Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor-lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins' constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.

Modelling the uptake and growth kinetics of Penicillium glabrum in a tannic acid-containing solid-state fermentation for tannase production

A mathematical growth model for the batch solid-state fermentation process for fungal tannase production was developed and tested experimentally. The unstructured model describes the uptake and growth kinetics of Penicillium glabrum in an impregnated polyurethane foam substrate system. In general, good agreement between the experimental data and model simulations was obtained. Biomass, tannase and spore production are described by logistic kinetics with a time delay between biomass production and tannase and spore formation. Possible induction mechanisms for the latter are proposed. Hydrolysis of tannic acid, the main carbon source in the substrate system, is reasonably well described with Michaelis-Menten kinetics with time-varying enzyme concentration but a more complex reaction mechanism is suspected. The metabolism of gallic acid, a tannase-hydrolysis product of tannic acid, was shown to be growth limiting during the main growth phase. (c) 2004 Elsevier Ltd. All rights reserved.

Modelling and validation of Lactobacillus plantarum fermentations in cereal-based media with different sugar concentrations and buffering capacities

An unstructured mathematical model is proposed to describe the fermentation kinetics of growth, lactic acid production, pH and sugar consumption by Lactobacillus plantarum as a function of the buffering capacity and initial glucose concentration of the culture media. Initially the experimental data of L plantarum fermentations in synthetic media with different buffering capacity and glucose were fitted to a set of primary models. Later the parameters obtained from these models were used to establish mathematical relationships with the independent variables tested. The models were validated with 6 fermentations of L. plantarum in different cereal-based media. In most cases the proposed models adequately describe the biochemical changes taking place during fermentation and are a promising approach for the formulation of cereal-based probiotic foods. (C) 2008 Elsevier B.V. All rights reserved.

Modelling the effect of fatty acids in odour development of cooked meat in vitro: part I - sensory perception

We have investigated the contribution of muscle components to the development of cooked meat odour in an aqueous model system using trained taste panels. Reaction mixtures were prepared with oleic, linoleic and linolenic acids with or without cysteine and ribose in a buffer with or without ferrous sulphate. Odour profiles were assessed and triangular tests were used to determine the ability of panellists to discriminate between mixtures. The presence of sugar and amino acid was highly detectable by panellists independently of the fatty acid considered (P < 0.001). However, the presence of C18:3 made differences. more obvious between mixtures than the presence of C18:1 or C18:2. `Meaty' notes were only associated with cysteine and ribose. `Fishy' notes were only apparent in C18:3 mixtures with or without sugar and amino acid, although the presence of cysteine and ribose decreased the perception. The addition of Fe+ +, a pro-oxidant present in the muscle, produced a reduction in the score of the attributes although the pattern was the same as when Fe was not used in the mixtures. Only `fishy' notes that were exclusively perceived in C18:3 mixtures showed a higher score in the presence of iron. Iron also produced a better discrimination in C18:3 mixtures, which were closely related to `grassy' notes in the presence of cysteine and ribose. (C) 2002 Published by Elsevier Science Ltd.

Modelling oil absorption during post-frying cooling - I: model development

Several studies have highlighted the importance of the cooling period in oil absorption in deep-fat fried products. Specifically, it has been established that the largest proportion of oil which ends up into the food, is sucked into the porous crust region after the fried product is removed from the oil bath, stressing the importance of this time interval. The main objective of this paper was to develop a predictive mechanistic model that can be used to understand the principles behind post-frying cooling oil absorption kinetics, which can also help identifying the key parameters that affect the final oil intake by the fried product. The model was developed for two different geometries, an infinite slab and an infinite cylinder, and was divided into two main sub-models, one describing the immersion frying period itself and the other describing the post-frying cooling period. The immersion frying period was described by a transient moving-front model that considered the movement of the crust/core interface, whereas post-frying cooling oil absorption was considered to be a pressure driven flow mediated by capillary forces. A key element in the model was the hypothesis that oil suction would only begin once a positive pressure driving force had developed. The mechanistic model was based on measurable physical and thermal properties, and process parameters with no need of empirical data fitting, and can be used to study oil absorption in any deep-fat fried product that satisfies the assumptions made.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Delineation and modelling of a nucleolar retention signal in the coronavirus nucleocapsid protein

Unlike nuclear localization signals, there is no obvious consensus sequence for the targeting of proteins to the nucleolus. The nucleolus is a dynamic subnuclear structure which is crucial to the normal operation of the eukaryotic cell. Studying nucleolar trafficking signals is problematic as many nucleolar retention signals (NoRSs) are part of classical nuclear localization signals (NLSs). In addition, there is no known consensus signal with which to inform a study. The avian infectious bronchitis virus (IBV), coronavirus nucleocapsid (N) protein, localizes to the cytoplasm and the nucleolus. Mutagenesis was used to delineate a novel eight amino acid motif that was necessary and sufficient for nucleolar retention of N protein and colocalize with nucleolin and fibrillarin. Additionally, a classical nuclear export signal (NES) functioned to direct N protein to the cytoplasm. Comparison of the coronavirus NoRSs with known cellular and other viral NoRSs revealed that these motifs have conserved arginine residues. Molecular modelling, using the solution structure of severe acute respiratory (SARS) coronavirus N-protein, revealed that this motif is available for interaction with cellular factors which may mediate nucleolar localization. We hypothesise that the N-protein uses these signals to traffic to and from the nucleolus and the cytoplasm.

The multidimensional measurement of the positive symptoms of psychosis

The measures most frequently used to assess psychotic symptoms fail to reflect important dimensions. The Psychotic Symptom Rating Scale (PSYRATS) aims to capture the multidimensional nature of auditory hallucinations and delusions. Individuals (N = 276) who had recently relapsed with positive symptoms completed the auditory hallucinations and delusions PSYRATS scales. These scores were compared with the relevant items from the SAPS and PANSS, and with measures of current mood. Total scores and distribution of items of the PSYRATS scales are presented and correlated with other measures. Positive symptom items from the SAPS and PANSS reflected the more objective aspects of PSYRATS ratings of auditory hallucinations and delusions (frequency and conviction) but were relatively poor at measuring distress. A major strength of the PSYRATS scales is the specific measurement of the distress dimension of symptoms, which is a key target of psychological intervention. It is advised that the PSYRATS should not be used as a total score alone, whilst further research is needed to clarify the best use of potential subscales. Copyright (c) 2007 John Wiley & Sons, Ltd.

Semiotic modelling for complex enterprise systems

An enterprise is viewed as a complex system which can be engineered to accomplish organisational objectives. Systems analysis and modelling will enable to the planning and development of the enterprise and IT systems. Many IT systems design methods focus on functional and non-functional requirements of the IT systems. Most methods are normally capable of one but leave out other aspects. Analysing and modelling of both business and IT systems may often have to call on techniques from various suites of methods which may be placed on different philosophic and methodological underpinnings. Coherence and consistency between the analyses are hard to ensure. This paper introduces the Problem Articulation Method (PAM) which facilitates the design of an enterprise system infrastructure on which an IT system is built. Outcomes of this analysis represent requirements which can be further used for planning and designing a technical system. As a case study, a finance system, Agresso, for e-procurement has been used in this paper to illustrate the applicability of PAM in modelling complex systems.

Modelling requirements of supplier selection for benchmarking service provision

Supplier selection has a great impact on supply chain management. The quality of supplier selection also affects profitability of organisations which work in the supply chain. As suppliers can provide variety of services and customers demand higher quality of service provision, the organisation is facing challenges for making the right choice of supplier for the right needs. The existing methods for supplier selection, such as data envelopment analysis (DEA) and analytical hierarchy process (AHP) can automatically perform selection of competitive suppliers and further decide winning supplier(s). However, these methods are not capable of determining the right selection criteria which should be derived from the business strategy. An ontology model described in this paper integrates the strengths of DEA and AHP with new mechanisms which ensure the right supplier to be selected by the right criteria for the right customer's needs.

Modelling energy consumption of relay-enabled MAC protocols in ad hoc networks

To enhance the throughput of ad hoc networks, dual-hop relay-enabled transmission schemes have recently been proposed. Since in ad hoc networks throughput is normally related to their energy consumption, it is important to examine the impact of using relay-enabled transmissions on energy consumption. In this paper, we present an analytical energy consumption model for dual-hop relay-enabled medium access control (MAC) protocols. Based on the recently reported relay-enabled distributed coordination function (rDCF), we have shown the efficacy of the proposed analytical model. This is a generalized model and can be used to predict energy consumption in saturated relay-enabled ad hoc networks via energy decomposition. This is helpful in designing MAC protocols for cooperative communications and it is shown that using a relay results not only in a better throughput but also better energy efficiency.