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

Effect of innate and adaptive immune mechanisms on treatment regimens in an AIDS-related Kaposi's Sarcoma model

Kaposi Sarcoma (KS) is the most common AIDS-defining cancer, even as HIV-positive people live longer. Like other herpesviruses, human herpesvirus-8 (HHV-8) establishes a lifelong infection of the host that in association with HIV infection may develop at any time during the illness. With the increasing global incidence of KS, there is an urgent need of designing optimal therapeutic strategies for HHV-8-related infections. Here we formulate two models with innate and adaptive immune mechanisms, relevant for non-AIDS KS (NAKS) and AIDS-KS, where the initial condition of the second model is given by the equilibrium state of the first one. For the model with innate mechanism (MIM), we define an infectivity resistance threshold that will determine whether the primary HHV-8 infection of B-cells will progress to secondary infection of progenitor cells, a concept relevant for viral carriers in the asymptomatic phase. The optimal control strategy has been employed to obtain treatment efficacy in case of a combined antiretroviral therapy (cART). For the MIM we have shown that KS therapy alone is capable of reducing the HHV-8 load. In the model with adaptive mechanism (MAM), we show that if cART is administered at optimal levels, that is, 0.48 for protease inhibitors, 0.79 for reverse transcriptase inhibitors and 0.25 for KS therapy, both HIV-1 and HHV-8 can be reduced. The predictions of these mathematical models have the potential to offer more effective therapeutic interventions in the treatment of NAKS and AIDS-KS

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

Macrophage and neutrophil interactions in the pancreatic tumor microenvironment drive the pathogenesis of pancreatic cancer

Despite modest improvements in survival in recent years, pancreatic adenocarcinoma remains a deadly disease with a 5-year survival rate of only 9%. These poor outcomes are driven by failure of early detection, treatment resistance, and propensity for early metastatic spread. Uncovering innovative therapeutic modalities to target the resistance mechanisms that make pancreatic cancer largely incurable are urgently needed. In this review, we discuss the immune composition of pancreatic tumors, including the counterintuitive fact that there is a significant inflammatory immune infiltrate in pancreatic cancer yet anti-tumor mechanisms are subverted and immune behaviors are suppressed. Here, we emphasize how immune cell interactions generate tumor progression and treatment resistance. We narrow in on tumor macrophage (TAM) spatial arrangement, polarity/function, recruitment, and origin to introduce a concept where interactions with tumor neutrophils (TAN) perpetuate the microenvironment. The sequelae of macrophage and neutrophil activities contributes to tumor remodeling, fibrosis, hypoxia, and progression. We also discuss immune mechanisms driving resistance to standard of care modalities. Finally, we describe a cadre of treatment targets, including those intended to overcome TAM and TAN recruitment and function, to circumvent barriers presented by immune infiltration in pancreatic adenocarcinoma

Single-nucleus RNA sequencing identifies new classes of proximal tubular epithelial cells in kidney fibrosis

Background Proximal tubular cells (PTCs) are the most abundant cell type in the kidney. PTCs are central to normal kidney function and to regeneration versus organ fibrosis following injury. This study used single-nucleus RNA sequencing (snRNAseq) to describe the phenotype of PTCs in renal fibrosis. Methods Kidneys were harvested from naïve mice and from mice with renal fibrosis induced by chronic aristolochic acid administration. Nuclei were isolated using Nuclei EZ Lysis buffer. Libraries were prepared on the 10× platform, and snRNAseq was completed using the Illumina NextSeq 550 System. Genome mapping was carried out with high-performance computing. Results A total of 23,885 nuclei were analyzed. PTCs were found in five abundant clusters, mapping to S1, S1–S2, S2, S2-cortical S3, and medullary S3 segments. Additional cell clusters (“new PTC clusters”) were at low abundance in normal kidney and in increased number in kidneys undergoing regeneration/fibrosis following injury. These clusters exhibited clear molecular phenotypes, permitting labeling as proliferating, New-PT1, New-PT2, and (present only following injury) New-PT3. Each cluster exhibited a unique gene expression signature, including multiple genes previously associated with renal injury response and fibrosis progression. Comprehensive pathway analyses revealed metabolic reprogramming, enrichment of cellular communication and cell motility, and various immune activations in new PTC clusters. In ligand-receptor analysis, new PTC clusters promoted fibrotic signaling to fibroblasts and inflammatory activation to macrophages. Conclusions These data identify unrecognized PTC phenotype heterogeneity and reveal novel PTCs associated with kidney fibrosis