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.     

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).     

Solid-phase microextraction gas chromatography/mass spectrometry: a new method for species identification of truffles

This study describes a rapid method to identify different truffle species by analysis of their volatile compound fraction using static headspace solid-phase microextraction gas chromatography/mass spectrometry. The volatile organic compounds (VOCs) were extracted using a new 2-cm 50/30 microm DVB/CAR/PDMS fiber placed for 10 min in the headspace of the truffle sample with the vial maintained at 20 degrees C (in a thermostatically controlled analysis room). The mass spectra of the VOC chromatograms were represented as 'fingerprints' of the analysed samples. Next, stepwise factorial discriminant analysis afforded a limited number of characteristic fragment ions that allowed a classification of the truffle species studied. This new method provides an effective approach to rapid quality control and identification of truffle species by analysis of their volatile fraction. Moreover, this method offers the advantage of minimizing thermal, mechanical, and chemical modifications of the truffles, thereby reducing the risk of analytical artifacts.     

Synthesis, structure, and properties of Cs(4)Th(4)P(4)Se(26): a quaternary thorium selenophosphate containing the (P(2)Se(9))(6-) anion

Orange crystals of Cs(4)Th(4)P(4)Se(26) were grown from the reaction of (232)Th and P in a Cs(2)Se(3)/Se molten salt flux at 750 degrees C. Cs(4)Th(4)P(4)Se(26) crystallizes in the orthorhombic space group Pbca with the unit cell parameters: a = 12.0130(6), b = 14.5747(7), c = 27.134(1) A; Z = 8. The compound exhibits a three-dimensional structure, consisting of dimeric [Th(2)Se(13)] polyhedral units. The two crystallographically independent, nine-coordinate, bicapped trigonal prismatic thorium atoms share a triangular face to form the dimer, and each dimer edge-shares two selenium atoms with two other dimers to form kinked chains along the [010] direction. While this structure shares features of the previously reported Rb(4)U(4)P(4)Se(26), including phosphorus in the 5+ oxidation state, careful inspection of the structure reveals that the selenophosphate anion that knits the structure together in three directions in both compounds is a unique (P(2)Se(9))(6-) anion. The formula may be described best as [Cs(2)Th(2)(P(2)Se(9))(Se(2))(2)](2). The (P(2)Se(9))(6-) anion features a nearly linear Se-Se-Se backbone with an angle of 171 degrees and Se-Se distances that are approximately 0.2-0.3 A longer than the typical single Se-Se bond. Magnetic studies confirm that this phase contains Th(IV). Raman data for this compound is reported, and structural comparisons will be drawn to its uranium analogue, Rb(4)U(4)P(4)Se(26).     

Fast Li-Ion Conduction in Spinel-Structured Solids

Spinel-structured solids were studied to understand if fast Li⁺ ion conduction can be achieved with Li occupying multiple crystallographic sites of the structure to form a “Li-stuffed” spinel, and if the concept is applicable to prepare a high mixed electronic-ionic conductive, electrochemically active solid solution of the Li⁺ stuffed spinel with spinel-structured Li-ion battery electrodes. This could enable a single-phase fully solid electrode eliminating multi-phase interface incompatibility and impedance commonly observed in multi-phase solid electrolyte–cathode composites. Materials of composition Li_1.25M(III)_0.25TiO₄, M(III) = Cr or Al were prepared through solid-state methods. The room-temperature bulk Li⁺-ion conductivity is 1.63 × 10⁻⁴ S cm⁻¹ for the composition Li_1.25Cr_0.25Ti_1.5O₄. Addition of Li₃BO₃ (LBO) increases ionic and electronic conductivity reaching a bulk Li⁺ ion conductivity averaging 6.8 × 10⁻⁴ S cm⁻¹, a total Li-ion conductivity averaging 4.2 × 10⁻⁴ S cm⁻¹, and electronic conductivity averaging 3.8 × 10⁻⁴ S cm⁻¹ for the composition Li_1.25Cr_0.25Ti_1.5O₄ with 1 wt. % LBO. An electrochemically active solid solution of Li_1.25Cr_0.25Mn_1.5O₄ and LiNi_0.5Mn_1.5O₄ was prepared. This work proves that Li-stuffed spinels can achieve fast Li-ion conduction and that the concept is potentially useful to enable a single-phase fully solid electrode without interphase impedance.     

Existence theory for nonclassical entropy solutions of scalar conservation laws

We establish a general existence theory for the Cauchy problem associated with a scalar conservation law in one-space dimension. The flux-function is assumed to be nonconvex and we consider nonclassical entropy solutions selected by a kinetic relation. To solve the Cauchy problem, we construct a sequence of approximate solutions using a wave-front tracking scheme. The main difficulty is deriving a uniform estimate on the total variation of the approximate solutions. This is achieved here by introducing a generalized total variation functional, which is decreasing in time and, additionally, reduces to the standard total variation functional when the solutions contain only classical shocks. This functional seems sufficiently robust to be useful for systems as well.Received: June 3, 2002; revised: November 12, 2002     

Synthesis and Biological Evaluation of Several Dephosphonated Analogues of CMP‐Neu5Ac as Inhibitors of GM3‐Synthase

Previous studies demonstrated that reducing the GM3 content in myoblasts increased the cell resistance to hypoxic stress, suggesting that a pharmacological inhibition of the GM3 synthesis could be instrumental for the development of new treatments for ischemic diseases. Herein, the synthesis of several dephosphonated CMP‐Neu5Ac congeners and their anti ‐ GM3‐synthase activity is reported. Biological activity testes revealed that some inhibitors almost completely blocked the GM3‐synthase activity in vitro and reduced the GM3 content in living embryonic kidney 293A cells, eventually activating the epidermal growth factor receptor (EGFR) signaling cascade.     

Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.     

Studies on photoinduced effects in pulse-electrodeposited Ag/Hg-1212/CdSe hetero-nanostructures

Metal/superconductor/semiconductor (Ag/Hg-1212/CdSe) hetero-nanostructures have been fabricated using pulse-electrodeposition technique and are characterized by X-ray diffraction (XRD), full-width at half-maximum (FWHM) and scanning electron microscopy (SEM) studies. The junction capacitance of Ag/Hg-1212, Hg-1212/CdSe and Ag/Hg-1212/CdSe heterojunctions is measured in dark and under laser irradiation at room temperature. The nature of the junction formed and built-in-junction potentials were determined. The increase in carrier concentration across the junction due to photo-irradiation has been observed.