High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Substituted m-phenylene bridges as strong ferromagnetic couplers for Cu(II)-bridge-Cu(II) magnetic interactions: new perspectives

Based on a combined theoretical-experimental study, we propose that substituted m-phenylene ligands (m-N-Phi-N) can act as tuneable strong ferromagnetic couplers connecting Cu(II) ions; a new complex presenting that bridge with J close to +15 cm(-1) has been suggested and synthesized.     

Rigidified calixarenes bearing four carbamoylmethylphosphineoxide or carbamoylmethylphosphoryl functions at the wide rim

Conformationally rigidified tetraCMPO derivatives have been prepared from calix[4]arene bis(crown ether) 4a in which adjacent oxygens are bridged at the narrow rim by two diethylene glycol links. Acylation of the tetraamine 4c with the CMPO-active ester 5b gave the tetraphosphine oxide 6a, while the tetraphosphinate 6b and the tetraphosphonate 6c were obtained by Arbuzov reaction of tetrabromoacetamido derivative 7 with PhP(OEt)2 or P(OEt)3. The extraction ability of these CMPO derivatives was checked for selected lanthanides and actinides and compared with the analogous compounds 1b, 10b and 10d derived from calix[4]arene tetrapentyl ether. All rigidified bis(crown ether) ligands are more effective extractants than their pentyl ether counterparts and require only 1/10 of the concentration (cL= 10 4M) to obtain the same distribution coefficients, while with CMPO itself a 2,000-fold concentration is necessary. This could be a consequence of a better preorganisation of the ligating functions owing to the rigidity which on the other hand did not change the observed selectivity for americium (DAm/DEu=9-19) and for light lanthanides over heavy ones. NMR relaxivity titration curves show that the complex of Gd3+ with ligand 6a is highly oligomerised in anhydrous acetonitrile over a large range of ligand:metal concentration ratios. Nuclear magnetic relaxation dispersion (NMRD) profiles also showed that large oligomers were formed, and their mean tumbling times were deduced from the Solomon-Bloembergen-Morgan equations. The NMR spectra of dia- and paramagnetic lanthanide complexes with 6a agreed with the presence of two conformers with an elongated calix[4]arene skeleton in which the distances between opposite methylene groups are different. Contrary to what was observed with ligand 2a, the addition of nitrate ions does not labilize the metal complexes, presumably because of the rigidification effect of the ether bridges. Single-crystal X-ray structures were obtained for the active ester 5b and for diphenylphosphorylacetic acid 5a.     

Aggregation of [Cu(II)4] building blocks into [Cu(II)8] clusters or a [Cu(II)4]infinity chain through subtle chemical control

Coordination complexes of the ligand H3L [1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene] with Cu(II) are reported. Clusters showing various nuclearities or modes of supramolecular organization have been prepared by slightly changing the reaction conditions and have been crystallographically characterized. The reaction of H3L with one equivalent of Cu(OAc)2 in DMF yields the dinuclear complex [Cu2(HL)2(dmf)2] (1). Reaction in MeOH of H3L with an increased amount of metal, in the form of Cu(NO3)2, and excess strong base (nBu4NOH) affords the cluster [Cu8(L)2(OMe)8(NO3)2] (2). Complex 2 is a dimer of two linear [Cu4] arrays bridged by methoxide ligands, where the polynucleating ligand is fully deprotonated. The [Cu4]2 clusters are linked to each other by NO3- bridges to form one-dimensional coordination polymers. The link between [Cu8] units and their relative spatial positioning can be modified by changing the anion of the Cu(II) salt, as demonstrated by the synthesis of the cluster polymers [Cu8(L)2(OMe)8Cl2] (3) and [Cu8(L)(OMe)7.86Br2.14] (4), where only NO3- has been replaced by Cl- or Br-, respectively. Similarly, when ClO4- is used, compound [Cu8(L)2(OMe)8(ClO4)2(MeOH)4] (5) can be isolated. It contains independent [Cu8] units. A slight change in the stoichiometry of the reaction leading to 2 affords the related complex catena-[Cu4(L)(OMe)3(NO3)2(H2O)0.36] (6). This polymer contains essentially the same [Cu4] moiety as 2, albeit organized in a completely different arrangement. Each [Cu4] unit in 6 is linked by OMe- ligands to two such equivalent groups to form an infinite chain. Magnetic susceptibility measurements reveal weak antiferromagnetic exchange between Cu(II) centers in 1 (J = -0.73 cm(-1)) and strong antiferromagnetic coupling within [Cu4] chains in 2, 5, and 6 (most negative J values of -113.8 and -177.3 cm(-1) for 2 and 6, respectively).     

A solvent-controlled switch of manganese complex assemblies with a beta-diketonate-based ligand

The coordination properties of the new polynucleating ligand H(3)L1 (1,3-bis(3-oxo-3-phenylpropionyl)-2-hydroxy-5-methylbenzene) with Mn(II/III) are described. Depending on the solvent used, the reaction of H(3)L1 with Mn(OAc)(2) yields either of the two new multinuclear assemblies [Mn(2)(HL1)(2)(py)(4)] (1) and [Mn(3)(HL1)(3)] (2), as revealed by X-ray crystallography. The structure of 2 is remarkable in that it shows a unique asymmetric triple-stranded helicate. Complexes 1 and 2 can be interconverted by controlling the solvent of the reaction system, and therefore, this ensemble constitutes an interesting externally addressable switch. In the presence of Mn(III)/pyridine, partial degradation of H(3)L1 occurs via oxidative cleavage, and the new complex [Mn(2)(L2)(2)(py)(4)] (3) is formed. The crystal structure of this complex has shown the fully deprotonated form of the new donor H(3)L2 (3-(3-oxo-3-phenylpropionyl)-5-methylsalicylic acid). From the same reaction, the Mn(II) complex 1 is also obtained. A rational synthesis of H(3)L2 is reported, and this has been used to prepare 3 in high yields, directly from its components. Variable-temperature magnetic susceptibility (chi(m)) measurements were performed on complexes 1-3 under a magnetic field of 1 kG. The data for each complex were fit to the appropriate chi(m) vs T theoretical equation, respectively. In 1, the Mn(II) ions are uncoupled, with g = 2.01. The data from 2 were fit by assuming the presence of an exchange coupled Mn(II)...Mn(II) pair next to a magnetically isolated Mn(II) center. The fit gave J = -2.75 cm(-1), g(12) = 1.97, and g(3) = 1.92, respectively. In 3, two models fit the experimental data. In the most satisfactory, the Mn(III) ions are coupled antiferromagnetically with J = -1.48 cm(-1) and g = 1.98 and a term for weak ferromagnetic intermolecular exchange is included with zJ' = 0.39 cm(-1). The other model contemplates the presence of two uncoupled zero field split Mn(III) ions.     

Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9)

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings. For [n]phenacenes, all indicators of aromaticity show that the external rings are the most aromatic. From the external to the central ring, the local aromaticity varies in a damped alternate way. The trends for the [n]helicene series are the same as those found for [n]phenacenes. Despite the departure from planarity in [n]helicenes, only a very slight loss of aromaticity is detected in [n]helicenes as compared to the corresponding [n]phenacenes. Finally, because of magnetic couplings between superimposed six-membered rings in the higher members of the [n]helicenes series, we have demonstrated that the NICS indicator of aromaticity artificially increases the local aromaticity of their most external rings.     

Gadolinium‐Decorated Silica Microspheres as Redox‐Responsive MRI Probes for Applications in Cell Therapy Follow‐Up

The redox microenvironment within a cell graft can be considered as an indicator to assess whether the graft is metabolically active or hypoxic. We present a redox‐responsive MRI probe based on porous silica microparticles whose surface has been decorated with a Gd‐chelate through a disulphide bridge. Such microparticles are designed to be interspersed with therapeutic cells within a biocompatible hydrogel. The onset of reducing conditions within the hydrogel is paralleled by an increased clearance of Gd, that can be detected by MRI.     

Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core

In this paper, the Ritz minimum energy method, based on the use of the Principle of Virtual Displacements (PVD), is combined with refined Equivalent Single Layer (ESL) and Zig Zag (ZZ) shell models hierarchically generated by exploiting the use of Carrera's Unified Formulation (CUF), in order to engender the Hierarchical Trigonometric Ritz Formulation (HTRF). The HTRF is then employed to carry out the free vibration analysis of doubly curved shallow and deep functionally graded material (FGM) shells. The PVD is further used in conjunction with the Gauss theorem to derive the governing differential equations and related natural boundary conditions. Donnell–Mushtari's shallow shell-type equations are given as a particular case. Doubly curved FGM shells and doubly curved sandwich shells made up of isotropic face sheets and FGM core are investigated. The proposed shell models are widely assessed by comparison with the literature results. Two benchmarks are provided and the effects of significant parameters such as stacking sequence, boundary conditions, length-to-thickness ratio, radius-to-length ratio and volume fraction index on the circular frequency parameters and modal displacements are discussed.     

Engineering strategy to improve peptide analogs: from structure-based computational design to tumor homing

We present a chemical strategy to engineer analogs of the tumor-homing peptide CREKA (Cys-Arg-Glu-Lys-Ala), which binds to fibrin and fibrin-associated clotted plasma proteins in tumor vessels (Simberg et al. in Proc Natl Acad Sci USA 104:932–936, 2007) with improved ability to inhibit tumor growth. Computer modeling using a combination of simulated annealing and molecular dynamics were carried out to design targeted replacements aimed at enhancing the stability of the bioactive conformation of CREKA. Because this conformation presents a pocket-like shape with the charged groups of Arg, Glu and Lys pointing outward, non-proteinogenic amino acids α-methyl and N-methyl derivatives of Arg, Glu and Lys were selected, rationally designed and incorporated into CREKA analogs. The stabilization of the bioactive conformation predicted by the modeling for the different CREKA analogs matched the tumor fluorescence results, with tumor accumulation increasing with stabilization. Here we report the modeling, synthetic procedures, and new biological assays used to test the efficacy and utility of the analogs. Combined, our results show how studies based on multi-disciplinary collaboration can converge and lead to useful biomedical advances.