Intrinsic and extrinsic noise of gene expression in lineage trees

AbstractIntrinsic and extrinsic noise sources in gene expression, originating respectively from transcriptional stochasticity and from differences between cells, complicate the determination of transcriptional models. In particularly degenerate cases, the two noise sources are altogether impossible to distinguish. However, the incorporation of downstream processing, such as the mRNA splicing and export implicated in gene expression buffering, recovers the ability to identify the relevant source of noise. We report analytical copy-number distributions, discuss the noise sources’ qualitative effects on lower moments, and provide simulation routines for both models.

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Inferring intrinsic and extrinsic noise from a dual fluorescent reporter

10.1101/049486 ◽

2016 ◽

Cited By ~ 1

Author(s):

Erik van Nimwegen

Keyword(s):

Gene Expression ◽

Bayesian Analysis ◽

Ad Hoc ◽

Intrinsic Noise ◽

Extrinsic Noise ◽

Fluorescent Reporter ◽

Gene Expression Noise ◽

Total Gene Expression ◽

Using Data ◽

Intrinsic And Extrinsic Noise

AbstractDual fluorescent reporter constructs, which measure gene expression from two identical promoters within the same cell, allow total gene expression noise to be decomposed into an extrinsic component, roughly associated with cell-to-cell fluctuations in cellular component concentrations, and intrinsic noise, roughly associated with inherent stochasticity of the biochemical reactions involved in gene expression [1]. A recent paper by Fu and Pachter presented frequentist statistical estimators for intrinsic and extrinsic noise using data from dual reporters [2]. For comparison, I here present results of a Bayesian analysis of this problem. I show that the orthodox estimators suffer from pathologies such as predicting negative values for a manifestly non-negative quantity, i.e. variance, and show that the Bayesian estimators do not suffer from such pathologies. In addition, I show that the Bayesian analysis automatically identifies that optimal estimates of intrinsic and extrinsic noise depend on a subtle combination of two statistics of the data, allowing for accuracies that are up to twice the accuracy of the orthodox estimators in some parameter regimes.I hope up this little worked out example contrasting orthodox statistical analysis based on ad hoc estimators with estimators resulting from a Bayesian analysis, will be educational for others in the field. I distribute a Mathematica Notebook with this paper that allows users to easily reproduce all results and figures of the paper.

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Population growth affects intrinsic and extrinsic noise in gene expression

10.1101/362368 ◽

2018 ◽

Cited By ~ 1

Author(s):

Philipp Thomas

Keyword(s):

Gene Expression ◽

Cell Cycle ◽

Intrinsic Noise ◽

Integrated Approach ◽

Time Lapse ◽

Biochemical Networks ◽

Intrinsic Variability ◽

Extrinsic Noise ◽

Growing Population ◽

Intrinsic And Extrinsic Noise

Clonal cells of exponentially growing populations vary substantially from cell to cell. The main drivers of this heterogeneity are the population dynamics and stochasticity in the intracellular reactions, which are commonly studied separately. Here we develop an agent-based framework that allows tracking of the biochemical dynamics in every single cell of a growing population that accounts for both of these factors. Apart from the common intrinsic variability of the biochemical reactions, the framework also predicts extrinsic noise arising from fluctuations in the histories of cells without the need to introduce fluctuating rate constants. Instead, these extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age, which are ubiquitously observed in growing populations. We give explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics as measured in two-colour experiments. We find that these statistics may differ significantly depending on the experimental setup used to observe the cells. We illustrate this fact using (i) averages over an isolated cell lineage tracked over many generations as observed in the mother machine, (ii) snapshots of a growing population with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots of unknown cell ages as measured from static images. Our integrated approach applies to arbitrary biochemical networks and generation time distributions. By employing models of stochastic gene expression and feedback regulation, we elucidate that isolated lineages, as compared to snapshot data, can significantly overestimate the mean number of molecules, overestimate extrinsic noise but underestimate intrinsic noise and have qualitatively different sensitivities to cell cycle fluctuations.

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Estimating intrinsic and extrinsic noise from single-cell gene expression measurements

Statistical Applications in Genetics and Molecular Biology ◽

10.1515/sagmb-2016-0002 ◽

2016 ◽

Vol 15 (6) ◽

Cited By ~ 13

Author(s):

Audrey Qiuyan Fu ◽

Lior Pachter

Keyword(s):

Gene Expression ◽

Single Cell ◽

Hierarchical Model ◽

Mean Squared Error ◽

Single Cells ◽

Geometric Interpretation ◽

Published Data ◽

Stochastic Gene Expression ◽

Extrinsic Noise ◽

Intrinsic And Extrinsic Noise

AbstractGene expression is stochastic and displays variation (“noise”) both within and between cells. Intracellular (intrinsic) variance can be distinguished from extracellular (extrinsic) variance by applying the law of total variance to data from two-reporter assays that probe expression of identically regulated gene pairs in single cells. We examine established formulas [Elowitz, M. B., A. J. Levine, E. D. Siggia and P. S. Swain (2002): “Stochastic gene expression in a single cell,” Science, 297, 1183–1186.] for the estimation of intrinsic and extrinsic noise and provide interpretations of them in terms of a hierarchical model. This allows us to derive alternative estimators that minimize bias or mean squared error. We provide a geometric interpretation of these results that clarifies the interpretation in [Elowitz, M. B., A. J. Levine, E. D. Siggia and P. S. Swain (2002): “Stochastic gene expression in a single cell,” Science, 297, 1183–1186.]. We also demonstrate through simulation and re-analysis of published data that the distribution assumptions underlying the hierarchical model have to be satisfied for the estimators to produce sensible results, which highlights the importance of normalization.

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Plasmids for Independently Tunable, Low-Noise Expression of Two Genes

mSphere ◽

10.1128/msphere.00340-19 ◽

2019 ◽

Vol 4 (3) ◽

Cited By ~ 1

Author(s):

João P. N. Silva ◽

Soraia Vidigal Lopes ◽

Diogo J. Grilo ◽

Zach Hensel

Keyword(s):

Gene Expression ◽

Protein Expression ◽

Low Noise ◽

Expression Systems ◽

Extrinsic Noise ◽

Gene Expression Noise ◽

Expression Noise ◽

Foreign Proteins ◽

Noise Limit ◽

Cell Variation

ABSTRACTSome microbiology experiments and biotechnology applications can be improved if it is possible to tune the expression of two different genes at the same time with cell-to-cell variation at or below the level of genes constitutively expressed from the chromosome (the “extrinsic noise limit”). This was recently achieved for a single gene by exploiting negative autoregulation by the tetracycline repressor (TetR) and bicistronic gene expression to reduce gene expression noise. We report new plasmids that use the same principles to achieve simultaneous, low-noise expression for two genes inEscherichia coli. The TetR system was moved to a compatible plasmid backbone, and a system based on thelacrepressor (LacI) was found to also exhibit gene expression noise below the extrinsic noise limit. We characterized gene expression mean and noise across the range of induction levels for these plasmids, applied the LacI system to tune expression for single-molecule mRNA detection under two different growth conditions, and showed that two plasmids can be cotransformed to independently tune expression of two different genes.IMPORTANCEMicrobiologists often express foreign proteins in bacteria in order study them or to use bacteria as a microbial factory. Usually, this requires controlling the number of foreign proteins expressed in each cell, but for many common protein expression systems, it is difficult to “tune” protein expression without large cell-to-cell variation in expression levels (called “noise” in protein expression). This work describes two protein expression systems that can be combined in the same cell, with tunable expression levels and very low protein expression noise. One new system was used to detect single mRNA molecules by fluorescence microscopy, and the two systems were shown to be independent of each other. These protein expression systems may be useful in any experiment or biotechnology application that can be improved with low protein expression noise.

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