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.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

DEA-R:ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea-Ratio Analysis. Our model, called DEA-R, treats all possible ratios "output/input" as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts' opinions via flexible restrictive conditions on individual "output/input" pairs. © 2007 Springer Science+Business Media, LLC.

Chemical modification of polymers

Based on the knowledge of PVC degradation and stabilisation, chemical modifications were imposed on degraded PVC and raw PVC with the aim of obtaining non-migrating additives. The modifications were carried out mainly in the presence of dibutyl maleate (DBM), and the resulting polymer contained dibutyl maleic residues. Such modifications result in a polymer which contain substantive additives which resist migration under aggressive environments. Previous studies have shown that stable nitroxyl radicals function as stabilisers in polymer during processing (e.g. PP, PVC) by deactivating a large number of kinetic chains via a redox process whereby the concentrations of the nitroxyl and its reduced form, the hydroxylamine, fluctuate reciprocally and rhythmically. In order to understand the major reactions involved in such systems, a simulation method was used which resulted in a mathematical model and some rate constants, explaining the kinetic behaviour exhibited by such system. In the process of forming a suitable model, two nonlinear oscillators were proposed, which could be of interest in the study of nonlinear phenomenon because of their chaotic behaviour.

A dynamic model for the activated sludge treatment of coke oven effluents

This is an Inter-Disciplinary Higher Degree (IHD) thesis about Water Pollution Control in the Iron and Steel Industry. After examining the compositions, and various treatment methods, for the major effluent streams from a typical Integrated Iron and Steel works, it was decided to concentrate investigative work on the activated-sludge treatment of coke-oven effluents. A mathematical model of this process was developed in an attempt to provide a tool for plant management that would enable improved performance, and enhanced control of Works Units. The model differs from conventional models in that allowance is made for the presence of two genera of microorganisms, each of which utilises a particular type of substrate as its energy source. Allowance is also made for the inhibitive effect of phenol on thiocyanate biodegradation, and for the self-toxicity of the bacteria when present in a high substrate concentration environment. The enumeration of the kinetic characteristics of the two groups of micro-organisms was shown to be of major importance. Laboratory experiments were instigated in an attempt to determine accurate values of these coefficients. The use of the Suspended Solids concentration was found to be too insensitive a measure of viable active mass. Other measures were investigated, and Adenosine Triphosphate concentration was chosen as the most effective measure of bacterial populations. Using this measure, a model was developed for phenol biodegradation from experimental results which implicated the possibility of storage of substate prior to metabolism. A model for thiocyanate biodegradation was also developed, although the experimental results indicate that much work is still required in this area.

A dynamic model of the hypoxia-inducible factor 1α (HIF-1α) network

Activation of the hypoxia-inducible factor (HIF) pathway is a critical step in the transcriptional response to hypoxia. Although many of the key proteins involved have been characterised, the dynamics of their interactions in generating this response remain unclear. In the present study, we have generated a comprehensive mathematical model of the HIF-1a pathway based on core validated components and dynamic experimental data, and confirm the previously described connections within the predicted network topology. Our model confirms previous work demonstrating that the steps leading to optimal HIF-1a transcriptional activity require sequential inhibition of both prolyl- and asparaginyl-hydroxylases. We predict from our model (and confirm experimentally) that there is residual activity of the asparaginyl-hydroxylase FIH (factor inhibiting HIF) at low oxygen tension. Furthermore, silencing FIH under conditions where prolyl-hydroxylases are inhibited results in increased HIF-1a transcriptional activity, but paradoxically decreases HIF-1a stability. Using a core module of the HIF network and mathematical proof supported by experimental data, we propose that asparaginyl hydroxylation confers a degree of resistance upon HIF-1a to proteosomal degradation. Thus, through in vitro experimental data and in silico predictions, we provide a comprehensive model of the dynamic regulation of HIF-1a transcriptional activity by hydroxylases and use its predictive and adaptive properties to explain counter-intuitive biological observations.

Improving minimax disparity model to determine the OWA operator weights

Determining the Ordered Weighted Averaging (OWA) operator weights is important in decision making applications. Several approaches have been proposed in the literature to obtain the associated weights. This paper provides an alternative disparity model to identify the OWA operator weights. The proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct OWA weights. The proposed disparity model can be used for a preference ranking aggregation. A numerical example in preference ranking and an application in search engines prove the usefulness of the generated OWA weights.