Introduction to Applied Mathematics for Environmental Science (2006)(1st ed.)(en)(317s)

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  1. Introduction
  2. NoZDR - Численные методы
  3. Исчисление
  4. Towards Efficient Analysis of Variation in Time and Space

Although the mechanisms of cell death are rather rarely pursued, there is evidence for the involvement of iron in the sequelae of exposure to toxic doses of gentamicin Petronilho et al. The most dangerous kinds of man-made toxic chemical agents, those that kill cells or organisms, exhibit a rich diversity of chemical structures and can bind to multiple cellular targets, to the extent that a unitary mode of action is not considered likely.

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This said, the same was thought to be true for the mode of action of general anaesthetics or narcotics, and they turn out to have a comparatively small number of rather specific protein targets Dobson et al. However, this does not mean that multiple initial events do not at some point converge to a comparatively small number of crucial events of cell death whether through necrosis or apoptosis, Vanden Berghe et al. A recent special issue on toxicants and neurodegeneration is also of interest here Gupta and Milatovic Acetaminophen paracetamol in the United Kingdom ChEBI is a well-known analgesic that is nevertheless highly toxic at concentrations in excess of the therapeutic dose, as it is converted to the electrophilic N-acetyl-p-benzoquinone imine NAPQI.

If glutathione is in insufficient supply, the NAPQI cannot be conjugated harmlessly by glutathione and so it reacts covalently with proteins, especially mitochondrial proteins Hinson et al. Barker et al. One of the effects of mitochondrial damage is iron release, and it has long been known that iron chelators help prevent this toxicity Sakaida et al.

Appropriate hydroxyl radical scavengers are also partly protective Chandrasekaran et al.


It is now clear Bomhard and Herbold ; Khan et al. Many mutagens are carcinogens, typically by intercalating into DNA, so it was not a priori obvious why asbestos fibres—enormously larger than the diameter of DNA—should be so toxic. The mystery was solved when it was realised that asbestos does in fact contain and bind iron, that the sharp surface of the iron-loaded fibres can catalyse hydroxyl radical formation and that it is this that provides the toxic mechanism Aljandali et al. It was found that mice low in iron are resistant to this hepatotoxicity however Poland and Knutson ; Sweeny et al.

In addition, iron enhances the toxicity of dioxin Al-Turk et al. While the exact details have still not been worked out, there is little doubt that iron is important in the toxicity of a wide variety of polyhalogenated aromatics Smith and Chernova ; Smith and Elder , including hexachlorobenzene ChEBI Franklin et al. Phenylhydrazine ChEBI like other hydrazines is a reactive substance that is commonly used in toxicity studies.

It is known Agrawal et al. Melatonin can be protective Sharma and Haldar Like most if not all other xenobiotics Dobson et al. There is certainly evidence that exposure to this agent causes oxidative stress Ali et al. Taken together, this does imply strongly a role for iron-mediated cytotoxicity of the type highlighted herein in the pathogenesis of methylmercury poisoning. As such, its toxicity may be expected to be exacerbated by iron, and this is the case Andersen ; Ayaki et al.

In addition, again as expected from the above and consistent with its structural similarity to the Parkinson-inducing agent MPTPmethylphenyl-1,2,3,6-tetrahydropyridine, ChEBI , it can induce Parkinson-like symptoms Kaur et al. The protection by molecules—such as ferritin Kaur et al. The list of known and potential toxicants is limitless, and part of the role of this review is to alert domain experts to the likelihood that iron, and dysregulation in iron metabolism, may mediate the toxicity of such molecules and thus that its chelation may be important, under both acute and chronic conditions, in assisting resolution of the toxicity.

Welding fumes are toxic and contain both iron and manganese Flynn and Susi ; Sriram et al. As is well known, cells can die by both necrosis and by a more regulated form, apoptosis. Brewer ; Cass et al. As it turns out, while there is a little evidence that iron overload can cause necrosis Babatasi et al.

NoZDR - Численные методы

Bergman et al. Aljandali et al. As reviewed in the previous survey Kell a and elsewhere e. Shoelson and Goldfine ; Shoelson et al. Ali and Mann ; Circu and Aw ; Granic et al. I have mentioned several times the idea that different proteins can bind unliganded iron to catalyse the production of hydroxyl radical, and it is certainly the case that the degree of liganding can affect these kinds of activities Kell a. Here it is appropriate to highlight the abilities of polypeptides and even poly aminoacids —whether binding metals or not —to exhibit catalytic activities, e.

The recent development of orthogonal ribosomes capable of incorporating novel amino acids into polypeptides Neumann et al. Developing novel pharmaceutical agents is a costly enterprise, and many candidate drugs fall by the wayside during the development process see e.


Dobson et al. As most recently reviewed Agarwal ; Berdoukas et al. Amit et al. The implications for this and other neurodegenerative diseases—and potentially for the more acute and even chronic effects of other toxins—are obvious. Note that—unlike the other two—Deferoxamine is not orally active and must be injected, and even then may fail to cross cellular membranes to exert its action appropriately Warkentin et al.

Allen and Cornforth , on nepetoidin caffeic acid esters Maioli et al. Many of the protective effects observed are likely due to the iron chelating, as well as directly antioxidative redox properties of these molecules e. Ferrali et al. Other molecules that are not themselves directly antioxidant, but have iron-binding characteristics, may also be of benefit. This is certainly true of phytic acid phytate; myo-inositol-1,2,3,4,5,6-hexakis phosphate; CHEBI Aljandali et al.

While phlebotomy is a very traditional nostrum, often assumed or considered to have rather dubious or at best modest scientific support, there is in fact increasing literature implying its benefits in a variety of conditions e. Aigner et al. Plausibly such benefits are due to its role in decreasing iron stores.

It is certainly the case that reasons for the co-occurrence of two or more observables are that one causes the other or they have the same, separate cause. Since I have argued strongly here for the essentiality of iron dysregulation in a variety of syndromes and have omitted many others, such as non-alcoholic Baptista-Gonzalez et al.

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There is considerable and increasing evidence for that see e. Adibhatla and Hatcher ; Baker et al. In a similar vein, it is not news Attwood et al. As previously discussed, it is well established on theoretical grounds alone that the activity of any step in a biochemical network can influence the concentration of any variable such as—fleetingly—the amount of hydroxyl radicals produced. Thus, while it is better to derive quantitative models e.

The extent of cell damage caused by the unliganded iron-catalysed production of ROSs and RNSs is determined by many factors, some of which promote and some of which act against it. While the existence of hormesis see text means that the see-saw illustrated here is an imperfect metaphor, the diagram serves to illustrate the complexity of the problem and the need for a systems biology approach to its solution.

Indeed, it is the very act of doing this that leads one to recognise these kinds of complex problems as problems of systems or network biology Alon ; Klipp et al. What do I mean by this? The implication of this is that to be more specific we need suitable network models of the biological systems of interest Kell , and of how toxicants of any kind can interact with their components. Of course in the steady state, the amount of a substance is governed both by the processes that create it and those that decompose it Fig. Hence, the need for accurate systems biology models.

The steady-state concentrations of a molecule depend on the rates of production and removal of the molecule in question. Both lowering creation and increasing removal represents a particularly effective strategy relative to doing just one of these alone. The latter decrease of concentration of C may sometimes better be effected by increasing the activities of enzymes yet further downstream.

The very fact that multiple reactions typically lead to the creation and destruction of a given metabolite such as the hydroxyl radical means that to minimise its concentration it is best to modify many reactions simultaneously. This exceptionally important point from systems biology should underpin any scientific and therapeutic programs. For the purposes of this discussion, I shall concentrate on metabolic networks in contrast to signalling networks they transfer both matter and information, Kell There may of course be other interactions such those that do not involve substrates or products but are mediated via molecules effectors that modify the rates of reactions.

The distinction between forward and inverse models is based on whether one starts with the parameters or variables of the system.

In metabolic networks, the parameters are typically the starting concentrations of substances present and the kinetic constants K m , K i , V max , etc. The variables are typically the concentrations of metabolic intermediates, and the metabolic fluxes that change over time until a steady state if such exists is attained.

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It is important to note that only the parameters control the system. The first qualitative stage is one in which are listed all the reactions that are known to occur in the system or organism of interest; in the modern era, and especially for metabolic networks, these reaction lists are often derived in part from genomic annotations Arakawa et al. A second stage, again qualitative, adds known effectors e. Armed with such information, it is then possible to provide stochastic and ordinary differential equation models of the entire metabolic network of interest.

Towards Efficient Analysis of Variation in Time and Space

In some cases, it is possible to make simplifying assumptions that require minimal knowledge of the kinetic parameters of the system and allow one to generate a time series of the system variables Smallbone et al. An attractive feature of metabolism, for the purposes of modelling, is that, in contrast to signalling pathways, metabolism is subject to direct thermodynamic and in particular stoichiometric constraints Palsson These constraints are extremely important in reducing the search space for the values of the kinetic parameters of the model, and indeed constrain significantly the states that the system can adopt Kell ; Palsson The modelling community has access to many tools, which are interoperable because they can be exchanged using community standards Kell of which the most popular Klipp et al.

Models are best made, and made available, in SBML. In addition, there is recognition that it is desirable to be clear about the meaning semantics of the elements in the model Ananiadou et al.