Mathematical Modeling of the Aging Process

Mathematical Modeling of the Aging Process

Axel Kowald (Medizinisches Proteom Center (MPC), Ruhr-Universität Bochum, Germany)
Copyright: © 2009 |Pages: 19
DOI: 10.4018/978-1-60566-076-9.ch018
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Abstract

Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality risk, which finally leads to the death of the organism. Modern hygiene and medicine has led to an amazing increase in average life expectancy over the last 150 years, but the underlying biochemical mechanisms of the aging process are still poorly understood. However, a better understanding of these mechanisms is increasingly important since the growing fraction of elderly people in the human population confronts our society with completely new and challenging problems. The aim of this chapter is to provide an overview of the aging process, discuss how it relates to system biological concepts, and explain how mathematical modeling can improve our understanding of biochemical processes involved in the aging process. We concentrate on the modeling of stochastic effects that become important when the number of involved entities (i.e., molecules, organelles, cells) is very small and the reaction rates are low. This is the case for the accumulation of defective mitochondria, which we describe mathematically in detail. In recent years several tools became available for stochastic modeling and we also provide a brief description of the most important of those tools. Of course, mitochondria are not the only target of modeling efforts in aging research. Therefore, the chapter concludes with a brief survey of other interesting computational models in this field of research.
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What Is Aging?

Looking at the enormous rise of average human lifespan over the last 150 years, one could get the impression that modern research actually has identified the relevant biochemical pathways involved in aging and has successfully reduced the pace of aging. Oeppen and Vaupel (2002) collected data on world wide life expectancy from studies going back to 1840. Figure 1 shows the life expectancy for males (squares) and females (circles) for the countries that had the highest life expectancy for the given year. Two points are remarkable. Firstly, there is an amazingly linear trend in life expectancy that corresponds to an increase of 3 months per year (!) and secondly there is no leveling off observable.

Figure 1.

Male (blue squares) and female (red circles) life expectancy in the world record holding country between 1840 and 2000 based on the annual data of countries world wide (reproduced with permission from Oeppen & Vaupel, 2002).

These impressive data suggest strongly that lifespan will also continue to rise in the next years, but it does not show that the actual aging rate has fallen during the last century. Aging can best be described as a gradual functional decline, leading to a constantly increasing risk to die within the next time interval (mortality). The Gompertz-Makeham equation (Gompertz, 1825; Makeham, 1867),, describes how the exponential increase of mortality depends on intrinsic vulnerability (I), actuarial aging rate (G) and environmental risk (E). All living organisms have a base mortality caused by environmental risks, but it is the aging rate, G, which causes human mortality to double approx. every 8 years. From this equation we can derive the following expression for the survivorship function: As expected we see that the number of remaining survivors depends on all three parameters and consequently a change of the average life expectancy (time until 50% of the population has died) can be caused by a modification of any of those parameters. This point is also discussed in more detail by (Kowald, 2002). And indeed, analyzing the survivorship data of the last 100 years more closely, it becomes clear that the aging rate, G, remained constant. The enormous increase in life expectancy was achieved exclusively by changes of intrinsic vulnerability and environmental risk!

Because of the drastic social, economical and political consequences that are brought about by the demographic changes of the age structure of the population, it is now more important than ever to understand what constitutes the biochemical basis for a non-zero aging rate, G. Systems biology might help to achieve this goal.

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Why Is Aging A Prime Candidate For Systems Biology?

Evolutionary theories of the aging process explain why aging has evolved, but unfortunately they don’t predict specific mechanisms to be involved in aging. As a consequence more than 300 mechanistic ideas have been developed (Medvedev, 1990), each centered around different biochemical processes. This is probably due to the fact that even the simplest multicellular organisms are such complex systems that many components have the potential to cause deterioration of the whole system in case of a malfunction. Figure 2 shows a small sample of the most popular mechanistic theories. The spatial arrangement of the diagram intends to reflect the various connections between the different theories. And it is exactly the large number of interactions that makes it so difficult to investigate aging experimentally and renders it ideal for systems biology. To understand this we will look at a few examples.

Figure 2.

Graphical representation of some mechanistic theories of aging. The topology of the diagram reflects logical and mechanistic overlaps and points of interaction between different theories.

Key Terms in this Chapter

Systems Biology Workbench: The Systems Biology Workbench (SBW) is a software systems that enables different modeling programs to communicate with each other and provide or use specialized analysis services. In this way SBW acts as broker for services like deterministic and stochastic simulation engines, stability and bifurcation analysis, model optimization and graphical model building. Popular tools that are SBW aware are among others JDesigner, CellDesigner and Dizzy.

Mitochondria: Cellular organelles present in most eukaryotic cells that are important for calcium homeostasis, apoptosis and energy production. Mitochondria are endosymbionts and probably derived from purple bacteria. A remnant of this origin is the small circular mitochondrial DNA (mtDNA) that is at the center of the mitochondrial theory of aging.

Aging: A biological phenomenon observed in most animals leading to increasing functional impairment and constantly rising mortality rate. Age related changes can be observed at intracellular, tissue and organismic level. Many theories about the mechanism of the aging process exist, but the details are currently still unresolved.

Life Expectancy: Time until 50% of a cohort of newborn individual have died. Also known as average life-span, although technically it is the median life-span. The life expectancy for humans in industrialized countries is currently between 75 and 80 years, and for women 2-3 years higher than for man.

Dizzy: A stochastic simulation tool written in Java. Models can be defined in systems biology markup language (SBML) or a proprietary language and simulated using various stochastic and deterministic algorithms. The GUI and the core engine are separate modules so that Dizzy can also be used for batch calculations on a computer cluster.

Disposable Soma Theory: Popular theory about the evolution of the aging process. Aging is explained as the result of an optimal resource allocation between reproduction and self-maintenance. That means, aging itself has no selection advantage, but is a side product of another selected trait. Species specific life-spans are readily explained by different environmental mortalities.

Stochastic Modeling: A modeling framework that takes care of microscopic random fluctuations and the discreteness of molecules. Stochastic models explicitly calculate the change of the number of molecules of the participating species during the time course of a chemical reaction. The first exact stochastic simulation algorithms were developed by Gillespie (1977) and are now part of several modeling tools. Stochastic simulations are normally more time consuming than deterministic simulations via differential equations.

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Table of Contents
Foreword
Ralf Herwig
Preface
Andriani Daskalaki
Acknowledgment
Andriani Daskalaki
Chapter 1
Peter Ghazal
An increasing number of biological experiments and more recently clinical based studies are being conducted using large-scale genomic, proteomic and... Sample PDF
Pathway Biology Approach to Medicine
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Chapter 2
Peter Wellstead, Sree Sreenath, Kwang-Hyun Cho
In this chapter the authors describe systems and control theory concepts for systems biology and the corresponding implications for medicine. The... Sample PDF
Systems and Control Theory for Medical Systems Biology
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Chapter 3
S. Nikolov
In this chapter we investigate how the inclusion of time delay alters the dynamic properties of (a) delayed protein cross talk model, (b) time delay... Sample PDF
Mathematical Description of Time Delays in Pathways Cross Talk
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Chapter 4
Elisabeth Maschke-Dutz
In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis... Sample PDF
Deterministic Modeling in Medicine
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Chapter 5
Andrew Kuznetsov
Biologists have used a reductionist approach to investigate the essence of life. In the last years, scientific disciplines have merged with the aim... Sample PDF
Synthetic Biology as a Proof of Systems Biology
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Chapter 6
Tuan D. Pham
Computational models have been playing a significant role for the computer-based analysis of biological and biomedical data. Given the recent... Sample PDF
Computational Models for the Analysis of Modern Biological Data
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Chapter 7
Vanathi Gopalakrishnan
This chapter provides a perspective on 3 important collaborative areas in systems biology research. These areas represent biological problems of... Sample PDF
Computer Aided Knowledge Discovery in Biomedicine
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Chapter 8
Thomas Meinel
The function of proteins is a main subject of research in systems biology. Inference of function is now, more than ever, required by the upcoming of... Sample PDF
Function and Homology of Proteins Similar in Sequence: Phylogenetic Profiling
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Chapter 9
Nikolaos G. Sgourakis, Pantelis G. Bagos, Stavros J. Hamodrakas
GPCRs comprise a wide and diverse class of eukaryotic transmembrane proteins with well-established pharmacological significance. As a consequence of... Sample PDF
Computational Methods for the Prediction of GPCRs Coupling Selectivity
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Chapter 10
Pantelis G. Bagos, Stavros J. Hamodrakas
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Bacterial ß-Barrel Outer Membrane Proteins: A Common Structural Theme Implicated in a Wide Variety of Functional Roles
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Chapter 11
L.K. Flack
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Clustering Methods for Gene-Expression Data
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Chapter 12
George Sakellaropoulos, Antonis Daskalakis, George Nikiforidis, Christos Argyropoulos
The presentation and interpretation of microarray-based genome-wide gene expression profiles as complex biological entities are considered to be... Sample PDF
Uncovering Fine Structure in Gene Expression Profile by Maximum Entropy Modeling of cDNA Microarray Images and Kernel Density Methods
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Chapter 13
Wasco Wruck
This chapter describes the application of the BeadArrayTM technology for gene expression profiling. It introduces the BeadArrayTM technology, shows... Sample PDF
Gene Expression Profiling with the BeadArrayTM Platform
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Chapter 14
Djork-Arné Clevert, Axel Rasche
Readers shall find a quick introduction with recommendations into the preprocessing of Affymetrix GeneChip® microarrays. In the rapidly growing... Sample PDF
The Affymetrix GeneChip® Microarray Platform
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Chapter 15
Jacek Majewski
Eukaryotic genes have the ability to produce several distinct products from a single genomic locus. Recent developments in microarray technology... Sample PDF
Alternative Isoform Detection Using Exon Arrays
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Chapter 16
Prerak Desai
The use of systems biology to study complex biological questions is gaining ground due to the ever-increasing amount of genetic tools and genome... Sample PDF
Gene Expression in Microbial Systems for Growth and Metabolism
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Chapter 17
Heike Stier
Alternative splicing is an important part of the regular process of gene expression. It controls time and tissue dependent expression of specific... Sample PDF
Alternative Splicing and Disease
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Chapter 18
Axel Kowald
Aging is a complex biological phenomenon that practically affects all multicellular eukaryotes. It is manifested by an ever increasing mortality... Sample PDF
Mathematical Modeling of the Aging Process
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Chapter 19
Evgenia Makrantonaki
This chapter introduces an in vitro model as a means of studying human hormonal aging. For this purpose, human sebaceous gland cells were maintained... Sample PDF
The Sebaceous Gland: A Model of Hormonal Aging
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Chapter 20
R. Seigneuric, N.A.W. van Riel, M.H.W. Starmans, A. van Erk
Complex diseases such as cancer have multiple origins and are therefore difficult to understand and cure. Highly parallel technologies such as DNA... Sample PDF
Systems Biology Applied to Cancer Research
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Chapter 21
Matej Orešic, Antonio Vidal-Puig
In this chapter the authors report on their experience with the analysis and modeling of data obtained from studies of animal models related to... Sample PDF
Systems Biology Strategies in Studies of Energy Homeostasis In Vivo
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Chapter 22
Axel Rasche
We acquired new computational and experimental prospects to seek insight and cure for millions of afflicted persons with an ancient malady. Type 2... Sample PDF
Approaching Type 2 Diabetes Mellitus by Systems Biology
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Chapter 23
Alia Benkahla, Lamia Guizani-Tabbane, Ines Abdeljaoued-Tej, Slimane Ben Miled, Koussay Dellagi
This chapter reports a variety of molecular biology informatics and mathematical methods that model the cell response to pathogens. The authors... Sample PDF
Systems Biology and Infectious Diseases
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Chapter 24
Daniela Albrecht, Reinhard Guthke
This chapter describes a holistic approach to understand the molecular biology and infection process of human-pathogenic fungi. It comprises the... Sample PDF
Systems Biology of Human-Pathogenic Fungi
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Chapter 25
Jessica Ahmed
Secretases are aspartic proteases, which specifically trim important, medically relevant targets such as the amyloid-precursor protein (APP) or the... Sample PDF
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Chapter 26
Paul Wrede
Peptides fulfill many tasks in controlling and regulating cellular functions and are key molecules in systems biology. There is a great demand in... Sample PDF
In Machina Systems for the Rational De Novo Peptide Design
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Chapter 27
Ferda Mavituna, Raul Munoz-Hernandez, Ana Katerine de Carvalho Lima Lobato
This chapter summarizes the fundamentals of metabolic flux balancing as a computational tool of metabolic engineering and systems biology. It also... Sample PDF
Applications of Metabolic Flux Balancing in Medicine
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Chapter 28
Roberta Alfieri, Luciano Milanesi
This chapter aims to describe data integration and data mining techniques in the context of systems biology studies. It argues that the different... Sample PDF
Multi-Level Data Integration and Data Mining in Systems Biology
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Chapter 29
Hendrik Hache
In this chapter, different methods and applications for reverse engineering of gene regulatory networks that have been developed in recent years are... Sample PDF
Methods for Reverse Engineering of Gene Regulatory Networks
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Chapter 30
Alok Mishra
This chapter introduces the techniques that have been used to identify the genetic regulatory modules by integrating data from various sources. Data... Sample PDF
Data Integration for Regulatory Gene Module Discovery
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Chapter 31
Elizabeth Santiago-Cortés
Biological systems are composed of multiple interacting elements; in particular, genetic regulatory networks are formed by genes and their... Sample PDF
Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation
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Chapter 32
A. Maffezzoli
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Chapter 33
Paolo Vicini
This chapter describes the System for Population Kinetics (SPK), a novel Web service for performing population kinetic analysis. Population kinetic... Sample PDF
The System for Population Kinetics: Open Source Software for Population Analysis
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Chapter 34
Julia Adolphs
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Photosynthesis: How Proteins Control Excitation Energy Transfer
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Chapter 35
Michael R. Hamblin
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Chapter 36
Andriani Daskalaki
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Chapter 37
Alexey R. Brazhe, Nadezda A. Brazhe, Alexey N. Pavlov, Georgy V. Maksimov
This chapter describes the application of interference microscopy and double-wavelet analysis to noninvasive study of cell structure and function.... Sample PDF
Interference Microscopy for Cellular Studies
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Chapter 38
Cathrin Dressler, Olaf Minet, Urszula Zabarylo, Jürgen Beuthan
This chapter deals with the mitochondrias’ stress response to heat, which is the central agent of thermotherapy. Thermotherapies function by... Sample PDF
Fluorescence Imaging of Mitochondrial Long-Term Depolarization in Cancer Cells Exposed to Heat-Stress
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Chapter 39
Athina Theodosiou, Charalampos Moschopoulos, Marc Baumann, Sophia Kossida
In previous years, scientists have begun understanding the significance of proteins and protein interactions. The direct connection of those with... Sample PDF
Protein Interactions and Diseases
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Chapter 40
Bernard de Bono
From a genetic perspective, disease can be interpreted in terms of a variation in molecular sequence or expression (dose) that impairs normal... Sample PDF
The Breadth and Depth of BioMedical Molecular Networks: The Reactome Perspective
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Chapter 41
Jorge Numata
Thermodynamics is one of the best established notions in science. Some recent work in biomolecular modeling has sacrificed its rigor in favor of... Sample PDF
Entropy and Thermodynamics in Biomolecular Simulation
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Chapter 42
Isabel Reinecke, Peter Deuflhard
In this chapter some model development concepts can be used for the mathematical modeling in physiology as well as a graph theoretical approach for... Sample PDF
Model Development and Decomposition in Physiology
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Chapter 43
Mohamed Derouich
Throughout the world, seasonal outbreaks of influenza affect millions of people, killing about 500,000 individuals every year. Human influenza... Sample PDF
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Chapter 44
Mohamed Derouich
Dengue fever is a re-emergent disease affecting more than 100 countries. Its incidence rate has increased fourfold since 1970 with nearly half the... Sample PDF
Dengue Fever: A Mathematical Model with Immunization Program
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Chapter 45
Ross Foley
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Automated Image Analysis Approaches in Histopathology
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