Models and Algorithms for Biomolecules and Molecular Networks

Bhaskar DasGupta, Jie Liang

• Publisher: Wiley-IEEE Press
• Year: 2016
• Print ISBN: 9780470601938
• eBook ISBN: 9781119162278
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biophysics
• Index: Biological Sciences

By providing expositions to modeling principles, theories, computational solutions, and open problems, this reference presents a full scope on relevant biological phenomena, modeling frameworks, technical challenges, and algorithms.

• Up-to-date developments of structures of biomolecules, systems biology, advanced models, and algorithms
• Sampling techniques for estimating evolutionary rates and generating molecular structures
• Accurate computation of probability landscape of stochastic networks, solving discrete chemical master equations
• End-of-chapter exercises

 

1
Geometric Models of Protein Structure and Function Prediction

1.1 Introduction

Three-dimensional atomic structures of protein molecules provide rich information for understanding how these working molecules of a cell carry out their biological functions. With the amount of solved protein structures rapidly accumulating, computation of geometric properties of protein structure becomes an indispensable component in studies of modern biochemistry and molecular biology. Before we discuss methods for computing the geometry of protein molecules, we first briefly describe how protein structures are obtained experimentally.

There are primarily three experimental techniques for obtaining protein structures: X-ray crystallography, solution nuclear magnetic resonance (NMR), and recently freeze-sample electron microscopy (cryo-EM). In X-ray crystallography, the diffraction patterns of X-ray irradiation of a high-quality crystal of the protein molecule are measured. Since the diffraction is due to the scattering of X-rays by the electrons of the molecules in the crystal, the position, the intensity, and the phase of each recorded diffraction spot provide information for the reconstruction of an electron density map of atoms in the protein molecule. Based on independent information of the amino acid sequence, a model of the protein conformation is then derived by fitting model conformations of residues to the electron density map. An iterative process called refinement is then applied to improve the quality of the fit of the electron density map. The final model of the protein conformation consists of the coordinates of each of the non-hydrogen atoms [46].

The solution NMR technique for solving protein structure is based on measuring the tumbling and vibrating motion of the molecule in solution. By assessing the chemical shifts of atomic nuclei with spins due to interactions with other atoms in the vicinity, a set of estimated distances between specific pairs of atoms can be derived from NOSEY spectra. When a large number of such distances are obtained, one can derive a set of conformations of the protein molecule, each being consistent with all of the distance constraints [10]. Although determining conformations from either X-ray diffraction patterns or NMR spectra is equivalent to solving an ill-posed inverse problem, a technique such as Bayesian Markov chain Monte Carlo with parallel tempering has been shown to be effective in obtaining protein structures from NMR spectra [52].

1.2 Theory and Model

1.2.1 Idealized Ball Model

The shape of a protein molecule is complex. The chemical properties of atoms in a molecule are determined by their electron charge distribution. It is this distribution that generates the scattering patterns of the X-ray diffraction. Chemical bonds between atoms lead to transfer of electronic charges from one atom to another, and the resulting isosurfaces of the electron density distribution depend not only on the location of individual nuclei but also on interactions between atoms. This results in an overall complicated isosurface of electron density [2].

The ge...

Table of contents

• Cover
• Series Page
• Title Page
• Copyright
• Dedication
• List of Figures
• List of Tables
• Foreword
• Acknowledgments
• Chapter 1: Geometric Models of Protein Structure and Function Prediction
• Chapter 2: Scoring Functions for Predicting Structure and Binding of Proteins
• Chapter 3: Sampling Techniques: Estimating Evolutionary Rates and Generating Molecular Structures
• Chapter 4: Stochastic Molecular Networks
• Chapter 5: Cellular Interaction Networks
• Chapter 6: Dynamical Systems and Interaction Networks
• Chapter 7: Case Study of Biological Models
• Glossary
• Index
• End User License Agreement