dimensions via image cross-correlation.

By monitoring stage drift via the normalized cross-correlation of an image of a stuck bead, obtained in real-time, with an out-of-focus "template" image of a similar immobile bead, stored in memory, we implement a simple approach to actively stabilize drift in all three dimensions for existing video microscopy setups. We demonstrate stability to 0.0062 nm along the Z-axis and 0.0031 nm along the X- and Y-axes for long (100 s) timescales.

Unwinding and rewinding the nucleosome inner turn: force dependence of the kinetic rate constants.

A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.

The molecular yo-yo method: live jump detection improves throughput of single-molecule force spectroscopy for out-of-equilibrium transitions.

By monitoring multiple molecular transitions, force-clamp, and trap-position-clamp methods have led to precise determinations of the free energies and free energy landscapes for molecular states populated in equilibrium at the same or similar forces. Here, we present a powerful new elaboration of the force-clamp and force-jump methods, applicable to transitions far from equilibrium. Specifically, we have implemented a live jump detection and force-clamp algorithm that intelligently adjusts and maintains the force on a single molecule in response to the measured state of that molecule. We are able to collect hundreds of individual molecular transitions at different forces, many times faster than previously, permitting us to accurately determine force-dependent lifetime distributions and reaction rates. Application of our method to unwinding and rewinding the nucleosome inner turn, using optical tweezers reveals experimental lifetime distributions that comprise a statistically meaningful number of transitions, and that are accurately single exponential. These measurements significantly reduce the error in the previously measured rates, and demonstrate the existence of a single, dominant free energy barrier at each force studied. A key benefit of the molecular yo-yo method for nucleosomes is that it reduces as far as possible the time spent in the tangentially bound state, which minimizes the loss of nucleosomes by dissociation.

Practical axial optical trapping.

We describe a new method for calibrating optical trapping measurements in which tension is applied in the direction of the laser beam to a molecule tethered between a surface and an optically trapped bead. Specifically, we present a generally-applicable procedure for converting from the measured scattering intensity and the measured stage displacement to applied tension and bead-coverslip separation, using measurements of the light intensity scattered from an untethered, trapped bead. Our calibration accounts for a number of effects, including aberrations and the interference of forward-reflected bead-scattered light with the trapping beam. To demonstrate the accuracy of our method, we show measurements of the DNA force-versus-extension relation using a range of laser intensities, and show that these measurements match the expected extensible wormlike-chain (WLC) behavior. Finally, we also demonstrate a force-clamp, in which the tension in a tether is held fixed while the extension varies as a result of molecular events.

Particle-scale structure in frozen colloidal suspensions from small-angle x-ray scattering.

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has concentrated mostly on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small-angle x-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high-density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by standard interparticle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium densification processes.

Allosteric conformational spread: exact results using a simple transfer matrix method.

A transfer matrix method is described for the conformational spread (CS) model of allosteric cooperativity within a one-dimensional arrangement of four-state binding sites. Each such binding site can realize one of two possible conformational states. Each of these states can either bind ligand or not bind ligand. Thus, analytical expressions that are exact within the context of the CS model are derived for the grand partition function, for the mean fraction of binding sites occupied by ligand versus ligand concentration, and for the mean fraction of binding sites in a given allosteric state versus ligand concentration. The utility of our analytical results is demonstrated by least-mean-square fitting of prior experimental results obtained on the bacterial flagellar motor for the fraction of FliM/FliG/FliN complexes with CheY-P bound [V. Sourjik and H. C. Berg, Proc. Natl. Acad. Sci. U.S.A. 99, 12669 (2002)] and for the cw bias [P. Cluzel, Science 287, 1652 (2000)], which plausibly may be identified as the fraction of protomers realizing state 2. Finally, the relationships between our analytical results and the classical Monod-Wyman-Changeaux, Koshland-Nemethy-Filmer, and McGhee-Von Hippel treatments of allosteric cooperativity are elucidated, as is the connection to an earlier approximate analytical treatment of the CS model.

Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors.

We describe a simple-to-construct programmable direct-digital-synthesis-based controller for use with acousto-optic deflectors. Our controller corrects for nonlinear diffraction efficiency versus diffraction angle, provides superior stability, functionality, and configurability, and costs a fraction of commercially available systems. Using this instrument, we move a 1 mum diameter bead by 1-nm-sized steps and resolve these steps.

How a liquid becomes a glass both on cooling and on heating.

The onset of structural arrest and glass formation in a concentrated suspension of silica nanoparticles in a water-lutidine binary mixture near its consolute point is studied by exploiting the near-critical fluid degrees of freedom to control the strength of an attraction between particles and multispeckle x-ray photon correlation spectroscopy to determine the particles' collective dynamics. This model system undergoes a glass transition both on cooling and on heating, and the intermediate liquid realizes unusual logarithmic relaxations. How vitrification occurs for the two different glass transitions is characterized in detail and comparisons are drawn to recent theoretical predictions for glass formation in systems with attractive interactions.

Optimizing the signal-to-noise ratio for X-ray photon correlation spectroscopy.

An analysis is presented of how to optimize the experimental beamline configuration for achieving the best possible signal-to-noise ratio (SNR) in X-ray photon correlation spectroscopy experiments using area detectors. It is shown that there exists an optimum detector distance; namely, the highest SNR is achieved by matching the angular pixel size with the angular source size. Binning several pixels together can increase the SNR by permitting to match the shape of a detector pixel to the shape of the source. It is also shown that collimating slits several times wider than the effective transverse coherence length are optimal; further, it is demonstrated that the energy dependence of the SNR is dictated by the energy dependence of detector efficiency and source brilliance. Ultimately the effects of focusing and low longitudinal coherence are discussed.

Crossover from stretched to compressed exponential relaxations in a polymer-based sponge phase.

X-ray photon correlation spectroscopy was used to characterize the wave vector- and temperature-dependent dynamics of spontaneous thermal fluctuations in a sponge (L3) phase that occurs in a blend of a symmetric poly(styrene-ethylene/butylene-styrene) triblock copolymer with a polystyrene homopolymer. Measurements of the intermediate scattering function reveal a crossover from stretched- to compressed-exponential relaxations as the temperature is lowered from 180 to 120 degrees C.

Fluctuation dynamics of block copolymer vesicles.

X-ray photon correlation spectroscopy was used to characterize the wave-vector- and temperature-dependent dynamics of spontaneous thermal fluctuations in a vesicle (L4) phase that occurs in a blend of a symmetric poly(styrene-ethylene/butylene-styrene) triblock copolymer with a polystyrene homopolymer. Measurements of the intermediate scattering function reveal stretched-exponential behavior versus time, with a stretching exponent slightly larger than 2/3. The corresponding relaxation rates show an approximate q(3) dependence versus wave vector. Overall, the experimental measurements are well described by theories that treat the dynamics of independent membrane plaquettes.

Statistical analysis of X-ray speckle at the NSLS.

A statistical analysis of the static speckle produced by illuminating a disordered aerogel sample by a nominally coherent X-ray beam at wiggler beamline X25 at the National Synchrotron Light Source is reported. The results of the analysis show that the coherence delivered to the X25 hutch is within 35% of what is expected. The rate of coherent photons is approximately two times smaller than expected on the basis of the X25 wiggler source brilliance.

Symmetric-to-asymmetric transition in triblock copolymer-homopolymer blends.

In blends of a symmetric poly(styrene-ethylene/butylene-styrene) tri-block-copolymer with a polystyrene homopolymer, small-angle x-ray scattering and cryotransmission electron microscopy measurements reveal a microstructure consisting of a disordered arrangement of poly(ethylene/butylene) membranes suspended in polystyrene. For triblock volume fractions less than 0.22, the membranes form an asymmetric sponge or L4 phase, consisting predominantly of equilibrium vesicles. For volume fractions greater than 0.22, they form a symmetric sponge-phase (L3 phase), separated from the L4 phase by a first-order transition.