Computer simulation of two polymers confined to a box-like cavity

Rehel, Desiree

Honours

2021

Polson, James

Bachelor of Science

Faculty of Science. Honours in Physics.

Physics

University of Prince Edward Island

Charlottetown, PE

In this study, we use computer simulations to examine the behaviour of systems of two polymers confined to a box-like cavity, with strong confinement in one dimension and a square cross-section. We also explore the effect that asymmetries in polymer size and box dimensions have on the system. The project is motivated by some recent experimental work (Z. Liu, M.Sc. thesis, McGill University Libraries, 2019) in which the behaviour of two DNA molecules confined to a box-like cavity with strong Show moreIn this study, we use computer simulations to examine the behaviour of systems of two polymers confined to a box-like cavity, with strong confinement in one dimension and a square cross-section. We also explore the effect that asymmetries in polymer size and box dimensions have on the system. The project is motivated by some recent experimental work (Z. Liu, M.Sc. thesis, McGill University Libraries, 2019) in which the behaviour of two DNA molecules confined to a box-like cavity with strong confinement in one dimension and either a square or elliptical cross-section was examined. Understanding the behaviour of systems of confined polymers may have applications in a fewareas. For example, such understanding may help guide the development and optimization of nanofluidic devices which use nanoconfinement to sort, manipulate and map DNA molecules. The information may also help elucidate the mechanism causing the segregation of DNA chromosomes during the division of prokaryotic cells, as there is no cellular machinery in prokaryotic cells to actively pull the chromosomes apart. We start by examining the behaviour of two identical polymers confined to a boxlike cavity with a square cross-section and strong confinement in one dimension. To examine the organization of the polymers, we measure probability distributions for the centre-of-mass positions of the polymer and the displacement between the centre-of-mass positions of the polymers. We measure the radius of gyration and asphericity of the polymers in the plane of the box to examine their conformation. We also measure the inter-polymer proximity and overlap. To examine the dynamics of the system, we measure the mean-square displacement, the position cross-correlation and the time correlations for the first few Rouse modes. As a reference, we measured the same quantities for a system with only one polymer as were measured for the system of two polymers and compared the results. We find that in the large box sizes, the behaviour of the system is unaffected by the presence of the second polymer. However, as the box becomes smaller, the dynamical behaviour of the polymers is slowed due to the presence of the second polymer. We find that as the box size decreases, the polymers first start to compress while remaining segregated but that as the box size decreases further, they start to have a higher probability of significant inter-polymer overlap. We found the general trends to be independent of polymer length. We also found that increasing the height of the box had the effect of decreasing the interaction between the polymers and thus allowing easier overlap. Since the interactions between polymers decrease with increasing box height, the dynamics of the system were found to be less affected when the box was taller. The results found in the simulations are qualitatively consistent with the results from the previously mentioned experiments in that the polymers are pushed away from the centre of the box, and the dynamics of the system are slowed due to the presence of the second polymer. The effects of asymmetries in the system were also examined. We looked at the non-dynamical behaviour of a system of two polymers confined to a box-like cavity with strong confinement in one dimension and a rectangular cross-section. Studying this type of asymmetry is motivated by the experiments performed in which the researchers investigated the behaviour of two !-DNA molecules confined to a cavity with an elliptical cross-section and strong confinement in one dimension (Z. Liu, MSc thesis, McGill University Libraries, 2019). It was found that the asymmetry caused the average shape anisometry of the polymer to increase. The asymmetry was also found to promote segregation of the polymers along the long axis of the box, with the two polymers periodically swapping between the segregated positions at the poles. These results are consistent with what was seen in the experiments: the anisometry of the cavity promotes polymer segregation. Finally, we examined the non-dynamical behaviour of two non-identical polymers confined to a box-like cavity with strong confinement in one dimension and a square-cross-section. This system is similar to howin the previously mentioned experiments, the researchers examined the behaviour of a larger !-DNA molecule confined to a box-like cavity with a plasmid, which is a smaller ring polymer. It was found that the larger polymers preferred the centre of the box, thus causing the smaller polymers to be pushed away from the centre. In cases with a larger asymmetry in polymer size, the smaller polymer was pushed into the corner of the box. It was also found that the size and shape of the larger polymers were more affected by the confinement than that of the smaller ones. Due to having very limited data for this system, a complete understanding of the effect due to the presence of the second polymers was not possible. However, the observed results are consistent with what was seen in the experiment in that the larger polymer tends to be more concentrated at the centre of the box while the smaller polymer tends to be pushed towards the edges. The results also shed light on an anomaly seen in the distribution of the two lambda-DNA molecules and suggest that one of the dyes used, YOYO-3, causes a smaller increase in the contour length of the molecule than the other dye, YOYO-1. Show less

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