The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu

Random geometric complexes

We study the expected topological properties of Cech and Vietoris-Rips complexes built on i.i.d. random points in R^d. We find higher dimensional analogues of known results for connectivity and component counts for random geometric graphs. However, higher homology H_k is not monotone when k > 0. In particular for every k > 0 we exhibit two thresholds, one where homology passes from vanishing to nonvanishing, and another where it passes back to vanishing. We give asymptotic formulas for the expectation of the Betti numbers in the sparser regimes, and bounds in the denser regimes. The main technical contribution of the article is in the application of discrete Morse theory in geometric probability.Comment: 26 pages, 3 figures, final revisions, to appear in Discrete & Computational Geometr

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Trastuzumab Mediated T-Cell Response against HER-2/Neu Overexpressing Esophageal Adenocarcinoma Depends on Intact Antigen Processing Machinery

BACKGROUND: Esophageal adenocarcinoma (EAC) is a highly aggressive disease with poor prognosis, which frequently exhibits HER-2 gene amplification. Trastuzumab, the humanized antibody against HER-2, has potent growth inhibitory effects on HER-2 overexpressing cancers. One effect of trastuzumab is that it causes HER-2 receptor internalization and degradation, enhancing presentation of HER-2 epitopes on MHC-Class I molecules. This enhances the ability of HER-2 specific cytotoxic T lymphocytes (CTLs) to recognize and kill cancer cells. Novel strategies targeting the HER-2 receptor either directly by trastuzumab and/or indirectly by inducing a CTL response against HER-2 epitopes with, for instance, DC immunotherapy and consequently combining these strategies might prove to be very effective. METHODOLOGY/PRINCIPAL FINDINGS: In this study we report that trastuzumab has potent growth inhibitory effects on two HER-2 overexpressing EAC cell lines OE33 and OE19. However, we found that trastuzumab and HER-2 specific CTLs act synergistically in inducing tumor lysis in OE33 but not in OE19. We discovered that in OE19 this deficient response is due to a down-regulation of the Transporter Associated with Antigen Processing-2 (TAP-2). TAP-2 is an important member of the Antigen Processing Machinery (APM), and is one of the essential elements for loading antigens on MHC class I molecules. Importantly, we demonstrated that by inducing re-expression of TAP-2 in OE19 with INF-γ treatment or by incubating the cells with INF-γ producing CTLs, the specific anti HER-2 CTL tumor lysis response and synergistic effect with trastuzumab can be restored. CONCLUSION: An inefficient response of HER-2 overexpressing EAC to trastuzumab and/or DC immunotherapy can be due to a down-regulated TAP-2 expression and thus a deficient APM. Future studies combining trastuzumab with IFN-γ and/or immune-therapies inducing potent anti HER-2 CTL responses could lead to an effective combinatorial strategy for successful treatment of HER-2 overexpressing but APM defective cancer

Local therapy of cancer with free IL-2

This is a position paper about the therapeutic effects of locally applied free IL-2 in the treatment of cancer. Local therapy: IL-2 therapy of cancer was originally introduced as a systemic therapy. This therapy led to about 20% objective responses. Systemic therapy however was very toxic due to the vascular leakage syndrome. Nevertheless, this treatment was a break-through in cancer immunotherapy and stimulated some interesting questions: Supposing that the mechanism of IL-2 treatment is both proliferation and tumoricidal activity of the tumor infiltrating cells, then locally applied IL-2 should result in a much higher local IL-2 concentration than systemic IL-2 application. Consequently a greater beneficial effect could be expected after local IL-2 application (peritumoral = juxtatumoral, intratumoral, intra-arterial, intracavitary, or intratracheal = inhalation). Free IL-2: Many groups have tried to prepare a more effective IL-2 formulation than free IL-2. Examples are slow release systems, insertion of the IL-2 gene into a tumor cell causing prolonged IL-2 release. However, logistically free IL-2 is much easier to apply; hence we concentrated in this review and in most of our experiments on the use of free IL-2. Local therapy with free IL-2 may be effective against transplanted tumors in experimental animals, and against various spontaneous carcinomas, sarcomas, and melanoma in veterinary and human cancer patients. It may induce rejection of very large, metastasized tumor loads, for instance advanced clinical tumors. The effects of even a single IL-2 application may be impressive. Not each tumor or tumor type is sensitive to local IL-2 application. For instance transplanted EL4 lymphoma or TLX9 lymphoma were not sensitive in our hands. Also the extent of sensitivity differs: In Bovine Ocular Squamous Cell Carcinoma (BOSCC) often a complete regression is obtained, whereas with the Bovine Vulval Papilloma and Carcinoma Complex (BVPCC) mainly stable disease is attained. Analysis of the results of local IL-2 therapy in 288 cases of cancer in human patients shows that there were 27% Complete Regressions (CR), 23% Partial Regressions (PR), 18% Stable Disease (SD), and 32% Progressive Disease (PD). In all tumors analyzed, local IL-2 therapy was more effective than systemic IL-2 treatment. Intratumoral IL-2 applications are more effective than peritumoral application or application at a distant site. Tumor regression induced by intratumoral IL-2 application may be a fast process (requiring about a week) in the case of a highly vascular tumor since IL-2 induces vascular leakage/edema and consequently massive tumor necrosis. The latter then stimulates an immune response. In less vascular tumors or less vascular tumor sites, regression may require 9–20 months; this regression is mainly caused by a cytotoxic leukocyte reaction. Hence the disadvantageous vascular leakage syndrome complicating systemic treatment is however advantageous in local treatment, since local edema may initiate tumor necrosis. Thus the therapeutic effect of local IL-2 treatment is not primarily based on tumor immunity, but tumor immunity seems to be useful as a secondary component of the IL-2 induced local processes. If local IL-2 is combined with surgery, radiotherapy or local chemotherapy the therapeutic effect is usually greater than with either therapy alone. Hence local free IL-2 application can be recommended as an addition to standard treatment protocols. Local treatment with free IL-2 is straightforward and can readily be applied even during surgical interventions. Local IL-2 treatment is usually without serious side effects and besides minor complaints it is generally well supported. Only small quantities of IL-2 are required. Hence the therapy is relatively cheap. A single IL-2 application of 4.5 million U IL-2 costs about 70 Euros. Thus combined local treatment may offer an alternative in those circumstances when more expensive forms of treatment are not available, for instance in resource poor countries

Glia-Pinealocyte Network: The Paracrine Modulation of Melatonin Synthesis by Tumor Necrosis Factor (TNF)

The pineal gland, a circumventricular organ, plays an integrative role in defense responses. The injury-induced suppression of the pineal gland hormone, melatonin, which is triggered by darkness, allows the mounting of innate immune responses. We have previously shown that cultured pineal glands, which express toll-like receptor 4 (TLR4) and tumor necrosis factor receptor 1 (TNFR1), produce TNF when challenged with lipopolysaccharide (LPS). Here our aim was to evaluate which cells present in the pineal gland, astrocytes, microglia or pinealocytes produced TNF, in order to understand the interaction between pineal activity, melatonin production and immune function. Cultured pineal glands or pinealocytes were stimulated with LPS. TNF content was measured using an enzyme-linked immunosorbent assay. TLR4 and TNFR1 expression were analyzed by confocal microscopy. Microglial morphology was analyzed by immunohistochemistry. In the present study, we show that although the main cell types of the pineal gland (pinealocytes, astrocytes and microglia) express TLR4, the production of TNF induced by LPS is mediated by microglia. This effect is due to activation of the nuclear factor kappa B (NF-kB) pathway. In addition, we observed that LPS activates microglia and modulates the expression of TNFR1 in pinealocytes. As TNF has been shown to amplify and prolong inflammatory responses, its production by pineal microglia suggests a glia-pinealocyte network that regulates melatonin output. The current study demonstrates the molecular and cellular basis for understanding how melatonin synthesis is regulated during an innate immune response, thus our results reinforce the role of the pineal gland as sensor of immune status

Measurement of melatonin in body fluids: Standards, protocols and procedures

Abstract: The circadian rhythm of melatonin in saliva or plasma, or of the melatonin metabolite 6‐ sulphatoxymelatonin in urine, is a defining feature of suprachiasmatic nucleus function, the endogenous oscillatory pacemaker. These measurements are useful to evaluate problems related to the onset or offset of sleep and for assessing phase delays or advances of rhythms in entrained individuals. Additionally, they have become an important tool for psychiatric diagnosis, its use being recommended for phase typing in patients suffering from sleep and mood disorders. Thus, the development of sensitive and selective methods for the precise detection of melatonin in tissues and fluids of animals emerges as necessary. Due to its low concentration and the co‐existence of many other endogenous compounds in blood, the determination of melatonin has been an analytical challenge. This review discusses current methodologies employed for detection and quantification of melatonin in biological fluids and tissues

Age-Related Changes in the Daily Rhythm of Photoreceptor Functioning and Circuitry in a Melatonin-Proficient Mouse Strain

Retinal melatonin is involved in the modulation of many important retinal functions. Our previous studies have shown that the viability of photoreceptors and ganglion cells is reduced during aging in mice that lack melatonin receptor type 1. This demonstrates that melatonin signaling is important for the survival of retinal neurons. In the present study, we investigate the effects of aging on photoreceptor physiology and retinal organization in CH3-f+/+ mice, a melatonin proficient mouse strain. Our data indicate that the amplitude of the a and b waves of the scotopic and photopic electroretinogram decreases with age. Moreover, the daily rhythm in the amplitude of the a- and b- waves is lost during the aging process. Similarly, the scotopic threshold response is significantly affected by aging, but only when it is measured during the night. Interestingly, the changes observed in the ERGs are not paralleled by relevant changes in retinal morphological features, and administration of exogenous melatonin does not affect the ERGs in C3H-f+/+ at 12 months of age. This suggests that the responsiveness of the photoreceptors to exogenous melatonin is reduced during aging