LAUSR

The mitochondrial DNA of trypanosomes, called kinetoplast DNA (kDNA) contains thousands of minicircles that are topologically linked into a single structure that resembles a medieval chainmail. This biological chainmail is characterized by two parameters: the link type between minicircles, and the number of minicircles linked to each minicircle (i.e. the minicircle valence). In previous works, a protocol was proposed to determine the mean value of the minicircle valence. In these experiments, minicircles were excised from the network and the products compared with those obtained from fragmenting idealized structures. These idealized structures assumed a negligible variance in the distribution of valences of the initial network. It is therefore unclear to what extent this theoretical analysis captures the true topology of the kDNA network when kDNA samples are extracted from unsynchronized cells or from cells with silenced kDNA replication genes. Subsequent studies proposed that there is a critical percolation density during network formation. We asked whether this density can be estimated using fragmentation reactions. The goal of this work is to develop a mathematical method that can be used to estimate the mean valence of networks when the variance of the valence is non-negligible. We first show microscopy data on Crithidia fasciculata that, in agreement with the original experimental results, show a distribution of valences with nonzero variance. Second, we use computer simulations of network fragmentation to show that the predicted and actual mean valence are different when the valence distribution has nonzero variance. We propose a more general mathematical formulation and computer simulations of kDNA fragmentation to estimate this value. Last, we show that fragmentation experiments may lead to errors in the estimation of the critical percolation density since the collapsing density depends on the initial density of the network, and on the fragmentation reaction.