A sigmoid functional response emerges when Cytotoxic T Lymphocytes start killing fresh target cells

Cytotoxic T lymphocyte (CTL)-mediated killing involves the formation of a synapse with a target cell, followed by delivery of perforin and granzymes. Previously, we derived a general functional response for CTL killing while considering that CTLs form stable synapses (i.e., single-stage) and that the number of conjugates remains at steady state. However, the killing of target cells sometimes requires multiple engagements (i.e., multistage). To study how multistage killing and a lack of steady state influence the functional response, we here analyze a set of differential equations as well as simulations employing the cellular Potts model, in both cases describing CTLs that kill target cells. We find that at steady state the total killing rate (i.e., the number of target cells killed by all CTLs) is well described by the previously derived double saturation function. Compared to single-stage killing, the total killing rate during multistage killing saturates at higher CTL and target cell densities. Importantly, when the killing is measured before the steady state is approached, a qualitatively different functional response emerges for two reasons: First, the killing signal of each CTL gets diluted over several targets and because this dilution effect is strongest at high target cell densities; this can result in a peak in the dependence of the total killing rate on the target cell density. Second, the total killing rate exhibits a sigmoid dependence on the CTL density when killing is a multistage process, because it takes typically more than one CTL to kill a target. In conclusion, a sigmoid dependence of the killing rate on the CTLs during initial phases of killing may be indicative of a multistage killing process. Observation of a sigmoid functional response may thus arise from a dilution effect and is not necessarily due to cooperative behavior of the CTLs

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Mathematical modeling provides kinetic details of the human immune response to vaccination

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data

Standing genetic variation and the evolution of drug resistance in HIV

Drug resistance remains a major problem for the treatment of HIV. Resistance can occur due to mutations that were present before treatment starts or due to mutations that occur during treatment. The relative importance of these two sources is unknown. We study three different situations in which HIV drug resistance may evolve: starting triple-drug therapy, treatment with a single dose of nevirapine and interruption of treatment. For each of these three cases good data are available from literature, which allows us to estimate the probability that resistance evolves from standing genetic variation. Depending on the treatment we find probabilities of the evolution of drug resistance due to standing genetic variation between 0 and 39%. For patients who start triple-drug combination therapy, we find that drug resistance evolves from standing genetic variation in approximately 6% of the patients. We use a population-dynamic and population-genetic model to understand the observations and to estimate important evolutionary parameters. We find that both, the effective population size of the virus before treatment, and the fitness of the resistant mutant during treatment, are key-parameters that determine the probability that resistance evolves from standing genetic variation. Importantly, clinical data indicate that both of these parameters can be manipulated by the kind of treatment that is used.Comment: 33 pages 6 figure

Taking Multiple Infections of Cells and Recombination into Account Leads to Small Within-Host Effective-Population-Size Estimates of HIV-1

Whether HIV-1 evolution in infected individuals is dominated by deterministic or stochastic effects remains unclear because current estimates of the effective population size of HIV-1 in vivo, Ne, are widely varying. Models assuming HIV-1 evolution to be neutral estimate Ne∼102–104, smaller than the inverse mutation rate of HIV-1 (∼105), implying the predominance of stochastic forces. In contrast, a model that includes selection estimates Ne>105, suggesting that deterministic forces would hold sway. The consequent uncertainty in the nature of HIV-1 evolution compromises our ability to describe disease progression and outcomes of therapy. We perform detailed bit-string simulations of viral evolution that consider large genome lengths and incorporate the key evolutionary processes underlying the genomic diversification of HIV-1 in infected individuals, namely, mutation, multiple infections of cells, recombination, selection, and epistatic interactions between multiple loci. Our simulations describe quantitatively the evolution of HIV-1 diversity and divergence in patients. From comparisons of our simulations with patient data, we estimate Ne∼103–104, implying predominantly stochastic evolution. Interestingly, we find that Ne and the viral generation time are correlated with the disease progression time, presenting a route to a priori prediction of disease progression in patients. Further, we show that the previous estimate of Ne>105 reduces as the frequencies of multiple infections of cells and recombination assumed increase. Our simulations with Ne∼103–104 may be employed to estimate markers of disease progression and outcomes of therapy that depend on the evolution of viral diversity and divergence

Experimental investigations on the drilling parameters to minimize delamination and taperness of hybrid GFRP/Al₂O₃ composites by using ANOVA approach

Purpose Drilling holes in composite materials is a complex and challenging process because of their intrinsic anisotropic characteristics and unevenness compared to conventional metals. Hybridization of composites enhances the strength and hardness of the material but makes it more difficult to drill a hole in it. The purpose of this study is to optimize the drilling to minimize the delamination and taperness of hybrid glass fiber reinforced plastic (GFRP)/Al2O3 composites. Design/methodology/approach The present study investigates the impact of drilling parameters on delamination of the drilled hole and the taperness of the hole on hybrid GFRP/Al2O3. Optimum drilling conditions for minimizing delamination and taperness of the hole are determined to enhance the hole quality. Feed (f), speed (N) and drill diameter (D) are the parameters taken into consideration for drilling operation. By applying Taguchi’s signal-to-noise ratio analysis, process parameters have been optimized to reduce the delamination and taperness of holes on Hybrid GFRP/Al2O3 composites. The effect of process parameters was analyzed using the analysis of variance method. Findings The investigational results confirmed that the delamination is positively affected by speed, drill diameter and feed rate. Also, the taperness of the hole is positively affected by the drill diameter. Regression-based models were developed to predict the delamination and taperness of the hole matched with the experimental results, which are attained with an order of 95% and 97%. Originality/value Minimum delamination was found at the optimum condition of drill diameter 10 mm, feed at 0.225 mm/rev and the speed at 151 rpm and minimum taperness were found at the optimum condition of drill diameter 10 mm, feed at level 0.3 mm/rev and speed at 86 rpm for hybrid laminate composite (S-glass+ GFRP/Al2O3) were evaluated. </jats:sec

DIAGNOSIS &amp; MANAGEMENT OF ALLERGIC FUNGAL SINUSITIS

BACKGROUND Chronic sinusitis is one of the common diagnosis in ENT practice. Allergic fungal sinusitis is a clinical entity with characteristic clinical, radiographic and histopathological findings. Allergic fungal sinusitis and eosinophilic mucin rhinosinusitis can easily be misdiagnosed. AIM OF STUDY A prospective clinical study of allergic Fungal Rhinosinusitis to use diagnostic criteria to confirm the disease with Radiological, Pathological & Microbiological investigations and their management. MATERIALS & METHODS A prospective study of allergic Fungal Rhinosinusitis in 2 years from November 2011 to October 2013. Among the patients who attended the ENT OPD during this period, 21 patients with symptoms and signs suggestive of Allergic Fungal Rhinosinusitis are selected