Counting single cells and computing their heterogeneity: from phenotypic frequencies to mean value of a quantitative biomarker

Abstract

This tutorial presents a mathematical theory that relates the probability of sample frequencies, of M phenotypes in an isogenic population of N cells, to the probability distribution of the sample mean of a quantitative biomarker, when the N is very large. An analogue to the statistical mechanics of canonical ensemble is discussed.

Keywords

large deviation principle / chemical kinetics / Boltzmann’s law / variational Bayesian method / maximum entropy principle

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ACKNOWLEDGEMENTS

We thank Ivana Bozic, Ken Dill, Hao Ge, Liu Hong, Matt Lorig and Wenning Wang for many helpful discussions. H. Q. is partially supported by NIH grant R01GM109964 (PI: Sui Huang) and the Olga Jung Wan Endowed Professorship.

COMPLIANCE WITH ETHICS GUIDELINES

The authors Hong Qian and Yu-Chen Cheng declare that they have no conflict of interests.ƒThis article does not contain any studies with human or animal subjects performed by any of the authors.

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