Applications of Little's Law to stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.Comment: Accepted by Physical Review

Digital gene expression analysis of the zebra finch genome

Background: In order to understand patterns of adaptation and molecular evolution it is important to quantify both variation in gene expression and nucleotide sequence divergence. Gene expression profiling in non-model organisms has recently been facilitated by the advent of massively parallel sequencing technology. Here we investigate tissue specific gene expression patterns in the zebra finch (Taeniopygia guttata) with special emphasis on the genes of the major histocompatibility complex (MHC). Results: Almost 2 million 454-sequencing reads from cDNA of six different tissues were assembled and analysed. A total of 11,793 zebra finch transcripts were represented in this EST data, indicating a transcriptome coverage of about 65%. There was a positive correlation between the tissue specificity of gene expression and non-synonymous to synonymous nucleotide substitution ratio of genes, suggesting that genes with a specialised function are evolving at a higher rate (or with less constraint) than genes with a more general function. In line with this, there was also a negative correlation between overall expression levels and expression specificity of contigs. We found evidence for expression of 10 different genes related to the MHC. MHC genes showed relatively tissue specific expression levels and were in general primarily expressed in spleen. Several MHC genes, including MHC class I also showed expression in brain. Furthermore, for all genes with highest levels of expression in spleen there was an overrepresentation of several gene ontology terms related to immune function. Conclusions: Our study highlights the usefulness of next-generation sequence data for quantifying gene expression in the genome as a whole as well as in specific candidate genes. Overall, the data show predicted patterns of gene expression profiles and molecular evolution in the zebra finch genome. Expression of MHC genes in particular, corresponds well with expression patterns in other vertebrates

A microfluidic processor for gene expression profiling of single human embryonic stem cells

The gene expression of human embryonic stem cells (hESC) is a critical aspect for understanding the normal and pathological development of human cells and tissues. Current bulk gene expression assays rely on RNA extracted from cell and tissue samples with various degree of cellular heterogeneity. These cell population averaging data are difficult to interpret, especially for the purpose of understanding the regulatory relationship of genes in the earliest phases of development and differentiation of individual cells. Here, we report a microfluidic approach that can extract total mRNA from individual single-cells and synthesize cDNA on the same device with high mRNA-to-cDNA efficiency. This feature makes large-scale single-cell gene expression profiling possible. Using this microfluidic device, we measured the absolute numbers of mRNA molecules of three genes (B2M, Nodal and Fzd4) in a single hESC. Our results indicate that gene expression data measured from cDNA of a cell population is not a good representation of the expression levels in individual single cells. Within the G0/G1 phase pluripotent hESC population, some individual cells did not express all of the 3 interrogated genes in detectable levels. Consequently, the relative expression levels, which are broadly used in gene expression studies, are very different between measurements from population cDNA and single-cell cDNA. The results underscore the importance of discrete single-cell analysis, and the advantages of a microfluidic approach in stem cell gene expression studies

Stochastic neural network models for gene regulatory networks

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in population of cells. The discussion suggest that stochastic neural network models can give better description of gene regulatory networks and provide criteria for measuring the reasonableness o mathematical models

Optimal decoding of information from a genetic network

Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary that translates expression levels into a map of implied positions. The optimal decoder makes use of graded variations in absolute expression level, resulting in positional estimates that are precise to ~1% of the embryo's length. We test this optimal decoder by analyzing gap gene expression in embryos lacking some of the primary maternal inputs to the network. The resulting maps are distorted, and these distortions predict, with no free parameters, the positions of expression stripes for the pair-rule genes in the mutant embryos

Parallelism and divergence in immune responses: a comparison of expression levels in two lakes

Question: How do immune phenotypes differ between infected and uninfected wild individuals, and is the effect the same in different populations? Organisms: Threespine stickleback (Gasterosteus aculeatus) from two lake populations on the island of North Uist, Scotland, sampled in May 2015. Methods: For each fish, we recorded length, sex, reproductive status, condition, and parasitic infection. We measured the expression levels of eight genes that act as key markers of immune system function using qPCR, and then examined the relationship between measured factors and immune gene expression profiles within each population. Conclusions: Populations differed significantly in their immune gene expression profiles. Within each population, multiple factors, including condition, reproductive status, and Schistocephalus solidus infection levels, were found to correlate with expression levels of different arms of the immune system

Sustained gene expression in the retina by improved episomal vectors

Gene and cellular therapies are nowadays part of therapeutic strategies for the treatment of diverse pathologies. The drawbacks associated with gene therapy-low levels of transgene expression, vector loss during mitosis, and gene silencing-need to be addressed. The pEPI-1 and pEPito family of vectors was developed to overcome these limitations. It contains a scaffold/matrix attachment region, which anchors its replication to cell division in eukaryotic cells while in an extrachromosomal state and is less prone to silencing, due to a lower number of CpG motifs. Recent success showed that ocular gene therapy is an important tool for the treatment of several diseases, pending the overcome of the aforementioned limitations. To achieve sustained gene delivery in the retina, we evaluated several vectors based on pEPito and pEPI-1 for their ability to sustain transgene expression in retinal cells. These vectors stably transfected and replicated in retinal pigment epithelial (RPE) cells. Expression levels were promoter dependent with constitutive promoters cytomegalovirus immediate early promoter (CMV) and human CMV enhancer/human elongation factor 1 alpha promoter yielding the highest levels of transgene expression compared with the retina-specific RPE65 promoter. When injected in C57Bl6 mice, transgene expression was sustained for at least 32 days. Furthermore, the retina-specific RPE65 promoter showed higher efficiency in vivo compared to in vitro. In this study, we demonstrate that by combining tissue-specific promoters with a mitotic stable system, less susceptible to epigenetic silencing such as pEPito-based plasmids, we can achieve prolonged gene expression and a sustained therapeutic effect.Fundacao para a Ciencia e Tecnologia, Portugal [PEst/OE/EQB-LA 0023/2013, SFRH/BD/76873/2011, SFRH/BD/70318/2010, PTDC/SAU/BEB/098475/2008]; European Union [PIRG-GA-2009-249314