Mathematical modelling of DNA
1st and 2nd year courses in math or physics, (or with teacher's permission)
Differential Geometry of Framed Curves (MATH-423)
This course is designed to be an introduction, within the particular context of DNA, to the interplay between analysis, computation and experiment that makes up the process called mathematical modelling. In addition to students whose primary interest is in DNA, the syllabus is intended for students wishing an introduction to the modelling process in general, and the course will describe a number of widely encountered mathematical and computational techniques.
The course will be a detailed introduction to the cgDNA sequence-dependent coarse grain model of DNA, including both how to use it to predict various biologically pertinent sequence-dependent expectations with an associated Monte Carlo code, and all the extensive underlying applied mathematics necessary to estimate cgDNA parameter sets from a library of Molecular Dynamics simulations. The cgDNA model is a research tool that has its own web page . The course will work through the details of publications described on that page, specifically, ,, and  below.
The course has five chapters.
0) Introduction to DNA and a brief overview of its coarse grain models.
1) The sequence-dependent, rigid-base cgDNA model.
2) Parameter estimation for the cgDNA model from Molecular Dynamics time series.
3) Monte Carlo methods with application to sampling cgDNA model equilibrium distributions.
4) Equality constrained nonlinear optimisation with application to computing cgDNA equilibria.
|Week 1 (26.2)||
Description of the basic structure of DNA, and multiscaling (or coarse graining) approaches. The need for a tertiary structure model of DNA, i.e. a sequence-dependent coarse grain model. Overview of the cgDNA coarse grain model to predict a Gaussian PDF for the configuration distribution of a DNA fragment of given sequence. (three periods lecture, one period exercises)
Here you have the link to the supplementary material for this first lecture.
The following references for the cgDNA model are available on the cgDNA web page .
-  A DNA Coarse-Grain Rigid Base Model and Parameter Estimation from Molecular Dynamics Simulations , D. Petkevičiūtė Thesis #5520, EPFL, (2012).
-  cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA , D. Petkevičiūtė, M. Pasi, O. Gonzalez and J. H. Maddocks Nucleic Acids Research 42, no. 20 (2014), p. e153, (2014) .
-  A sequence-dependent rigid-base model of DNA , O. Gonzalez, D. Petkevičiūtė, and J. H. Maddocks, Journal of Chemical Physics 138, no. 5 (2013), p. 055122 1-28 .
References for general books on DNA.
 Understanding DNA, The molecule & how it work C. R. Calladine, H. R. Drew, B. F. Luisi, A. A. Travers, Third Edition, 2004, Academic Press, ISBN 9780121550893 .
Summary: Understanding DNA explains, step by step, why DNA forms specific structures, the form of these structures and how they fundamentally affect the biological processes of transcription and replication.
 Unraveling Dna: The Most Important Molecule Of Life M. D. Frank-Kamenetskii, Revised and Updated Edition, 1997, Perseus Publishing, ISBN 9780201155846.
Summary: A curious blend of history, biographical details to cover the development of molecular biology from the influence of physicists earlier in the century, through the central dogma of molecular biology to discussion of social issues raised by genetic engineering.
 DNA topology A. D. Bates & A. Maxwell, 2005, Oxford University Press, ISBN 9780198506553.
Summary: A clear, concise explanation of the relevance of supercoiling and catenation in the context of biological activity of the DNA molecule.
 DNA structure and Function R. R. Sinden, 1994, Academic Press, ISBN 9780126457506.
Summary: a timely and comprehensive resource, that provides a simple yet comprehensive introduction to nearly all aspects of DNA structure. It also explains current ideas on the biological significance of classic and alternative DNA conformations.