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

Abstract Gene 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.

[1]  Heinz Koeppl,et al.  Accounting for extrinsic variability in the estimation of stochastic rate constants , 2012 .

[2]  Johan Paulsson,et al.  Separating intrinsic from extrinsic fluctuations in dynamic biological systems , 2011, Proceedings of the National Academy of Sciences.

[3]  Jeffrey W. Smith,et al.  Stochastic Gene Expression in a Single Cell , 2022 .

[4]  Debora S. Marks,et al.  MicroRNA control of protein expression noise , 2015, Science.

[5]  Clive G. Bowsher,et al.  Identifying sources of variation and the flow of information in biochemical networks , 2012, Proceedings of the National Academy of Sciences.

[6]  David A. Rand,et al.  Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data , 2013, 1401.1640.

[7]  Nam Ki Lee,et al.  Contribution of RNA polymerase concentration variation to protein expression noise , 2014, Nature Communications.

[8]  A Geometrical Interpretation of an Alternative Formula for the Sample Covariance , 2011 .

[9]  Marc S. Sherman,et al.  Cell-to-cell variability in the propensity to transcribe explains correlated fluctuations in gene expression. , 2015, Cell systems.

[10]  Michael P H Stumpf,et al.  Decomposing noise in biochemical signaling systems highlights the role of protein degradation. , 2011, Biophysical journal.

[11]  S. Teichmann,et al.  Computational and analytical challenges in single-cell transcriptomics , 2015, Nature Reviews Genetics.

[12]  Markus Kollmann,et al.  Quantifying origins of cell-to-cell variations in gene expression. , 2008, Biophysical journal.

[13]  Peter M. Heffernan New Measures of Spread and a Simpler Formula for the Normal Distribution , 1988 .

[14]  D. Volfson,et al.  Origins of extrinsic variability in eukaryotic gene expression , 2006, Nature.

[15]  C. Stein,et al.  Estimation with Quadratic Loss , 1992 .