Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type

summary:In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction $$\ddot{u}= - \gamma \dot{u} + m(\|\nabla u\|^2) \Delta u - \delta |u|^{\alpha }u + f,$$ which is known as degenerate if $m(\cdot )\ge 0$, and non-degenerate if $m(\cdot )\ge m_0 > 0$. We would like to point out that, to the author's knowledge, exponential decay for this type of equations has been studied just for the special cases of $\alpha$. Our aim is to extend the validity of previous results in [5] to $\alpha \ge 0$ both to the degenerate and non-degenerate cases of $m$. We extend our results to equations with $\Delta^2$

Co-receptor CD8-mediated modulation of T-cell receptor functional sensitivity and epitope recognition degeneracy

The interaction between T-cell receptors (TCRs) and peptide epitopes is highly degenerate: a TCR is capable of interacting productively with a wide range of different peptide ligands, involving not only cross-reactivity proper (similar epitopes elicit strong responses), but also polyspecificity (ligands with distinct physicochemical properties are capable of interacting with the TCR). Degeneracy does not gainsay the fact that TCR recognition is fundamentally specific: for the vast majority of ligands, the functional sensitivity of a given TCR is virtually null whereas this TCR has an appreciable functional sensitivity only for a minute fraction of all possible ligands. Degeneracy can be described mathematically as the probability that the functional sensitivity, of a given TCR to a randomly selected ligand, exceeds a set value. Variation of this value generates a statistical distribution that characterizes TCR degeneracy. This distribution can be modeled on the basis of a Gaussian distribution for the TCR/ligand dissociation energy. The kinetics of the TCR and the MHCI molecule can be used to transform this underlying Gaussian distribution into the observed distribution of functional sensitivity values. In the present paper, the model is extended by accounting explicitly for the kinetics of the interaction between the co-receptor and the MHCI molecule. We show that T-cells can modulate the level of degeneracy by varying the density of co-receptors on the cell surface. This could allow for an analog of avidity maturation during incipient T-cell responses

Systems approaches to cell culture-derived extracellular vesicles for acute kidney injury therapy: Prospects and challenges

Acute kidney injury (AKI) is a heterogeneous syndrome, comprising diverse etiologies of kidney insults that result in high mortality and morbidity if not well managed. Although great efforts have been made to investigate underlying pathogenic mechanisms of AKI, there are limited therapeutic strategies available. Extracellular vesicles (EV) are membrane-bound vesicles secreted by various cell types, which can serve as cell-free therapy through transfer of bioactive molecules. In this review, we first overview the AKI syndrome and EV biology, with a particular focus on the technical aspects and therapeutic application of cell culture-derived EVs. Second, we illustrate how multi-omic approaches to EV miRNA, protein, and genomic cargo analysis can yield new insights into their mechanisms of action and address unresolved questions in the field. We then summarize major experimental evidence regarding the therapeutic potential of EVs in AKI, which we subdivide into stem cell and non-stem cell-derived EVs. Finally, we highlight the challenges and opportunities related to the clinical translation of animal studies into human patients

Systems Biology Approaches for the Improvement of Oncolytic Virus-Based Immunotherapies

Oncolytic virus (OV)-based immunotherapy is mainly dependent on establishing an efficient cell-mediated antitumor immunity. OV-mediated antitumor immunity elicits a renewed antitumor reactivity, stimulating a T-cell response against tumor-associated antigens (TAAs) and recruiting natural killer cells within the tumor microenvironment (TME). Despite the fact that OVs are unspecific cancer vaccine platforms, to further enhance antitumor immunity, it is crucial to identify the potentially immunogenic T-cell restricted TAAs, the main key orchestrators in evoking a specific and durable cytotoxic T-cell response. Today, innovative approaches derived from systems biology are exploited to improve target discovery in several types of cancer and to identify the MHC-I and II restricted peptide repertoire recognized by T-cells. Using specific computation pipelines, it is possible to select the best tumor peptide candidates that can be efficiently vectorized and delivered by numerous OV-based platforms, in order to reinforce anticancer immune responses. Beyond the identification of TAAs, system biology can also support the engineering of OVs with improved oncotropism to reduce toxicity and maintain a sufficient portion of the wild-type virus virulence. Finally, these technologies can also pave the way towards a more rational design of armed OVs where a transgene of interest can be delivered to TME to develop an intratumoral gene therapy to enhance specific immune stimuli

Responses of Salmonella biofilms to oxidizing biocides: evidence of spatial clustering

The spatial organization of biofilm bacterial communities can be influenced by several factors, including growth conditions and challenge with antimicrobials. Differential survival of clusters of cells within biofilms has been observed. In this work, we present a variety of methods to identify, quantify and statistically analyse clusters of live cells from images of two Salmonella strains with differential biofilm forming capacity exposed to three oxidizing biocides. With a support vector machine approach, we showed spatial separation between the two strains, and, using statistical testing and high‐performance computing (HPC), we determined conditions which possess an inherent cluster structure. Our results indicate that there is a relationship between biocide potency and inherent biofilm formation capacity with the tendency to select for spatial clusters of survivors. There was no relationship between positions of clusters of live or dead cells within stressed biofilms. This work identifies an approach to robustly quantify clusters of physiologically distinct cells within biofilms and suggests work to understand how clusters form and survive is needed. Significance statement: Control of biofilm growth remains a major challenge and there is considerable uncertainty about how bacteria respond to disinfection within a biofilm and how clustering of cells impacts survival. We have developed a methodological approach to identify and statistically analyse clusters of surviving cells in biofilms after biocide challenge. This approach can be used to understand bacterial behaviour within biofilms under stress and is widely applicable

Hotspot autoimmune T cell receptor binding underlies pathogen and insulin peptide cross-reactivity

The cross-reactivity of T cells with pathogen- and self-derived peptides has been implicated as a pathway involved in the development of autoimmunity. However, the mechanisms that allow the clonal T cell antigen receptor (TCR) to functionally engage multiple peptide–major histocompatibility complexes (pMHC) are unclear. Here, we studied multiligand discrimination by a human, preproinsulin reactive, MHC class-I–restricted CD8+ T cell clone (1E6) that can recognize over 1 million different peptides. We generated high-resolution structures of the 1E6 TCR bound to 7 altered peptide ligands, including a pathogen-derived peptide that was an order of magnitude more potent than the natural self-peptide. Evaluation of these structures demonstrated that binding was stabilized through a conserved lock-and-key–like minimal binding footprint that enables 1E6 TCR to tolerate vast numbers of substitutions outside of this so-called hotspot. Highly potent antigens of the 1E6 TCR engaged with a strong antipathogen-like binding affinity; this engagement was governed though an energetic switch from an enthalpically to entropically driven interaction compared with the natural autoimmune ligand. Together, these data highlight how T cell cross-reactivity with pathogen-derived antigens might break self-tolerance to induce autoimmune disease