Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Lack of directed V alpha 14-J alpha 281 rearrangements in NK1+ T cells.

NK1.1+ T cells are an unusual subset of TCR alpha beta cells distinguished by their highly restricted V beta repertoire and predominant usage of an invariant V alpha 14-J alpha 281 chain. To assess whether a directed rearrangement mechanism could be responsible for this invariant alpha chain, we have analyzed V alpha 14 rearrangements by polymerase chain reaction and Southern blot in a panel of cloned T-T hybrids derived from thymic NK1.1+ T cells. As expected a high proportion (17/20) of the hybrids had rearranged V alpha 14 to J alpha 281. However, V alpha 14-J alpha 281 rearrangements always occurred on only one chromosome and were accompanied by other V alpha-J alpha rearrangements (not involving V alpha 14) on the homologous chromosome. These data argue that rigorous ligand selection rather than directed rearrangement is responsible for the high frequency of V alpha 14-J alpha 281 rearrangements in NK1.1+ T cells.

Absolute requirement for the pre-T cell receptor alpha chain during NK1.1+ TCRalphabeta cell development.

Most natural killer T (NKT) cells express a highly skewed alphabeta TCR repertoire, consisting of an invariant V alpha14-J alpha281 chain paired preferentially with a polyclonal Vbeta8.2 chain. This repertoire is positively selected by the monomorphic CD1d molecule expressed on cells of hematopoietic origin. The origin of NKT cells and their lineage relationship to conventional T cells is controversial. We show here that the development of NKT cells is absolutely dependent on expression of the pre-TCRalpha chain, in marked contrast to conventional T cells which arise in significant numbers even in the absence of a functional pre-TCR. Distinct developmental requirements for pre-TCR expression in the NKT and T cell lineages may reflect differences in the ability of the TCRalphabeta to substitute functionally for the pre-TCR in immature precursor cells.

Selective induction of NK cell proliferation and cytotoxicity by activated NKT cells.

NK T cells produce cytokines when their semi-invariant TCR engages glycolipids associated with CD1d. The physiological consequences of NKT cell activation remain controversial, although they have been implicated in control of autoimmunity, parasites and tumors. We show here that specific activation of NKT cells in liver and spleen leads to a rapid induction of extensive NK cell proliferation and cytotoxicity. This NK cell activation is dependent, at least in part, on IFN-gamma production by NKT cells and IL-12 production by antigen-presenting cells. Remarkably, activation of NK cells by NKT cells is highly selective, since bystander T and B lymphocytes show transient expression of activation markers but almost no proliferation. Collectively our data suggest that CD1d-dependent NKT cells regulate innate immunity by sampling blood-borne glycolipid antigens and rapidly activating NK cells.

Biased V beta usage in immature thymocytes is independent of DJ beta proximity and pT alpha pairing.

During thymus development, the TCR beta locus rearranges before the TCR alpha locus. Pairing of productively rearranged TCR beta-chains with an invariant pT alpha chain leads to the formation of a pre-TCR and subsequent expansion of immature pre-T cells. Essentially nothing is known about the TCR V beta repertoire in pre-T cells before or after the expression of a pre-TCR. Using intracellular staining, we show here that the TCR V beta repertoire is significantly biased at the earliest developmental stage in which VDJ beta rearrangement has occurred. Moreover (and in contrast to the V(H) repertoire in immature B cells), V beta repertoire biases in immature T cells do not reflect proximity of V beta gene segments to the DJ beta cluster, nor do they depend upon preferential V beta pairing with the pT alpha chain. We conclude that V gene repertoires in developing T and B cells are controlled by partially distinct mechanisms.

Visual representation of food in the brain : effects of repeated exposure and gut hormone secretion

The thesis at hand is concerned with the spatio-temporal brain mechanisms of visual food perception as investigated by electrical neuroimaging. Due to the increasing prevalence of obesity and its associated challenges for public health care, there is a need to better understand behavioral and brain processes underlying food perception and food-based decision-making. The first study (Study A) of this thesis was concerned with the role of repeated exposure to visual food cues. In our everyday lives we constantly and repeatedly encounter food and these exposures influence our food choices and preferences. In Study A, we therefore applied electrical neuroimaging analyses of visual evoked potentials to investigate the spatio-temporal brain dynamics linked to the repeated viewing of high- and low-energy food cues (published manuscript: "The role of energetic value in dynamic brain response adaptation during repeated food image viewing" (Lietti et al., 2012)). In this study, we found that repetitions differentially affect behavioral and brain mechanisms when high-energy, as opposed to low-energy foods and non-food control objects, were viewed. The representation of high-energy food remained invariant between initial and repeated exposures indicating that the sight of high-energy dense food induces less behavioral and neural adaptation than the sight of low-energy food and non-food control objects. We discuss this finding in the context of the higher salience (due to greater motivation and higher reward or hedonic valuation) of energy- dense food that likely generates a more mnemonically stable representation. In turn, this more invariant representation of energy-dense food is supposed to (partially) explain why these foods are over-consumed despite of detrimental health consequences. In Study Β we investigated food responsiveness in patients who had undergone Roux-en-Y gastric bypass surgery to overcome excessive obesity. This type of gastric bypass surgery is not only known to alter food appreciation, but also the secretion patterns of adipokines and gut peptides. Study Β aimed at a comprehensive and interdisciplinary investigation of differences along the gut-brain axis in bypass-operated patients as opposed to weight-matched non-operated controls. On the one hand, the spatio-temporal brain dynamics to the visual perception of high- vs. low-energy foods under differing states of motivation towards food intake (i.e. pre- and post-prandial) were assessed and compared between groups. On the other hand, peripheral gut hormone measures were taken in pre- and post-prandial nutrition state and compared between groups. In order to evaluate alterations in the responsiveness along the gut-brain-axis related to gastric bypass surgery, correlations between both measures were compared between both participant groups. The results revealed that Roux-en- Y gastric bypass surgery alters the spatio-temporal brain dynamics to the perception of high- and low-energy food cues, as well as the responsiveness along the gut-brain-axis. The potential role of these response alterations is discussed in relation to previously observed changes in physiological factors and food intake behavior post-Roux-en-Y gastric bypass surgery. By doing so, we highlight potential behavioral, neural and endocrine (i.e. gut hormone) targets for the future development of intervention strategies for deviant eating behavior and obesity. Together, the studies showed that the visual representation of foods in the brain is plastic and that modulations in neural activity are already noted at early stages of visual processing. Different factors of influence such as a repeated exposure, Roux-en-Y gastric bypass surgery, motivation (nutrition state), as well as the energy density of the visually perceived food were identified. En raison de la prévalence croissante de l'obésité et du défi que cela représente en matière de santé publique, une meilleure compréhension des processus comportementaux et cérébraux liés à la nourriture sont nécessaires. En particulier, cette thèse se concentre sur l'investigation des mécanismes cérébraux spatio-temporels liés à la perception visuelle de la nourriture. Nous sommes quotidiennement et répétitivement exposés à des images de nourriture. Ces expositions répétées influencent nos choix, ainsi que nos préférences alimentaires. La première étude (Study A) de cette thèse investigue donc l'impact de ces exposition répétée à des stimuli visuels de nourriture. En particulier, nous avons comparé la dynamique spatio-temporelle de l'activité cérébrale induite par une exposition répétée à des images de nourriture de haute densité et de basse densité énergétique. (Manuscrit publié: "The role of energetic value in dynamic brain response adaptation during repeated food image viewing" (Lietti et al., 2012)). Dans cette étude, nous avons pu constater qu'une exposition répétée à des images représentant de la nourriture de haute densité énergétique, par opposition à de la nourriture de basse densité énergétique, affecte les mécanismes comportementaux et cérébraux de manière différente. En particulier, la représentation neurale des images de nourriture de haute densité énergétique est similaire lors de l'exposition initiale que lors de l'exposition répétée. Ceci indique que la perception d'images de nourriture de haute densité énergétique induit des adaptations comportementales et neurales de moindre ampleur par rapport à la perception d'images de nourriture de basse densité énergétique ou à la perception d'une « catégorie contrôle » d'objets qui ne sont pas de la nourriture. Notre discussion est orientée sur les notions prépondérantes de récompense et de motivation qui sont associées à la nourriture de haute densité énergétique. Nous suggérons que la nourriture de haute densité énergétique génère une représentation mémorielle plus stable et que ce mécanisme pourrait (partiellement) être sous-jacent au fait que la nourriture de haute densité énergétique soit préférentiellement consommée. Dans la deuxième étude (Study Β) menée au cours de cette thèse, nous nous sommes intéressés aux mécanismes de perception de la nourriture chez des patients ayant subi un bypass gastrique Roux- en-Y, afin de réussir à perdre du poids et améliorer leur santé. Ce type de chirurgie est connu pour altérer la perception de la nourriture et le comportement alimentaire, mais également la sécrétion d'adipokines et de peptides gastriques. Dans une approche interdisciplinaire et globale, cette deuxième étude investigue donc les différences entre les patients opérés et des individus « contrôles » de poids similaire au niveau des interactions entre leur activité cérébrale et les mesures de leurs hormones gastriques. D'un côté, nous avons investigué la dynamique spatio-temporelle cérébrale de la perception visuelle de nourriture de haute et de basse densité énergétique dans deux états physiologiques différent (pre- et post-prandial). Et de l'autre, nous avons également investigué les mesures physiologiques des hormones gastriques. Ensuite, afin d'évaluer les altérations liées à l'intervention chirurgicale au niveau des interactions entre la réponse cérébrale et la sécrétion d'hormone, des corrélations entre ces deux mesures ont été comparées entre les deux groupes. Les résultats révèlent que l'intervention chirurgicale du bypass gastrique Roux-en-Y altère la dynamique spatio-temporelle de la perception visuelle de la nourriture de haute et de basse densité énergétique, ainsi que les interactions entre cette dernière et les mesures périphériques des hormones gastriques. Nous discutons le rôle potentiel de ces altérations en relation avec les modulations des facteurs physiologiques et les changements du comportement alimentaire préalablement déjà démontrés. De cette manière, nous identifions des cibles potentielles pour le développement de stratégies d'intervention future, au niveau comportemental, cérébral et endocrinien (hormones gastriques) en ce qui concerne les déviances du comportement alimentaire, dont l'obésité. Nos deux études réunies démontrent que la représentation visuelle de la nourriture dans le cerveau est plastique et que des modulations de l'activité neurale apparaissent déjà à un stade très précoce des mécanismes de perception visuelle. Différents facteurs d'influence comme une exposition repetee, le bypass gastrique Roux-en-Y, la motivation (état nutritionnel), ainsi que la densité énergétique de la nourriture qui est perçue ont pu être identifiés.

Education of Murine NK Cells Requires Both cis and trans Recognition of MHC Class I Molecules.

Although NK cells use invariant receptors to identify diseased cells, they nevertheless adapt to their environment, including the presence of certain MHC class I (MHC-I) molecules. This NK cell education, which is mediated by inhibitory receptors specific for MHC-I molecules, changes the responsiveness of activating NK cell receptors (licensing) and modifies the repertoire of MHC-I receptors used by NK cells. The fact that certain MHC-I receptors have the unusual capacity to recognize MHC-I molecules expressed by other cells (trans) and by the NK cell itself (cis) has raised the question regarding possible contributions of the two types of interactions to NK cell education. Although the analysis of an MHC-I receptor variant suggested a role for cis interaction for NK cell licensing, adoptive NK cell transfer experiments supported a key role for trans recognition. To reconcile some of these findings, we have analyzed the impact of cell type-specific deletion of an MHC-I molecule and of a novel MHC-I receptor variant on the education of murine NK cells when these mature under steady-state conditions in vivo. We find that MHC-I expression by NK cells (cis) and by T cells (trans), and MHC-I recognition in cis and in trans, are both needed for NK cell licensing. Unexpectedly, modifications of the MHC-I receptor repertoire are chiefly dependent on cis binding, which provides additional support for an essential role for this unconventional type of interaction for NK cell education. These data suggest that two separate functions of MHC-I receptors are needed to adapt NK cells to self-MHC-I.

Impact of normalization on miRNA microarray expression profiling.

Profiling miRNA levels in cells with miRNA microarrays is becoming a widely used technique. Although normalization methods for mRNA gene expression arrays are well established, miRNA array normalization has so far not been investigated in detail. In this study we investigate the impact of normalization on data generated with the Agilent miRNA array platform. We have developed a method to select nonchanging miRNAs (invariants) and use them to compute linear regression normalization coefficients or variance stabilizing normalization (VSN) parameters. We compared the invariants normalization to normalization by scaling, quantile, and VSN with default parameters as well as to no normalization using samples with strong differential expression of miRNAs (heart-brain comparison) and samples where only a few miRNAs are affected (by p53 overexpression in squamous carcinoma cells versus control). All normalization methods performed better than no normalization. Normalization procedures based on the set of invariants and quantile were the most robust over all experimental conditions tested. Our method of invariant selection and normalization is not limited to Agilent miRNA arrays and can be applied to other data sets including those from one color miRNA microarray platforms, focused gene expression arrays, and gene expression analysis using quantitative PCR.

Targeted expression of human CD1d in transgenic mice reveals independent roles for thymocytes and thymic APCs in positive and negative selection of Valpha14i NKT cells.

CD1d-dependent invariant Valpha14 (Valpha14i) NKT cells are innate T lymphocytes expressing a conserved semi-invariant TCR, consisting, in mice, of the invariant Valpha14-Jalpha18 TCR alpha-chain paired mostly with Vbeta8.2 and Vbeta7. The cellular requirements for thymic positive and negative selection of Valpha14i NKT cells are only partially understood. Therefore, we generated transgenic mice expressing human CD1d (hCD1d) either on thymocytes, mainly CD4+ CD8+ double positive, or on APCs, the cells implicated in the selection of Valpha14i NKT cells. In the absence of the endogenous mouse CD1d (mCD1d), the expression of hCD1d on thymocytes, but not on APCs, was sufficient to select Valpha14i NKT cells that proved functional when activated ex vivo with the Ag alpha-galactosyl ceramide. Valpha14i NKT cells selected by hCD1d on thymocytes, however, attained lower numbers than in control mice and expressed essentially Vbeta8.2. The low number of Vbeta8.2+ Valpha14i NKT cells selected by hCD1d on thymocytes was not reversed by the concomitant expression of mCD1d, which, instead, restored the development of Vbeta7+ Valpha14i NKT cells. Vbeta8.2+, but not Vbeta7+, NKT cell development was impaired in mice expressing both hCD1d on APCs and mCD1d. Taken together, our data reveal that selective CD1d expression by thymocytes is sufficient for positive selection of functional Valpha14i NKT cells and that both thymocytes and APCs may independently mediate negative selection.

VAX1 mutation associated with microphthalmia, corpus callosum agenesis and orofacial clefting-the first description of a VAX1 phenotype in humans.

Vax1 and Vax2 have been implicated in eye development and the closure of the choroid fissure in mice and zebrafish. We sequenced the coding exons of VAX1 and VAX2 in 70 patients with anophthalmia/microphthalmia. In VAX1, we observed homozygosity for two successive nucleotide substitutions c.453G>A and c.454C>A, predicting p.Arg152Ser, in a proband of Egyptian origin with microphthalmia, small optic nerves, cleft lip/palate and corpus callosum agenesis. This mutation affects an invariant residue in the homeodomain of VAX1 and was absent from 96 Egyptian controls. It is likely that the mutation results in a loss of function, as the mutation results in a phenotype similar to the Vax1 homozygous null mouse. We did not identify any mutations in VAX2. This is the first description of a phenotype associated with a VAX1 mutation in humans and establishes VAX1 as a new causative gene for anophthalmia/microphthalmia. ©2011 Wiley Periodicals, Inc.

NKT cells: In the beginning...

Invariant natural killer T (iNKT) cells as we know them today are a unique subset of mature T cells co-expressing a semi-invariant Valpha14/Vbeta8 TCR and surface markers characteristic of NK cells. The semi-invariant TCR on iNKT cells recognizes glycolipids bound to monomorphic CD1d molecules, leading to rapid cytokine production. The purpose of this historical perspective is to describe how a series of seemingly unrelated findings in the late 1980s and early 1990s crystallized in the discovery of iNKT cells. The story is told from a personal viewpoint, with a particular effort to place both breakthroughs and misinterpretations in the context of their era.

Quantization of energy and writhe in self-repelling knots

Probably the most natural energy functional to be considered for knotted strings is that given by electrostatic repulsion. In the absence of counter-charges, a charged, knotted string evolving along the energy gradient of electrostatic repulsion would progressively tighten its knotted domain into a point on a perfectly circular string. However, in the presence of charge screening self-repelling knotted strings can be stabilized. It is known that energy functionals in which repulsive forces between repelling charges grow inversely proportionally to the third or higher power of their relative distance stabilize self-repelling knots. Especially interesting is the case of the third power since the repulsive energy becomes scale invariant and does not change upon Mobius transformations (reflections in spheres) of knotted trajectories. We observe here that knots minimizing their repulsive Mobius energy show quantization of the energy and writhe (measure of chirality) within several tested families of knots.

Sustained activation and tumor targeting of NKT cells using a CD1d-anti-HER2-scFv fusion protein induce antitumor effects in mice

Invariant NKT (iNKT) cells are potent activators of DCs, NK cells, and T cells, and their antitumor activity has been well demonstrated. A single injection of the high-affinity CD1d ligand alpha-galactosylceramide (alphaGalCer) leads to short-lived iNKT cell activation followed, however, by long-term anergy, limiting its therapeutic use. In contrast, we demonstrated here that when alphaGalCer was loaded on a recombinant soluble CD1d molecule (alphaGalCer/sCD1d), repeated injections led to sustained iNKT and NK cell activation associated with IFN-gamma secretion as well as DC maturation in mice. Most importantly, when alphaGalCer/sCD1d was fused to a HER2-specific scFv antibody fragment, potent inhibition of experimental lung metastasis and established s.c. tumors was obtained when systemic treatment was started 2-7 days after the injection of HER2-expressing B16 melanoma cells. In contrast, administration of free alphaGalCer at this time had no effect. The antitumor activity of the CD1d-anti-HER2 fusion protein was associated with HER2-specific tumor localization and accumulation of iNKT, NK, and T cells at the tumor site. Targeting iNKT cells to the tumor site thus may activate a combined innate and adaptive immune response that may prove to be effective in cancer immunotherapy

iNKT/CD1d-antitumor immunotherapy significantly increases the efficacy of therapeutic CpG/peptide-based cancer vaccine.

BACKGROUND: Therapeutic cancer vaccines aim to boost the natural immunity against transformed cancer cells, and a series of adjuvants and co-stimulatory molecules have been proposed to enhance the immune response against weak self-antigens expressed on cancer cells. For instance, a peptide/CpG-based cancer vaccine has been evaluated in several clinical trials and was shown in pre-clinical studies to favor the expansion of effector T versus Tregs cells, resulting in a potent antitumor activity, as compared to other TLR ligands. Alternatively, the adjuvant activity of CD1d-restricted invariant NKT cells (iNKT) on the innate and adaptive immunity is well demonstrated, and several CD1d glycolipid ligands are under pre-clinical and clinical evaluation. Importantly, additive or even synergistic effects have been shown upon combined CD1d/NKT agonists and TLR ligands. The aim of the present study is to combine the activation and tumor targeting of activated iNKT, NK and T cells. METHODS: Activation and tumor targeting of iNKT cells via recombinant α-galactosylceramide (αGC)-loaded CD1d-anti-HER2 fusion protein (CD1d-antitumor) is combined or not with OVA peptide/CpG vaccine. Circulating and intratumoral NK and H-2Kb/OVA-specific CD8 responses are monitored, as well as the state of activation of dendritic cells (DC) with regard to activation markers and IL-12 secretion. The resulting antitumor therapy is tested against established tumor grafts of B16 melanoma cells expressing human HER2 and ovalbumin. RESULTS: The combined CD1d/iNKT antitumor therapy and CpG/peptide-based immunization leads to optimized expansion of NK and OVA-specific CD8 T cells (CTLs), likely resulting from the maturation of highly pro-inflammatory DCs as seen by a synergistic increase in serum IL-12. The enhanced innate and adaptive immune responses result in higher tumor inhibition that correlates with increased numbers of OVA-specific CTLs at the tumor site. Antibody-mediated depletion experiments further demonstrate that in this context, CTLs rather than NK cells are essential for the enhanced tumor inhibition. CONCLUSIONS: Altogether, our study in mice demonstrates that αGC/CD1d-antitumor fusion protein greatly increases the efficacy of a therapeutic CpG-based cancer vaccine, first as an adjuvant during T cell priming and second, as a therapeutic agent to redirect immune responses to the tumor site.

The role of energetic value in dynamic brain response adaptation during repeated food image viewing.

The repeated presentation of simple objects as well as biologically salient objects can cause the adaptation of behavioral and neural responses during the visual categorization of these objects. Mechanisms of response adaptation during repeated food viewing are of particular interest for better understanding food intake beyond energetic needs. Here, we measured visual evoked potentials (VEPs) and conducted neural source estimations to initial and repeated presentations of high-energy and low-energy foods as well as non-food images. The results of our study show that the behavioral and neural responses to food and food-related objects are not uniformly affected by repetition. While the repetition of images displaying low-energy foods and non-food modulated VEPs as well as their underlying neural sources and increased behavioral categorization accuracy, the responses to high-energy images remained largely invariant between initial and repeated encounters. Brain mechanisms when viewing images of high-energy foods thus appear less susceptible to repetition effects than responses to low-energy and non-food images. This finding is likely related to the superior reward value of high-energy foods and might be one reason why in particular high-energetic foods are indulged although potentially leading to detrimental health consequences.