MAT 580 Special Topics in Materials Science and Engineering I:

Network Models in Self-Organized Molecular Systems

The course is about the construction of network models for the solution of current molecular physics problems so as to relate the molecular structure to its dynamical properties. It includes a review of basic network models and their extension to weighted networks. Self-organized macromolecular structures (surfactants, proteins, RNA, etc.) are introduced and fundamental results that may be obtained from all-atom methods are outlined. Approaches to coarse-graining of macromolecules are discussed and these coarse-grained models are examined within the scope of network models in general. Applications include statistical and spectral analysis using descriptive network parameters, and dynamical response analysis through equilibrium relaxations of the nodes of the network. The ideas conveyed in the course may be generalized to any type of soft-matter with self-organization capacity as well as larger scale networks with dynamic properties common to the currently analyzed systems.

Intended Audience: An introductory graduate level course for all interested FENS students. No preliminary knowledge on any of the major components of the course (e.g. graph theory) is necessary.

Scope: To expose the students to network models and network theory as applied to the field of structure - function relationships in the physics of macromolecules, and to create an interface to current research problems in diverse fields of study.

Aims: To use the tools of network theory for studying current molecular physics problems. To furnish the students with the basic understanding to choose between all-atom versus coarse grained models for obtaining a given system property. To extend the ideas conveyed in the course to any type of soft-matter with self-organization capacity as well as larger scale networks with dynamic properties common to the currently analyzed systems.

Instructor: Canan ATILGAN - office: 2058; phone: 9523; e-mail: canan@sabanciuniv.edu

Hours: M 9:40 - 10:30; W 15:40 - 17:30 (these times are subject to change)

Reading materials: Papers from the current literature (to be specified in the detailed course outline)

Evaluation will be based on regular assignments (code & report); students are expected to write their own codes in a programming language of their own choice.

Brief outline:

Introduction to Networks	Random networks. Networks with Poisson and scale-free distributions. Small-world networks.	2 weeks
Networks with arbitrary degree distributions	Generating functions for studying the basic network properties.	1 week
Weighted networks	Methods for assigning weights to links; modification of network parameters to incorporate weights.	1 week
Introduction to macromolecular structure	Polymers, proteins, DNA, RNA.	1 week
Bio-macromolecules as weighted networks	Statistics on large amounts of experimental structural data; Thomas - Dill and Miyazawa - Jernigan potentials.	1 week
All-atom approaches to the structure and dynamics of macromolecules	Force fields, molecular mechanics (including basic optimization techniques), molecular dynamics.	2 weeks
Modal analysis	Elastic network models. High and low frequency filtering in relation to molecular-level function.	2 weeks
Perturbation - response analysis	Probing the landscape of macromolecules; stability analysis. Domain movements.	2 weeks
Dynamical analysis	Predicting local relaxations on different time scales.	2 weeks