Computer simulation of confined polymers and 2D catenated-ring networks

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Polymers are flexible, chain-like molecules that are ubiquitous in nature.  An especially significant polymer of biological relevance is DNA, whose sequence of nucleotides contains the genetic blueprint of an organism. In recent years, there has been intense research activity focused on the development of novel technologies for manipulating and characterizing the physical properties of DNA. Many of these "nanofluidics" technologies involve the transport of DNA into very compact regions of of space. The confinement of polymers in such regions is known to affect their physical properties, an understanding of which is essential for rational design of devices for DNA analysis, as well as for understanding biological phenomena such as chromosome segregation in bacteria. DNA can exist in exotic forms in some organisms. For example, kinetoplasts are structures found in the mitochondria of trypanosome parasites that are composed of thousands of interlocking rings of DNA in two-dimensional "chain-mail" membranes. Recent experiments have characterized some of the unique properties of these objects, which behave like thermalized elastic membranes. Kinetoplasts could serve as an inspiration for the development of novel two-dimensional materials with technological applications.  I will use computer simulation methods to model DNA systems studied in recent experiments. A simulation is a virtual experiment on a model system carried out on a computer. Simulations can be used to interpret the results of experiments and test the validity of theoretical descriptions of experimental systems. The simulations will employ very simple molecular models in order to make the calculations feasible. I will focus on two broad themes. In the first, I will employ 2D networks of interlocking hard rings to model kinetoplasts. I will address the following questions: (1) What is the physical origin of the concave shapes of kinetoplasts? (2) What are the effects of the flexibility of the kinetoplast DNA, the solvent conditions, the presence of perforations, and the linking topology on the average size and shape of the membranes?  The second theme focuses on confinement effects in systems of one or two polymers. I will address the following questions: (1) How does confinement affect the organization and dynamics of two strongly confined polymers under conditions similar to those recently examined in DNA nanofluidics experiments? (2) How can explicitly calculated free-energy functions help elucidate the recently observed behaviour of a single DNA molecule confined to a complex nanofluidic geometry? (3) Is it possible to extract quantitatively accurate estimates of the entropic force for a DNA molecule tethered to an atomic force microscope (AFM) cantilever tip interacting with a nearby surface, as attempted in a recent AFM experiment? My research should help contribute to the development of such technological tools for analyzing DNA.