Phase separation reduces cell-to-cell variability of transcriptional bursting

Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics.

A phenomenological model of non-genomic variability of luminescent bacterial cells

The light emitted by a luminescent bacterium serves as a unique native channel of information regarding the intracellular processes within the individual cell. In the presence of highly sensitive equipment, it is possible to obtain the distribution of bacterial culture cells by the intensity of light emission, which correlates with the amount of luciferase in the cells. When growing on rich media, the luminescence intensity of individual cells of brightly luminous strains of the luminescent bacteria Photobacterium leiognathi and Ph. phosporeum reaches 104-105 quanta/s. The signal of such intensity can be registered using sensitive photometric equipment. All experiments were carried out with bacterial clones (genetically homogeneous populations). A typical dynamics of luminous bacterial cells distributions with respect to intensity of light emission at various stages of batch culture growth in a liquid medium was obtained. To describe experimental distributions, a phenomenological model that links the light of a bacterial cell with the history of events at the molecular level was constructed. The proposed phenomenological model with a minimum number of fitting parameters (1.5) provides a satisfactory description of the complex process of formation of cell distributions by luminescence intensity at different stages of bacterial culture growth. This may be an indication that the structure of the model describes some essential processes of the real system. Since in the process of division all cells go through the stage of release of all regulatory molecules from the DNA molecule, the resulting distributions can be attributed not only to luciferase, but also to other proteins of constitutive (and not only) synthesis.

Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks

Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.

Stable maintenance of hidden switches as a strategy to increase the gene expression stability

In response to severe genetic and environmental perturbations, wild-type organisms can express hidden alternative phenotypes adaptive to such adverse conditions. While our theoretical understanding of the population-level fitness advantage and evolution of phenotypic switching under variable environments has grown, the mechanism by which these organisms maintain phenotypic switching capabilities under static environments remains to be elucidated. Here, using computational simulations, we analyzed the evolution of gene circuits under natural selection and found that different strategies evolved to increase the gene expression stability near the optimum level. In a population comprising bistable individuals, a strategy of maintaining bistability and raising the potential barrier separating the bistable regimes was consistently taken. Our results serve as evidence that hidden bistable switches can be stably maintained during environmental stasis-an essential property enabling the timely release of adaptive alternatives with small genetic changes in the event of substantial perturbations.

Special function methods for bursty models of transcription

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.

Time-dependent solutions for a stochastic model of gene expression with molecule production in the form of a compound Poisson process

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability distribution and the model parameters depend on time in an arbitrary (e.g., oscillatory) manner, and for arbitrary initial conditions. We show that in the case of periodic external activation and constant protein degradation rate, the response of the gene is analogous to the resistor-capacitor low-pass filter, where slow oscillations of the external driving have a greater effect on gene expression than the fast ones. We also demonstrate that the nth cumulant of the protein number distribution depends on the nth moment of the burst size distribution. We use these results to show that different measures of noise (coefficient of variation, Fano factor, fractional change of variance) may vary in time in a different manner. Therefore, any biological hypothesis of evolutionary optimization based on the nonmonotonic dependence of a chosen measure of noise on time must justify why it assumes that biological evolution quantifies noise in that particular way. Finally, we show that not only for exponentially distributed burst sizes but also for a wider class of burst size distributions (e.g., Dirac delta and gamma) the control of gene expression level by burst frequency modulation gives rise to proportional scaling of variance of the protein number distribution to its mean, whereas the control by amplitude modulation implies proportionality of protein number variance to the mean squared.