Optimal vaccine scheduling in cancer immunotherapy

Cancer immunotherapy aims at stimulating the immune system to react against cancer stealth capabilities. It consists of repeatedly injecting small doses of a tumor-associated molecule one wants the immune system to recognize, until a consistent immune response directed against the tumor cells is observed.

We have applied the theory of optimal control to the problem of finding the optimal schedule of injections of an immunotherapeutic agent against cancer. The method employed works for a general ODE system and can be applied to find the optimal protocol in a variety of clinical problems where the kinetics of the drug or treatment and its influence on the normal physiologic functions have been described by a mathematical model.

We show that the choice of the cost function has dramatic effects on the kind of solution the optimization algorithm is able to find. This provides evidence that a careful ODE model and optimization schema must be designed by mathematicians and clinicians using their proper different perspectives.     

5-Spirocyclopropane Isoxazolidines as Versatile Intermediates in Organic Synthesis

The review outlines the various different azaheterocycles available from 5-spirocyclopropane isoxazolidines. These compounds can be regarded as versatile direct precursors of tetrahydro-, dihydropyridone and azetidinone derivatives. The current scope and limitations, and the selectivity aspects of the different processes are discussed therein.     

Solid-state interactions and drug release of teicoplanin in binary combinations with peracetylated α-, β-, and γ-cyclodextrins

Triacetyl α-cyclodextrin, triacetyl β-cyclodextrin and triacetyl γ-cyclodextrin were tested as possible hydrophobic carriers to prolong the release of hydrophilic teicoplanin (TCP). Physical–chemical characterization of individual components, drug-carrier physical mixtures at 0.5, 0.67 and 0.75 mass fraction of carrier, and the respective interaction products by kneading or evaporative crystallization under microwave irradiation was carried out using differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). In vitro drug release in pH 7.4 phosphate buffer at 37 °C was determined by intrinsic dissolution rate (IDR) measurements on non disintegrating compressed discs. Solid-state interactions of TCP with triacetyl α-cyclodextrin by evaporative crystallization and kneading and with triacetyl β-cyclodextrin by evaporative crystallization (probably resulting in carrier amorphization) were demonstrated. The role of carrier hydrophobicity, carrier mass fraction and preparation method of solid drug-carrier combinations on solid-state drug-carrier interactions and slowing down of TCP release was assessed. Modulation of drug release can be achieved using TCP-triacetyl γ-cyclodextrin combinations at 0.5 mass fraction of carrier.     

Understanding the role of stereoelectronic effects in determining collagen stability. 2. A quantum mechanical/molecular mechanical study of (Proline-Proline-Glycine)(n) polypeptides

The importance of vicinal and long-range interresidue effects in determining the stability of the collagen triple helix has been investigated by quantum mechanical (QM) and molecular mechanical (MM) computations on suitable model polypeptides, taking into account solvent effects by the polarizable continuum model (PCM). At the QM level, the PII conformation corresponds to an energy minimum for pentapeptide analogues incorporating the sequence Gly-Pro-Pro-Gly, irrespective of the down or up puckering of the pyrrolidine ring. However, our computations indicate that the alternation of down and up prolines characterizing collagen and collagen-like peptides is not due to an intrinsic preference of the Pro-Pro-Gly sequence. This result is confirmed by MM computations of longer polypeptides. Next, MM computations on model triple helices show that a better packing is obtained for specific values of backbone dihedrals, which, in turn, favor the alternation of down and up prolines along each chain.     

Coordination properties of 6-deoxy-6-[1-(2-amino) ethylamino]-β-cyclodextrin and the ability of its copper(II) complex to recognize and separate amino acid enantiomeric pairs

The functionalized cyclodextrin 6-deoxy-6-[1-(2-amino)ethylamino]--cyclodextrin was synthesized, and an NMR, EPR, pH-metric, and calorimetric investigation was carried out in aqueous solution in order to ascertain its behaviour towards protonation and copper(II) complex formation. The thermodynamic parameters of the ternary complex formation with alanine, phenylalanine and tryptophan enantiomeric pairs were also determined (25° C andI=0.1 mol dm^–3). No thermodynamic enantioselectivity was observed in these systems, while a chiral, though poor, discrimination was observed in LEC: c.d. spectra also show enantiomeric stereoselectivity. The results of the present investigation, compared with previously reported results, suggest the occurence of acis-complex trans-complex equilibrium in such systems.     

Soft agonist receptor interactions: Theoretical and experimental simulation of the active site of the receptor of sweet molecules

The structure-activity relationship of sweet molecules is chosen as an example to illustrate a mechanistic approach of soft agonist-receptor interactions. It is shown that an essentially geometric model of the receptor site can explain the activity of most sweet molecules, both rigid and flexible. The relevant conformations of flexible molecules in solution are extracted from a combination of NMR data and of energy calculations. A possible experimental simulation of the receptor environment in solution is illustrated by the complex of a dipeptide sweetener with a crown-ether.     

Structure elucidation and 3D solution conformation of the antibiotic enduracidin determined by NMR spectroscopy and molecular dynamics

Enduracidin and ramoplanin belong to the large family of cyclodepsipeptide antibiotics, highly effective against Gram-positive bacteria. The primary and 3D solution structure of ramoplanin is already well known, and the primary structure of enduracidin has been determined by a combination of chemical and NMR spectroscopic methods. Both antibiotics share a similar peptide core of 17 amino acids and differ mainly in the length of the acyl chain and the presence of two D-mannose moieties in ramoplanin. Based on the high sequence homology with ramoplanin, the structure in solution of enduracidin is modeled as a cyclic peptide. The tertiary structure thus obtained was refined through molecular dynamics (MD) simulation, in which the interatomic NOE-derived distance restraints were imposed. MD simulations yielded a family of representative 3D structures (RMSD = 0.89), which highlighted a backbone geometry similar to that of ramoplanin in its beta-hairpin arrangement. In contrast, enduracidin displays a different arrangement of the side-chain and of the residues forming the hydrophobic core.     

Thermal behavior of Cu(II)-, Cd(II)-, and Hg(II)-exchanged montmorillonite complexedwith cysteine

The thermal behavior of montmorillonite and organically modified montmorillonite, both treated with heavy metal cations [Cu(II), Cd(II) and Hg(II)], was characterized via thermal analyses (TG, DTG and DTA) combined with evolved species gas mass spectrometry (MS-EGA), and X-ray diffraction at in situ controlled temperature (HTXRD). The reactions involving Cu(II)- and Cd(II)-montmorillonite samples are mostly related to H₂O and OH loss, unlike Hg(II)-montmorillonite, where effects associated to Hg(II) loss are also present. Finally reactions related to dehydration, dehydroxylation and to organic matter decomposition can be observed in montmorillonite samples treated with cysteine.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.