Time course solutions of the Sax-Markov binary eurejoining/misrejoining model of DNA double-strand breaks

The Sax-Markov binary eurejoining/misrejoining (SMBE) model is a stochastic representation of Sax's breakage-and-reunion mechanism of misrejoining DNA double-strand breaks (DSBs). In this model, to approximate DSB misrejoining probabilities that decrease with increasing distance, the nucleus is treated as a collection of eta isolated nuclear subvolumes called sites; DSB free ends within the same site interact with a probability that is independent of distance, and DSB free ends within different sites never interact. In our previous work, SMBE steady-state solutions were used to estimate eta from a combination of high-dose PFGE (pulsed-field gel electrophoresis) data and moderate-dose chromosomal aberration data. Here, analytic SMBE transient solutions (i.e., time courses of DSBs and misrejoinings) are derived and used to estimate eta from various sets of misrejoining DSB kinetic data. The time courses are multiexponentials with rate constants kappa, 6kappa, 15kappa, ... j(2j-1)kappa corresponding to different nuclear site states and not different types of DSBs. For example, the kappa component corresponds to nuclear sites with two DSB free ends and thus only one possible rejoining interaction, and the 6kappa component corresponds to sites with four DSB free ends and thus six (four choose two) potential rejoining interactions--four of these six potential interactions lead to a final state of two misrejoinings and the other two of six lead to a final state of correct repair (unrejoinable DSBs are not represented in the SMBE model). The SMBE time course solutions provide site number estimates that fall in the range of eta approximately equals 10-100 for premature chromosome condensation (PCC) data and eta approximately equals 1,000 for PFGE data.