| Description |
1 online resource (268 p.) |
| Series |
Techniques in Life Science and Biomedicine for the Non-Expert |
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Techniques in life science and biomedicine for the non-expert.
|
| Contents |
Intro -- Preface -- Contents -- Part I Biological Networks and Graph Theory -- 1 Introduction to Graph Theory -- 1.1 Definitions and Examples -- 1.2 Spectral Graph Theory -- 1.3 Centrality Measures -- 1.3.1 Geometric Centralities -- 1.3.1.1 Clustering Coefficient -- 1.3.2 Closeness -- 1.3.2.1 Lin's Index -- 1.3.2.2 Harmonic Centrality -- 1.3.3 Path-Based Centralities -- 1.3.3.1 Betweenness Centrality -- 1.3.3.2 Subgraph Centrality -- 1.3.3.3 Information Centrality -- 1.3.4 Spectral Measures -- 1.3.4.1 Eigenvector Centrality -- 1.3.4.2 Hub Centrality -- 1.3.4.3 Katz's Index |
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1.3.4.4 Vibrational Centrality -- 1.4 Axioms for Centrality -- 1.4.1 The Size Axiom -- 1.4.2 The Density Axiom -- 1.4.3 The Score-Monotonicity Axiom -- 2 Biological Networks -- 2.1 Networks: The Representation of a System at the Basis of Systems Biology -- 2.2 Biochemical Networks -- 2.2.1 Metabolic Networks -- 2.2.2 Protein-Protein Interaction Networks -- 2.2.3 Genetic Regulatory Networks -- 2.2.4 Neural Networks -- 2.3 Phylogenetic Networks -- 2.4 Signalling Networks -- 2.5 Ecological Networks -- 2.6 Challenges in Computational Network Biology -- 3 Network Inference for Drug Discovery |
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3.1 How Network Biology Helps Drug Discovery -- 3.2 Computational Methods -- 3.2.1 Classifier-Based Methods -- 3.2.2 Reverse Engineering Methods -- 3.2.3 Integrating Static and Dynamic Data: A PromisingVenue -- Part II Calculus and Chemical Reactions -- 4 An Introduction to Differential and Integral Calculus -- 4.1 Derivative of a Real Function -- 4.2 Examples of Derivatives -- 4.3 Geometric Interpretation of the Derivative -- 4.4 The Algebra of Derivatives -- 4.5 Definition of Integral -- 4.6 Relation Between Integral and Derivative -- 4.7 Methods of Integration -- 4.7.1 Integration by Parts |
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4.7.2 Integration by Substitution -- 4.7.3 Integration by Partial Fraction Decomposition -- 4.7.4 The Reverse Chain Rule -- 4.7.5 Using Combinations of Methods -- 4.8 Ordinary Differential Equations -- 4.8.1 First-Order Linear Equations -- 4.8.2 Initial Value Problems -- 4.9 Partial Differential Equations -- 4.10 Discretization of Differential Equations -- 4.10.1 The Implicit or Backward Euler Method -- 4.10.2 The Runge-Kutta Method -- 4.11 Systems of Differential Equations -- 5 Modelling Chemical Reactions -- 5.1 Modelling in Systems Biology -- 5.2 The Different Types of Mathematical Models |
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5.3 Chemical Kinetics: From Diagrams to Mathematical Equations -- 5.4 Kinetics of Chemical Reactions -- 5.4.1 The Law of Mass Action -- 5.4.2 Example 1: the Lotka-Volterra System -- 5.4.2.1 Equilibrium -- 5.4.3 Example 2: the Michaelis-Menten Reactions -- 5.5 Conservation Laws -- 5.6 Markov Processes -- 5.7 The Master Equation -- 5.7.1 The Chemical Master Equation -- 5.8 Molecular Approach to Chemical Kinetics -- 5.8.1 Reactions Are Collisions -- 5.8.2 Reaction Rate -- 5.8.3 Zeroth-, First-, and Second-Order Reactions -- 5.8.4 Higher-Order Reactions |
| Summary |
This introductory guide provides a thorough explanation of the mathematics and algorithms used in standard data analysis techniques within systems biology, biochemistry, and biophysics. Each part of the book covers the mathematical background and practical applications of a given technique. Readers will gain an understanding of the mathematical and algorithmic steps needed to use these software tools appropriately and effectively, as well how to assess their specific circumstance and choose the optimal method and technology. Ideal for students planning for a career in research, early-career researchers, and established scientists undertaking interdiscplinary research |
| Notes |
5.9 Fundamental Hypothesis of Stochastic Chemical Kinetics |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed September 26, 2023) |
| Subject |
Computational biology -- Mathematics
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| Form |
Electronic book
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| Author |
Carpentieri, B.
|
| ISBN |
9783031365669 |
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3031365666 |
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