Stochastic model of transcription factor-regulated gene expression

Decoding the grammar of transcriptional regulation from RNA polymerase measurements: models and their applications

The genomic revolution has indubitably brought about a paradigm shift in the field of molecular biology, wherein we can sequence, write and re-write genomes. In spite of achieving such feats, we still lack a quantitative understanding of how cells integrate environmental and intra-cellular signals at the promoter and accordingly regulate the production of messenger RNAs. This current state of affairs is being redressed by recent experimental breakthroughs which enable the counting of RNA polymerase molecules (or the corresponding nascent RNAs) engaged in the process of transcribing a gene at the single-cell level. Theorists, in conjunction, have sought to unravel the grammar of transcriptional regulation by harnessing the various statistical properties of these measurements. In this review, we focus on the recent progress in developing falsifiable models of transcription that aim to connect the molecular mechanisms of transcription to single-cell polymerase measurements. We discuss studies where the application of such models to the experimental data have led to novel mechanistic insights into the process of transcriptional regulation. Such interplay between theory and experiments will likely contribute towards the exciting journey of unfurling the governing principles of transcriptional regulation ranging from bacteria to higher organisms.

Mechanistic Modeling of Genetic Circuits for ArsR Arsenic Regulation

Bioreporters are living cells that generate an easily measurable signal in the presence of a chemical compound. They acquire their functionality from synthetic gene circuits, the configuration of which defines the response signal and signal-to-noise ratio. Bioreporters based on the Escherichia coli ArsR system have raised significant interest for quantifying arsenic pollution, but they need to be carefully optimized to accurately work in the required low concentration range (1-10 μg arsenite L^-1). To better understand the general functioning of ArsR-based genetic circuits, we developed a comprehensive mechanistic model that was empirically tested and validated in E. coli carrying different circuit configurations. The model accounts for the different elements in the circuits (proteins, DNA, chemical species), and their detailed affinities and interactions, and predicts the (fluorescent) output from the bioreporter cell as a function of arsenite concentration. The model was parametrized using existing ArsR biochemical data, and then complemented by parameter estimations from the accompanying experimental data using a scatter search algorithm. Model predictions and experimental data were largely coherent for feedback and uncoupled circuit configurations, different ArsR alleles, promoter strengths, and presence or absence of arsenic efflux in the bioreporters. Interestingly, the model predicted a particular useful circuit variant having steeper response at low arsenite concentrations, which was experimentally confirmed and may be useful as arsenic bioreporter in the field. From the extensive validation we expect the mechanistic model to further be a useful framework for detailed modeling of other synthetic circuits.

Genetics of the ceramide/sphingosine-1-phosphate rheostat in blood pressure regulation and hypertension

BACKGROUND

Several attempts to decipher the genetics of hypertension of unknown causes have been made including large-scale genome-wide association analysis (GWA), but only a few genes have been identified. Unsolved heterogeneity of the regulation of blood pressure and the shortcomings of the prevailing monogenic approach to capture genetic effects in a polygenic condition are the main reasons for the modest results. The level of the blood pressure is the consequence of the genotypic state of the presumably vast network of genes involved in regulating the vascular tonus and hence the blood pressure. Recently it has been suggested that components of the sphingolipid metabolism pathways may be of importance in vascular physiology. The basic metabolic network of sphingolipids has been established, but the influence of genetic variations on the blood pressure is not known. In the approach presented here the impact of genetic variations in the sphingolipid metabolism is elucidated by a two-step procedure. First, the physiological heterogeneity of the blood pressure is resolved by a latent class/structural equation modelling to obtain homogenous subpopulations. Second, the genetic effects of the sphingolipid metabolism with focus on de novo synthesis of ceramide are analysed. The model does not assume a particular genetic model, but assumes that genes operate in networks.

RESULTS

The stratification of the study population revealed that (at least) 14 distinct subpopulations are present with different propensity to develop hypertension. Main effects of genes in the de novo synthesis of ceramides were rare (0.14% of all possible). However, epistasis was highly significant and prevalent amounting to approximately 70% of all possible two-gene interactions. The phenotypic variance explained by the ceramide synthesis network were substantial in 4 of the subpopulations amounting to more than 50% in the subpopulation in which all subjects were hypertensive. Construction of the network using the epistatic values revealed that only 17% of the interactions detected were in the direct metabolic pathway, the remaining jumping one or more intermediates.

CONCLUSIONS

This study established the components of the ceramide/sphingosine-1-phosphate rheostat as central to blood pressure regulation. The results in addition confirm that epistasis is of paramount importance and is most conspicuous in the regulation of the rheostat network. Finally, it is shown that applying a simple case-control approach with single gene association analysis is bound to fail, short of identifying a few potential genes with small effects.

Bimodal gene expression in noncooperative regulatory systems

Bimodality of gene expression, as a mechanism contributing to phenotypic diversity, enhances the survival of cells in a fluctuating environment. To date, the bimodal response of a gene regulatory system has been attributed to the cooperativity of transcription factor binding or to feedback loops. It has remained unclear whether noncooperative binding of transcription factors can give rise to bimodality in an open-loop system. We study a theoretical model of gene expression in a two-step cascade (a deterministically monostable system) in which the regulatory gene produces transcription factors that have a nonlinear effect on the activity of the target gene. We show that a unimodal distribution of transcription factors over the cell population can generate a bimodal steady-state output without cooperative transcription factor binding. We introduce a simple method of geometric construction that allows one to predict the onset of bimodality. The construction only involves the parameters of bursting of the regulatory gene and the dose-response curve of the target gene. Using this method, we show that the gene expression may switch between unimodal and bimodal as the concentration of inducers or corepressors is varied. These findings may explain the experimentally observed bimodal response of cascades consisting of a fluorescent protein reporter controlled by the tetracycline repressor. The geometric construction provides a useful tool for designing experiments and for interpretation of their results. Our findings may have important implications for understanding the strategies adopted by cell populations to survive in changing environments.

The role of noise and positive feedback in the onset of autosomal dominant diseases

Background

Autosomal dominant (AD) diseases result when a single mutant or non-functioning gene is present on an autosomal chromosome. These diseases often do not emerge at birth. There are presently two prevailing theories explaining the expression of AD diseases. One explanation originates from the Knudson two-hit theory of hereditary cancers, where loss of heterozygosity or occurrence of somatic mutations impairs the function of the wild-type copy. While these somatic second hits may be sufficient for stable disease states, it is often difficult to determine if their occurrence necessarily marks the initiation of disease progression. A more direct consequence of a heterozygous genetic background is haploinsufficiency, referring to a lack of sufficient gene function due to reduced wild-type gene copy number; however, haploinsufficiency can involve a variety of additional mechanisms, such as noise in gene expression or protein levels, injury and second hit mutations in other genes. In this study, we explore the possible contribution to the onset of autosomal dominant diseases from intrinsic factors, such as those determined by the structure of the molecular networks governing normal cellular physiology.

Results

First, simple models of single gene insufficiency using the positive feedback loops that may be derived from a three-component network were studied by computer simulation using Bionet software. The network structure is shown to affect the dynamics considerably; some networks are relatively stable even when large stochastic variations in are present, while others exhibit switch-like dynamics. In the latter cases, once the network switches over to the disease state it remains in that state permanently. Model pathways for two autosomal dominant diseases, AD polycystic kidney disease and mature onset diabetes of youth (MODY) were simulated and the results are compared to known disease characteristics.

Conclusions

By identifying the intrinsic mechanisms involved in the onset of AD diseases, it may be possible to better assess risk factors as well as lead to potential new drug targets. To illustrate the applicability of this study of pathway dynamics, we simulated the primary pathways involved in two autosomal dominant diseases, Polycystic Kidney Disease (PKD) and mature onset diabetes of youth (MODY). Simulations demonstrate that some of the primary disease characteristics are consistent with the positive feedback - stochastic variation theory presented here. This has implications for new drug targets to control these diseases by blocking the positive feedback loop in the relevant pathways.

Conversion of graded to binary response in an activator-repressor system

Appropriate regulation of gene expression is essential to ensure that protein synthesis occurs in a selective manner. The control of transcription is the most dominant type of regulation mediated by a complex of molecules such as transcription factors. In general, regulatory molecules are of two types: activator and repressor. Activators promote the initiation of transcription whereas repressors inhibit transcription. In many cases, they regulate the gene transcription on binding the promoter mutually exclusively and the observed gene expression response is either graded or binary. In experiments, the gene expression response is quantified by the amount of proteins produced on varying the concentration of an external inducer molecules in the cell. In this paper, we study a gene regulatory network where activators and repressors both bind the same promoter mutually exclusively. The network is modeled by assuming that the gene can be in three possible states: repressed, unregulated, and active. An exact analytical expression for the steady-state probability distribution of protein levels is then derived. The exact result helps to explain the experimental observations that in the presence of activator molecules the response is graded at all inducer levels, whereas in the presence of both activator and repressor molecules, the response is graded at low and high inducer levels and binary at an intermediate inducer level.

Amplification and detection of single-molecule conformational fluctuation through a protein interaction network with bimodal distributions

A protein undergoes conformational dynamics with multiple time scales, which results in fluctuating enzyme activities. Recent studies in single-molecule enzymology have observe this "age-old" dynamic disorder phenomenon directly. However, the single-molecule technique has its limitation. To be able to observe this molecular effect with real biochemical functions in situ, we propose to couple the fluctuations in enzymatic activity to noise propagations in small protein interaction networks such as a zeroth-order ultrasensitive phosphorylation-dephosphorylation cycle. We show that enzyme fluctuations can indeed be amplified by orders of magnitude into fluctuations in the level of substrate phosphorylation, a quantity of wide interest in cellular biology. Enzyme conformational fluctuations sufficiently slower than the catalytic reaction turnover rate result in a bimodal concentration distribution of the phosphorylated substrate. In return, this network-amplified single-enzyme fluctuation can be used as a novel biochemical "reporter" for measuring single-enzyme conformational fluctuation rates.

Analysis of heterogeneity and epistasis in physiological mixed populations by combined structural equation modelling and latent class analysis

BACKGROUND

Biological systems are interacting, molecular networks in which genetic variation contributes to phenotypic heterogeneity. This heterogeneity is traditionally modelled as a dichotomous trait (e.g. affected vs. non-affected). This is far too simplistic considering the complexity and genetic variations of such networks.

METHODS

In this study on type 2 diabetes mellitus, heterogeneity was resolved in a latent class framework combined with structural equation modelling using phenotypic indicators of distinct physiological processes. We modelled the clinical condition "the metabolic syndrome", which is known to be a heterogeneous and polygenic condition with a clinical endpoint (type 2 diabetes mellitus). In the model presented here, genetic factors were not included and no genetic model is assumed except that genes operate in networks. The impact of stratification of the study population on genetic interaction was demonstrated by analysis of several genes previously associated with the metabolic syndrome and type 2 diabetes mellitus.

RESULTS

The analysis revealed the existence of 19 distinct subpopulations with a different propensity to develop diabetes mellitus within a large healthy study population. The allocation of subjects into subpopulations was highly accurate with an entropy measure of nearly 0.9. Although very few gene variants were directly associated with metabolic syndrome in the total study sample, almost one third of all possible epistatic interactions were highly significant. In particular, the number of interactions increased after stratifying the study population, suggesting that interactions are masked in heterogenous populations. In addition, the genetic variance increased by an average of 35-fold when analysed in the subpopulations.

CONCLUSION

The major conclusions from this study are that the likelihood of detecting true association between genetic variants and complex traits increases tremendously when studied in physiological homogenous subpopulations and on inclusion of epistasis in the analysis, whereas epistasis (i.e. genetic networks) is ubiquitous and should be the basis in modelling any biological process.

Haploinsufficient prostate tumor suppression by Nkx3.1: a role for chromatin accessibility in dosage-sensitive gene regulation

Transcription factor haploinsufficiency plays a role in the pathogenesis of many diseases, including cancer. In a mouse model of prostate tumor initiation, loss of a single allele of the tumor suppressor Nkx3.1 stochastically inactivates the expression of a class of dosage-sensitive target genes. Here we show that dosage sensitivity is associated with the differential histone H3/H4 acetylation states of Nkx3.1 target genes. When histone acetylation is induced in Nkx3.1+/- mouse prostates with the histone deacetylase inhibitor Trichostatin A, Nkx3.1 can bind to and reactivate the expression of dosage-sensitive target genes. We incorporated our findings into a mathematical model that entails the association of Nkx3.1 with histone acetyltransferase activity. Subsequent experiments indicate that Nkx3.1 associates with and recruits the histone acetyltransferase p300/CREB-binding protein-associated factor to chromatin. Finally, we demonstrate a role for the dosage-sensitive target gene intelectin/omentin in suppressing prostate tumorigenicity. Our results reveal how the interplay between transcription factor dosage and chromatin affects target gene expression in tumor initiation.