Influence of Reaction and Diffusion Processes on the Intracellular Distribution of Mitochondria in Muscle Fibers

Extensive research in the fields of biochemistry, biological sciences, genetics and molecular biology has helped scientists delve into the molecular machinery of cell function. However, the unity and common features of living organisms that have evolved over millennia suggests that more general principles may dictate how cell components are arranged in space and time. In this context, analysis of the mechanisms governing cellular organization forms the central theme of the present research. Muscle fibers being highly plastic and the most organized cells in the biological world are chosen for the present study. The primary goal of this research is to develop mathematical models to analyze governing factors of organization of mitochondria in muscle fibers. Knowledge of such governing principles on muscles from a wide spectrum of animals provides vital insights to engineer new muscle, to develop tissue and metabolic engineering approaches for muscle regeneration and to develop gene therapy strategies to directly treat muscle diseases. A major challenge is that there exists no mathematical model governing mitochondrial spatial organization within the context of both energy metabolism and mitochondrial life cycles. Moreover, since muscle fibers are highly adaptive, experimental studies of their organization are limited. The present work provides a detailed analysis of mitochondrial spatial distribution and life-cycle dynamics performed for fibers subjected to various conditions, including metabolic demand for ATP, oxygen supply from surrounding capillaries, and fiber size. The mathematical modeling approach uses a reaction-diffusion analysis of oxygen, ATP, ADP and PCr involved in energy metabolism and mitochondrial function as governed by oxygen supply, volume fraction of mitochondria, and rates of reaction. Superimposed upon and coupled to the continuum species material balances is a cellular automata (CA) approach describing the mitochondrial life cycle. The CA is a discrete computational approach within a defined lattice framework. The fate of the discrete entities is governed by a set of local rules pertinent to the system. Proposing rules in order to mimic mitochondrial dynamics in muscle fibers is another area in theoretical muscle biology that has not been explored. The developed mathematical model is solved numerically with a code specifically written in MATLAB and run on high performance computing. The continuum species material balances are solved using an alternating direction implicit finite difference scheme. Probabilistic Gaussian distribution functions simulating important biological phenomenon such as targeted mitophagy and mitochondrial fission are proposed as CA rules to describe the lifecycle of mitochondria. In order to assess diffusional constraints in the fiber, the effectiveness factor, defined as the ratio of the reaction rate in the system with finite rates of diffusion to that in the absence of diffusion limits is evaluated. The model results show significant shifts and redistribution of mitochondria near the capillaries where there is an increased availability of oxygen. The shifts in mitochondrial distribution allow the fiber to function more efficiently, i.e. with minimal diffusion limitations and higher cellular energy state and greater aerobic capacity. The model results describing the spatial distribution of mitochondria effectively predicted the experimentally observed heterogeneous distributions. The experimentally validated model is used to study mitochondrial distribution in a wide range of fiber types, and to analyze the growth of fibers and the effects of hypoxia. The utilization of a quantitative bioengineering analysis in the present work demonstrates the importance of reaction and diffusion processes in muscle organization and function.