Foreword

Rigorous description of biological phenomena through physics and mathematics is a daunting task both theoretically and computationally. One has to simplify usually very complex biological systems so as to be able to write equations that can be solved at least via numerical methods. There is always a high level of difficulty in physical understanding of a complicated biological process: how much the system is simplified, which degrees of freedom are chosen and which are discarded, and then how the numerical solution methods are implemented all contribute to the success or failure in understanding the particular biological system through physics and mathematics. Biological systems with their many degrees of freedom thus bring a highest possible challenge to a working physicist. This book contains state of the art theoretical and numerical techniques for analysis of several biological phenomena by a biophysical approach. In it, readers would find many invaluable insights into the biological processes, which can be utilized in diverse applications, including the spread of disease in a pandemic situation.

This book discusses three biological processes utilizing the techniques of biophysics: melting and vitrification of DNA molecules which can be described collectively as the chemistry of nucleic acids, theoretical discussion of percolation model and the description of folding of protein Crambin via two different methods. In chapter 1, Morse potential is used to describe the hydrogen bond interaction between nucleic acid base pairs in DNA molecule, and then a metropolis algorithm is used for the total potential energy as well as including the quantum fluctuation in terms of random displacement of the 𝜋 electrons. This way the melting temperature of base pairs is calculated. Then in chapter 5, the same principles are used together with the inclusion of effect of longitudinal phonon vibrations to calculate the vitrification temperature of the base pairs. In chapter 2, an analytical analysis for a percolation simulation is presented: in a bit-string model of invading species in a random environment, the Hausdorff dimensions are calculated for the fractals and the conditions on invasion are analyzed analytically. Chapters 3 and 4 are reserved for analysis of the folding dynamics of the plant-seed protein Crambin in a liquid environment. A stochastic approach used to take into account the viscosity results in a 2D-Langevin equation, solution of which is established with a Molecular Dynamics simulation, accompanied by a delicate Monte Carlo technique. The final image of folded protein is found to be in very good geometric agreement with the real shape of the protein chain. Finally, a much useful discussion of the well known 10-12 potential of hydrogenhydrogen covalent bond is shared in the appendix.

This book consists of the research articles the author published during his postdoc studies at the Feza Gürsey Institute. Feza Gürsey Institute was a major center for theoretical physics and mathematics in Turkey. During the first decade of this century many top level research was conducted in this institute, and Dr. Taneri’s work was up there with the very best. As in any good work, this book has many layers. It can be a valuable tool for the graduate students learning the subject, or it can be equally useful for established researchers.