Regulation of Gene Activation by Competitive Cross Talking Pathways

Nascent RNA kinetics with complex promoter architecture: Analytic results and parameter inference

Transcription is a stochastic process that involves several downstream operations which make it difficult to model and infer transcription kinetics from mature RNA numbers in individual cell. However, recent advances in single-cell technologies have enabled a more precise measurement of the fluctuations of nascent RNA that closely reflect transcription kinetics. In this paper we introduce a general stochastic model to mimic nascent RNA kinetics with complex promoter architecture. We derive the exact distribution and moments of nascent RNA using queuing theory techniques, which provide valuable insights into the effect of the molecular memory created by the multistep activation and deactivation on the stochastic kinetics of nascent RNA. Moreover, based on the analytical results, we develop a statistical method to infer the promoter memory from stationary nascent RNA distributions. Data analysis of synthetic data and a realistic example, the HIV-1 gene, verifies the validity of this inference method.

What can we learn when fitting a simple telegraph model to a complex gene expression model?

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Effects of bursty synthesis in organelle biogenesis

A fundamental question of cell biology is how cells control the number of organelles. The processes of organelle biogenesis, namely de novo synthesis, fission, fusion, and decay, are inherently stochastic, producing cell-to-cell variability in organelle abundance. In addition, experiments suggest that the synthesis of some organelles can be bursty. We thus ask how bursty synthesis impacts intracellular organelle number distribution. We develop an organelle biogenesis model with bursty de novo synthesis by considering geometrically distributed burst sizes. We analytically solve the model in biologically relevant limits and provide exact expressions for the steady-state organelle number distributions and their means and variances. We also present approximate solutions for the whole model, complementing with exact stochastic simulations. We show that bursts generally increase the noise in organelle numbers, producing distinct signatures in noise profiles depending on different mechanisms of organelle biogenesis. We also find different shapes of organelle number distributions, including bimodal distributions in some parameter regimes. Notably, bursty synthesis broadens the parameter regime of observing bimodality compared to the 'non-bursty' case. Together, our framework utilizes number fluctuations to elucidate the role of bursty synthesis in producing organelle number heterogeneity in cells.

Using steady-state formula to estimate time-dependent parameters of stochastic gene transcription models

When studying stochastic gene transcription, it is important to understand how system parameters are temporally modulated in response to varying environments. Experimentally, the dynamic distribution data of RNA copy numbers measured at multiple time points are often fitted to stochastic transcription models to estimate time-dependent parameters. However, current methods require determining which parameters are time-dependent, as well as their analytical formulas, before the optimal fit. In this study, we developed a method to estimate time-dependent parameters in a classical two-state model without prior assumptions regarding the system parameters. At each measured time point, the method fitted the dynamic distribution data using a steady-state distribution formula, in which the estimated constant parameters were approximated as time-dependent parameter values at the measured time point. The accuracy of this method can be guaranteed for RNA molecules with relatively high degradation rates and genes with relatively slow responses to induction. We quantify the accuracy of the method and implemented this method on two sets of dynamic distribution data from prokaryotic and eukaryotic cells, and revealed the temporal modulation of transcription burst size in response to environmental changes.

Gene-Function-Based Clusters Explore Intricate Networks of Gene Expression of Circulating Tumor Cells in Patients with Colorectal Cancer

Colorectal cancer (CRC) is a complex disease characterized by dynamically deregulated gene expression and crosstalk between signaling pathways. In this study, a new approach based on gene-function-based clusters was introduced to explore the CRC-associated networks of gene expression. Each cluster contained genes involved in coordinated regulatory activity, such as RAS signaling, the cell cycle process, transcription, or translation. A retrospective case-control study was conducted with the inclusion of 119 patients with histologically confirmed colorectal cancer and 308 controls. The quantitative expression data of 15 genes were obtained from the peripheral blood samples of all participants to investigate cluster-gene and gene-gene interactions. DUSP6, MDM2, and EIF2S3 were consistently selected as CRC-associated factors with high significance in all logistic models. CPEB4 became an insignificant factor only when combined with the clusters for cell cycle processes and for transcription. The CPEB4/DUSP6 complex was a prerequisite for the significance of MMD, whereas EXT2, RNF4, ZNF264, WEE1, and MCM4 were affected by more than two clusters. Intricate networks among MMD, RAS signaling factors (DUSP6, GRB2, and NF1), and translation factors (EIF2S3, CPEB4, and EXT2) were also revealed. Our results suggest that limited G1/S transition, uncontrolled DNA replication, and the cap-independent initiation of translation may be dominant and concurrent scenarios in circulating tumor cells derived from colorectal cancer. This gene-function-based cluster approach is simple and useful for revealing intricate CRC-associated gene expression networks. These findings may provide clues to the metastatic mechanisms of circulating tumor cells in patients with colorectal cancer.

Stochastic gene transcription with non-competitive transcription regulatory architecture

The transcription factors, such as activators and repressors, can interact with the promoter of gene either in a competitive or non-competitive way. In this paper, we construct a stochastic model with non-competitive transcriptional regulatory architecture and develop an analytical theory that re-establishes the experimental results with an improved data fitting. The analytical expressions in the theory allow us to study the nature of the system corresponding to any of its parameters and hence, enable us to find out the factors that govern the regulation of gene expression for that architecture. We notice that, along with transcriptional reinitiation and repressors, there are other parameters that can control the noisiness of this network. We also observe that, the Fano factor (at mRNA level) varies from sub-Poissonian regime to super-Poissonian regime. In addition to the aforementioned properties, we observe some anomalous characteristics of the Fano factor (at mRNA level) and that of the variance of protein at lower activator concentrations in the presence of repressor molecules. This model is useful to understand the architecture of interactions which may buffer the stochasticity inherent to gene transcription.

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.

Using average transcription level to understand the regulation of stochastic gene activation

Gene activation is a random process, modelled as a framework of multiple rate-limiting steps listed sequentially, in parallel or in combination. Together with suitably assumed processes of gene inactivation, transcript birth and death, the step numbers and parameters in activation frameworks can be estimated by fitting single-cell transcription data. However, current algorithms require computing master equations that are tightly correlated with prior hypothetical frameworks of gene activation. We found that prior estimation of the framework can be facilitated by the traditional dynamical data of mRNA average level M(t), presenting discriminated dynamical features. Rigorous theory regarding M(t) profiles allows to confidently rule out the frameworks that fail to capture M(t) features and to test potential competent frameworks by fitting M(t) data. We implemented this procedure for a large number of mouse fibroblast genes under tumour necrosis factor induction and determined exactly the 'cross-talking n-state' framework; the cross-talk between the signalling and basal pathways is crucial to trigger the first peak of M(t), while the following damped gentle M(t) oscillation is regulated by the multi-step basal pathway. This framework can be used to fit sophisticated single-cell data and may facilitate a more accurate understanding of stochastic activation of mouse fibroblast genes.

A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Approximating gene transcription dynamics using steady-state formulas

Understanding how genes in a single cell respond to dynamically changing signals has been a central question in stochastic gene transcription research. Recent studies have generated massive steady-state or snapshot mRNA distribution data of individual cells, and inferred a large spectrum of kinetic transcription parameters under varying conditions. However, there have been few algorithms to convert these static data into the temporal variation of kinetic rates. Real-time imaging has been developed to monitor stochastic transcription processes at the single-cell level, but the immense technicality has prevented its application to most endogenous loci in mammalian cells. In this article, we introduced a stochastic gene transcription model with variable kinetic rates induced by unstable cellular conditions. We approximated the transcription dynamics using easily obtained steady-state formulas in the model. We tested the approximation against experimental data in both prokaryotic and eukaryotic cells and further solidified the conditions that guarantee the robustness of the method. The method can be easily implemented to provide convenient tools for quantifying dynamic kinetics and mechanisms underlying the widespread static transcription data, and may shed a light on circumventing the limitation of current bursting data on transcriptional real-time imaging.

A delayed HIV-1 model with cell-to-cell spread and virus waning

In this paper, we propose and analyse a delayed HIV-1 model with both viral and cellular transmissions and virus waning. We obtain the threshold dynamics of the proposed model, characterized by the basic reproduction number R0 . If R0<1 , the infection-free steady state is globally asymptotically stable; whereas if R0>1 , the system is uniformly persistent. When the delays are positive, we show that the intracellular delays in both viral and cellular infections may lead to stability switches of the infected steady state. Both analytical and numerical results indicate that if the effect of cell-to-cell transmission is ignored, then the risk of HIV-1 infection will be underestimated. Moreover, the viral load of model without virus waning is higher than the one of model with virus waning. These results highlight the important role of two ways of viral transmission and virus waning on HIV-1 infection.