Abstract
Two things Tunde loved were dynamics and probability. The work described herein combined them both, which explains why Tunde invariably asked me each time we talked how this work was proceeding. However, as I've come to appreciate as reminiscent of a surprisingly large amount of work in almost any researcher's career, I did not complete a peer-reviewed article on the matter while he could see it. We were broadly motivated by analysis of data for total DNA content in single cells, across thousands of cells. From such data one can estimate the proportions of cells in different phases of the cell cycle by fitting a mixture model for subpopulations of G(0)/G(1) phase cells (1 relative copy of the genome), S phase cells (between 1 and 2 relative copies of the genome), and G(2)/M phase cells (2 relative copies of the genome). Given an asynchronously cycling population, Gaussian models are reasonable for the G(0)/G(1) and G(2)/M subpopulations, but an appropriate functional form for the S-phase subpopulation was unclear. Since the probability of observing an S-phase cell is intimately related to the dynamics of DNA replication, we worked to derive a model for DNA replication dynamics from first principles, resulting in a closed-form, analytic expression for the dynamics of DNA synthesis. While quite arguably a somewhat superfluous effort, there is a certain satisfaction and academic beauty to modeling systems from a first-principles approach, and it can sometimes lead to unexpected scientific insights. Yet, while mathematically elegant, there was a fundamental issue with a key assumption that the so-called inter-origin distance distribution (distances between DNA replication initiation sites) was time-invariant. First, I present the model as developed previously. Then, to address the time-invariant inter-origin distance distribution issue, I provide a treatment of time-varying inter-origin distance distributions that, while mathematically simple, provides (i) mechanistic predictions for how all the DNA in a fertilized frog egg can be replicated "on time" despite some inter-origin distances initially exceeding the corresponding amount of allowable time and (ii) evidence that, based only on data from DNA content versus time and average inter-origin distances, somatic cell DNA is parsed into distinct regions whose replication is temporally separate.