Coupling gene expression dynamics to cell size dynamics and cell cycle events: exact and approximate solutions of the extended telegraph model

Abstract

The standard model describing the fluctuations of mRNA numbers in single cells is the telegraph model which includes synthesis and degradation of mRNA, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by the cell cycle phase, cellular growth and division, and other crucial aspects of cellular biology. Here we derive the analytical time-dependent solution of a stochastic model that explicitly considers various sources of intrinsic and extrinsic noise: switching between inactive and active states, doubling of gene copy numbers upon DNA replication, dependence of the mRNA synthesis rate on cellular volume, gene dosage compensation, partitioning of molecules during cell division, cell-cycle duration variability, and cell-size control strategies. We show that generally the analytical distribution of transcript numbers in steady-state growth cannot be accurately approximated by the steady-state solution of extrinsic noise models, i.e. a telegraph model with parameters drawn from probability distributions. This is because the mRNA lifetime is often not small enough compared to the cell cycle duration to erase the memory of division and replication. Accurate approximations are possible when this memory is weak, e.g. for genes with bursty expression and for which there is sufficient gene dosage compensation when replication occurs.

RNA velocity unraveled

“…We have restricted our discussion to regulatory modulation in terminally differentiated cells. In a variety of contexts, cell division, which involves molecule partitioning and transcriptional dosage compensation [ 93 , 156 ], plays a significant role in differentiation, and it is inappropriate to omit its effects. Considerable literature exists on cell cycle models [ 93 , 157 , 158 ], but they are fairly challenging to solve, and the appropriate way to integrate them with occupation measures is unclear at this time.…”

Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis

“…This pattern is strongly influenced by various sources of noise including the variability in cell cycle durations, the doubling of gene copy numbers upon DNA replication, and the partitioning of molecules during cell division. How noise in gene expression is regulated by different aspects of cell cycle, growth, and division have been extensively studied in the literature [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Analytical time-dependent distributions for gene expression models with complex promoter switching mechanisms

“…While we have considered an implicit description of gene product dilution due to cell division, via the effective gene product decay rate, it has recently been shown that in some parameter regimes, this type of model cannot capture the stochastic dynamics predicted by models with an explicit description of the cell cycle [62]. We hence anticipate that a more detailed gene expression model with the inclusion of feedback loops [17][18][19][20][21] and cell cycle events, such as cell growth, cell division, and gene replication [63][64][65][66][67][68] may display more complex behavior of time-evolution and may even introduce novel dynamical phases hitherto undescribed. These effects are currently under investigation.…”