Type III secretion contact-dependent model for the intracellular development of Chlamydia

The medically significant genus Chlamydia is a class of obligate intracellular bacterial pathogens that replicate within vacuoles in host eukaryotic cells termed inclusions. Chlamydia's developmental cycle involves two forms; an infectious extracellular form, known as an elementary body (EB), and a non-infectious form, known as the reticulate body (RB), that replicates inside the vacuoles of the host cells. The RB surface is covered in projections that are in intimate contact with the inclusion membrane. Late in the developmental cycle, these reticulate bodies differentiate into the elementary body form. In this paper, we present a hypothesis for the modulation of these developmental events involving the contact-dependent type III secretion (TTS) system. TTS surface projections mediate intimate contact between the RB and the inclusion membrane. Below a certain number of projections, detachment of the RB provides a signal for late differentiation of RB into EB. We use data and develop a mathematical model investigating this hypothesis. If the hypothesis proves to be accurate, then we have shown that increasing the number of inclusions per host cell will increase the number of infectious progeny EB until some optimal number of inclusions. For more inclusions than this optimum, the infectious yield is reduced because of spatial restrictions. We also predict that a reduction in the number of projections on the surface of the RB (and as early as possible during development) will significantly reduce the burst size of infectious EB particles. Many of the results predicted by the model can be tested experimentally and may lead to the identification of potential targets for drug design. © Society for Mathematical Biology 2006.

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.

About Methods of Mathematical Modelling in the Development of Information Systems

This article describes the approach, which allows to develop information systems without taking into consideration details of physical storage of the relational model and type database management system. Described in terms of graph model, this approach allows to construct several algorithms, for example, for verification application domain. This theory was introduced into operation testing as a part of CASE-system METAS.

Mathematical Models of Domain Ontologies

* This paper was made according to the program No 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project "Intellectual Systems Based on Multilevel Domain Models".

An Information Model for Pension Fund Management

In this paper the issues of Ukrainian new three-level pension system are discussed. First, the paper presents the mathematical model that allows calculating the optimal size of contributions to the non-state pension fund. Next, the non-state pension fund chooses an Asset Management Company. To do so it is proposed to use an approach based on Kohonen networks to classify asset management companies that work in Ukrainian market. Further, when the asset management company is chosen, it receives the pension contributions of the participants of the non-pension fund. Asset Management Company has to invest these contributions profitably. This paper proposes an approach for choosing the most profitable investment project using decision trees. The new pension system has been lawfully ratified only four years ago and is still developing, that is why this paper is very important.

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Development of An Enhanced Oil Sands Fluid Tailings Generation Model

Bitumen extraction from surface-mined oil sands results in the production of large volumes of Fluid Fine Tailings (FFT). Through Directive 085, the Province of Alberta has signaled that oil sands operators must improve and accelerate the methods by which they deal with FFT production, storage and treatment. This thesis aims to develop an enhanced method to forecast FFT production based on specific ore characteristics. A mass relationship and mathematical model to modify the Forecasting Tailings Model (FTM) by using fines and clay boundaries, as the two main indicators in FFT accumulation, has been developed. The modified FTM has been applied on representative block model data from an operating oil sands mining venture. An attempt has been made to identify order-of-magnitude associated tailings treatment costs, and to improve financial performance by not processing materials that have ultimate ore processing and tailings storage and treatment costs in excess of the value of bitumen they produce. The results on the real case study show that there is a 53% reduction in total tailings accumulations over the mine life by selectively processing only lower tailings generating materials through eliminating 15% of total mined ore materials with higher potential of fluid fines inventory. This significant result will assess the impact of Directive 082 on mining project economic and environmental performance towards the sustainable development of mining projects.

Mathematical Modeling to Assess the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi

BACKGROUND: Multiyear epidemics of Salmonella enterica serovar Typhi have been reported from countries across eastern and southern Africa in recent years. In Blantyre, Malawi, a dramatic increase in typhoid fever cases has recently occurred, and may be linked to the emergence of the H58 haplotype. Strains belonging to the H58 haplotype often exhibit multidrug resistance and may have a fitness advantage relative to other Salmonella Typhi strains.

METHODS: To explore hypotheses for the increased number of typhoid fever cases in Blantyre, we fit a mathematical model to culture-confirmed cases of Salmonella enterica infections at Queen Elizabeth Central Hospital, Blantyre. We explored 4 hypotheses: (1) an increase in the basic reproductive number (R0) in response to increasing population density; (2) a decrease in the incidence of cross-immunizing infection with Salmonella Enteritidis; (3) an increase in the duration of infectiousness due to failure to respond to first-line antibiotics; and (4) an increase in the transmission rate following the emergence of the H58 haplotype.

RESULTS: Increasing population density or decreasing cross-immunity could not fully explain the observed pattern of typhoid emergence in Blantyre, whereas models allowing for an increase in the duration of infectiousness and/or the transmission rate of typhoid following the emergence of the H58 haplotype provided a good fit to the data.

CONCLUSIONS: Our results suggest that an increase in the transmissibility of typhoid due to the emergence of drug resistance associated with the H58 haplotype may help to explain recent outbreaks of typhoid in Malawi and similar settings in Africa.

The use of mathematical modelling in fire safety engineering

Fire is a form of uncontrolled combustion which generates heat, smoke, toxic and irritant gases. All of these products are harmful to man and account for the heavy annual cost of 800 lives and £1,000,000,000 worth of property damage in Britain alone. The new discipline of Fire Safety Engineering has developed as a means of reducing these unacceptable losses. One of the main tools of Fire Safety Engineering is the mathematical model and over the past 15 years a number of mathematical models have emerged to cater for the needs of this discipline. Part of the difficulty faced by the Fire Safety Engineer is the selection of the most appropriate modelling tool to use for the job. To make an informed choice it is essential to have a good understanding of the various modelling approaches, their capabilities and limitations. In this paper some of the fundamental modelling tools used to predict fire and evacuation are investigated as are the issues associated with their use and recent developments in modelling technology.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Applying Mathematical Models to Study the Role of the Immune System in Chronic Myelogenous Leukemia

Although tyrosine kinase inhibitors (TKIs) such as imatinib have transformed chronic myelogenous leukemia (CML) into a chronic condition, these therapies are not curative in the majority of cases. Most patients must continue TKI therapy indefinitely, a requirement that is both expensive and that compromises a patient's quality of life. While TKIs are known to reduce leukemic cells' proliferative capacity and to induce apoptosis, their effects on leukemic stem cells, the immune system, and the microenvironment are not fully understood. A more complete understanding of their global therapeutic effects would help us to identify any limitations of TKI monotherapy and to address these issues through novel combination therapies. Mathematical models are a complementary tool to experimental and clinical data that can provide valuable insights into the underlying mechanisms of TKI therapy. Previous modeling efforts have focused on CML patients who show biphasic and triphasic exponential declines in BCR-ABL ratio during therapy. However, our patient data indicates that many patients treated with TKIs show fluctuations in BCR-ABL ratio yet are able to achieve durable remissions. To investigate these fluctuations, we construct a mathematical model that integrates CML with a patient's autologous immune response to the disease. In our model, we define an immune window, which is an intermediate range of leukemic concentrations that lead to an effective immune response against CML. While small leukemic concentrations provide insufficient stimulus, large leukemic concentrations actively suppress a patient's immune system, thus limiting it's ability to respond. Our patient data and modeling results suggest that at diagnosis, a patient's high leukemic concentration is able to suppress their immune system. TKI therapy drives the leukemic population into the immune window, allowing the patient's immune cells to expand and eventually mount an efficient response against the residual CML. This response drives the leukemic population below the immune window, causing the immune population to contract and allowing the leukemia to partially recover. The leukemia eventually reenters the immune window, thus stimulating a sequence of weaker immune responses as the two populations approach equilibrium. We hypothesize that a patient's autologous immune response to CML may explain the fluctuations in BCR-ABL ratio that are regularly seen during TKI therapy. These fluctuations may serve as a signature of a patient's individual immune response to CML. By applying our modeling framework to patient data, we are able to construct an immune profile that can then be used to propose patient-specific combination therapies aimed at further reducing a patient's leukemic burden. Our characterization of a patient's anti-leukemia immune response may be especially valuable in the study of drug resistance, treatment cessation, and combination therapy.

Numerical and analytical study of an atherosclerosis inflammatory disease model

We study a reaction–diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction–diffusion system and lead to the complete characterisation of the ωω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study