Universiteit Leiden

nl en


Enumeration and Simulation of Lattice Polymers as Models for Compact Biological Macromolecules

Promotores: H. Schiessel, G.T. Barkema

Raoul Diederick Schram
15 december 2015
Thesis in Leiden Repository

Polymers are the main building blocks of many biological systems, and thus polymer models are important tools for our understanding. One such biological system is the large scale organisation of chromatin. A key question here, is how during cell division the chromosomes can separate without entanglement and knotting. One proposal is that this achieved by a specific spatial organisation of the chromosomes, known as the "fractal globule". Using Monte Carlo simulations, we found that fractal globules are unstable and thus cannot represent the biological system without further ingredients. Another proposal is that topological effects cause spatial separation of the chromosomes. These topological effects can be studied using simulations of nonconcatenated ring polymers. Using a compute device called the Graphics Processing Unit, very detailed and long simulations were carried out. From these a picture emerged in which ring polymers behave much slower than was found in previous studies. A second biological system studied here is the folded state of the protein. This is modeled by the Hamiltonian walk. Here, instead of simulations, we exactly enumerated all Hamiltonian walks of the 4x4x4 cube. Interestingly, simulations show that for larger systems many more walks exist than previously estimated.