MATHEMATICAL MODELLING OF ENERGY GENERATION IN THE MITOCHONDRIA

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ABSTRACT

Most of the energy carrying molecules adenosine triphosphate (ATP) synthesized during cellular respiration is produced in the mitochondria through oxidative phosphorylation. By considering properly the process through which the bio-energy is generated in the mitochondria, we have developed a mathematical model for the energy generation based on the physics that would provide insights into the operations in the mitochondria and limiting mechanism. We hope that, with the model, it will be possible for an individual to predict the behavior of the mitochondria and thus energy requirement under certain conditions. 


TABLE OF CONTENTS

Title Page
Abstract
Table of Contents

CHAPTER ONE
3.0       Introduction
3.1       Work Objectives
3.2       Scope/Limitations of Study

CHAPTER TWO
2.0       Literature Review

CHAPTER THREE
3.0       Cellular respiration
3.1       Aerobic respiration
3.2       Anaerobic respiration
 3.3      Glycolysis
3.4       Citric acid cycle
3.5       Oxidative phosphorylation
3.6       Electron transport chain
3.7       Electron transport chains in mitochondria
3.8       Coupling with oxidative phosphorylation
3.9       ATP synthase (complex V)
3.10     The Chemiosmotic Theory
3.11     The proton-motive force

CHAPTER FOUR
4.0       Model Formulation/ Solution

CHAPTER FIVE
 5.0      Discussion
 5.1      Conclusion

5.2       References

CHAPTER ONE
1.0   INTRODUCTION
            In other to function, every machine requires specific parts such as screws, springs, cams, gears, and pulleys. Likewise, all biological machines must have many well-engineered parts to work. Examples include units called organs such as the liver, kidney and heart. This complex life units are from still smaller parts called cells which in turn are constructed from yet smaller machines known as organelles.
            In cell biology, a mitochondrion (plural mitochondria) is member-enclosed organelles found in most eukaryotic cells (Henze and Martin 2003).This organelles ranges from 0.5 to 10 micrometer (mm) in diameter. Mitochondria are sometimes described as “cellular power plants” because, they generate most of the cells supply of adenosine triphosphate (ATP), used as a source of chemical energy (Campbell et al 2006). In addition to supplying cellular energy, mitochondria are involved in a range of other processes, such as signaling, cell differentiation, cell death, as well as the control of cell cycle and cell growth (Mc Bride et al 2006). Mitochondria have been implicated in several human diseases, including mitochondria disorders (Garde and Roles 2005) and cordial dysfunction (Lesnefsky et al (2001), and plays a role in the aging process.
                        Mitochondrial energy generation (production) is a foundation for health and wellbeing. It is necessary for physical strengths, stamina and consciousness. Subtle deficits in mitochondrial function can cause weakness, fatigue and cognitive difficulties. Basically, the mitochondria supply almost all the energy to the cell (90%). Without mitochondria, there is no life, because, as we all know, life requires energy.
            Mitochondrial energy production (generation) is accomplished by two closely lined metabolic processes. First, the citric acid cycle which converts biological fuel (carbohydrates and fatty acids) into adenosine triphosphate (ATP) and hydrogen (in the form of nicotinamide-adenine dinuclotide NADH and flavine-adenine dinucleotide  FADH2). Secondly, the  electron transport chain which combines hydrogen with oxygen to generate abundant ATP in a highly efficient controlled manner.
 The process of generating ATP with oxygen is called “oxidative phosphorylation”. This process generates approximately ten times more ATP than the citric acid cycle alone, and generates more ATP than any other energy-producing pathway (e.g. glycolysis). Oxidative phosphorylation is the primary energy process for all aerobic organisms”.
            Mitochondrial electronnr healthy transport is not perfect. Even under ideal conditions, some electron leak from the electron transport chain. These leaking elections interact with oxygen to produce superoxide radicals. Since it is the interest of this work to approach the study of the energy generation in the mitochondria of a cell from a mathematical modeling point, understanding the process of oxidation of glucose (hydrocarbons) in the mitochondria where most of the ATPs are produced is most fundamental. 

1.1   WORK OBJECTIVES:
·         To develop a mathematical model for energy generation in the mitochondria based on the physics that would provide insights into the operation in the mitochondria and limiting mechanisms. We hope that, with the model, it will be possible for an individual to predict the behavior of he mitochondria under wide range of operating conditions.


 1.2   SCOPE/LIMITATIONS OF STUDY
            In other for us to understand properly the processes through which this bio-energy is generated in the mitochondria so as to build the mathematical model for the operation; it is important for us to study and understand in details the structural regulatory and functional proteins involved in a variety of task that ranges from enzymatic constituent of bioenergetics pathways. These pathways include
a.       Glycolytic pathway (substrate).
b.      The trycaboxylic acid (TCA) cycle
c.       Oxidative phosphoxylation (oxophouse) and the
d.      Nucleotide transport membrane channel.

 Details of the above mentioned pathways shall be discussed in the third chapter of this works......

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