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

Author

Listed:
  • Fu Audrey Qiuyan

    (Department of Genetics, Stanford University, Stanford, CA 94305, United States of America)

  • Pachter Lior

    (Departments of Mathematics, Molecular & Cell Biology and Computer Science, University of California, Berkeley, Berkeley, CA 94720, United States of America)

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.

Suggested Citation

  • Fu Audrey Qiuyan & Pachter Lior, 2016. "Estimating intrinsic and extrinsic noise from single-cell gene expression measurements," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(6), pages 447-471, December.
    • Handle: RePEc:bpj:sagmbi:v:15:y:2016:i:6:p:447-471:n:2
    DOI: 10.1515/sagmb-2016-0002
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    References listed on IDEAS

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    1. Dmitri Volfson & Jennifer Marciniak & William J. Blake & Natalie Ostroff & Lev S. Tsimring & Jeff Hasty, 2006. "Origins of extrinsic variability in eukaryotic gene expression," Nature, Nature, vol. 439(7078), pages 861-864, February.
    2. Hayes, Kevin, 2011. "A Geometrical Interpretation of an Alternative Formula for the Sample Covariance," The American Statistician, American Statistical Association, vol. 65(2), pages 110-112.
    3. Sora Yang & Seunghyeon Kim & Yu Rim Lim & Cheolhee Kim & Hyeong Jeon An & Ji-Hyun Kim & Jaeyoung Sung & Nam Ki Lee, 2014. "Contribution of RNA polymerase concentration variation to protein expression noise," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
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