Fractals in Molecular Biophysics

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Overview

Historically, science has sought to reduce complex problems to their simplest components, but more recently it has recognized the merit of studying complex phenomena in situ. Fractal geometry is one such appealing approach, and this book discusses its application to complex problems in molecular biophysics. The book provides a detailed, unified treatment of fractal aspects of protein and structure dynamics, fractal reaction kinetics in biochemical systems, sequence correlations in DNA and proteins, and descriptors of chaos in enzymatic systems. In an area that has been slow to acknowledge the use of fractals, this is an important addition to the literature, offering a glimpse of the wealth of possible applications to complex problems.

The book contains black-and-white illustrations.

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Editorial Reviews

From the Publisher
"The book is devoted to various applications of the modern concept of fractals to molecular, cellular, and metabolic systems. First, the basic terminology of self-similarity, polymer statistics, renormalization groups, and multifractality is introduced . . . Then temporal phenomena . . . are considered. One chapter discusses correlations and entropies of sequence data. Another chapter deals with applications of percolation theory: antibody receptor clustering, microdomains in biomembranes, and the hydration of proteins. The final chapter reviews chaos in enzymatic systems. The chapters constitute almost self-contained reviews, each with an introduction, a summary, and references. The book should be of interest to a broad readership—specialists in fractals can learn about interesting biological applications, and people familiar with biochemistry are introduced to the unifying formalism of statistical mechanics and fractals."—Mathematical Reviews

"Ever since fractals became a popular concept about 25 years ago, researchers have struggled to discover how to apply the concepts to various other scientific studies. The key idea is that the fractal approach offers ways of carefully measuring the dimension and scaling properties of various phenomena in order to classify them. . . . Although the first chapter of the book summarizes fractal concepts in a fairly intuitive way, it is not an elementary tutorial. . . . Successive chapters cover protein structure, polymer statistics and loops, multifractality, diffusion, dynamics, sequence data, percolation, and chaos. Dewey has succeeded in giving a thorough account of how the tools of fractal mathematics can enhance the study of polymer structure and dynamics. The book will be most useful for researchers or serious students with a strong mathematical background."—The Quarterly Review of Biology

"This is a volume in the series Topics in Physical Chemistry. It is its goal to pull together diverse applications and to present a unified exposition how fractals can be used in molecular biophysics. The book is intended for two audiences: the biophysical chemist who is unfamiliar with fractals, and the expert in fractals who is unfamiliar with biophysical problems. A theme that runs through the book is the close association of fractals and renormalization group theory, the latter being intimately associated with phase behavior of polymers and aggregates."—Quarterly of Applied Mathematics

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Product Details

  • ISBN-13: 9780195084474
  • Publisher: Oxford University Press, USA
  • Publication date: 2/28/1998
  • Series: Topics in Physical Chemistry Series
  • Edition description: New Edition
  • Pages: 288
  • Product dimensions: 6.40 (w) x 9.20 (h) x 0.90 (d)

Table of Contents

1. What Are Fractals?
2. Fractal Aspects of Protein Structure
3. Loops, Polymer Statistics, and Helix-Coil Transitions
4. The Multifractality of Biomacromolecules
5. Fractal Diffusion and Chemical Kinetics
6. Are Protein Dynamics Fractal?
7. Fractons and Vibrational Relaxation in Proteins
8. Encoded Walks and Correlations in Sequence Data
9. Percolation
10. Chaos in Biochemical Systems
Index

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