The nonlinear dynamics and fluctuations of mRNA levels in cell cycle coupled transcription

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

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 an extended telegraph model that explicitly considers the 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. Based on the time-dependent solution, we obtain the analytical distributions of transcript numbers for lineage and population measurements in steady-state growth and also find a linear relation between the Fano factor of mRNA fluctuations and cell volume fluctuations. We show that generally the lineage and population distributions 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.

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

Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast.

Stochastic Transcription with Alterable Synthesis Rates

Background: Gene transcription is a random bursting process that leads to large variability in mRNA numbers in single cells. The main cause is largely attributed to random switching between periods of active and inactive gene transcription. In some experiments, it has been observed that variation in the number of active transcription sites causes the initiation rate to vary during elongation. Results: We established a mathematical model based on the molecular reaction mechanism in single cells and studied a stochastic transcription system consisting of two active states and one inactive state, in which mRNA molecules are produced with two different synthesis rates. Conclusions: By calculation, we obtained the average mRNA expression level, the noise strength, and the skewness of transcripts. We gave a necessary and sufficient condition that causes the average mRNA level to peak at a limited time. The model could help us to distinguish an appropriate mechanism that may be employed by cells to transcribe mRNA molecules. Our simulations were in agreement with some experimental data and showed that the skewness can measure the deviation of the distribution of transcripts from the mean value. Especially for mature mRNAs, their distributions were almost able to be determined by the mean, the noise (or the noise strength), and the skewness.

A Novel Dynamical Regulation of mRNA Distribution by Cross-Talking Pathways

In this paper, we use a similar approach to the one proposed by Chen and Jiao to calculate the mathematical formulas of the generating function V(z,t) and the mass function Pm(t) of a cross-talking pathways model in large parameter regions. Together with kinetic rates from yeast and mouse genes, our numerical examples reveal novel bimodal mRNA distributions for intermediate times, whereby the mode of distribution Pm(t) displays unimodality with the peak at m=0 for initial and long times, which has not been obtained in previous works. Such regulation of mRNA distribution exactly matches the transcriptional dynamics for the osmosensitive genes in Saccharomyces cerevisiae, which has not been generated by those models with one single pathway or feedback loops. This paper may provide us with a novel observation on transcriptional distribution dynamics regulated by multiple signaling pathways in response to environmental changes and genetic perturbations.

Quantification of transcription noise’s impact on cell fate commitment with digital resolutions

Motivation

Gene transcription is a random and noisy process. Tremendous efforts in single cell studies have been mapping transcription noises to phenotypic variabilities between isogenic cells. However, the exact role of the noise in cell fate commitment remains largely descriptive or even controversial.

Results

For a specified cell fate, we define the jumping digit I of a critical gene as a statistical threshold that a single cell has approximately an equal chance to commit the fate as to have at least I transcripts of the gene. When the transcription is perturbed by a noise enhancer without changing the basal transcription level E  0, we find a crossing digit k such that the noise catalyzes cell fate change when I > k while stabilizes the current state when I < k; k remains stable against enormous variations of kinetic rates. We further test the reactivation of latent HIV in 22 integration sites by noise enhancers paired with transcriptional activators. Strong synergistic actions are observed when the activators increase transcription burst frequency, whereas no synergism, but antagonism, is often observed if activators increase burst size. The synergistic efficiency can be predicted accurately by the ratio I / E0. When the noise enhancers double the noise, the activators double the burst frequency, and I / E0 ≥ 7, their combination is 10 times more effective than their additive effects across all 22 sites.

Availability and implementation

The jumping digit I may provide a novel probe to explore the phenotypic consequences of transcription noise in cell functions. Code is freely available at http://cam.gzhu.edu.cn/info/1014/1223.htm.

Supplementary information

Supplementary data are available at Bioinformatics online.

Mean trapping time for an arbitrary trap site on a class of fractal scale-free trees

Fractals are ubiquitous in nature and random walks on fractals have attracted lots of scientific attention in the past several years. In this work, we consider discrete random walks on a class of fractal scale-free trees (FST), whose topologies are controlled by two integer parameters (i.e., u≥2 and v≥1) and exhibit a wide range of topological properties by suitably varying the parameters u and v. The mean trapping time (MTT), referred to as T_{y}, which is the mean time it takes the walker to be absorbed by the trap fixed at site y of the FST, is addressed analytically on the FST, and the effects of the trap location y on the MTT for the FST and for the general trees are also analyzed. First, a method, which is based on the connection between the MTT and the effective resistances, to derive analytically T_{y} for an arbitrary site y of the FST is presented, and some examples are provided to show the effectiveness of the method. Then, we compare T_{y} for all the possible site y of the trees, and find the sites where T_{y} achieves the minimum (or maximum) on the FST. Finally, we analyze the effects of trap location on the MTT in general trees and find that the average path length (APL) from an arbitrary site to the trap is the decisive factor which dominates the difference in the MTTs for different trap locations on general trees. We find, for any tree, the MTT obtains the minimum (or maximum) at sites where the APL achieves the minimum (or maximum).