Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation

Abstract

Positively skewed distributions common in biology are often approximated with lognormal or gamma functions. It is shown here that for some classes of phenomena, including intermitotic time and protein expression variabilities, exponentially modified Gaussian (EMG) may provide better fit. EMG is generated by processes involving normally distributed entry rates and exponentially distributed exit rates; therefore, its parameters may be straightforwardly interpreted in biologically meaningful terms and thus may help to choose between theoretical models of the respective phenomena. In particular, EMG is consistent with the transition probability model of cell cycle and may be used to estimate its deterministic and probabilistic parts. EMG is also consistent with the assumption that the probabilistic part is determined by competing stochastic transcriptional events committing cells to proliferative mitoses, differentiation, or apoptosis. Discrete event simulation modelling of this situation suggests that cell differentiation rate is primarily increased by decreasing the frequencies of the events that result in the realisation of the competing options, including proliferation, rather than by the direct changes in the differentiation-inducing events.