How do these computational models account for the radically different aging rates that occur in different species? Our simulations show that the time required for the clonal expansions of mtDNA mutations by random drift is proportional to the number of mtDNA molecules per cell, N, and the mtDNA half-life, Thaf (Chinnery and Samuels, 1999). However, neither of these parameters is believed to vary significantly across mammalian species. The simulations indicate that there is no biologically reasonable way to speed up the process of clonal expansion of mtDNA mutations in short-lived species. The long time scale necessary for clonal expansion by random drift leads us to reconsider the two hypotheses illustrated in Figure 48.1. Although the clonal expansion hypothesis may be the best explanation for the increase in mtDNA mutations with age in the long-lived species, such as humans, for the short-lived species we have to return to the error-cascade hypothesis.
The relative importance of the clonal expansion and error cascade mechanisms in the mtDNA aging simulations is controlled by the parameter Pmut, the probability of de novo mutation formation in mtDNA. At low mtDNA mutation rates clonal expansions dominate (Taylor et al., 2003), whereas at high mutation rates the error cascade mechanism of enhanced ROS production should be included in the simulations. There is good reason to believe that the mtDNA mutation rate is higher in short-lived species than it is in humans. This has been repeatedly observed in experiments on aging in rodents (Wang et al., 1997; Herrero and Barja, 1999). Finally, our own analysis of the mtDNA sequences of mammals indicates that the mitochondrial genomes of the short-lived species are physically more susceptible to mutations than are those in the long-lived species (Samuels, 2004, 2005).
There are only a few other research groups that have recently worked on simulations of mtDNA dynamics and the aging process. The simulation research program of Tom Kirkwood (Kowald and Kirkwood, 1993; Kowald and Kirkwood, 2000; Sozou and Kirkwood, 2001; Kirkwood and Proctor, 2003) is based on a different general hypothesis than that of our modeling efforts. Their work uses the delayed degradation hypothesis, which assumes that mitochondria carrying a large fraction of mutated mtDNA suffer less damage and are thus degraded more slowly than the mitochondria with a larger proportion of wild-type mtDNA. This gives the mutant mtDNA a competitive advantage over the wildtype mtDNA. Another research group that is active in this area of simulation is headed by Konstatin Khrapko (Nekhaeva et al., 2002; Kraytsberg, et al., 2003). The simulations of this group follow the same general hypotheses as we do in our modeling.
For an idea of the future challenges to be dealt with in mtDNA simulations, take another look at Table 48.2. The simulation methods described in this chapter cover only a small range of the scales important to the role of mtDNA in the aging process. In particular, building on simulations of aging at the cellular level to develop an understanding of the aging process at the organism level is a grand challenge.
There are significant challenges to be faced even within the scale range covered by these simulations, between the mtDNA molecule level and the cell level. The complicated spatial organization of mtDNA in separate organelles, and even further into nucleoids (small groupings of 1-5 mtDNA molecules), is a challenge to simulation. The simulations described here do not deal with these intermediate levels of organization, though those of Kirkwood do include the organelle level.
Although there are many off-the-shelf simulation packages for biochemical models, there are few such packages available for the types of simulations described in this chapter. For this reason, the research in this area is still primarily done by writing original programs in either C or Fortran. Until a very flexible and general simulation package is available, I recommend that you write your own programs for this research. However, this does not mean writing every line of simulation code from scratch. Here are two excellent sources of code for basic simulation methods, such as the Poisson and Binomial routines used repeatedly in this chapter.
For advice on programming methods for simulation I recommend the very popular series of Numerical Recipes books (Press et al., 1988), now available in Fortran, C, C++, and Fortran 90. These books take a very practical approach to numerical methods, not a theoretical one, describing routines that are both effective and relatively simple. The books contain example codes for each numerical method discussed. These codes can be used directly in your simulation for convenience, though often an expert programmer can improve on their efficiency.
For an alternative to the Numerical Recipes books, I recommend the GNU Scientific Library (or GSL), available for free download at www.gnu.org/software/gsl. This software library contains over 1000 routines, in C and C++, which can be used as basic building blocks for developing simulation code. The most effective approach may be to read the Numerical Recipes books for an understanding of the methods, and use the GSL code in your programs.
Finally, for cross-species comparisons of mitochon-drial genomes, the National Center for Biotechnology Information (NCBI), a part of the National Institutes of Health, is the standard repository for all sequenced mitochondrial genomes. These genomes are available at www.ncbi.nlm.nih.gov/genomes/ORGANELLES/ organelles.html, in a convenient taxonomic organization. As of this writing (mid-2005), this database contained complete mitochondrial genomes from 713 different species, including 639 metazoa species.
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For centuries, ever since the legendary Ponce de Leon went searching for the elusive Fountain of Youth, people have been looking for ways to slow down the aging process. Medical science has made great strides in keeping people alive longer by preventing and curing disease, and helping people to live healthier lives. Average life expectancy keeps increasing, and most of us can look forward to the chance to live much longer lives than our ancestors.