Life sciences through mathematical models

Understanding mitochondria and the utility of optimization as a canonical framework for identifying and modeling mitochondrial pathways

The goal of this paper is to provide an overview of our current understanding of mitochondrial function as a framework to motivate the hypothesis that mitochondrial behavior is governed by optimization principles that are constrained by the laws of the physical and biological sciences. Then, mathematical optimization tools can generally be useful to model some of these processes under reasonable assumptions and limitations. We are specifically interested in optimizations via variational methods, which are briefly summarized. Within such an optimization framework, we suggest that the numerous mechanical instigators of cell and intracellular functioning can be modeled utilizing some of the principles of mechanics that govern engineered systems, as well as by the frequently observed feedback and feedforward mechanisms that coordinate the multitude of processes within cells. These mechanical aspects would need to be coupled to governing biochemical rules. Of course, biological systems are significantly more complex than engineered systems, and require considerably more experimentation to ascertain and characterize parameters and subsequent behavior. That complexity requires well-defined limitations and assumptions for any derived models. Optimality is being motivated as a framework to help us understand how cellular decisions are made, especially those that transition between physiological behaviors and dysfunctions along pathophysiological pathways. We elaborate on our interpretation of optimality and cellular decision making within the body of this paper, as we revisit these ideas in the numerous different contexts of mitochondrial functions.

Brain energetics, mitochondria, and traumatic brain injury

We review current thinking about, and draw connections between, brain energetics and metabolism, and between mitochondria and traumatic brain injury. Energy is fundamental to proper brain function. Its creation in a useful form for neurons and glia, and consistently in response to the brain's high energy needs, is critical for physiological pathways. Dysfunction in the mechanisms of energy production is at the center of neurological and neuropsychiatric pathologies. We examine the connections between energetics and mitochondria - the organelle responsible for almost all the energy production in the cell - and how secondary pathologies in traumatic brain injury result from energetic dysfunction. This paper interweaves these topics, a necessity since they are closely coupled, and identifies where there exist a lack of understanding and of data. In addition to summarizing current thinking in these disciplines, our goal is to suggest a framework for the mathematical modeling of mechanisms and pathways based on optimal energetic decisions.