Random variability in quantities arising in cellular biology
Cellular noise is random variability in quantities arising in cellular biology. For example, cells which are genetically identical, even within the same tissue, are often observed to have different expression levels of proteins, different sizes and structures. These apparently random differences can have important biological and medical consequences.
Cellular noise was originally, and is still often, examined in the context of gene expression levels – either the concentration or copy number of the products of genes within and between cells. As gene expression levels are responsible for many fundamental properties in cellular biology, including cells' physical appearance, behaviour in response to stimuli, and ability to process information and control internal processes, the presence of noise in gene expression has profound implications for many processes in cellular biology.
Definitions.
The most frequent quantitative definition of noise is the coefficient of variation:
 formula_1
where formula_2 is the noise in a quantity formula_3, formula_4 is the mean value of formula_3 and formula_6 is the standard deviation of formula_3. This measure is dimensionless, allowing a relative comparison of the importance of noise, without necessitating knowledge of the absolute mean.
Other quantities often used for mathematical convenience are the Fano factor:
 formula_8
and the normalized variance:
 formula_9
Experimental measurement.
The first experimental account and analysis of gene expression noise in prokaryotes is from Becskei &amp; Serrano and from Alexander van Oudenaarden's lab. The first experimental account and analysis of gene expression noise in eukaryotes is from James J. Collins's lab.
Intrinsic and extrinsic noise.
Cellular noise is often investigated in the framework of "intrinsic" and "extrinsic" noise. Intrinsic noise refers to variation in identically regulated quantities within a single cell: for example, the intra-cell variation in expression levels of two identically controlled genes. Extrinsic noise refers to variation in identically regulated quantities between different cells: for example, the cell-to-cell variation in expression of a given gene.
Intrinsic and extrinsic noise levels are often compared in dual reporter studies, in which the expression levels of two identically regulated genes (often fluorescent reporters like GFP and YFP) are plotted for each cell in a population.
An issue with the general depiction of extrinsic noise as a spread along the main diagonal in dual-reporter studies is the assumption that extrinsic factors cause positive expression correlations between the two reporters. In fact, when the two reporters compete for binding of a low-copy regulator, the two reporters become anomalously anticorrelated, and the spread is perpendicular to the main diagonal. In fact, any deviation of the dual-reporter scatter plot from circular symmetry indicates extrinsic noise. Information theory offers a way to avoid this anomaly.
Sources.
"Note": These lists are illustrative, not exhaustive, and identification of noise sources is an active and expanding area of research.
Note that extrinsic noise can affect levels and types of intrinsic noise: for example, extrinsic differences in the mitochondrial content of cells lead, through differences in ATP levels, to some cells transcribing faster than others, affecting the rates of gene expression and the magnitude of intrinsic noise across the population.
Effects.
"Note": These lists are illustrative, not exhaustive, and identification of noise effects is an active and expanding area of research.
Analysis.
As many quantities of cell biological interest are present in discrete copy number within the cell (single DNAs, dozens of mRNAs, hundreds of proteins), tools from discrete stochastic mathematics are often used to analyse and model cellular noise. In particular, master equation treatments – where the probabilities formula_10 of observing a system in a state formula_11 at time formula_12 are linked through ODEs – have proved particularly fruitful. A canonical model for noise gene expression, where the processes of DNA activation, transcription and translation are all represented as Poisson processes with given rates, gives a master equation which may be solved exactly (with generating functions) under various assumptions or approximated with stochastic tools like Van Kampen's system size expansion.
Numerically, the Gillespie algorithm or stochastic simulation algorithm is often used to create realisations of stochastic cellular processes, from which statistics can be calculated.
The problem of inferring the values of parameters in stochastic models (parametric inference) for biological processes, which are typically characterised by sparse and noisy experimental data, is an active field of research, with methods including Bayesian MCMC and approximate Bayesian computation proving adaptable and robust. Regarding the two-state model, a moment-based method was described for parameters inference from mRNAs distributions.
References.
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