CD8 T-cell induction against vascular endothelial growth factor receptor 2 by Salmonella for vaccination purposes against a murine melanoma.

The Salmonella type III secretion system (T3SS) efficiently translocates heterologous proteins into the cytosol of eukaryotic cells. This leads to an antigen-specific CD8 T-cell induction in mice orally immunized with recombinant Salmonella. Recently, we have used Salmonella's T3SS as a prophylactic and therapeutic intervention against a murine fibrosarcoma. In this study, we constructed a recombinant Salmonella strain translocating the immunogenic H-2D(b)-specific CD8 T-cell epitope VILTNPISM (KDR2) from the murine vascular endothelial growth factor receptor 2 (VEGFR2). VEGFR2 is a member of the tyrosine protein kinase family and is upregulated on proliferating endothelial cells of the tumor vasculature. After single orogastric vaccination, we detected significant numbers of KDR2-tetramer-positive CD8 T cells in the spleens of immunized mice. The efficacy of these cytotoxic T cells was evaluated in a prophylactic setting to protect mice from challenges with B16F10 melanoma cells in a flank tumor model, and to reduce dissemination of spontaneous pulmonary melanoma metastases. Vaccinated mice revealed a reduction of angiogenesis by 62% in the solid tumor and consequently a significant decrease of tumor growth as compared to non-immunized mice. Moreover, in the lung metastasis model, immunization with recombinant Salmonella resulted in a reduction of the metastatic melanoma burden by approximately 60%

Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems

In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume in Regular and Chaotic Dynamics in honor of Richard Cushma

Vanishing Twist near Focus-Focus Points

We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-momentum map are spirals determined by the eigenvalue of the equilibrium. From this representation of the rotation number we derive that the twist condition for the isoenergetic KAM condition vanishes on a curve in the image of the energy-momentum map that is transversal to the line of constant energy. In contrast to this we also show that the frequency map is non-degenerate for every point in a neighborhood of a focus-focus point.Comment: 13 page

KAM \`{a} la R

Recently R\"ussmann proposed a new new variant of KAM theory based on a slowly converging iteration scheme. It is the purpose of this note to make this scheme accessible in an even simpler setting, namely for analytic perturbations of constant vector fields on a torus. As a side effect the result may be the shortest complete KAM proof for perturbations of integrable vector fields available so far.Comment: 11 pages, version 2.

A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Optimal stability and instability for near-linear Hamiltonians

In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover, in the same spirit as the notion of KAM stable integrable Hamiltonians, we will introduce a notion of effectively stable integrable Hamiltonians, conjecture a characterization of these Hamiltonians and show that our result prove this conjecture in the linear case

Holomorphic linearization of commuting germs of holomorphic maps

Let $f_1, ..., f_h$ be $h\ge 2$ germs of biholomorphisms of \C^n fixing the origin. We investigate the shape a (formal) simultaneous linearization of the given germs can have, and we prove that if $f_1, ..., f_h$ commute and their linear parts are almost simultaneously Jordanizable then they are simultaneously formally linearizable. We next introduce a simultaneous Brjuno-type condition and prove that, in case the linear terms of the germs are diagonalizable, if the germs commutes and our Brjuno-type condition holds, then they are holomorphically simultaneously linerizable. This answers to a multi-dimensional version of a problem raised by Moser.Comment: 24 pages; final version with erratum (My original paper failed to cite the work of L. Stolovitch [ArXiv:math/0506052v2]); J. Geom. Anal. 201

Aspects of the planetary Birkhoff normal form

The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the dynamics of this problem. Remarkably, it allowed to give a {\sl direct} proof of the celebrated Arnold's Theorem [V. I. Arnold. Uspehi Math. Nauk. 1963] on the stability of planetary motions. In this paper, using a "ad hoc" set of symplectic variables, we develop an asymptotic formula for this normal form that may turn to be useful in applications. As an example, we provide two very simple applications to the three-body problem: we prove a conjecture by [V. I. Arnold. cit] on the "Kolmogorov set"of this problem and, using Nehoro{\v{s}}ev Theory [Nehoro{\v{s}}ev. Uspehi Math. Nauk. 1977], we prove, in the planar case, stability of all planetary actions over exponentially-long times, provided mean--motion resonances are excluded. We also briefly discuss perspectives and problems for full generalization of the results in the paper.Comment: 44 pages. Keywords: Averaging Theory, Birkhoff normal form, Nehoro{\v{s}}ev Theory, Planetary many--body problem, Arnold's Theorem on the stability of planetary motions, Properly--degenerate kam Theory, steepness. Revised version, including Reviewer's comments. Typos correcte

The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems

The Fermi-Pasta-Ulam $\alpha$-model of harmonic oscillators with cubic anharmonic interactions is studied from a statistical mechanical point of view. Systems of N= 32 to 128 oscillators appear to be large enough to suggest statistical mechanical behavior. A key element has been a comparison of the maximum Lyapounov coefficient $\lambda_{max}$ of the FPU $\alpha$-model and that of the Toda lattice. For generic initial conditions, $\lambda_{max}(t)$ is indistinguishable for the two models up to times that increase with decreasing energy (at fixed N). Then suddenly a bifurcation appears, which can be discussed in relation to the breakup of regular, soliton-like structures. After this bifurcation, the $\lambda_{max}$ of the FPU model appears to approach a constant, while the $\lambda_{max}$ of the Toda lattice appears to approach zero, consistent with its integrability. This suggests that for generic initial conditions the FPU $\alpha$-model is chaotic and will therefore approach equilibrium and equipartition of energy. There is, however, a threshold energy density $\epsilon_c(N)\sim 1/N^2$, below which trapping occurs; here the dynamics appears to be regular, soliton-like and the approach to equilibrium - if any - takes longer than observable on any available computer. Above this threshold the system appears to behave in accordance with statistical mechanics, exhibiting an approach to equilibrium in physically reasonable times. The initial conditions chosen by Fermi, Pasta and Ulam were not generic and below threshold and would have required possibly an infinite time to reach equilibrium.Comment: 24 pages, REVTeX, 8 PostScript figures. Published versio

Direct Injection of Functional Single-Domain Antibodies from E. coli into Human Cells

Intracellular proteins have a great potential as targets for therapeutic antibodies (Abs) but the plasma membrane prevents access to these antigens. Ab fragments and IgGs are selected and engineered in E. coli and this microorganism may be also an ideal vector for their intracellular delivery. In this work we demonstrate that single-domain Ab (sdAbs) can be engineered to be injected into human cells by E. coli bacteria carrying molecular syringes assembled by a type III protein secretion system (T3SS). The injected sdAbs accumulate in the cytoplasm of HeLa cells at levels ca. 105–106 molecules per cell and their functionality is shown by the isolation of sdAb-antigen complexes. Injection of sdAbs does not require bacterial invasion or the transfer of genetic material. These results are proof-of-principle for the capacity of E. coli bacteria to directly deliver intracellular sdAbs (intrabodies) into human cells for analytical and therapeutic purposes