Computational Biology

A Statistical Mechanics Perspective, Second Edition

Ralf Blossey

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429994609
• Edition: 2
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

Computational biology has developed rapidly during the last two decades following the genomic revolution which culminated in the sequencing of the human genome. More than ever it has developed into a field which embraces computational methods from different branches of the exact sciences: pure and applied mathematics, computer science, theoretical physics. This Second Edition provides a solid introduction to the techniques of statistical mechanics for graduate students and researchers in computational biology and biophysics.

• Material has been reorganized to clarify equilbrium and nonequilibrium aspects of biomolecular systems

• 
  
  

• Content has been expanded, in particular in the treatment of the electrostatic interactions of biomolecules and the application of non-equilibrium statistical mechanics to biomolecules

• 
  
  

• New network-based approaches for the study of proteins are presented.

• 
  
  

All treated topics are put firmly in the context of the current research literature, allowing the reader to easily follow an individual path into a specific research field. Exercises and Tasks accompany the presentations of the topics with the intention of enabling the readers to test their comprehension of the developed basic concepts.

I

Equilibrium Statistical Mechanics

Chapter 1

Equilibrium Statistical Mechanics

Après tout, vous êtes ici, c’est l’essentiel! Nous allons faire du bon travail ensemble […]! D’ici peu, le monde ébloui decouvrira la puissance du grand Z!

Franquin, Z comme Zorglub (1961)

1.1Z: The partition function

This section introduces the basic physical concepts and mathematical quantities needed to describe systems composed of many particles, when only a statistical description remains possible.

Already for an apparently trivial system such as a gas of identical atoms, composed of N ∼ 1023 particles/mole (Avogadro’s number), the description of each particle’s trajectory is illusory and not even desirable, and hence only a statistical approach feasible. In biology, as we will see, things are more complicated: not only is the number of relevant interacting components large, but in addition the components are very often ‘individuals’.

Suppose we can characterize our system of interest by a given number of ‘state variables’, which can be finite or infinite. An example of such a state variable can be the spatial position of a particle, hence a continuous variable, but in principle it can be any other of its distinguishing characteristics. We call the set of these state variables x, irrespective of their physical nature, and treat x here as a set of discrete variables;1 we call such a collection of variables characterizing the state of a system a microstate. The possible microstates a system can assume, typically under certain constraints, can be subsumed under the name of a statistical ensemble. One has to distinguish the microstate the system can assume in each of its realisations from the ultimate macrostate that is to be characterized by a macroscopic physical observable after a suitable averaging procedure over the microstates.2

Example. We give a simple illustration of the concept by considering the conformations of a linear molecule such as DNA. The macrostate is the chain conformation we will most probably observe when we image the molec...