Implications of stochastic inheritance

Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes.

Rate of segregation due to plasmid incompatibility

We calculated the rates of segregation due to plasmid incompatibility under several simple models. A common feature of all the models that we considered is that incompatibility is caused by the inability of the segregation mechanism to distinguish between two incompatible plasmids.

We measured the rate of segregation due to incompatibility of a pair of ColE1 derivatives under two conditions: (1) One plasmid was introduced into cells carrying the other by conjugation. (2) Cells carrying both plasmids were maintained by selection and then selection was released.

Interpretation of the results was made more difficult by effects of the Plasmids on the host cell's growth rate. These experiments gave results in agreement with the predictions of a random pool replication model. Published results were also in reasonable agreement with this model.

Modeling cellular systems and aging processes: I. Mathematics of cell system models-a review

A review of the literature on mathematical models of populations of cellular systems is presented. Continuous, discrete, and stochastic models are presented in a semihistorical manner as a prelude to answering the question of how to model an asynchronously dividing cellular system. This analysis is then broadened, in an attempt to broach the more general question of modeling the distribution of a set or collection of cell properties through an asynchronously dividing cellular system. Such properties might be cell motility, cell cycle length, time to mitosis, or number of epigenetic particles. It is shown that one fruitful approach to this modeling question is a coupled continuous-probabilistic model. The ramifications of this type of formalism are discussed.

Loss of gene repression activity: a theory of cellular senescence

Recent evidence bearing on cellular senescence has come from cell fusion and clonal lifespan studies. To date, no model has been developed that is consistent with the recent findings. The purpose of this paper is to present a mechanism for cell senescence that is qualitatively consistent with the experimental evidence.