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E-raamat: Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models

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Edited by (Western Michigan University, Kalamazoo, MI, USA), Edited by (Professor of Mathematical Sciences, Sweet Briar College, VA, USA)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 26-Feb-2013
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780124157934
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Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete ModelsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 26-Feb-2013
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780124157934
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Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology.

Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software.

  • Features self-contained chapters with real biological research examples using freely available computational tools
  • Spans several mathematical techniques at basic to advanced levels
  • Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology

Arvustused

"Contributors in biology, in mathematics, and in bioinformatics introduce undergraduate students and their instructors to more applications of discrete mathematics to biology than can be found in standard textbooks. The goal is not to be comprehensive, but to open the door to more advanced and specialized resources." --Reference and Research Book News, August 2013

Muu info

Expand your access to the set of mathematical tools and techniques for understanding and solving problems in the biological sciences
Contributors xi
Preface xiii
Chapter 1 Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli
1(36)
Raina Robeva
Bessie Kirkwood
Robin Davies
1.1 Introduction
1(2)
1.2 E. coli and the lac operon
3(3)
1.3 Boolean Network Models of the Lac Operon
6(19)
1.3.1 Identifying the Model Variables and Parameters
7(2)
1.3.2 Boolean Network Models
9(5)
1.3.3 Creating a Boolean Model of the Lac Operon
14(2)
1.3.4 Initial Testing of the Boolean Model of the Lac Operon from Eqs. (1.4)
16(1)
1.3.5 Using Discrete Visualizer of Dynamics (DVD) to Test a Boolean Model
17(4)
1.3.6 How to Recognize a Deficient Model
21(2)
1.3.7 A More Refined Boolean Model of the Lac Operon
23(2)
1.4 Determining the Fixed Points of Boolean Networks
25(6)
1.5 Conclusions and Discussion
31(3)
1.6 Supplementary Materials
34(1)
References
34(3)
Chapter 2 Bistability in the Lactose Operon of Escherichia coli: A Comparison of Differential Equation and Boolean Network Models
37(38)
Raina Robeva
Necmettin Yildirim
2.1 Introduction
37(2)
2.2 The Lactose Operon of Escherichia Coli
39(1)
2.3 Modeling Biochemical Reactions with Differential Equations
40(7)
2.3.1 Enzymatic Reactions and the Michaelis-Menten Equation
42(2)
2.3.2 Multi-Molecule Binding and Hill Equations
44(3)
2.4 The Yildirim-Mackey Differential Equation Models for the Lactose Operon
47(10)
2.4.1 Model Justification
47(5)
2.4.2 Numerical Simulation of the Yildirim-Mackey Models and Bistability
52(5)
2.5 Boolean Modeling of Biochemical Interactions
57(3)
2.6 Boolean Approximations of the Yildirim-Mackey Models
60(10)
2.6.1 Boolean Variants of the 3-Variable Model
60(5)
2.6.2 Boolean Variants of the 5-Variable Model
65(5)
2.7 Conclusions and Discussion
70(3)
2.8 Supplementary Materials
73(1)
References
73(2)
Chapter 3 Inferring the Topology of Gene Regulatory Networks: An Algebraic Approach to Reverse Engineering
75(30)
Brandilyn Stigler
Elena Dimitrova
3.1 Introduction
75(3)
3.1.1 Gene Regulatory Networks in Molecular Biology
75(1)
3.1.2 Reverse Engineering of Gene Regulatory Networks
76(2)
3.2 Polynomial Dynamical Systems (PDSs)
78(4)
3.3 Computational Algebra Preliminaries
82(3)
3.4 Construction of the Model Space: A Reverse Engineering Algorithm
85(4)
3.5 Model Selection
89(7)
3.5.1 Preprocessing: Minimal Sets Algorithm
91(2)
3.5.2 Postprocessing: The Grobner Fan Method
93(3)
3.6 Discretization
96(4)
References
100(5)
Chapter 4 Global Dynamics Emerging from Local Interactions: Agent-Based Modeling for the Life Sciences
105(38)
David Gammack
Elsa Schaefer
Holly Gaff
4.1 Introduction
105(8)
4.1.1 Agent-Based Modeling and the Biology Mind Set
105(1)
4.1.2 A Brief Note About Platforms
106(3)
4.1.3 A Brief History of Agent-Based Modeling
109(4)
4.2 Axon Guidance
113(6)
4.2.1 Background
113(1)
4.2.2 Understanding the Domain: Axon Biology
114(2)
4.2.3 Breaking Down the Problem
116(1)
4.2.4 Constructing a Model of Axon Development
117(2)
4.3 An Agent-Based Model for Cholera and the Importance of Replication
119(9)
4.3.1 Model Description
120(3)
4.3.2 ABM Modeling Exercises: Cholera and the NetLogo BehaviorSpace
123(5)
4.4 Use and Description of ABM in Research: Tick-Borne Disease Agent-Based Models
128(6)
4.4.1 The Model
129(1)
4.4.2 Purpose
130(1)
4.4.3 State Variables and Scales
130(1)
4.4.4 Process Overview and Scheduling
130(1)
4.4.5 Design Concepts
131(1)
4.4.6 Input
132(1)
4.4.7 Simulation Experiments
132(2)
4.5 Comments for Instructors
134(3)
4.6 Supplementary Materials
137(1)
References
137(6)
Chapter 5 Agent-Based Models and Optimal Control in Biology: A Discrete Approach
143(36)
Reinhard Laubenbacher
Franziska Hinkelmann
Matt Oremland
5.1 Introduction
143(4)
5.2 A First Example
147(1)
5.3 Netlogo: An Introduction
148(1)
5.4 An Introduction to Agent-Based Models
149(3)
5.5 Optimization and Optimal Control
152(5)
5.6 Scaling and Aggregation
157(6)
5.6.1 Correlating Data Sets
158(1)
5.6.2 Cost Function Analysis When Scaling
159(4)
5.7 A Heuristic Approach
163(4)
5.7.1 Genetic Algorithms
164(3)
5.7.2 Other Heuristic Algorithms
167(1)
5.8 Mathematical Framework for Representing Agent-Based Models
167(4)
5.9 Translating Agent-Based Models into Polynomial Dynamical Systems
171(4)
5.9.1 Basic Movement Function
171(2)
5.9.2 Uphill and Downhill Movement
173(2)
5.10 Summary
175(1)
5.11 Supplementary Materials
176(1)
References
176(3)
Chapter 6 Neuronal Networks: A Discrete Model
179(34)
Winfried Just
Sungwoo Ahn
David Terman
6.1 Introduction and Overview
179(1)
6.2 Neuroscience in a Nutshell
180(3)
6.2.1 Neurons, Synapses, and Action Potentials
180(1)
6.2.2 Firing Patterns
181(1)
6.2.3 Olfaction
182(1)
6.2.4 Mathematical Models
183(1)
6.3 The Discrete Model
183(6)
6.4 Exploring the Model for Some Simple Connectivities
189(8)
6.4.1 Acyclic Digraphs
190(1)
6.4.2 Directed Cycle Graphs
191(2)
6.4.3 Complete Loop-Free Digraphs
193(2)
6.4.4 Other Connectivities
195(1)
6.4.5 Discussion: Advantages and Limitations of the Approach in this Section
196(1)
6.5 Exploring the Model for Some Random Connectivities
197(5)
6.5.1 Erdos-Renyi Random Digraphs
197(4)
6.5.2 Discussion: Other Models of Random Digraphs
201(1)
6.6 Another Interpretation of the Model: Disease Dynamics
202(3)
6.7 More Neuroscience: Connection with ODE Models
205(3)
6.8 Directions of Further Research
208(2)
6.9 Supplementary Materials
210(1)
References
210(3)
Chapter 7 Predicting Population Growth: Modeling with Projection Matrices
213(26)
Janet Steven
James Kirkwood
7.1 Introduction
213(1)
7.2 Life Cycles and Population Growth
214(1)
7.3 Determining Stages in the Life Cycle
215(1)
7.4 Determining the Number of Individuals in a Stage at Time to + 1
215(1)
7.5 Constructing a Projection Matrix
216(6)
7.6 Predicting How a Population Changes After One Year
222(4)
7.7 The Stable Distribution of Individuals Across Stages
226(1)
7.8 Theory Supporting the Calculation of Stable Distributions
227(7)
7.8.1 Eigenvalues and Eigenvectors
227(1)
7.8.2 The Perron-Frobenius Theorem
228(3)
7.8.3 Raising a Matrix to a Power in MATLAB and R
231(1)
7.8.4 Finding the Stable Distribution
231(3)
7.9 Determining Population Growth Rate and the Stable Distribution
234(3)
7.9.1 Calculating Eigenvalues and Eigenvectors in MATLAB
235(1)
7.9.2 Calculating Eigenvalues and Eigenvectors in R
236(1)
7.10 Further Applications of the Projection Matrix
237(1)
References
237(2)
Chapter 8 Metabolic Pathways Analysis: A Linear Algebraic Approach
239(28)
Terrell L. Hodge
8.1 Introduction
239(3)
8.2 Biochemical Reaction Networks, Metabolic Pathways, and the Stoichiometry Matrix
242(16)
8.2.1 Stoichiometric Matrix I: Nullspaces, Linear Dependence, and Spanning Sets
242(9)
8.2.2 More on the Nullspace of the Stoichiometric Matrix: Spanning with Biochemical Pathways and Base Changing
251(5)
8.2.3 Conclusion
256(2)
8.3 Extreme Paths and Model Improvements
258(7)
8.3.1 Downloading and Installing expa.exe
258(2)
8.3.2 Analyzing a Modeling Decision: Directed Graphs
260(5)
8.4 Supplementary Data
265(1)
References
265(2)
Chapter 9 Identifying CpG Islands: Sliding Window and Hidden Markov Model Approaches
267(40)
Raina Robeva
Aaron Garrett
James Kirkwood
Robin Davies
9.1 Introduction
267(3)
9.1.1 Biochemistry Background
267(1)
9.1.2 CpG Islands
268(2)
9.1.3 DNA Methylation in Cancer
270(1)
9.2 Quantitative Characteristics of the CpG Island Regions and Sliding Windows Algorithms
270(4)
9.3 Definition and Basic Properties of Markov Chains and Hidden Markov Models
274(8)
9.3.1 Finite State Markov Chains
274(3)
9.3.2 Hidden Markov Models (HMMs)
277(2)
9.3.3 Viewing DNA Sequences As Outputs of a HMM
279(3)
9.4 Three Canonical Problems for HMMs with Applications to CGI Identification
282(19)
9.4.1 Decoding: The Viterbi algorithm
283(6)
9.4.2 Evaluation and Posterior Decoding: The Forward-Backward Algorithm
289(6)
9.4.3 Training: The Baum-Welch Algorithm
295(4)
9.4.4 Post-Processing
299(2)
9.5 Conclusions and Discussion
301(1)
9.6 Supplementary Materials
302(1)
References
302(5)
Chapter 10 Phylogenetic Tree Reconstruction: Geometric Approaches
307(36)
David Haws
Terrell L. Hodge
Ruriko Yoshida
10.1 Introduction
307(3)
10.2 Basics on Trees and Phylogenetic Trees
310(8)
10.3 Tree Space
318(11)
10.3.1 Trees as Points
318(2)
10.3.2 Fitting Trees: A Distance-Based Approach
320(4)
10.3.3 Tree Metrics and Tree Space
324(5)
10.4 Neighbor-Joining and BME
329(10)
10.4.1 Neighbor-Joining
329(5)
10.4.2 Balanced Minimum Evolution
334(5)
10.5 Summary
339(1)
References
340(3)
Index 343
Raina Robeva was born in Sofia, Bulgaria. She holds a PhD in Mathematics from the University of Virginia and has broad research interests spanning theoretical mathematics, applied probability, and systems biology. Robeva is the founding Chief Editor of the journal Frontiers in Systems Biology and the lead author/editor of the books An Invitation to Biomathematics (2008), Mathematical Concepts and Methods in Modern Biology: Using Modern Discrete Models (2013), and Algebraic and Discrete Mathematical Methods for Modern Biology (2015), all published by Academic Press. She is Professor of Mathematical Sciences and Director of the Center for Science and Technology in Society at Sweet Briar College.
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