between the production of ROS and their oxidation, which then affects mitochondrial respiratory chain function. Cumulative oxidative stress is viewed as the critical factor that precedes a cascade to dysfunction (Elfawy and Das 2019).
Mitochondrial diseases have a major relevance to military personnel health. For example, approximately one-third of the 1990–1991 US Gulf War veterans – in the range of 175,000–250,000 soldiers – developed chronic multisymptom health problems, known by the term “Gulf War Illness”, with mechanisms that adversely affect mitochondria (Koslik et al. 2014; Chen et al. 2017).
1.8. Modeling
More generally, and rounding out the above discussion, when compared to the tremendous number of papers that describe experimental results and hypothesize causes, effects and couplings, there have been a comparatively small number of works on the mathematical modeling of various aspects of mitochondrial function. Early examples of such models (Magnus and Keizer 1997, 1998a, 1998b) are quite complex, with simpler derivative models attempted (Bertram et al. 2006; Saa and Siqueira 2013). Derived equations govern ATP production during glucose metabolism via oxidative phosphorylation. There have also been efforts to relate mitochondrial dynamics to neuronal spike generation, providing a powerful tool for disease modeling and potentially enabling clinical interventions (Venkateswaran et al. 2012). A computational model for the mitochondrial respiratory chain is derived to appropriately balance mass, charge and free energy transduction (Beard 2005). Evidence exists of optimal decisions occurring within the mitochondria. The challenge of formulating even a simple model is a serious undertaking.
Mathematical modeling has been attempted for other critically related aspects of energetics, but are beyond our scope here, which has been to provide background on the mitochondria, where optimizations appear to have been the governing framework for processes.
Due to the formidable challenges in gathering biological data, understanding cause and effect, and even identifying all the components and constituents of cells, it is fully understandable and logical that these have taken precedence in the research community. As these aspects have become better understood and deeper, we have seen that mathematical modeling efforts have started to take hold and bear fruit.
1.9. Concluding summary
Mitochondria play a central role in cellular energetics, and are involved in almost all neurological disorders. Thus, mitochondrial function is at the core of our understanding of neurological health. How dysfunction leads to many of the most debilitating and fatal neurodegenerative diseases is still poorly understood. Some understanding may be garnered if the processes that occur within the cell can be placed in an optimization framework, which may then lead to therapeutic interventions to improve the health of the many millions of people who suffer from these diseases.
Mitochondria move, stop and anchor, undergo fusion and fission, and degrade on the spatial and temporal scales needed to meet the broad spectrum of cellular energy needs, as well as Ca++ buffering needs, throughout the neuron. Any lack of these functions can lead to mitochondrial and neuronal death. Based on the literature, of which only a very small fraction is referenced here, it appears that there are energy-based mechanisms that operate locally (sub-optimizations) and globally across multiple cells and beyond (perhaps full optimizations). Such a constrained optimization framework appears to be a reasonable way to better understand very complex subcellular processes.
It appears that among numerous progression paths, some lead to dysfunction, in particular, due to ineffective energy production. These paths, we believe, satisfy some optimalities in order to become the chosen progression path. We may conclude that physiological, as well as pathological paths, in conjunction with other environmental factors, can be optimal choices for the organism. Perhaps, depending on the combination of intracellular and extracellular environments, such optimizations can be based on different cellular/subcellular states, characteristics and constraints. Clearly, due to the criticality of energy production and usage, we expect that these are fundamental aspects of any optimal decision-making. There may not be any global optimizations, only local sub-optimizations. Understanding these optimality decisions may provide clues and eventually paths for clinical interventions and cures for some of humanity’s most serious neurodegenerative diseases.
Approaching such problems with the view of an applied mechanician may provide new perspectives on cell modeling and intracellular processes. We trust that this chapter will motivate others to try their hand at biological modeling.
1.10. Acknowledgments
It is a pleasure to thank the editors of this volume for their effort in organizing the authors and chapters, and for considering a chapter on a topic that may be considered outside the mainstream focus of this book, as well as the very useful feedback on the first draft of this chapter.
1.11. Appendix
This volume acknowledges the professional life and accomplishments of Isaac Elishakoff. I knew of his work before I met him in 1982, when I gave a talk at the Technion, in Haifa, where Isaac was a faculty member. He was very kind to a novice; at the time I worked for a consulting engineering firm in New York. It would be another seven years before I would join Rutgers University. But during that consulting period, I continued my friendship with Isaac, and we and two additional colleagues published a paper on the use of MACSYMA, one of the early symbolic codes, in problems of random vibration.
Isaac and I continued our near-periodic interactions, randomly exchanging ideas and holiday greetings. He eventually came to Florida Atlantic University, not missing a beat in his extraordinary productivity. He writes books as others write papers. His interest in mechanics goes beyond the technical aspects, intersecting with the historical provenance of the fundamental ideas that shape our disciplines. His works continue to add insights and dimension to our understanding of complex physical processes.
While my professional interests very much overlap with Isaac’s, I have recently become interested in the biological sciences, in particular, brain energetics, and whether we can apply some of our engineering and mathematical modeling skills to the fantastic and very complex processes, by which the cells in our bodies create energy. I am pleased to honor Isaac by presenting a summary of some interesting aspects of the functioning of the mitochondria, an organelle that exists in large numbers in most of our cells. It creates the energy that our bodies require in order to live, survive and think. This community has much to offer in helping to increase our understanding of these beyond-complicated processes. I am sure that Isaac would agree.
Congratulations Isaac, for what you have achieved so far, and for what you will continue to contribute!
1.12. References
Adiele, R.C. and Adiele, C.A. (2019). Metabolic defects in multiple sclerosis. Mitochondrion, 44, 7–14.
Baker, N., Patel, J., Khacho, M. (2019). Linking mitochondrial dynamics, cristae remodeling and supercomplex formation: How mitochondrial structure can regulate bioenergetics. Mitochondrion, 49, 259–268.
Beard, D.A. (2005). A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation. PLoS Comput. Biol., 1(4), 252–264.
Benard, G., Bellance, N., James, D., Parrone, P., Fernandez, H., Letellier, T., Rossignol, R. (2007). Mitochondrial bioenergetics and structural network organization. J. Cell Sci., 120(5), 838–848.
Benaroya, H. (2020). Brain energetics, mitochondria, and traumatic brain injury. Rev. Neurosci. [Online]. Available at: https://doi.org/10.1515/revneuro-2019-0086.
Bertram, R., Pedersen, M.G., Luciani, D.S., Sherman, A. (2006). A simplified model for mitochondrial ATP production. J. Theor. Biol., 243, 575–586.
Buhlman, L.M. (2016). Mitochondrial Mechanisms of Degeneration