Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Early marketing matters:a time-varying parameter approach to persistence modeling

Are persistent marketing effects most likely to appear right after the introduction of a product? The authors give an affirmative answer to this question by developing a model that explicitly reports how persistent and transient marketing effects evolve over time. The proposed model provides managers with a valuable tool to evaluate their allocation of marketing expenditures over time. An application of the model to many pharmaceutical products, estimated through (exact initial) Kalman filtering, indicates that both persistent and transient effects occur predominantly immediately after a brand's introduction. Subsequently, the size of the effects declines. The authors theoretically and empirically compare their methodology with methodology based on unit root testing and demonstrate that the need for unit root tests creates difficulties in applying conventional persistence modeling. The authors recommend that marketing models should either accommodate persistent effects that change over time or be applied to mature brands or limited time windows only.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

Modelling stock volatilities during financial crises:a time varying coefficient approach

We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying model which provides the platform upon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure.

Exploring the biological basis for Salmonella persistence in food manufacturing environments

The persistence of Salmonella spp. in low moisture foods is a challenge for the food industry as despite control strategies already in place, notable outbreaks still occur. The aim of this study was to characterise isolates of Salmonella, known to be persistent in the food manufacturing environment, by comparing their microbiological characteristics with a panel of matched clinical and veterinary isolates. The gross morphology of the challenge panel was phenotypically characterised in terms of cellular size, shape and motility. In all the parameters measured, the factory isolates were indistinguishable from the human, clinical and veterinary strains. Further detailed metabolic profiling was undertaken using the biolog Microbial ID system. Multivariate analysis of the metabolic microarray revealed differences in metabolism of the factory isolate of S.Montevideo, based on its upregulated ability to utilise glucose and the sugar alcohol groups. The remainder of the serotype-matched isolates were metabolically indistinguishable. Temperature and humidity are known to influence bacterial survival and through environmental monitoring experimental parameters were defined. The results revealed Salmonella survival on stainless steel was affected by environmental temperatures that may be experienced in a food processing environment; with higher survival rates (D25=35.4) at temperatures at 25°C and lower humidity levels of 15% RH, however a rapid decline in cell count (D10=3.4) with lower temperatures of 10°C and higher humidity of 70% RH. Several resident factories strains survived in higher numbers on stainless steel (D25=29.69) compared to serotype matched clinical and veterinary isolates (D25=22.98). Factory isolates of Salmonella did not show an enhanced growth rate in comparison to serotype matched solates grown in Luria broth, Nutrient broth and M9 minimal media indicating that as an independent factor, growth was unlikely to be a major factor driving Salmonella persistence. Using a live / dead stain coupled with fluorescence microscopy revealed that when no longer culturable, isolates of S.Schwarzengrund entered into a viable nonculturable state. The biofilm forming capacity of the panel was characterised and revealed that all were able to form biofilms. None of the factory isolates showed an enhanced capability to form biofilms in comparison to serotype-matched isolates. In disinfection studies, planktonic cells were more susceptible to disinfectants than cells in biofilm and all the disinfectants tested were successful in reducing bacterial load. Contact time was one of the most important factors for reducing bacterial populations in a biofilm. The genomes of eight strains were sequenced. At the nucleotide and amino acid level the food factory isolates were similar to those of isolates from other environments; no major genomic rearrangements were observed, supporting the conclusions of the phenotypic and metabolic analysis. In conclusion, having investigated a variety of morphological, biochemical and genomic factors, it is unlikely that the persistence of Salmonella in the food manufacturing environment is attributable to a single phenotypic, metabolic or genomic factor. Whilst a combination of microbiological factors may be involved it is also possible that strain persistence in the factory environment is a consequence of failure to apply established hygiene management principles.