levels: subcellular, cellular, tissue and organism. Dysfunction in the mechanisms of energy production appears to be at the center of neurological and neuropsychiatric pathologies. Thus, the profound interest is in understanding how these organelles function and govern their operations. One example of dysfunction is how secondary pathologies in traumatic brain injuries result from energetic dysfunction.
Neurons and glia are the components of brain function, but energy homeostasis must be maintained in order to assure proper functioning, and begins within the subcellular organelle, the mitochondria. This homeostasis is the product of metabolic reactions that are coupled to energy demands in space and time throughout the brain, and are regulated by feedforward and feedback mechanisms. Any mismatch between supply and demand over significant time intervals invariably initiates cascades of dysfunction leading to well-known neurodegenerative and neuropsychiatric pathologies.
These mechanisms, at all scales, “choose” from numerous progression paths, some of which lead to dysfunction due, in large part, to ineffective energy production. Understanding how these “choices” are made requires us to formulate models of the mechanisms alluded to above. If there are governing optimal “choices” or mechanisms, then dysfunction and defects may also sometimes be optimal choices for the organism, and perhaps the optimizations are energy-dependent given the criticality of energy production and usage. Perhaps, optimal choices can lead to negative outcomes. Given the multiple constraints for a successful living organism, there may only be local sub-optimizations. Thus, when we refer to optimization, we are having the above discussion, about how we frame the multitude of progression paths within the cell and external to it. Evolution governed which organisms survived, and which did not, based on their fitness for the environment. At the cellular level, this may entail a minimization of energy use, or perhaps the quickest transfer of information between two neurons.
Understanding these optimality decisions can provide clues for clinical interventions and eventually, cures for some of humanity’s most serious neurodegenerative diseases. Optimal pathways may be identified via the multitude of techniques that have been developed for the physical sciences and engineering, taking the morphological (and mechanical), biochemical and metabolic constraints into account. Constraints such as signaling mechanisms at all scales, cell and organelle morphology, feedback mechanisms, and imbalances of energetics and other intermediate products of mitochondrial functioning are part of a possible formulation. The community is at the beginning of formulating such models. This overview aims to pull together a very brief summary of current thoughts and evidence that, at least for the mitochondrial organelle at the subcellular level, the responses are evolutionarily conserved local and global optimizations.
In the following sections, we discuss some of the key functions of the mitochondria and identify, or suggest how these appear to be evolutionarily conserved properties that are based on an optimization. While optimization in biology has been discussed for decades, the application of optimization methodologies to such systems has been slow to develop, in part due to an incomplete understanding of significant aspects of functioning and an incomplete dataset.
We also refer to the work of Elishakoff (e.g. 1994, 2003, and with Qiu 2001). Elishakoff developed the concept of anti-optimization, where system uncertainties are studied by combining conventional optimization methods with interval analysis. In this approach, the optimal solution is a domain, rather than a point and is a two-level process. At one level, the optimal values of system parameters are obtained, and at the other level, uncertainties are anti-optimized. The anti-optimization yields the least favorable and most favorable system response and relies on knowledge of the bounds of uncertainty, rather than probability density functions. Such an approach can be potentially useful in biological systems where data can be sparse, with uncertainties only known via the upper and lower bounds.
1.2. Mitochondria
Our brief overview is about the very exciting area of the intense biological research of the mitochondria, an intracellular organelle. The mitochondria’s primary functions include the maintenance of energy homeostasis, cell integrity and survival (Simcox and Reeve 2016). The mitochondria variably comprise between about 20% of the cell, up to most of the cell volume, dynamically depending on the energetic needs of the cell. In the aggregate, mitochondria account for about 10% of body weight, attesting to their importance. These organelles produce up to 95% of a eukaryotic cell’s energy through oxidative phosphorylation (Tzameli 2012), driven by an electrochemical proton gradient created by the respiratory chain housed within the mitochondria’s inner membrane. Oxidative phosphorylation is the metabolic pathway in the mitochondrial matrix containing the cristae, where enzymes oxidize nutrients. Energy is released, producing adenosine triphosphate (ATP), a complex organic chemical that provides energy for many cellular processes. The human body consumes, on average, a quantity of ATP per day that approximates its body weight (Zick and Reichert 2011).
Eukaryotes are organisms with cells that have a nucleus enclosed within membranes, unlike prokaryotes (bacteria and archaea). Eukaryotes may also be multicellular and consist of many cell types.
The cristae are tight folds of the inner membrane studded with proteins, with the folds providing a significant increase in surface area (much in the same way as the folded cerebral cortex), over which the above energy-producing processes can occur. Cristae biogenesis, regulated through the large enzyme ATP synthase, closely links mitochondrial morphology to energy demand (Simcox and Reeve 2016).
Mitochondrial functions also include quality control through fission (division) and fusion (merging), iron–sulfur cluster formation, calcium handling, cell signaling, cell repair and maintenance, and reactive oxygen species (ROS) production (Simcox and Reeve 2016). ROS emission is harmful to the mitochondrial DNA, which is a byproduct of energy production (Kembro et al. 2013) and is at least partially eliminated. As part of their metabolic functions, mitochondria also perform critical programmed cell death functions called apoptosis (Vakifahmetoglu-Norberg et al. 2017), which are related to the function of fission. Figure 1.1 summarizes some of these functions.
Figure 1.1. Mitochondria shown undergoing fission/fusion. The respiratory complexes are shown, identified using roman numerals. Various mechanisms are also shown, including signaling, Ca2+ transport across the membrane, and others outside of our current scope (Vakifahmetoglu-Norberg et al. 2017, with permission). For a color version of this figure, see www.iste.co.uk/challamel/mechanics3.zip
Mitochondria are believed to be the reason why complex cellular beings evolved from single celled entities. They originated as individual cell bacteria, but eventually integrated with our ancestral cells, leading to the current eukaryotic cells with nuclei. This ancestry partially explains why mitochondria, to this day, contain mtDNA, remnants of their own DNA.
The goal of this chapter is to refer to aspects of mitochondrial behavior that appear to be governed by optimization principles, which are constrained by biological limitations. It is reasonable to assume that the mathematical machinery of optimization can be useful in modeling some of these processes. Also, given that there are numerous mechanistic determinants of cell and intracellular functioning, we believe that these can be modeled using some of the principles of mechanics that govern engineered systems, as well as the frequently observed feedback and feedforward mechanisms that coordinate the multitude of processes within cells. Of course, biological systems are significantly more complex and require considerably more experimentation in order to ascertain behavior. We suggest the ideas herein with humility. A more detailed review of some of these ideas is available (Benaroya 2020), where the links between mitochondria, cellular energy production and the coupling of these to diseases and the body’s response to injury are discussed.
1.3. General morphology; fission and fusion
Mitochondria exist in varying numbers, dependent on cell type, and sometimes form intracellular networks of interconnecting organelles called a reticulum, extending throughout the cytosol and in close contact with