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.     

Synthesis of an asymmetric fullerene dimer via sequential cycloadditions

A single isomer of a monofunctionalised C₇₀ fullerene is isolated and characterised using variable temperature NMR spectroscopy. Pendant methylene bromide groups allow for further cycloaddition reactions and a C₆₀-C₇₀ asymmetric fullerene dimer is thus prepared.     

Nonlinear dynamics of charged particles interacting with combined ac-dc electromagnetic fields

A nonlinear Lorenz model describing interactions between charged particles and combined ac-dc electromagnetic fields is studied for various combinations of frequencies, field strengths and relative angle (θ) between the ac and dc magnetic fields. Strong directional effects on the magnitude and location of resonant particle motion are observed when θ is varied and the regular resonance windows in the aligned field (θ = 0) and linear version of the model studied previously by Durney etaal., break up to form irregular and less well pronounced regions of large and small particle displacements when nonlinearities are taken into account. The length of time takne to achieve resonant behaviour also becomes larger and more variable when nonlinearities are present. The possible relevance of these effects to interactions between electromagnetic fields and biological media is briefly discussed.     

Mapping of possible prion protein self-interaction domains using peptide arrays

Background  

The common event in transmissible spongiform encephalopathies (TSEs) or prion diseases is the conversion of host-encoded protease sensitive cellular prion protein (PrP^C) into strain dependent isoforms of scrapie associated protease resistant isoform (PrP^Sc) of prion protein (PrP). These processes are determined by similarities as well as strain dependent variations in the PrP structure. Selective self-interaction between PrP molecules is the most probable basis for initiation of these processes, potentially influenced by chaperone molecules, however the mechanisms behind these processes are far from understood. We previously determined that polymorphisms do not affect initial PrP^C to PrP^Sc binding but rather modulate a subsequent step in the conversion process. Determining possible sites of self-interaction could elucidate which amino acid(s) or amino acid sequences contribute to binding and further conversion into other isoforms. To this end, ovine – and bovine PrP peptide-arrays consisting of 15-mer overlapping peptides were probed with recombinant sheep PrP^C fused to maltose binding protein (MBP-PrP).     

The observation of a large gauche preference when 2-fluoroethylamine and 2-fluoroethanol become protonated

The energies of the gauche and anti conformers of 2-fluoroethylamine, 2-fluoroethanol and their protonated analogues are calculated using density functional theory. Unlike the non protonated systems, the protonated systems show a strong gauche effect where the C-F and the C-(+)NH(3) or C-F and C-(+)OH(2) bonds are gauche rather than anti to each other. Single crystal X-ray diffraction studies of 2-fluoroethylammonium compounds identify the same conformational preference.     

Structural and rate studies of the 1,2-additions of lithium phenylacetylide to lithiated quinazolinones: influence of mixed aggregates on the reaction mechanism

The 1,2-addition of lithium phenylacetylide (PhCCLi) to quinazolinones was investigated using a combination of structural and rate studies. (6)Li, (13)C, and (19)F NMR spectroscopies show that deprotonation of quinazolinones and phenylacetylene in THF/pentane solutions with lithium hexamethyldisilazide affords a mixture of lithium quinazolinide/PhCCLi mixed dimer and mixed tetramer along with PhCCLi dimer. Although the mixed tetramer dominates at high mixed aggregate concentrations and low temperatures used for the structural studies, the mixed dimer is the dominant form at the low total mixed aggregate concentrations, high THF concentrations, and ambient temperatures used to investigate the 1,2-addition. Monitoring the reaction rates using (19)F NMR spectroscopy revealed a first-order dependence on mixed dimer, a zeroth-order dependence on THF, and a half-order dependence on the PhCCLi concentration. The rate law is consistent with the addition of a disolvated PhCCLi monomer to the mixed dimer. Investigation of the 1,2-addition of PhCCLi to an O-protected quinazolinone implicates reaction via trisolvated PhCCLi monomers.     

Optical rotatory dispersion studies—CIV Low-temperature circular dichroism behavior of various chromophoric derivatives of alcohols and amines

The low-temperature circular dichroism behavior of various cyclic and alicyclic systems containing the methyl xanthato-, N,N-diethyl-N′-acylthioureyl-, N-phthalimido-, nitrito- and dithio-carbalkoxy- chromophores is discussed. Rotational strength (R₀^T) values are reported where possible and changes in this parameter upon variation of the temperature are interpreted, where relevant, in terms of the degree of steric inhibition to free rotation about the various bonds connected to the asymmetric center bearing (or nearest to) the chromophore moiety.     

Synthesis of a short-chain fullerene dimer

The synthesis of a short-chain fullerene dimer via bifunctional cycloaddition is demonstrated. A mono-functionalised C₆₀ species is isolated, and has the potential for further organic functionalisation.