Deterministic Modeling in Medicine

Deterministic Modeling in Medicine

Elisabeth Maschke-Dutz (Max Planck Institute for Molecular Genetics, Germany)
Copyright: © 2009 |Pages: 23
DOI: 10.4018/978-1-60566-076-9.ch004
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Abstract

In this chapter basic mathematical methods for the deterministic kinetic modeling of biochemical systems are described. Mathematical analysis methods, the respective algorithms, and appropriate tools and resources, as well as established standards for data exchange, model representations and definitions are presented. The methods comprise time-course simulations, steady state search, parameter scanning, and metabolic control analysis among others. An application is demonstrated using a test case model that describes parts of the extrinsic apoptosis pathway and a small example network demonstrates an implementation of metabolic control analysis.
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Introduction

We can observe the molecular background of complex disease processes with systems biology. Today, drug development plays a central role in the interdisciplinary area of systems biology. Scientists from various disciplines, such as biology, bioinformatics, medical research, chemistry, physics, computer science and mathematics, work together to analyze complex disease processes by studying molecular interaction networks. The aim is to understand and analyze the complex behavior of human diseases. Through this collaborative research we can obtain specific methods and results that can lead to new predictions and assumptions about the observed diseases and processes.

Metabolic pathways like the citric acid cycle and glycolysis, for example, are important processes that may be used to analyze the complex mechanism in living biological systems. The modeling of these pathways provides appropriate structures for observing the behavior of metabolic diseases, i.e. diabetes. Gene regulatory networks describe protein-DNA interactions or indirectly as the interaction between DNA and DNA. Here, we can also examine the regulation of the activity of single genes and the behavior of single molecules, as well as observe the interaction and regulation between different genes and proteins in complex structures. The normal function of single genes is affected in several diseases. A lot of information is available about the functionality of single genes in different diseases and also the roles of mutations in these genes are comprehensively described (Weinberg 1994). Many project studies about this topic are currently underway, and we expect more interesting results in the future (Futreal et al. 2004). Multiprotein complexes are the result of numerous protein-protein interactions. These interactions are essential for physiological processes. In biological networks, diffusion and the molecular transport across cell membranes are also important physiological processes. In different compartments of the cell the function of a protein can change, because the functionality of a protein depends also on the existing targets in the appropriate compartments. For example the p53 protein acts in the nucleus as a transcription factor of apoptosis. The protein Mdm2 in turn can bind to p53 and initiates its ubiquitination and subsequent degradation in the cytoplasm. In the cytoplasm p53 can not act as a transcription factor and instead the degradation of p53 is initialized in this compartment. Signaling pathways play an important role in many diseases. For example the cell signaling mechanism regulates cell proliferation and cell differentiation. The main structures that are responsible for the progression of cancer are interferences in signaling pathways (Cui et al. 2007). The reasons for these inferences in turn are founded in mutated proteins.

Using mathematical models we can describe complex cellular processes. This chapter gives an overview of the possibilities available to analyze these molecular, cellular and physiological processes with mathematical modeling, and outlines how we can integrate experimental data. We demonstrate the utilization of the mathematical model analysis in two examples. Time-course simulation and parameter scanning are applied to a model for the extrinsic apoptosis pathways and metabolic control analysis is applied to a small sample network.

Key Terms in this Chapter

Topology: The topology defines the properties of spaces and maps. Dependent on the described space arbitrary complex structures used.

Euclidean Norm: The Euclidean space denotes an n-dimensional space that can be characterized through Euclidean geometry. An n-dimensional vector describes a point in this space. The Euclidean norm defines the length of a vector and the distance function between two vectors is called an Euclidean metric.

Stoichiometry: The quantitative relationship between the reactant and the product in a chemical reaction is described by the stoichiometry. It can be used to calculate the quantitative amount of the product or the educt of a reaction, where one of both measurable quantities is known.

ODE: An ordinary differential equation is an equation that contains a function and the derivates of this function. It differs from partial differential equations in that, in an ordinary differential equation, the included function depends on only one variable.

Protein Complex: A group of two or more chemically bound proteins formed by stable protein-protein interactions.

Eigenvalues: In linear algebra the equation defines the eigenvalues ? and the corresponding eigenvectors v of a linear transformation represented by a quadratic matrix A. ? is a complex value and v is a complex valued vector. The eigenvalues describe essential characteristics of the linear map.

Kinetics: In this chapter the term kinetic is used in a chemical sense and describes the principles of reaction velocities.

DAE: A differential-algebraic equation (DAE) is a special kind of differential equation and expressed by means of differential algebra. This equation does not necessarily include all dependent variables, and their derivates must not be expressed explicitly.

Object-Oriented: Object-oriented programming uses abstract objects and their interactions to describe the contents and the functionalities of the program, according to its design.

Python: The high-level programming script language Python supports functional, object-oriented and imperative programming paradigms.

Fortran: The name of a programming language derived from FORmula TRANSlation. Fortran was developed in the 1950s and was especially used for numerical programming. The programming language directly supports numerical operations and because of this, optimized compiler calculations can be performed. Up to now, various numerical programming libraries are available and used in mathematical, physical and chemical science.

Bcl2: Is the prototype for a protein family of mammalian genes and the proteins coded by these genes. The name is derived from B-cell lymphoma 2.

C++: The programming language C++ was developed in 1979 by Bjane Stroustrup. It supports object-oriented programming and is an enhancement to the programming language C.

Enzyme: Protein molecules that catalyze chemical reactions. They play an important role in most metabolic processes and are responsible for activation and control of biochemical reactions in living systems.

Linearization: In mathematics, linearization describes the linear approximation of a function at a given point.

Deterministic: An algorithm is called deterministic when the same results are always obtained under identical conditions. In this respect, deterministic mathematical modeling describes systems without any random possibility function. Identical starting conditions always provide the same output.

Experimental Data: Gene expression profiles derived from micro array based experiments with different study foci, i.e. prostate cancer, compound testing or diabetes.

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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
$37.50
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
ß-barrel outer membrane proteins constitute the second and less well-studied class of transmembrane proteins. They are present exclusively in the... Sample PDF
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
Clustering methods are used to place items in natural patterns or convenient groups. They can be used to place genes into clusters to have similar... Sample PDF
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
Development of Specific Gamma Secretase Inhibitors
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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
In this chapter, authors review main methods, approaches, and models for the analysis of neuronal network data. In particular, the analysis concerns... Sample PDF
Investigating the Collective Behavior of Neural Networks: A Review of Signal Processing Approaches
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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
This chapter introduces the theory of optical spectra and excitation energy transfer of light harvesting complexes in photosynthesis. The light... Sample PDF
Photosynthesis: How Proteins Control Excitation Energy Transfer
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Chapter 35
Michael R. Hamblin
Photodynamic therapy (PDT) is a rapidly advancing treatment for multiple diseases. PDT involves the administration of a nontoxic drug or dye known... Sample PDF
Photodynamic Therapy: A Systems Biology Approach
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Chapter 36
Andriani Daskalaki
Photodynamic Therapy (PDT) involves administration of a photosensitizer (PS) either systemically or locally, followed by illumination of the lesion... Sample PDF
Modeling of Porphyrin Metabolism with PyBioS
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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
A Pandemic Avian Influenza Mathematical Model
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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
The field of histopathology has encountered a key transition point with the progressive move towards use of digital slides and automated image... Sample PDF
Automated Image Analysis Approaches in Histopathology
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About the Contributors