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 the nucleus, the endoplasmic reticulum, the Golgi network and the cytoskeleton (Benard et al. 2007). The cytosol is the intracellular fluid that surrounds all the organelles and other components of the cell. The endoplasmic reticulum, an organelle, has protein-related functions, and works with the Golgi network to deliver proteins to where they are needed within the cell.
The mitochondrial network is a net-like formation. “Mitochondrion” traces back to the Greek word meaning “thread grain”. Mitochondria may exist as small isolated particles, or as extended filaments, networks or clusters connected via intermitochondrial junctions. Serial-section three-dimensional images showed filamentous mitochondria frequently linked into networks (Skulachev 2001).
Extended mitochondria, and electrically coupled mitochondrial clusters, can transmit power in the form of membrane potential between remote parts of the cell. The coupled clusters are switched on and off as needed, in order to avoid local damage due to a simultaneous discharge of too many of the organelles at once. As energy demand increases, isolated mitochondria unite into extended mitochondrial systems. In tissues composed of large cells with high energy demands, such as the brain, heart and kidneys, the so-called mitochondrial reticulum occupies much of the cell volume.
Certain physiological and pathological conditions lead to the decoupling of mitochondrial filaments and networks into single mitochondria. Extended mitochondrial systems of various topologies exist only when their energy coupling and transmitting machineries are functioning normally (Skulachev 2001). Muscle fibers require a specialized spatial organization of the mitochondrial network (Vinogradskaya et al. 2014).
Mitochondrial fission, fusion, motility and tethering, the four conserved and interdependent mitochondrial activities, alter the mitochondrial network shape and its distribution in the cell. A dysfunction of one activity can have consequences on another. For example, it is observed that the attenuation of fission disrupts the transport of mitochondria to neuronal synapses, resulting in detrimental effects on cell function. Tethering defects can reduce fission rates (Lackner 2014). Relative rates of mitochondrial fission and fusion govern the connectivity of the network, where energetic needs coordinate the two processes. Feedforward and feedback mechanisms coordinate the complex relationships between energy supply and demand. We anticipate that these activities operate within an optimal domain.
In complex polarized cells such as neurons, mitochondria must be actively transported and tethered to, and maintained in, active synaptic regions. Tethers are important for positioning mitochondria within the overall cell structure and also relative to other organelles.
Mitochondrial morphology (network organization) and bioenergetic functions are coupled bidirectionally (Benard et al. 2007). The metabolic needs of the cell optimize the organelle’s bioenergetic capacity using frequent cycles of fusion and fission to adapt the morphology of the mitochondrial compartment to current supply and demand, as well as other required functions, of which there are many (Pagliuso et al. 2018). A disruption of these, for example, unopposed fission or fusion, adversely impacts cellular and organismal metabolism, leading to potentially devastating dysfunction (Wai and Langer 2016).
Fusion engages the entire mitochondrial compartment in respiratory active cells, maximizing ATP synthesis by mixing the matrix and the inner membrane, allowing close cooperation within the respiratory machinery. Metabolites, enzymes and mitochondrial gene products are spread throughout the mitochondrial compartment. Extensive adaptations of mitochondria to bioenergetic conditions occur at the level of the inner membrane ultrastructure and the remodeling of mitochondria cristae. A sudden need for metabolic energy results in cell stress and can lead to the formation of hyperfused mitochondrial networks. Such short-term stress exposure in starvation results in fusion that optimizes mitochondrial function and plays a beneficial role for the long-term maintenance of bioenergetic capacity. In a complementary way, irreversibly damaged mitochondria are eliminated by fission (autophagy), contributing to the maintenance of bioenergetic capacity (Westermann 2012). It is interesting, as a practical matter, that stresses to the cells benefit mitochondria in the same way as exercising in the gym benefits our muscles. Whether keeping the body at a proper range of temperatures when it is too cold, keeping up energy production during reduced caloric intake or matching energy needs during strenuous activity, the mitochondria comes out stronger and healthier, with larger numbers. Stress is an optimization mechanism.
Extensive disturbances to the dynamic balance between fission and fusion are linked to neurodegenerative and metabolic diseases (Chauhan et al. 2014). One purpose of this cycle between fission and fusion is to minimize the accumulation of reactive oxygen species (ROS). ROS are formed as a natural byproduct of the normal metabolism of oxygen and have important roles in cell signaling and homeostasis. However, during times of stress, ROS levels can increase dramatically, resulting in significant damage to cell structures. Cumulatively, this is known as oxidative stress.
Mitochondrial performance can be estimated by its bioenergetic capacity (ATP generation), metabolic capacity (mTOR activity) and damage accumulation (ROS production and/or mutation accumulation in mtDNA). Several nutrient sensing pathways link glucose metabolism to mitochondrial ATP, mTOR and ROS levels, which, in turn, directly or indirectly control proteins of fission–fusion machinery, like the fission proteins Drp1 and Fis1. The system flow chart is shown in Figure 1.2.
Figure 1.2. Derivation of mitochondrial performance phenomenologically (Chauhan et al. (2014), with permission)
The ATP module in the network above can, for example, be modeled by the following three first-order ordinary differential rate equations (Chauhan et al. 2014):
The quantities in the square brackets represent concentrations. JGlyc, JResp and Jcons are the respective fluxes of glycolysis, mitochondrial respiration and ATP consumption in other cellular processes, derived phenomenologically. q1 is the fission rate, k1 and k2 are the respective synthesis rates, and d1 and d2 are the respective degradation rates. p1 to p12 are the rate constants. Even at the micro-level of the elements shown in Figure 1.2, optimal performance requires a balance between numerous processes governed by coupled equations of the form of equation [1.1].
System biology modeling approaches address such complex interactions between components of
