Zinc-phosphate nanoparticles with reversibly attached TNF-α analogs: an interesting concept for potential use in active immunotherapy

The authors’ intention was to prepare nanometer-sized zinc-phosphate nanoparticles that would be capable of binding histidine-rich TNF-α analogs onto their surface via a coordinative bond. Zinc-phosphate nanoparticles with a size of around 60 nm were prepared by a wet precipitation method and characterized using SEM, EDX, XRD, and DLS. First, BSA was bound as a testing protein, afterward two TNF-α analogs with decreased activity were bound to the described nanoparticles. The efficiency of binding and the existence of coordinative bond were confirmed with SDS-PAGE analysis. During binding, particle storage, and release experiments, the prepared TNF-α analogs retained their biological activity—hence the epitopes necessary for formation of antibodies stayed intact. The particle size did not change within a period of 2 weeks. No significant agglomeration was observed, the particles could be quickly dispersed in ultrasound. The present nanoparticles and the general approach of coordinative binding are widely applicable for natural and engineered histidine-rich proteins. The nanoparticles bearing appropriate TNF-α analogs could also be potentially used for active immunotherapy to tackle the chronic inflammatory diseases associated with pathogenically elevated levels of TNF-α.     

Picture change error correction in the radial distributions of canonical orbital densities and total electron density of radon atom: the effect of the size of nucleus and the basis set limit

The 2nd order Douglas-Kroll-Hess (DKH2) and the Infinite Order Two Component (IOTC) radial distributions of electron density of canonical Hartree-Fock (HF) orbitals of radon atom are presented. Furthermore, the total electron density is revisited. The picture change error (PCE) correction is investigated by analytical means. The point charge model of nucleus and the Gaussian nucleus model are employed. The basis set is extrapolated by means of including tight s and also p Gaussians within the original triple zeta basis set. It is found that the DKH1 PCE corrected DKH2 total electron and s orbital contact densities are negative for the point charge model of nucleus if tight enough s Gaussians are included in the basis set. It is shown that this failure is caused due to the missing terms of the second order Douglas-Kroll transformation for the DKH2 electron density. PCE is found the most striking in the DKH2/IOTC electron density of s orbitals close to the nucleus. The radial distributions of the 2-component p _1/2 orbital densities are considerably affected by PCE at the nucleus as well. Furthermore, the PCE corrected DKH2/IOTC scalar p orbital densities have a non-zero value of electron density at nucleus and can be considered as an spin-orbit (SO) average of the p _1/2 and p _3/2 orbitals. The d and f orbitals are affected by PCE in the vicinity of the nucleus only little. The PCE corrected DKH2 and IOTC radial distributions of orbital densities are nodeless, which is completely in agreement with the radial distribution of the analytic or numeric DCH orbital densities.     

Low-density polyethylene in mixtures of hexane and benzene derivates

Preferential sorption, equilibrium swelling degree, and volume of the swollen membrane in systems low-density polyethylene + hexane + aromatic compound (benzene, methylbenzene, or ethylbenzene) were studied using gravimetric and dilatometric methods at the temperature of 25 °C. Aromatic compounds are preferentially sorbed in low-density polyethylene compared to hexane. Experimental volume changes of the membrane were found to be noticeably different from those calculated on the basis of mass sorption data under the assumption of additivity. This difference points to the existence of the interactions between the polymer and the surrounding liquid mixture. The volume swelling degree curves are close to each other in the whole concentration range of the binary liquid mixture (hexane + aromatics) suggesting that the attractive forces between the polymer chains are the deciding factor limiting the volume expansion of the membrane in all three systems to the same extent.     

Families of optimal packings in real and complex Grassmannian spaces

A construction based on a \(4l \times 4l\) Hadamard matrix leads to a new family of optimal orthoplex packings in Grassmannian spaces \(G_{\mathbb {R}}(8l, 4l)\) and \(G_{\mathbb {C}}(4l, 2l)\). A related construction gives an optimal simplex packings in \(G_{\mathbb {R}}(8 l-1, 4 l - 1)\) and \(G_{\mathbb {R}}(8l-1, 4l)\) with the additional assumption of an \(8l \times 8l\) skew Hadamard matrix and a related 1-factorization of a complete graph. A construction of a maximal optimal simplex packings in \(G_{\mathbb {C}}(2l-1, l- 1)\) and \(G_{\mathbb {C}}(2l-1,l)\) is given.     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

An SQP method for mathematical programs with vanishing constraints with strong convergence properties

We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of \({\mathcal {Q}}\)-stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how \({\mathcal {Q}}_M\)-stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of \({\mathcal {Q}}_M\)-stationarity of the limit points.     

Determination of activation effect of Ca(OH)<Subscript>2</Subscript> upon the hydration of BFS and related heat by isothermal calorimeter

Isothermal conduction calorimetry, differential thermal analysis (DTA)–thermogravimetric analysis (TG) analysis, and SEM observations have proved the activation effect of Ca(OH)₂ released from the C₃S hydration upon blast furnace slag (BFS). Five sample mixtures of BFS and C₃S and two samples of pure BFS and C₃S were submitted to reaction with water inside the calorimeter at room temperature. The values of hydration heat were recorded up to 7 days. Samples were stored in humidity during 28 days and then were submitted to DTA–TG and SEM analysis. The effect of Ca(OH)₂ upon heat evolution of sample mixtures has been quantified and its influence upon the formation of new hydrates and microstructure of pastes was evidenced.     

On multiplication groups of relatively free quasigroups isotopic to Abelian groups

If Q is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group Mlt Q is a Frobenius group. Conversely, if Mlt Q is a Frobenius group, Q a quasigroup, then Q has to be isotopic to an Abelian group. If Q is, in addition, finite, then it must be a central quasigroup (a T-quasigroup).This work was supported by institutional grant MSM 113200007, and by Grant Agency of Czech Republic, grant number 201/99/0263.