Mathematical Approaches to Molecular Structural Biology
- 1st Edition - November 19, 2022
- Imprint: Academic Press
- Author: Subrata Pal
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 0 3 9 7 - 4
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 0 6 6 3 - 0
Mathematical Approaches to Molecular Structural Biology offers a comprehensive overview of the mathematical foundations behind the study of biomolecular structure. Initial c… Read more
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Request a sales quoteMathematical Approaches to Molecular Structural Biology offers a comprehensive overview of the mathematical foundations behind the study of biomolecular structure. Initial chapters provide an introduction to the mathematics associated with the study of molecular structure, such as vector spaces and matrices, linear systems, matrix decomposition, vector calculus, probability and statistics. The book then moves on to more advanced areas of molecular structural biology based on the mathematical concepts discussed in earlier chapters. Here, key methods such as X-ray crystallography and cryo-electron microscopy are explored, in addition to biomolecular structure dynamics within the context of mathematics and physics.
This book equips readers with an understanding of the fundamental principles behind structural biology, providing researchers with a strong groundwork for further investigation in both this and related fields.
- Includes a detailed introduction to key mathematical principles and their application to molecular structural biology
- Explores the mathematical underpinnings behind advanced techniques such as X-ray crystallography and Cryo-electron microscopy
- Features step-by-step protocols that illustrate mathematical and statistical principles for studying molecular structure and dynamics
- Provides a basis for further investigation into the field of computational molecular biology
- Includes figures and graphs throughout to visually demonstrate the concepts discussed
Researchers working in the areas of structural biology, molecular biology, biophysics, and related areas. Graduate and PhD students involved in structural biology, computational molecular biology, mathematics or statistics of molecular and structural biology and related disciplines
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- About the author
- Preface
- Acknowledgments
- Table of symbols
- Chapter 1. Mathematical preliminaries
- Abstract
- 1.1 Functions
- 1.2 Vectors
- 1.3 Matrices and determinants
- 1.4 Calculus
- 1.5 Series and limits
- Exercise 1
- Further reading
- Chapter 2. Vector spaces and matrices
- Abstract
- 2.1 Linear systems
- Exercises 2.1
- 2.2 Sets and subsets
- Exercise 2.2
- 2.3 Vector spaces and subspaces
- Exercise 2.3
- 2.4 Liner combination/linear independence
- Exercise 2.4
- 2.5 Basis vectors
- Exercise 2.5
- 2.6 Dimension and rank
- Exercise 2.6
- 2.7 Inner product space
- Exercise 2.7
- 2.8 Orthogonality
- Exercise 2.8
- 2.9 Mapping and transformation
- Exercise 2.9
- 2.10 Change of basis
- Exercise 2.10
- Further reading
- Chapter 3. Matrix decomposition
- Abstract
- 3.1 Eigensystems from different perspectives
- Exercise 3.1
- 3.2 Eigensystem basics
- Exercise 3.2
- 3.3 Singular value decomposition
- Exercises 3.3
- Further reading
- Chapter 4. Vector calculus
- Abstract
- 4.1 Derivatives of univariate functions
- 4.2 Derivatives of multivariate functions
- 4.3 Gradients of scalar- and vector-valued functions
- 4.4 Gradients of matrices
- 4.5 Higher-order derivates – Hessian
- 4.6 Linearization and multivariate Taylor series
- Exercise 4
- Further Reading
- Chapter 5. Integral transform
- Abstract
- 5.1 Fourier transform
- 5.2 Dirac delta function
- 5.3 Convolution and deconvolution
- 5.4 Discrete Fourier transform
- 5.5 Laplace transform
- Exercise 5
- Further reading
- Chapter 6. Probability and statistics
- Abstract
- 6.1 Probability—definitions and properties
- 6.2 Random variables and distribution
- 6.3 Multivariate distribution
- 6.4 Covariance and correlation
- 6.5 Principal component analysis
- Exercise 6
- Further reading
- Chapter 7. X-ray crystallography
- Abstract
- 7.1 X-ray scattering
- 7.2 Scattering by an atom
- 7.3 Diffraction from a crystal – Laue equations
- 7.4 Diffraction and Fourier transform
- 7.5 Convolution and diffraction
- 7.6 The electron density equation
- Exercise 7
- Further reading
- Chapter 8. Cryo-electron microscopy
- Abstract
- 8.1 Quantum physics
- 8.2 Wave optics of electrons—scattering
- 8.3 Theory of image formation
- 8.4 Image processing by multivariate statistical analysis—principal component analysis
- 8.5 Clustering
- 8.6 Maximum likelihood
- Exercise 8
- Reference
- Further reading
- Chapter 9. Biomolecular structure and dynamics
- Abstract
- 9.1 Comparison of biomolecular structures
- 9.2 Conformational optimization
- 9.3 Molecular dynamics
- 9.4 Normal mode analysis
- Exercise 9
- References
- Further reading
- Index
- Edition: 1
- Published: November 19, 2022
- No. of pages (Paperback): 310
- No. of pages (eBook): 310
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9780323903974
- eBook ISBN: 9780323906630
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Subrata Pal
Subrata Pal obtained his bachelor’s and master’s degrees, both in physics, from Calcutta University. Subsequently, he pursued his predoctoral research in molecular biology and received a PhD degree from the same university in 1982. He carried out his postdoctoral research in DNA replication and gene expression at two of the premiere institutions in the USA: the National Institutes of Health, Bethesda, Maryland and Harvard Medical School, Boston Massachusetts. At Harvard, he received a Claudia Adams Barr special investigator award for basic contribution to cancer research. Professor Pal has a long teaching experience at the undergraduate and graduate levels – the areas of his teaching include physics, molecular biology and genomics.
Affiliations and expertise
Professor (retired), Jadavpur University, Kolkata, IndiaRead Mathematical Approaches to Molecular Structural Biology on ScienceDirect