Modeling Kinetoplast Dynamics

A kinetoplast is a network of connected circular DNA molecules. The planar structure of a kinetoplast makes it an ideal model to study 2D materials. This system can be modeled using Monte Carlo simulation as a linked ring system implemented in C. In the simulation, different configurations of the ring network are generated through random displacement and rotation of randomly selected rings. Allowed movements for each ring are determined by the parameters and initial conditions of our system. Movements are accepted if the rings do not overlap and their linking connectivity is unchanged. During the simulation, we calculate the gyration tensor of the ring network, which gives us information regarding the equilibrium properties of kinetoplasts. We measure the relationship between the eigenvalues of the gyration tensor, corresponding to the principal radii of gyration, and the parameters for the model. As free parameters, we vary the number of rings and their width. Here, we discuss the scaling behavior of the planar and transverse components of the gyration tensor and compare them to existing models of elastic membranes, to determine the physical effects of linked-ring connectivity.