Mathematical foundations of variation in gene expression

摘要

A key challenge in engineering biological organisms is the high degree of cell-to-cell variation commonly observed in gene expression. The inherently discrete and stochastic nature of the chemical reactions that underly gene expression has been proposed as an explanation for the highly asymmetric distributions that are frequently observed, with bursts of expression leading to a Gamma distribution. While this may explain the behaviour of systems with very low expression, it is insufficient to account for the high degree of cell-to-cell variation that is typically still observed even with strong expression (e.g., more than 2-fold standard deviation with a mean of many millions of molecules). In essence, with strong expression there are typically so many molecules involved that the law of large numbers will generally render the impact of chemical stochasticity largely insignificant. Stochasticity, however, is only one potential source of variation in observed gene expression levels from cell to cell. A typically much stronger source of variation is the indisputable fact that cells have at least small variations in their state (size, health, available resources, etc.). These small variations are then amplified by composition of chemical reactions to produce a broad log-normal distribution of expression levels at all levels of expression.