(651f) Sarcopenia in Silico

Sarcopenia refers to the age-related pathological loss of muscle mass and strength, a condition that contributes significantly to frailty as muscle loss often limits mobility and strength in elderly individuals. In the year 2000, the health care costs related to sarcopenia in the United States alone was estimated to exceed US$ 18.5 billion [1]. Given the increasing proportion of the elderly in populations worldwide, it is vital to establish a better understanding of age-dependent conditions, such as sarcopenia. While the retardation of sarcopenia has been shown to be possible, to date, there is no validated treatment for sarcopenia in humans.

The molecular etiology of sarcopenia is currently not fully understood. One of the main hypotheses of mechanism underlying sarcopenia is the progressive atrophy and loss of muscle fibres due to focal dysfunction of mitochondria. Mitochondria are cellular organelles responsible for energy generation and their DNA (mitochondrial DNA) while short, encode important proteins necessary for oxidative phosphorylation. Large-scale deletions in mtDNA have been found to be frequently associated with sarcopenia [2]. While the overall mtDNA deletion load in most tissues is relatively low, recent single cell studies have shown that high levels of mtDNA deletions can accumulate focally in sarcopenia [2-4]. Experimental techniques like histochemical or immuno-histochemical methods by in situ hybridization and laser capture micro-dissection followed by PCR have convincingly shown a mosaic-like cellular distribution of mtDNA deletions and associated age-related decline of mitochondrial respiratory enzyme activity [5]. Focal mtDNA deletions will eventually lead to mitochondrial dysfunction and apoptosis, and the loss of even a small part of a muscle fiber can cause whole-fibre dysfunction, giving reason to why low level mtDNA deletions can affect whole tissue functionality.

Devising treatment methods for sarcopenia thus require a critical understanding of the etiology and dynamics of mtDNA deletion accumulation in the muscle fibres. Currently, very limited experimental data are available on the etiology of sarcopenia and the possible interventions to reduce its progression in vertebrate animal models. This is due to significant challenges in obtaining such data for long-lived mammalian animal models (high cost) and also harvesting tissue sample for clinical trials is invasive in nature and therefore not feasible for human studies. Therefore, to better understand the influence of stochastic dynamics of mtDNA deletion accumulation on the focal accumulation of mtDNA deletions observed in the muscle fibre, we have developed a hybrid model that describes (1) the stochastic expansion of mtDNA deletion in a myo-nuclear region, (2) the spread of mtDNA across a muscle fibre, and (3) the progressive loss of muscle functionality. The hybrid model combines deterministic and stochastic models and can be further utilized as a work-bench to analyse the influence of different parametric perturbations on the severity of sarcopenia, thereby providing insight into the possible interventions.

2. RESULTS

2.1 Stochastic simulation of the developmental cell lineage

Embryonic cell divisions begin after fertilization of an oocyte. Initially, mouse oocytes harbor a large number of mitochondria, which allow the zygote to multiply initially without the need to replicate mtDNA. During the later stages of development, there is enormous amount of replication in the dividing embryonic cells. Thus, mtDNA proliferation during development acts to seed mtDNA deletions and aids the expansion of these deletions.

In the developmental cell lineage, the number of wild-type mtDNA (W) and mutant mtDNA (M) are tracked for each progenitor cells of mouse skeletal muscle. The model simulates two mtDNA-related maintenance processes: mitochondrial turnover, comprising of relaxed replication and degradation of mitochondria, and de novo deletions arising from errors during mtDNA replication, following our previous study [4]. The in silico stochastic mouse model is simulated such that each mtDNA-related process is a jump Markov process. A modified version of the SSA that incorporates the details of mtDNA turnover processes is used to simulate mtDNA deletion burden in a single heart tissue ( 25 million cells) during development. The parameters were obtained from reported values based on experimental data for mice and we have ensured that they are consistent with the current literature and the state of the art measurement techniques.

Our simulation indicated a wide spectrum of mtDNA deletion loads mimicking mosaicity seen in the experiments. These initial deletions can clonally expand during the natural life span of mouse as captured by our post-natal model below.

2.2 Post-natal skeletal muscle reaction-diffusion model

In mice, it has been found that during development skeletal muscle mass increases by 50-fold and this causes almost 50% increase in total mass of the organism at birth. The increase arises due to the action of a population of muscle stem cells, called satellite cells, which form the embryonic somatic progenitor cells. During myogenesis, the primitive cells are arranged in clusters and they further undergo fusion to form small multinucleated cells known as the myotubes. Elongation of myotubes occurs by end-to-end fusion with the adjacent tubes. Finally, these early differentiated myotubes are bundled together forming the muscle fibers. The reaction-diffusion model developed in this work is defined over a region with shape and attribute of a muscle fibre.

In post-development, individual satellite cells generated from stochastic simulations of cell lineage above are selected randomly and arranged end-to-end to form a muscle fibre. A reaction-diffusion equation is simulated to describe the concentration of wild-type and mutant mtDNA (W and M) in myonuclear domains along the length of the fiber during mouse's natural life span. The simulation results were validated against histochemical analysis of skeletal muscle tissue of mice, in which some of the fibres underwent atrophy or showed red-ragged phenotype due to mitochondrial dysfunction [7]. The model predictions demonstrated an excellent agreement with these experimental results. In addition, there were two interesting observations from further model simulations:

? De novo mtDNA deletions and their expansion during development are a significant contributor to the cell-to-cell heterogeneity of mtDNA deletion accumulation in the tissue seen post-natally. Most of the clonal expansion observed in the post mitotic cells is associated with the mtDNA deletion occurring and accumulating during development.

? Mitochondrial DNA diffusion modulated by mitochondrial fusion-fission plays a crucial role in determining the mtDNA deletion spread and its severity in sarcopenia. Here, faster diffusion, though intuitively not desirable as it enhances the spread of deletions, in fact leads to fewer focal accumulations of mtDNA deletions.

3. REFERENCES

1. I. Janssen, D. S. Shepard, P. T. Katzmarzyk et al., J Am Geriatr Soc 52 (1), 80 (2004).

2. L. A. Herndon, P. J. Schmeissner, J. M. Dudaronek et al., Nature 419 (6909), 808 (2002).

3. K. Khrapko, N. Bodyak, W. G. Thilly et al., Nucleic Acids Res 27 (11), 2434 (1999).

4. S. K. Poovathingal, J. Gruber, B. Halliwell et al., PLoS Comput Biol 5 (11), e1000572 (2009).

5. J. Muller-Hocker, Am J Pathol 134 (5), 1167 (1989).

6. Daniel T. Gillespie, Markov Processes: An Introduction for Physical Scientists. (Academic Press, San Diego, 1991).

7. S. H. McKiernan, E. Bua, J. McGorray et al., FASEB J 18 (3), 580 (2004).