Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression

Abstract

A panel of published distributions of cell interdivision times (IDT) comprising 77 datasets related to 16 cell types, some studied under different conditions, was used to evaluate their conformance to the exponentially modified gamma distribution (EMGD) in comparison with distributions suggested for IDT data earlier. Lognormal, gamma, inverse Gaussian, and shifted Weibull and gamma distributions were found to be generally inferior to EMGD. Exponentially modified Gaussian (EMG) performed equally well. Although EMGD or EMG may be worse than some other distributions in specific cases, the reason that IDT distributions must be generated by a common mechanism of the cell cycle makes it unlikely that they differ essentially in different cell types. Therefore, exponentially modified peak functions, such as EMGD or EMG, are most appropriate if the use of a single distribution for IDT data is reasonable. EMGD is also shown to be the best descriptive tool for published data on the distribution of times between the bursts of mRNA synthesis at defined genes in single cells. EMG is inadequate to such data because its Gaussian component markedly extends to the negative time domain. The applicability of EMGD to comparable features of cells and genes behaviors are discussed to support the validity of the transition probability model and to relate the exponential component of EMGD to the times of cell dwelling in the restriction point of the cell cycle.