An integrated mathematical model to evaluate nutrient partition in dairy cattle between the animal and its environment

In the past decade, a number of mechanistic, dynamic simulation models of several components of the dairy production system have become available. However their use has been limited due to the detailed technical knowledge and special software required to run them, and the lack of compatibility between models in predicting various metabolic processes in the animal. The first objective of the current study was to integrate the dynamic models of [Brit. J. Nutr. 72 (1994) 679] on rumen function, [J. Anim. Sci. 79 (2001) 1584] on methane production, [J. Anim. Sci. 80 (2002) 2481 on N partition, and a new model of P partition. The second objective was to construct a decision support system to analyse nutrient partition between animal and environment. The integrated model combines key environmental pollutants such as N, P and methane within a nutrient-based feed evaluation system. The model was run under different scenarios and the sensitivity of various parameters analysed. A comparison of predictions from the integrated model with the original simulation models showed an improvement in N excretion since the integrated model uses the dynamic model of [Brit. J. Nutr. 72 (1994) 6791 to predict microbial N, which was not represented in detail in the original model. The integrated model can be used to investigate the degree to which production and environmental objectives are antagonistic, and it may help to explain and understand the complex mechanisms involved at the ruminal and metabolic levels. A part of the integrated model outputs were the forms of N and P in excreta and methane, which can be used as indices of environmental pollution. (C) 2004 Elsevier B.V All rights reserved.

Use and abuse of mathematical models: an illustration from the 2001 foot and mouth disease epidemic in the United Kingdom

Foot and mouth disease (FMD) is a major threat, not only to countries whose economies rely on agricultural exports, but also to industrialised countries that maintain a healthy domestic livestock industry by eliminating major infectious diseases from their livestock populations. Traditional methods of controlling diseases such as FMD require the rapid detection and slaughter of infected animals, and any susceptible animals with which they may have been in contact, either directly or indirectly. During the 2001 epidemic of FMD in the United Kingdom (UK), this approach was supplemented by a culling policy driven by unvalidated predictive models. The epidemic and its control resulted in the death of approximately ten million animals, public disgust with the magnitude of the slaughter, and political resolve to adopt alternative options, notably including vaccination, to control any future epidemics. The UK experience provides a salutary warning of how models can be abused in the interests of scientific opportunism.

Successful long-term ultra dry storage of seed of 15 species of Brassicaceae in a genebank: variation in ability to germinate over 40 years and dormancy

Seed of 15 species of Brassicaceae were stored hermetically in a genebank (at -5 degrees C to -10 degrees C with c. 3% moisture content) for 40 years. Samples were withdrawn at intervals for germination tests. Many accessions showed an increase in ability to germinate over this period. due to loss in dormancy. Nevertheless, some dormancy remained after 40 years' storage and was broken by pre-applied gibberellic acid. The poorest seed survival occurred in Hormatophylla spinosa. Even in this accession the ability to germinate declined by only 7% between 1966 and 2006. Comparison of seeds from 1966 stored for 40 years with those collected anew in 2006 from the original sampling sites, where possible, showed few differences, other than a tendency (7 of 9 accessions) for the latter to show greater dormancy. These results for hermetic storage at sub-zero temperatures and low moisture contents confirm that long-term seed storage can provide a successful technology for ex situ plant biodiversity conservation.

A mathematical model of the in vitro keratinocyte response to chromium and nickel exposure

A mathematical model describing the main mechanistic processes involved in keratinocyte response to chromium and nickel has been developed and compared to experimental in vitro data. Accounting for the interactions between the metal ions and the keratinocytes, the law of mass action was used to generate ordinary differential equations which predict the time evolution and ion concentration dependency of keratinocyte viability, the amount of metal associated with the keratinocytes and the release of cytokines by the keratinocytes. Good agreement between model predictions and existing experimental data of these endpoints was observed, supporting the use of this model to explore physiochemical parameters that influence the toxicological response of keratinocytes to these two metals.

Understanding post-operative temperature drop in cardiac surgery: a mathematical model

A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central core containing the majority of organs, the rectal region containing the intestines and the outer peripheral region of skin and muscle. In particular, we focus on the issue of afterdrop: a drop in core temperature following patient re-warming, which can lead to serious post-operative complications. Model results for a typical cooling and re-warming procedure during surgery are in qualitative agreement with experimental data in producing the afterdrop effect and the observed dynamical variation in temperature between the core, rectal and peripheral regions. The influence of heat transfer processes and the volume of each compartmental region on the afterdrop effect is discussed. We find that excess fat on the peripheral and rectal regions leads to an increase in the afterdrop effect. Our model predicts that, by allowing constant re-warming after the core temperature has been raised, the afterdrop effect will be reduced.

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

Common variants of apolipoprotein A-IV differ in their ability to inhibit low density lipoprotein oxidation

Apolipoprotein A-IV (apoA-IV) inhibits lipid peroxidation, thus demonstrating potential anti-atherogenic properties. The aim of this study was to investigate how the inhibition of low density lipoprotein (LDL) oxidation was influenced by common apoA-IV isoforms. Recombinant wild type apoA-IV (100 mu g/ml) significantly inhibited the oxidation of LDL (50 mu g protein/ml) by 5 mu M CuSO4 (P < 0.005), but not by 100 mu M CuSO4, suggesting that it may act by binding copper ions. ApoA-IV also inhibited the oxidation of LDL by the water-soluble free-radical generator 2,2'-azobis(amidinopropane) dihydrochloride (AAPH; I mM), as shown by the two-fold increase in the time for half maximal conjugated diene formation (T-1/2; P < 0.05) suggesting it can also scavenge free radicals in the aqueous phase. Compared to wild type apoA-IV, apoA-IV-S347 decreased T-1/2 by 15% (P = 0.036) and apoA-IV-H360 increased T-1/2 by 18% (P = 0.046). All apoA-IV isoforms increased the relative electrophoretic mobility of native LDL, suggesting apoA-IV can bind to LDL and acts as a site-specific antioxidant. The reduced inhibition of LDL oxidation by apoA-IV-S347 compared to wild type apoA-IV may account for the previous association of the APOA4 S347 variant with increased CHD risk and oxidative stress. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

Analysing the ability to retain sidechain hydrogen-bonds in mutant proteins

Motivation: Hydrogen bonds are one of the most important inter-atomic interactions in biology. Previous experimental, theoretical and bioinformatics analyses have shown that the hydrogen bonding potential of amino acids is generally satisfied and that buried unsatisfied hydrogen-bond-capable residues are destabilizing. When studying mutant proteins, or introducing mutations to residues involved in hydrogen bonding, one needs to know whether a hydrogen bond can be maintained. Our aim, therefore, was to develop a rapid method to evaluate whether a sidechain can form a hydrogen-bond. Results: A novel knowledge-based approach was developed in which the conformations accessible to the residues involved are taken into account. Residues involved in hydrogen bonds in a set of high resolution crystal structures were analyzed and this analysis is then applied to a given protein. The program was applied to assess mutations in the tumour-suppressor protein, p53. This raised the number of distinct mutations identified as disrupting sidechain-sidechain hydrogen bonding from 181 in our previous analysis to 202 in this analysis.

Variation in the ability of human influenza A viruses to induce and inhibit the IFN-beta pathway

We investigated the ability of a selection of human influenza A viruses, including recent clinical isolates, to induce IFN-beta production in cultured cell lines. In contrast to the well-characterized laboratory strain A/PR/8/34, several, but not all, recent isolates of H3N2 viruses resulted in moderate IFN-beta stimulation. Through the generation of recombinant viruses, we were able to show that this is not due to a loss of the ability of the NS1 genes to suppress IFN-beta induction; indeed, the NS1 genes behaved similarly with respect to their abilities to block dsRNA signaling. Interestingly, replication of A/Sydney/5/97 virus was less Susceptible to pre-treatment with IFN-alpha than the other viruses. In contrast to the universal effect on dsRNA signaling, we noted differences in the effect of NS1 proteins on expression of interferon stimulated genes and also genes induced by a distinct pathway. The majority of NS1 proteins blocked expression From both IFN-dependent and TNF-dependent promoters by an apparent post-transcriptional mechanism. The NS1 gene of A/PR/8/34 NS1 did not confer these blocks. We noted striking differences in the Cellular localization of different influenza A virus NS1 proteins during infection, which might explain differences in biological activity. (C) 2005 Elsevier Inc. All rights reserved.

The glycosylation pattern of baculovirus expressed envelope protein E2 affects its ability to prevent infection with bovine viral diarrhoea virus

We have investigated the role of glycosylation of the envelope glycoprotein E2 of bovine viral diarrhoea virus (BVDV), produced in insect cells, in BVDV infection. When amino acids predicated to code for the C-terminal N-linked glycosylation site were mutated the resulting protein was less efficient than wild type protein at preventing infection of susceptible cells with BVDV. In addition, mutational analysis showed that a further two predicted N-terminal N-linked glycosylation sites of E2 are required for efficient production of recombinant protein. (c) 2005 Elsevier B.V. All rights reserved.

Evaluation of the binding ability of a novel dioxatetraazamacrocyclic receptor that contains two phenanthroline units: selective uptake of carboxylate anions

The novel dioxatetraaza macrocycle [26]phen(2)N(4)O(2), which incorporates two phenanthroline units, has been synthesized, and its acid-base behavior has been evaluated by potentiometric and H-1 NMR methods. Six protonation constants were determined, and the protonation sequence was established by NMR. The location of the fifth proton on the phen nitrogen was confirmed by X-ray determinations of the crystal structures of the receptor as bromide and chloride salts. The two compounds have the general molecular formula {(H-5[26]phen(2)N(4)O(2))X-n(H2O)(5-n)}X(n-1)(.)mH(2)O, where X = Cl, n = 3, and m = 6 or X = Br, n = 4, and m = 5.5. In the solid state, the (H-5[26]phen(2)N(4)O(2))(5+) cation adopts a "horseshoe" topology with sufficient room to encapsulate three or four halogen anions through the several N-(HX)-X-... hydrogen-bonding interactions. Two supermolecules {(H-5[26]phen(2)N(4)O(2))X-n(H2O)(5-n)}((5-n)+) form an interpenetrating dimeric species, which was also found by ESI mass spectrum. Binding studies of the protonated macrocycle with aliphatic (ox(2-), mal(2-), suc(2-), cit(3-), cta(3-)) and aromatic (bzc(-), naphc(-), anthc(-), pyrc(-), ph(2-), iph(2-), tph(2-), btc(3-)) anions were determined in water by potentiometric methods. These studies were complemented by H-1 NMR titrations in D2O of the receptor with selected anions. The H-i[26]phen(2)N(4)O(2)(i+) receptor can selectively uptake highly charged or extended aromatic carboxylate anions, such as btc(3-) and pyrc(-), in the pH ranges of 4.0-8.5 and < 4.0, respectively, from aqueous solution that contain the remaining anions as pollutants or contaminants. To obtain further insight into these structural and experimental findings, molecular dynamics (MD) simulations were carried out in water solution.

Past, present and future mathematical models for buildings (i)

This is the first of two articles presenting a detailed review of the historical evolution of mathematical models applied in the development of building technology, including conventional buildings and intelligent buildings. After presenting the technical differences between conventional and intelligent buildings, this article reviews the existing mathematical models, the abstract levels of these models, and their links to the literature for intelligent buildings. The advantages and limitations of the applied mathematical models are identified and the models are classified in terms of their application range and goal. We then describe how the early mathematical models, mainly physical models applied to conventional buildings, have faced new challenges for the design and management of intelligent buildings and led to the use of models which offer more flexibility to better cope with various uncertainties. In contrast with the early modelling techniques, model approaches adopted in neural networks, expert systems, fuzzy logic and genetic models provide a promising method to accommodate these complications as intelligent buildings now need integrated technologies which involve solving complex, multi-objective and integrated decision problems.

Past, present and future mathematical models for buildings (ii)

This article is the second part of a review of the historical evolution of mathematical models applied in the development of building technology. The first part described the current state of the art and contrasted various models with regard to the applications to conventional buildings and intelligent buildings. It concluded that mathematical techniques adopted in neural networks, expert systems, fuzzy logic and genetic models, that can be used to address model uncertainty, are well suited for modelling intelligent buildings. Despite the progress, the possible future development of intelligent buildings based on the current trends implies some potential limitations of these models. This paper attempts to uncover the fundamental limitations inherent in these models and provides some insights into future modelling directions, with special focus on the techniques of semiotics and chaos. Finally, by demonstrating an example of an intelligent building system with the mathematical models that have been developed for such a system, this review addresses the influences of mathematical models as a potential aid in developing intelligent buildings and perhaps even more advanced buildings for the future.

Mathematical model for low density lipoprotein (LDL) endocytosis by hepatocytes

Individuals with elevated levels of plasma low density lipoprotein (LDL) cholesterol (LDL-C) are considered to be at risk of developing coronary heart disease. LDL particles are removed from the blood by a process known as receptor-mediated endocytosis, which occurs mainly in the liver. A series of classical experiments delineated the major steps in the endocytotic process; apolipoprotein B-100 present on LDL particles binds to a specific receptor (LDL receptor, LDL-R) in specialized areas of the cell surface called clathrin-coated pits. The pit comprising the LDL-LDL-R complex is internalized forming a cytoplasmic endosome. Fusion of the endosome with a lysosome leads to degradation of the LDL into its constituent parts (that is, cholesterol, fatty acids, and amino acids), which are released for reuse by the cell, or are excreted. In this paper, we formulate a mathematical model of LDL endocytosis, consisting of a system of ordinary differential equations. We validate our model against existing in vitro experimental data, and we use it to explore differences in system behavior when a single bolus of extracellular LDL is supplied to cells, compared to when a continuous supply of LDL particles is available. Whereas the former situation is common to in vitro experimental systems, the latter better reflects the in vivo situation. We use asymptotic analysis and numerical simulations to study the longtime behavior of model solutions. The implications of model-derived insights for experimental design are discussed.