Distance Distribution Function Research Articles

Dipolar-coupled moment correlations in clusters of magnetic nanoparticles

Here, we investigate the nature of the moment coupling between 10-nm DMSA-coated magnetic nanoparticles, in both colloidal dispersion and in powder form. The individual iron oxide cores were composed of > 95% maghemite and agglomerated to clusters. At room temperature the ensemble behaved as a superparamagnet according to M\"ossbauer and magnetization measurements, however, with clear signs of dipolar interactions at low temperatures. Analysis of temperature-dependent AC susceptibility data in the superparamagnetic regime indicates a tendency for dipolar coupled anticorrelations of the core moments within the clusters. To resolve the directional correlations between the particle moments we performed polarized small-angle neutron scattering and determined the magnetic spin-flip cross-section of the powder in low magnetic field at 300 K. We extract the underlying pair distance distribution function of the magnetization vector field by an indirect Fourier transform of the cross-section, and which suggests positive as well as negative correlations between nearest neighbor moments, with anticorrelations clearly dominating for next-nearest moments. These tendencies are confirmed by Monte Carlo simulations of such core-clusters.

Nonlocal statistical field theory of dipolar particles forming chain-like clusters

We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the ’head-to-tail’ mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the point-like test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.

Interactions among trioctylamine-sulfuric acid-water: experiments and molecular dynamics simulations

Trioctylamine (TOA) has been widely regarded as a cost effective extractant and received extensive applications in the metallurgical industry. However, TOA is prone to aggregate and form something like viscoelastic material when it meets the sulfuric acid. However, there is no unified understanding of the mechanism of aggregation. Based on the possible molecular interaction model proposed in our previous work, we are going to probe the interaction of TOA and the sulfuric acid as well as to obtain a chemical structure corresponding to various molar ratios through molecular dynamics calculations together with a specific distance distribution function. The results show that the hydrogen bonding of the whole system strengthens with the increase of the molar ratio of sulfuric acid and water to TOA. When the molar ratio of sulfuric acid and water to TOA is comparatively low, the hydrogen bonds interactions between TOA and water was predominated. When the ratio is high, TOA will react with sulfuric acid through protonation. The results of the simulation is consistent with our previous studies.

A deterministic multifractal model for complex structures

An idealized deterministic multifractal-based model is suggested for describing the structure of complex hierarchical materials. The corresponding pair distance distribution function and the small-angle scattering form factor is calculated from a system containing a macroscopic number of randomly oriented multifractals with uncorrelated positions. We show how to extract various structural information of the fractal both from real and reciprocal space data, such as: the scaling factors, the overall and fractal dimensions, and the size of the basic objects composing the fractal. The obtained results give additional insights into the structure of multifractal systems at nano- and micro-scales.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard–Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson–Boltzmann–Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the ‘Yukawa’-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Coil-to-globule transition of thermo-responsive γ-substituted poly (ɛ-caprolactone) in water: A molecular dynamics simulation study

The coil-to-globule behavior of poly{γ-2-[2-(2methoxyethoxy)ethoxy]ethoxy-3-caprolactone} (PMEEECL) as a γ-substituted poly (ɛ-caprolactone) was investigated via atomistic molecular dynamics (MD) simulation. For this purpose, radius of gyration, end-to-end distance and radial distribution function of the chain in the presence of water were calculated. Consequently, the lower critical solution temperature (LCST) of PMEEECL chain at which the coil-to-globule transition takes place, was determined in each calculated parameter curve. The simulation results indicated that the LCST of PMEEECL was occurred at close to 320 K, which is in a good agreement with previous experimental results. Additionally, the appearance of sudden change in both Flory-Huggins interaction parameter (χ) and interaction energy between the PMEEECL chain and water molecules at about 320 K confirmed the calculated LCST result. The radial distribution function (RDF) results showed that the affinity of the PMEEECL side chain to water molecules is lower than its backbone.

Benchmarking earthquake location algorithms: A synthetic comparison

A priori assessment of the expected location accuracy of a sensor network is typically done through inversion of the traveltime spatial gradients. This approach assumes that the applied location algorithm successfully recovers the global minimum of the objective function. However, even for accurate and precise phase picks, complexity in the velocity model and limitations in the network layout may inhibit the finding of a global minimum. The location algorithms may end up in a local minimum instead. We compare the location performance of various objective functions and minimization approaches. Although most of the analyzed location approaches mostly lead to good location results, none of the analyzed approaches recovered the correct location for all event locations. This implies that (microseismic) event locations estimates include an additional inherent error, which is linked to the applied location approach. This aspect is often neglected when interpreting event locations. Our site comprises a sensor network of two vertical strings, in a 1D velocity model of the Groningen gas field (The Netherlands), complicated by two thin, very high-velocity layers. For a series of synthetic event locations, we calculate arrival times, add picking errors, and then feed these synthetic picks into a set of different location routines. We also determine a novel way to analyze this approach-dependent location error of the sensor network for the given velocity model and a set of event locations: We compare the distances between a set of assumed event locations to resulting locations in the target region of the subsurface. From the cumulative distribution function of that mislocation distance, we determine the [Formula: see text] and [Formula: see text] confidence distances for each method. This results in scalar values representing the location confidence distances for a given method. In turn, this can be used to easily compare the location capabilities of different sensor layouts.

End-to-end distance and contour length distribution functions of DNA helices.

I present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible configurations for each dimer in the sequence, selects the global equilibrium twist conformation for the molecule, and determines the average base pair distances along the molecule backbone. Integrating over the base pair radial and angular fluctuations, I derive the room temperature distribution functions as a function of the sequence length. The obtained values for the most probable end-to-end distance and contour length distance, providing a measure of the global molecule size, are used to examine the DNA flexibility at short length scales. It is found that, also in molecules with less than ∼60 base pairs, coiled configurations maintain a large statistical weight and, consistently, the persistence lengths may be much smaller than in kilo-base DNA.

3D super-resolution microscopy reflects mitochondrial cristae alternations and mtDNA nucleoid size and distribution

3D super-resolution microscopy based on the direct stochastic optical reconstruction microscopy (dSTORM) with primary Alexa-Fluor-647-conjugated antibodies is a powerful method for accessing changes of objects that could be normally resolved only by electron microscopy. Despite the fact that mitochondrial cristae yet to become resolved, we have indicated changes in cristae width and/or morphology by dSTORM of ATP-synthase F1 subunit α (F1α). Obtained 3D images were analyzed with the help of Ripley's K-function modeling spatial patterns or transferring them into distance distribution function. Resulting histograms of distances frequency distribution provide most frequent distances (MFD) between the localized single antibody molecules. In fasting state of model pancreatic β-cells, INS-1E, MFD between F1α were ~80 nm at 0 and 3 mM glucose, whereas decreased to 61 nm and 57 nm upon glucose-stimulated insulin secretion (GSIS) at 11 mM and 20 mM glucose, respectively. Shorter F1α interdistances reflected cristae width decrease upon GSIS, since such repositioning of F1α correlated to average 20 nm and 15 nm cristae width at 0 and 3 mM glucose, and 9 nm or 8 nm after higher glucose simulating GSIS (11, 20 mM glucose, respectively). Also, submitochondrial entities such as nucleoids of mtDNA were resolved e.g. after bromo-deoxyuridine (BrDU) pretreatment using anti-BrDU dSTORM. MFD in distances distribution histograms reflected an average nucleoid diameter (<100 nm) and average distances between nucleoids (~1000 nm). Double channel PALM/dSTORM with Eos-lactamase-β plus anti-TFAM dSTORM confirmed the latter average inter-nucleoid distance. In conclusion, 3D single molecule (dSTORM) microscopy is a reasonable tool for studying mitochondrion.

Recent advances in the UltraScan SOlution MOdeller(US-SOMO) hydrodynamic and small-angle scattering data analysis and simulation suite.

The UltraScan SOlution MOdeller (US-SOMO) is a comprehensive, public domain, open-source suite of computer programs centred on hydrodynamic modelling and small-angle scattering (SAS) data analysis and simulation. We describe here the advances that have been implemented since its last official release (#3087, 2017), which are available from release #3141 for Windows, Linux and Mac operating systems. A major effort has been the transition from the legacy Qt3 cross platform software development and user interface library to the modern Qt5 release. Apart from improved graphical support, this has allowed the direct implementation of the newest, almost two-orders of magnitude faster version of the ZENO hydrodynamic computation algorithm for all operating systems. Coupled with the SoMo-generated bead models with overlaps, ZENO provides the most accurate translational friction computations from atomic-level structures available (Rocco and Byron Eur Biophys J 44:417-431, 2015a), with computational times comparable with or faster than those of other methods. In addition, it has allowed us to introduce the direct representation of each atom in a structure as a (hydrated) bead, opening interesting new modelling possibilities. In the small-angle scattering (SAS) part of the suite, an indirect Fourier transform Bayesian algorithm has been implemented for the computation of the pairwise distance distribution function from SAS data. Finally, the SAS HPLC module, recently upgraded with improved baseline correction and Gaussian decomposition of not baseline-resolved peaks and with advanced statistical evaluation tools (Brookes et al. J Appl Cryst 49:1827-1841, 2016), now allows automatic top-peak frame selection and averaging.

Interpretation of solution scattering data from lipid nanodiscs.

The structural information contained in solution scattering data from empty lipid nanodiscs is examined in the context of a multi-component geometric model. X-ray scattering data were collected on nanodiscs of different compositions at scattering vector magnitudes up to 2.0 Å-1. Through the calculation of the partial form factor for each of the nanodisc components before the isotropic average, structural parameters in the model were correlated to the features observed in the X-ray scattering data and to the corresponding distance distribution function. It is shown that, in general, the features at ∼0.3-0.6 Å-1 in the scattering data correlate to the bilayer structure. The data also support the argument that the elliptical shape of nanodiscs found in model fitting is physical, rather than an artefact due to the nanodisc size distribution. The lipid chain packing peak at ∼1.5 Å-1 is visible in the data and reflects the lipid bilayer phase transition. The shape change in the distance distribution function across the phase transition suggests that the nanodiscs are more circular in the fluid phase. The implication of these findings for model fitting of empty and protein-loaded nanodiscs is discussed.

Reply to the 'Comment on "On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility" Phys. Chem. Chem. Phys., 2018, 20, DOI: '.

In his comment on a recent publication by us, G. Graziano claims that solubility differences of indole in methanol and water can be rationalized by the reversible work needed to create a cavity in the solvent of the size of the solute, in this case indole. This quantity, he argues, is closely related to the solvent accessible surface area, which is greater for methanol compared with water, thus making indole more soluble in the former solvent. G. Graziano asserts that it is this property which is responsible for the large difference between the solubilities of indole in methanol and water. Further, G. Graziano claims that the differences in excess entropies and in distance distribution functions of indole in methanol and water and in methanol and water as a cosolvent found in our original work (Henao, et al., Phys. Chem. Chem. Phys., 2016, 18, 23006) are too "small" to be able to account for the differences in solubility of the indole molecule. We show in this work that the differences found by us are not small, by displaying some selected distance distribution functions in an alternative way to that described in our original paper. In fact we conclude that the differences in these functions are quantitatively greater than those found by Graziano in his comment. Secondly, we show in this reply that although the increase of the solvent accessible surface area may rationalize the differences in the indole-methanol and indole-water binary systems, and thus the work required for cavity creation, it is insufficient to fully account for the increase of indole solubility in water by the addition of very small quantities of methanol in the ternary system indole-methanol-water. In other words, as stated in our original paper, methanol is actively changing the solvation shell and not just passively increasing the solvent accessible surface area around indole. As a result of these additional analyses, we conclude that our work on the solvation differences of indole in water and methanol successfully captures differences in the solvation shells of both solvents around indole in both binary and ternary systems. Finally, while we do agree that Graziano's calculations are able to capture the role of cavity creation to explain differences in solubility, we think that our results concerning the quantification of changes in molecular interaction should be added to the calculations suggested by him to lead to a full description of the solubility.

A Molecular Level Understanding of Template Effects in Ionic Liquids

The structure-directing or template effect has been invoked several times for ionic liquids to explain the different outcome in material synthesis, namely, different scaffolds or geometrical arrangements with varying ionic liquids. It is obvious to assume that such an effect can originate from the most likely complex microstructure, being present within the ionic liquid itself. In that regard, ionic liquids have already been shown to undergo a nanosegregation into polar and nonpolar phases, which is commonly known and denoted as microheterogeneity. In order to provide detailed insight on the molecular level and to understand the effects rising from this structuring, we performed molecular dynamics simulations on selected very simple model systems composed of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, considering ethyl, butyl, hexyl, and octyl side chains attached to the cations, mixed with either n-dodecanol or n-butanol. By analyzing snapshots of the simulation boxes and calculating spatial distribution functions, we can visualize that with increasing side chains, the systems show considerable nanosegregation into polar and nonpolar domains. Combined angular and distance distribution functions show that in case of the nanosegregating systems the side chains of the cations are preferentially arranged in a parallel fashion, which indicates a micelle-like structure for the ionic liquids. The alcohol molecules participate in and are, therefore, influenced by this microheterogeneity. It can be shown that in the case of the short IL alkyl side chains, the self-aggregation of the nonpolar units of the alcohols is much stronger, while for the long chain cations, the nonpolar entities of the alcohols are most often connected to the nonpolar units of the ionic liquids. Using our domain analysis tool, we can quantify these observations by tracking the number, size, and shape of the polar and nonpolar entities present in the different investigated systems. The aforementioned combined angular-distance distribution functions reveal a structure-directing effect of the ionic liquids on the alcohol molecules within our simple model systems. The ionic liquids act as template and order the alcohol molecules according to their own structure, resulting in a parallel alignment of the alkyl side chains of the alcohols and ionic liquid cations, with both polar groups being at the same side. These observations show that the microheterogeneous structure of ionic liquids can indeed be applied to order substrates with respect to each other or, for example, to catalysts in a predetermined fashion, opening new possibilities for explaining or enhancing selectivities of chemical reactions in ionic liquids.

Impact of polymer geometry on the interactions of protein-PEG conjugates

The conjugation of high molecular weight polyethylene glycol (PEG) to an active pharmaceutical ingredient (API) is an attractive strategy for the modification of biophysical and biodistribution properties of the API. Indeed, several therapeutic proteins conjugated to PEG have been safely administered in the clinic. While there have been studies on the configuration of these conjugates in solution, investigations on the impact of PEG geometry on protein-PEG conjugate interactions is limited. In this study, we use dynamic light scattering (DLS), rheology, and small-angle neutron scattering (SANS) to investigate the biophysical solution and interaction behavior of a 50kDa Fab protein attached to either a linear or tetrameric (branched) 40kDa PEG molecule. The hydrodynamic radii, diffusivity, viscosity and pair distance distribution function (PDDF) were obtained for the protein-PEG conjugates in solution. An analysis revealed that interactions between unconjugated proteins were quite attractive, however linear PEG-protein conjugates exhibited net repulsive interactions, similar to that of the unconjugated polymer. Tetramer PEG-protein conjugates on the other hand, exhibited a net weak attractive interaction, indicating a more balanced distribution of repulsive and attractive interaction states. Further analysis of the SANS data using geometric models consistent with the PDDF elucidated the conjugates' equilibrium configuration in solution. Insights gained from measurements and analysis used here can also be useful in predicting how conjugate geometries affect viscosity and aggregation behavior, which are important in determining suitable protein-polymer drug formulations.

Quantale-valued topological spaces via closure and convergence

For a quantale V we introduce V-valued topological spaces via V-valued point-set-distance functions and, when V is completely distributive, characterize them in terms of both, so-called closure towers and ultrafilter convergence relations. When V is the two-element chain 2, the extended real half-line [0,∞], or the quantale Δ of distance distribution functions, the general setting produces known and new results on topological spaces, approach spaces, and the only recently considered probabilistic approach spaces, as well as on their functorial interactions with each other.

Tight Lower Bounds on the Contact Distance Distribution in Poisson Hole Process

In this letter, we derive new lower bounds on the cumulative distribution function (CDF) of the contact distance in the Poisson hole process (PHP) for two cases: 1) reference point is selected uniformly at random from $\mathbb {R}^{\boldsymbol {2}}$ independently of the PHP and 2) reference point is located at the center of a hole selected uniformly at random from the PHP. While one can derive upper bounds on the CDF of contact distance by simply ignoring the effect of holes, deriving lower bounds is known to be relatively more challenging. As a part of our proof, we introduce a tractable way of bounding the effect of all the holes in a PHP, which can be used to study other properties of a PHP as well.

Simple Model for the Benzene Hexafluorobenzene Interaction.

While the experimental intermolecular distance distribution functions of pure benzene and pure hexafluorobenzene are well described by transferable all-atom force fields, the interaction between the two molecules (in a 1:1 mixture) is not well simulated. We demonstrate that the parameters of the transferable force fields are adequate to describe the intermolecular distance distribution if the charges are replaced by a set of charges that are not located at the atoms. The simplest model that well describes the experimental distance distribution, between benzene and hexafluorobenzene, is that of a single ellipsoid for each molecule, representing the van der Waals interactions, and a set of three point charges (on the axis perpendicular to the arene plane) which give the same quadrupole moment as do the all atom charges from the transferable force fields.

Reduction of small-angle scattering profiles to finite sets of structural invariants.

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters called Kn which are related to the shape of the object of study. These Kn, together with a radius R, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and the Dmax parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

Novel Melt-Spun Polymer-Optical Poly(methyl methacrylate) Fibers Studied by Small-Angle X-ray Scattering.

The structural properties of novel melt-spun polymer optical fibers (POFs) are investigated by small-angle X-ray scattering. The amorphous PMMA POFs were subjected to a rapid cooling in a water quench right after extrusion in order to obtain a radial refractive index profile. Four fiber samples were investigated with small-angle X-ray scattering (SAXS). The resulting distance-distribution functions obtained from the respective equatorial and meridional SAXS data exhibit a real-space correlation peak indicative of periodic cross-sectional and axial variations in the scattering density contrast. Simple model calculations demonstrate how the structural information contained particularly in the equatorial distance distribution function can be interpreted. The respective results are qualitatively verified for one of the fiber samples by comparison of the model curve with the measured SAXS data. Eventually, the study confirms that the cross-sectional variation of the (scattering-) density is the main reason for the formation of radial refractive-index profiles in the POFs.

Scattering model for tetrapods with cylindrical arms

A scattering model for regular tetrapods, which are the endoskeleton structure of regular tetrahedrons, is presented. Since a tetrapod, unlike spheres and cylinders, is an anisotropic structure formed by four cylinders branching out from the centroid to the vertices of a tetrahedron, additional symmetry elements and random orientation must be accounted for to develop its scattering model. The scattering function of tetrapods was derived from the modification of the scattering model for cylinders and their structural regularity was simplified. Scattering intensity profiles and pair distance distribution functions were obtained by numerical calculation and compared with the experimental data from small angle X-ray measurements of CdSe tetrapod nanocrystals.