Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

A pH-Sensitive Zwitterionic Iron Complex Probe with High Biocompatibility for Tumor-Specific Magnetic Resonance Imaging

Accurate diagnosis of tumor characteristics, including its location and boundary, is of immense value to subsequent therapy. Activatable magnetic resonance imaging (MRI) contrast agents that respond to tumor-specific microenvironments, such as the redox state, pH, and enzyme activity, enable better mapping of tumor tissue. However, the practical application of most reported activatable agents is hampered by problems including potential toxicity, inefficient elimination, and slow activation. In this study, we developed a zwitterionic iron complex (Fe-ZDS) as a positive MRI contrast agent for tumor-specific imaging. Fe-ZDS could dissociate in weakly acidic solution rapidly, accompanied by clear longitudinal relaxivity (r₁) enhancement, which enabled the complex to act as a pH-sensitive contrast agent for tumor-specific MR imaging. In vivo experiments showed that Fe-ZDS rapidly enhanced the tumor-to-normal contrast ratio by >40 %, which assisted in distinguishing the tumor boundary. Furthermore, Fe-ZDS circulated freely in the bloodstream and was excreted relatively safely via kidneys owing to its zwitterionic nature. Therefore, Fe-ZDS is an ideal candidate for a tumor-specific MRI contrast agent and holds considerable potential for clinical translation.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

Some preliminary observations on a defect Navier–Stokes system

Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier–Stokes equations are explored, leading to connections between classical elasticity, the elastic theory of defects, plasticity theory, and classical fluid mechanics.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

Conformational Dynamics Underlies Different Functions of Human KDM7 Histone Demethylases

The human KDM7 subfamily histone H3 Nϵ-methyl lysine demethylases PHF8 (KDM7B) and KIAA1718 (KDM7A) have different substrate selectivities and are linked to genetic diseases and cancer. We describe experimentally based computational studies revealing that flexibility of the region linking the PHD finger and JmjC domains in PHF8 and KIAA1718 regulates interdomain interactions, the nature of correlated motions, and ultimately H3 binding and demethylation site selectivity. F279S an X-linked mental retardation mutation in PHF8 is involved in correlated motions with the iron ligands and second sphere residues. The calculations reveal key roles of a flexible protein environment in productive formation of enzyme-substrate complexes and suggest targeting the flexible KDM7 linker region is of interest from a medicinal chemistry perspective.     

The effect of cationic groups on the stability of 19F MRI contrast agents in nanoparticles

Fluorine‐19 (¹⁹F)‐based contrast agents are increasingly used for magnetic resonance imaging. Conjugated to polymers, they provide an excellent quantitative imaging tool to detect the movement of the polymeric nanoparticles in vivo as there is no background signal in tissue. One of the challenges is the decline in signal intensity when the conjugated hydrophobic fluorinated functionalities aggregate. Therefore, a new fluorinated monomer was prepared from l ‐arginine that carries a 2,2,2‐trifluoroethyl functional group for imaging. The resulting monomer, 2,2,2‐trifluoroethylamide l ‐arginine methacrylamide (3FArgMA), was copolymerized with poly(ethylene glycol) methyl ether methacrylate (PEGMEMA), [2‐(2,3,4,6‐tetra‐O‐acetyl‐α‐d ‐mannopyranosyloxy)ethyl methacrylate or 1‐O‐methacryloyl‐2,3:4,5‐di‐O‐isopropylidene‐β‐d ‐fructopyranose, respectively, using poly(methyl methacrylate) macro‐reversible addition–fragmentation chain transfer polymerization agent. The resulting block copolymers, which varied in 3FArgMA content, were self‐assembled into micelles of hydrodynamic diameters from 25 to 60 nm. The permanently positively charged arginine functionality on the 3FArgMA displayed repulsive forces against aggregation enabling high spin–spin relaxation times (T₂) in acidic as well as alkaline solutions. However, the longer poly(ethylene glycol) side functionality in PEGMEMA enabled better steric stabilization (T₂~30 ms) while the short fructose side chain was not enough to maintain high T₂ values, in particular when a higher 3FArgMA content was used. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1994–2001     

Correlating Charge-Carrier Dynamics with Efficiency in Quantum-Dot Solar Cells: Can Excitonics Lead to Highly Efficient Devices?

The photovoltaic performance of quantum-dot solar cells strongly depends on the charge-carrier relaxation and recombination processes, which need to be modulated in a favorable way to obtain maximum efficiency. Recently, significant efforts have been devoted to investigate the carrier dynamics of nanocrystal sensitizers, both in solution and deposited on TiO₂ photoanodes, with the aim to correlate the excitonics with solar-energy conversion efficiency. This Minireview summarizes some proof of the concepts that efficiency can be directly correlated to the exciton dynamics of quantum-dot solar cells. The presented findings are based on CdSeS alloy, CdSe/CdS core/shell, Au/CdSe nanohybrids, and Mn-doped CdZnSSe nanocrystals, where the favourable excitonic processes are optimized to enhance the efficiency. Future prospects and limitations are addressed as well.