Superoxide production by cytochrome bc1 complex: a mathematical model.

Reactive oxygen species (ROS) are involved in the pathophysiology of several diseases (e.g. Alzheimer or atherosclerosis) and also in the aging process. The main source of ROS in aerobic organisms is the electron transport chain (ETC) in the inner mitochondrial membrane. Superoxide is produced at complexes I and III of the ETC, starting a complex network of ROS reactions. To achieve a deeper mechanistic understanding of how ROS are generated by complex III, we developed a mathematical model that successfully describes experimental data of complex III activity in various rat tissues, the production of ROS with and without antimycin and ROS generation depending on different values of the membrane potential ∆Ψ. The model also reinforces the idea of ubiquinone acting as a redox mediator between heme bL and oxygen, as proposed earlier.

Possible mechanisms for the regulation of telomere length.

Since DNA polymerases can only synthesise a new DNA strand in the 5'-3' direction and need a primer that provides a free 3' OH end, the cellular replication machinery is unable to duplicate the 3' ends of linear chromosomes unless special mechanisms are operative. While the telomeres seem to shorten continuously in human somatic cells because of the "end replication" problem, it appears that telomere length is maintained in cancer cells, the germ line and unicellular organisms like yeast and Tetrahymena by a mechanism involving the enzyme telomerase, which elongates the 3' ends of telomeres. However, telomerase must be part of a more complicated mechanism to ensure that there is no net gain or loss of telomeric ends. Here we describe a simple theoretical model that can explain several experimental findings. The simulations show that (i) the proposed mechanism is able to maintain telomeres at a constant length, (ii) this length constancy is independent of the initial telomere length, (iii) mutations of the telomeric sequence lead to an elongation of telomeres, (iv) inhibition of telomerase causes telomeric shortening, and (v) it reproduces and explains the experimental result that the addition of oligonucleotides to the culture medium leads to an increase of telomere length.

Theoretical Gompertzian implications on life span variability among genotypically identical animals.

Aging is a highly polygenic trait (Kirkwood, T.B.L., Franceschi, C., 1992. Is aging as complex as it would appear? Annals of the New York Academy of Sciences 663, 412-417) who's underlying mechanisms are still unresolved. Animal models are an important help for understanding this process and a recent report drew attention to a putative gene which causes variability in the life span among genotypically identical mice (de Haan, G., Gelman, R., Watson, A., Yunis, E., van Zant, G., 1998. A putative gene causes variability in life span among genotypically identical mice. Nature Genetics 19, 114-116). De Haan et al. observed that the time between the death of the first and last member of a group of inbred mice (the death range) is controlled by a locus, which they mapped to chromosome 11. The authors conclude that well-known effects like modifiers, suppressors or epistatic genes might not be able to explain how this variability in genetically identical organisms is generated and that such a trait has broad implications for genetic studies of the aging process. Here we give a possible answer to the question of what mechanism could cause such a phenotype. We show that all genes which affect the Gompertz parameters are possible candidates.

The mitochondrial theory of aging: do damaged mitochondria accumulate by delayed degradation?

The mitochondrial theory of aging states that the slow accumulation of impaired mitochondria is the driving force of the aging process. In recent years, this theory has gained new support with the discovery of age-related mitochondrial DNA deletions. However, the underlying mechanism of the accumulation of defective mitochondria remained unclear. This has changed recently with the proposal of de Grey that damaged mitochondria have a decreased degradation rate. The resulting increase in biological half-life would be a strong selection advantage leading to the accumulation of defective mitochondria. In this article, I summarize current ideas on how damaged organelles can build up in a cell as well as the shortcomings of these ideas. Then the new hypothesis and its justification are described. It appears that de Grey's hypothesis is a very promising concept that elegantly solves inconsistencies of current models and is in accordance with experimental findings.

Network theory of aging.

Evolution theory indicates that investment in mechanisms of somatic maintenance and repair is likely to be limited, suggesting that aging may result from the accumulation of unrepaired somatic defects. An important corollary of this hypothesis is that multiple mechanisms of aging operate in parallel. We describe a recently developed "network theory of aging" that integrates the contributions of defective mitochondria, aberrant proteins, and free radicals in the aging process and that includes the protective effects of antioxidant enzymes and proteolytic scavengers. Possibilities for further extension of the theory and its role in prediction and simulation of experimental results are discussed.

Mitotic brain cells are just as prone to mitochondrial deletions as neurons: a large-scale single-cell PCR study of the human caudate nucleus.

Mitochondria are considered a key element in the process of organismic aging, because of their fundamental role in cellular energy generation. In the course of oxidative phosphorylation, harmful free radicals are continuously produced damaging the mitochondrial (mt) genome. One of the consequences is the occurrence of large-scale deletions in mtDNA molecules. The 4977 bp common deletion accumulates exponentially with age, in a mosaic pattern, especially in postmitotic tissues. In order to investigate whether certain cell characteristics underlie this pattern of distribution, and to look for possible age-related changes, two cell types in the caudate nucleus of the human brain from five young and five senescent subjects were analysed by single-cell PCR.MAP2-positive neurons and GFAP-positive astrocytes were isolated by micromanipulation. For each of the 10 cases, at least 30 cells of each type were collected and subjected to PCR individually. Screening for the presence of the common deletion yielded no significant differences in relative distribution, neither between astrocytes and neurons, nor between healthy young and old humans. Our results imply that the age-dependent increase of the common deletion cannot come about by an increase of independent deletion events in a greater proportion of cells, and that mitotic rate is not a major cellular risk factor for deletion accumulation in the caudate nucleus.

Mitochondrial mutations, cellular instability and ageing: modelling the population dynamics of mitochondria.

All eukaryotic cells rely on mitochondrial respiration as their major source of metabolic energy (ATP). However, the mitochondria are also the main cellular source of oxygen radicals and the mutation rate of mtDNA is much higher than for chromosomal DNA. Damage to mtDNA is of great importance because it will often impair cellular energy production. However, damaged mitochondria can still replicate because the enzymes for mitochondrial replication are encoded entirely in the cell nucleus. For these reasons, it has been suggested that accumulation of defective mitochondria may be an important contributor to loss of cellular homoeostasis underlying the ageing process. We describe a mathematical model which treats the dynamics of a population of mitochondria subject to radical-induced DNA mutations. The model confirms the existence of an upper threshold level for mutations beyond which the mitochondrial population collapses. This threshold depends strongly on the division rate of the mitochondria. The model also reproduces and explains (i) the decrease in mitochondrial population with age, (ii) the increase in the fraction of damaged mitochondria in old cells, (iii) the increase in radical production per mitochondrion, and (iv) the decrease in ATP production per mitochondrion.

A network theory of ageing: the interactions of defective mitochondria, aberrant proteins, free radicals and scavengers in the ageing process.

Evolution theory indicates that ageing is caused by progressive accumulation of defects, since the evolutionary optimal level of maintenance is always below the minimum required for indefinite survival. Evolutionary theories also suggest that multiple processes are operating in parallel, but unfortunately they make no predictions about specific mechanisms. To understand and evaluate the many different mechanistic theories of ageing which have been proposed, it is therefore important to understand and study the network of maintenance processes which control cellular homeostasis. In this paper we describe a Network Theory of Ageing which integrates the contributions of defective mitochondria, aberrant proteins, and free radicals to the ageing process, and which includes the protective effects of antioxidant enzymes and proteolytic scavengers. The model simulations not only confirm and explain many experimental, age related findings like an increase in the fraction of inactive proteins, a significant rise in protein half-life, an increase in the amount of damaged mitochondria, and a drop in the energy generation per mitochondrion, but they also show interactions between the different theories which could not have been observed without the network approach. In some simulations, for example, the mechanism of the final breakdown seems to be a consequence of the cooperation of mitochondrial and cytoplasmic reactions, the mitochondria being responsible for a long term, gradual change which eventually triggers a short lived cytoplasmic error loop.

A comparison of amino acid distance measures using procrustes analysis.

Four methods to convert an amino acid similarity matrix into a metric distance matrix were compared using procrustes analysis. Procrustes analysis is a rotational fit technique, which assesses the degree of fit between two configurations after optimal matching of the two matrices under translation, rotation and scaling. The analysis shows that not all conversion methods are equivalent, but that the results of two methods are more similar than the others.

Biometrical evaluation of bioequivalence trials using a bootstrap individual direct curve comparison method.

Bioequivalence of two medicinal, or veterinary, products is established by comparing the mean of bioavailability measures, such as AUC and Cmax, following administration of the test (T) and reference (R) products. However, the use of these parameters has several drawbacks, e.g. they do not take into consideration the overall pharmacokinetic profile shape. Therefore, concerns have been raised regarding their appropriateness for assessment of bioequivalence. To overcome the limitations of these bioequivalence parameters, direct curve comparison metrics methods were recently proposed on an average basis. In this paper, an individual based direct curve comparison method for assessing bioequivalence is proposed. The bioequivalence of T and R in each subject is evaluated by a new curve comparison metrics delta. The metrics delta is the absolute sum of the difference between two curves. The significance of the metrics for each subject is assessed by bootstrapping. An overall bioequivalence of T and R may be considered if less than 25% of the subjects show statistically different profiles.

The mitochondrial theory of aging.

Mitochondria are not only the main source of energy for most eukaryotic cells, but also the main source of free radicals. These reactive molecules can damage all components of a cell such as membranes, proteins and DNA. Therefore they have long been suspected to be involved in the biological aging process. The fact that mitochondria posses their own genetic material (mtDNA) and that they only have a limited arsenal of DNA repair processes makes them one of the prime targets for reactive oxygen species. The idea that genetically damaged mitochondria accumulate with time and are causally responsible for the aging phenotype via a disturbed energy budget is at the core of the so called mitochondrial theory of aging. In recent years this idea has gained impetus from the discovery of mitochondrial diseases and mtDNA deletions in old organisms. However, there are still many open questions regarding the mechanism of the accumulation of these deletions and their physiological relevance. This review is therefore intended to give an overview of the current state of the mitochondrial theory of aging and to discuss some recent experimental findings.

Towards a network theory of ageing: a model combining the free radical theory and the protein error theory.

Many different theories of ageing have been proposed, based often on highly specific molecular causes. Recent advances in evolutionary theory support the idea that ageing is caused by progressive accumulation of defects, but indicate that multiple processes are likely to operate in parallel. This calls for an understanding of ageing and longevity in terms of a network of maintenance processes that controls the capability of the system to preserve homeostasis. Here we develop a theoretical model which begins the task of implementing a Network Theory of Ageing. To do this the model integrates the ideas of the Free Radical Theory, describing the reactions of free radicals, antioxidants and proteolytic enzymes, with the Protein Error Theory, describing the error propagation loops within the cellular translation machinery. The simulations show that an increased radical production and/or insufficient radical protection can destabilize an otherwise stable translation system. The model supports the idea that caloric restriction prolongs life via a reduction of the generation of radicals. Another result of the model is that protein half-life increases with time as a natural consequence of the interaction between proteolytic enzymes and radicals. Finally the model strengthens certain evolutionary ageing theories by showing that there is a positive correlation between maintenance related energy consumption and lifespan.

Accumulation of defective mitochondria through delayed degradation of damaged organelles and its possible role in the ageing of post-mitotic and dividing cells.

The mitochondrial theory of ageing proposes that an accumulation of defective mitochondria is a major contributor to the cellular deterioration that underlies the ageing process. The plausibility of the mitochondrial theory depends critically upon the population dynamics of intact and mutant mitochondria in different cell types. Earlier work suggested that mutant mitochondria might have a replication advantage but failed to account for the fact that mutants accumulate faster in post-mitotic than in dividing cells. We describe a new mathematical model that allows for damaged mitochondria to replicate more slowly, which accommodates experimental evidence of impaired energy generation and a reduced proton gradient in defective mitochondria. However, this is compensated for by a slower degradation rate of damaged mitochondria than intact ones, as suggested by de Grey (1997), which gives damaged mitochondria a selective advantage and leads to a clonal expansion of damaged mitochondria. This theoretical result is important because it agrees with evidence that, during ageing, single muscle fibres are taken over by one or only a few types of mtDNA mutants. The model also shows that cell division can rejuvenate and stabilize the mitochondrial population, consistent with data that post-mitotic tissues accumulate mitochondrial damage faster than mitotically active tissues.

Accuracy of tRNA charging and codon: anticodon recognition; relative importance for cellular stability.

Cellular homeostasis and the mechanisms which control homeostasis are important for understanding such fundamental processes as ageing and the origin of life. Several models have studied the importance of accurate protein synthesis for cellular stability, but these models have not considered the complexities of the translation process in any detail. Here we develop a new model which describes the interplay between aminoacyl-tRNA (aatRNA) synthetases, the cellular pool of charged tRNAs and the process of codon: anticodon recognition. We also take the processive character of the ribosomes into account. In common with previous work, our model predicts that the cellular translation apparatus can either be stable or deteriorate progressively with time. However, because our model explicitly describes different subreactions of the overall translation process, we are also able to assess the relative importance of accurate tRNA charging and codon: anticodon recognition for cellular stability. It appears that the tRNA charging by the aatRNA synthetases plays the key role in controlling the long-term stability of the cell. Ribosomal errors are less important because error-prone ribosomes, being processive, produce mainly inactive proteins which do not contribute to error propagation within the translation machinery.

Growing a classification tree using the apparent misclassification rate.

A method to determine the size of a classification tree is proposed. This method is based on the change of the apparent misclassification rate (AMR) of the tree at each growing stage. The method is simple and fast compared to the other classification tree methods, which are based on minimizing a cost complexity function. To test the method, it was used to classify species of fungi, and the results are in good agreement with those obtained by linear discriminant analysis. Also, 21 proteins with known structures and functions were classified using the proposed method. For this purpose the coefficient of variation for several properties of the secondary structures of these proteins has been used. Again, the results were in good agreement with the classification obtained previously using dynamic programming.

Inhibition of skin 5 alpha-reductase by oral contraceptive progestins in vitro.

Androgenic disorders of female skin such as hirsutism, acne and alopecia are etiologically caused by androgen excess. Skin 5 alpha-reductase activity is a major factor influencing the manifestation of endogenous androgen excess in women. Oral contraceptives have proven useful for the treatment of androgen disorders of the skin. The mechanisms of action by which oral contraceptives correct skin androgen levels may include inhibition of 5 alpha-reductase and androgen receptor activity. We investigated the inhibitory effect of oral contraceptive progestins and ethinyl estradiol on skin 5 alpha-reductase and their influence on androgen receptor activity and affinity, using three different in vitro assay systems. It was shown that norgestimate blocked 5 alpha-reductase activity with an IC50 value of 10 microM, followed by levonorgestrel (IC50 52 microM), dienogest (IC50 55 microM), cyproterone acetate (IC50 87 microM) and gestodene (IC50 98 microM). To determine the full androgenic potential of the progestins, androgen receptor binding affinities and activation potentials were determined. The progestins norgestimate and dienogest in particular combined 5 alpha-reductase inhibition with minimal androgenic potential. These data demonstrate that the progestins norgestimate and dienogest might help in the treatment of clinical hyperandrogeny in women.