Mathematical concepts and methods in modern biology: using modern discrete models
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| Format: | Book |
| Language: | English |
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Amsterdam ; Heidelberg [u.a.]
Elsevier, Academic Press
2013
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 349 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9780124157804 |
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| 245 | 1 | 0 | |a Mathematical concepts and methods in modern biology |b using modern discrete models |c ed. by Raina Robeva ... |
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| adam_text | Titel: Mathematical concepts and methods in modern biology
Autor: Robeva, Raina
Jahr: 2013
Contents
Contributors..............................................................................................................xi
Preface ...................................................................................................................xiii
CHAPTER 1 Mechanisms of Gene Regulation: Boolean Network
Models of the Lactose Operon in Escherichia coli.... 1
Raina Robeva, Bessie Kirkwood and Robin Davies
1.1 Introduction.............................................................................1
1.2 E. coli and the lac Operon........................................................3
1.3 Boolean Network Models of the Lac Operon.........................6
1.3.1 Identifying the Model Variables and
Parameters......................................................................7
1.3.2 Boolean Network Models...............................................9
1.3.3 Creating a Boolean Model ofthe Lac Operon.............14
1.3.4 Initial Testing of the Boolean Model of the Lac
Operon from Eqs. (1.4).................................................16
1.3.5 Using Discrete Visualizer of Dynamics (DVD)
to Test a Boolean Model...............................................17
1.3.6 How to Recognize a Deficient Model..........................21
1.3.7 A More Refined Boolean Model of the
Lac Operon...................................................................23
1.4 Determining the Fixed Points of Boolean Networks............25
1.5 Conclusions and Discussion..................................................31
1.6 Supplementary Materials......................................................34
References.....................................................................................34
CHAPTER 2 Bistability in the Lactose Operon of Escherichia coli:
A Comparison of Differential Equation and Boolean
Network Models...................................................37
Raina Robeva and Necmettin Yüdirim
2.1 Introduction...........................................................................37
2.2 The Lactose Operon of Escherichia Coli..............................39
2.3 Modeling Biochemical Reactions with
Differential Equations...........................................................40
2.3.1 Enzymatic Reactions and the Michaelis-Menten
Equation.......................................................................42
2.3.2 Multi-Molecule Binding and Hill Equations................44
vi Contents
2.4 The Yildirim-Mackey Differential Equation Models
for the Lactose Operon..........................................................47
2.4.1 Model Justification.......................................................47
2.4.2 Numerical Simulation of the Yildirim-Mackey
Models and Bistability.................................................52
2.5 Boolean Modeling of Biochemical Interactions...................57
2.6 Boolean Approximations ofthe Yildirim-Mackey Models.......60
2.6.1 Boolean Variants ofthe 3-Variable Model...................60
2.6.2 Boolean Variants ofthe 5-Variable Model...................65
2.7 Conclusions and Discussion..................................................70
2.8 Supplementary Materials......................................................73
References.....................................................................................73
CHAPTER 3 Inferring the Topology of Gene Regulatory Networks:
An Algebraic Approach to Reverse Engineering......75
Brandilyn Stigler and Elena Dimitrova
3.1 Introduction...........................................................................75
3.1.1 Gene Regulatory Networks in Molecular Biology........75
3.1.2 Reverse Engineering of Gene Regulatory Networks.......76
3.2 Polynomial Dynamical Systems (PDSs)...............................78
3.3 Computational Algebra Preliminaries...................................82
3.4 Construction of the Model Space:
A Reverse Engineering Algorithm.......................................85
3.5 Model Selection....................................................................89
3.5.1 Preprocessing: Minimal Sets Algorithm......................91
3.5.2 Postprocessing: The Gröbner Fan Method...................93
3.6 Discretization........................................................................96
References...................................................................................100
CHAPTER 4 Global Dynamics Emerging from Local Interactions:
Agent-Based Modeling for the Life Sciences........105
David Gammack, Elsa Schaefer and Holly Gaff
4.1 Introduction.........................................................................105
4.1.1 Agent-Based Modeling and the
Biology Mind Set.......................................................105
4.1.2 A Brief Note About Platforms....................................106
4.1.3 A Brief History of Agent-Based Modeling.................109
4.2 Axon Guidance....................................................................113
4.2.1 Background................................................................113
4.2.2 Understanding the Domain: Axon Biology................114
Contents vii
4.2.3 Breaking Down the Problem......................................116
4.2.4 Constructing a Model of Axon Development.............117
4.3 An Agent-Based Model for Cholera and the Importance of
Replication...........................................................................119
4.3.1 Model Description......................................................120
4.3.2 ABM Modeling Exercises: Cholera and
the NetLogo BehaviorSpace.......................................123
4.4 Use and Description of ABM in Research:
Tick-Borne Disease Agent-Based Models..........................128
4.4.1 The Model..................................................................129
4.4.2 Purpose.......................................................................130
4.4.3 State Variables and Scales..........................................130
4.4.4 Process Overview and Scheduling.............................130
4.4.5 Design Concepts.........................................................131
4.4.6 Input...........................................................................132
4.4.7 Simulation Experiments.............................................132
4.5 Comments for Instructors.....................................................134
4.6 Supplementary Materials....................................................137
References...................................................................................137
CHAPTER 5 Agent-Based Models and Optimal Control in
Biology: A Discrete Approach..............................143
Reinhard Laubenbacher, Franziska Hinkelmann and Matt Oremland
5.1 Introduction.........................................................................143
5.2 A First Example...................................................................147
5.3 Netlogo: An Introduction....................................................148
5.4 An Introduction to Agent-Based Models.............................149
5.5 Optimization and Optimal Control......................................152
5.6 Scaling and Aggregation.....................................................157
5.6.1 Correlating Data Sets..................................................158
5.6.2 Cost Function Analysis When Scaling.......................159
5.7 A Heuristic Approach..........................................................163
5.7.1 Genetic Algorithms....................................................164
5.7.2 Other Heuristic Algorithms........................................167
5.8 Mathematical Framework for Representing
Agent-Based Models..........................................................167
5.9 Translating Agent-Based Models into Polynomial
Dynamical Systems............................................................171
5.9.1 Basic Movement Function..........................................171
5.9.2 Uphill and Downhill Movement.................................173
vüi Contents
5.10 Summary...........................................................................175
5.11 Supplementary Materials..................................................176
References...................................................................................176
CHAPTER 6 Neuronal Networks: A Discrete Model..................179
Winfried Just, Sungwoo Ahn and David Terman
6.1 Introduction and Overview..................................................179
6.2 Neuroscience in a Nutshell..................................................180
6.2.1 Neurons, Synapses, and Action Potentials.................180
6.2.2 Firing Patterns............................................................181
6.2.3 Olfaction.....................................................................182
6.2.4 Mathematical Models.................................................183
6.3 The Discrete Model.............................................................183
6.4 Exploring the Model for Some Simple Connectivities.......189
6.4.1 Acyclic Digraphs........................................................190
6.4.2 Directed Cycle Graphs...............................................191
6.4.3 Complete Loop-Free Digraphs...................................193
6.4.4 Other Connectivities...................................................195
6.4.5 Discussion: Advantages and Limitations
of the Approach in this Section..................................196
6.5 Exploring the Model for Some Random Connectivities.........197
6.5.1 Erdös-Renyi Random Digraphs..................................197
6.5.2 Discussion: Other Models of Random Digraphs........201
6.6 Another Interpretation of the Model:
Disease Dynamics...............................................................202
6.7 More Neuroscience: Connection with ODE Models..........205
6.8 Directions of Further Research...........................................208
6.9 Supplementary Materials....................................................210
References...................................................................................210
CHAPTER 7 Predicting Population Growth: Modeling with
Projection Matrices............................................213
Janet Steven and James Kirkwood
7.1 Introduction.........................................................................213
7.2 Life Cycles and Population Growth....................................214
7.3 Determining Stages in the Life Cycle...:.............................215
7.4 Determining the Number of Individuais
in a Stage atTime to + 1......................................................215
7.5 Constructing a Projection Matrix........................................216
Contents ix
7.6 Predicting How a Population Changes After One Year.......222
7.7 The Stable Distribution of Individuais Across Stages.........226
7.8 Theory Supporting the Calculation of Stable
Distributions........................................................................227
7.8.1 Eigenvalues and Eigenvectors....................................227
7.8.2 The Perron-Frobenius Theorem.................................228
7.8.3 Raising a Matrix to a Power in MATLAB and R.......231
7.8.4 Finding the Stable Distribution..................................231
7.9 Determining Population Growth Rate and
the Stable Distribution.........................................................234
7.9.1 Calculating Eigenvalues and
Eigenvectors in MATLAB..........................................235
7.9.2 Calculating Eigenvalues and Eigenvectors in R.........236
7.10 Further Applications ofthe Projection Matrix...................237
References...................................................................................237
CHAPTER 8 Metabolie Pathways Analysis: A Linear
Algebraic Approach............................................239
Terrell L. Hodge
8.1 Introduction.........................................................................239
8.2 Biochemical Reaction Networks, Metabolie
Pathways, and the Stoichiometry Matrix............................242
8.2.1 Stoichiometric Matrix I: Nullspaces,
Linear Dependence, and Spanning Sets.....................242
8.2.2 More on the Nullspace ofthe Stoichiometric
Matrix: Spanning with Biochemical Pathways
and Base Changing.....................................................251
8.2.3 Conclusion..................................................................256
8.3 Extreme Paths and Model Improvements...........................258
8.3.1 Downloading and Installing expa.exe........................258
8.3.2 Analyzing a Modeling Decision: Directed Graphs........260
8.4 Supplementary Data............................................................265
References...................................................................................265
CHAPTER 9 Identifying CpG Islands: Sliding Window and
Hidden Markov Model Approaches......................267
Raina Robeva, Aaron Garrett, James Kirkwood and Robin Davies
9.1 Introduction..........................................................................267
9.1.1 Biochemistry Background..........................................267
9.1.2 CpG Islands................................................................268
Contents
9.1.3 DNA Methylation in Cancer......................................270
9.2 Quantitative Characteristics of the CpG
Island Regions and Sliding Windows Algorithms...............270
9.3 Definition and Basic Properties of Markov
Chains and Hidden Markov Models....................................274
9.3.1 Finite State Markov Chains........................................274
9.3.2 Hidden Markov Models (HMMs)..............................277
9.3.3 Viewing DNA Sequences As Outputs of a HMM......279
9.4 Three Canonical Problems for HMMs with
Applications to CGI Identification......................................282
9.4.1 Decoding: The Viterbi algorithm................................283
9.4.2 Evaluation and Posterior Decoding:
The Forward-Backward Algorithm............................289
9.4.3 Training: The Baum-Welch Algorithm.......................295
9.4.4 Post-Processing..........................................................299
9.5 Conclusions and Discussion................................................301
9.6 Supplementary Materials....................................................302
References...................................................................................302
CHAPTER 10 Phylogenese Tree Reconstruction:
Geometric Approaches........................................307
David Haws, Terrell L. Hodge and Ruriko Yoshida
10.1 Introduction.......................................................................307
10.2 Basics onTrees and Phylogenetic Trees...........................310
10.3 Tree Space.........................................................................318
10.3.1 Trees as Points..........................................................318
10.3.2 Fitting Trees: A Distance-Based Approach..............320
10.3.3 Tree Metrics and Tree Space....................................324
10.4 Neighbor-Joining and BME..............................................329
10.4.1 Neighbor-Joining......................................................329
10.4.2 Balanced Minimum Evolution.................................334
10.5 Summary...........................................................................339
References...................................................................................340
Index......................................................................................................................343
|
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| spelling | Mathematical concepts and methods in modern biology using modern discrete models ed. by Raina Robeva ... Amsterdam ; Heidelberg [u.a.] Elsevier, Academic Press 2013 XXI, 349 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Biologie (DE-588)4006851-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Biomathematics Biomathematik (DE-588)4139408-2 s Biologie (DE-588)4006851-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Robeva, Raina S. edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026737426&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical concepts and methods in modern biology using modern discrete models Biologie (DE-588)4006851-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4006851-1 (DE-588)4114528-8 (DE-588)4139408-2 |
| title | Mathematical concepts and methods in modern biology using modern discrete models |
| title_auth | Mathematical concepts and methods in modern biology using modern discrete models |
| title_exact_search | Mathematical concepts and methods in modern biology using modern discrete models |
| title_full | Mathematical concepts and methods in modern biology using modern discrete models ed. by Raina Robeva ... |
| title_fullStr | Mathematical concepts and methods in modern biology using modern discrete models ed. by Raina Robeva ... |
| title_full_unstemmed | Mathematical concepts and methods in modern biology using modern discrete models ed. by Raina Robeva ... |
| title_short | Mathematical concepts and methods in modern biology |
| title_sort | mathematical concepts and methods in modern biology using modern discrete models |
| title_sub | using modern discrete models |
| topic | Biologie (DE-588)4006851-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Biologie Mathematisches Modell Biomathematik |
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