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Fold change is a measure describing how much a quantity changes between an original and a subsequent measurement. It is defined as the
ratio In mathematics, a ratio shows how many times one number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in lan ...
between the two quantities; for quantities ''A'' and ''B'' the fold change of ''B'' with respect to ''A'' is ''B''/''A''. In other words, a change from 30 to 60 is defined as a fold-change of 2. This is also referred to as a "one fold increase". Similarly, a change from 30 to 15 is referred to as a "0.5-fold decrease". Fold change is often used when analysing multiple measurements of a biological system taken at different times as the change described by the ratio between the time points is easier to interpret than the difference. Fold change is so called because it is common to describe an increase of multiple ''X'' as an "''X''-fold increase". As such, several dictionaries, including the Oxford English Dictionary and Merriam-Webster Dictionary, as well as Collins's Dictionary of Mathematics, define "-fold" to mean "times", as in "2-fold" = "2 times" = "double". Likely because of this definition, many scientists use not only "fold", but also "fold change" to be synonymous with "times", as in "3-fold larger" = "3 times larger". Fold change is often used in analysis of
gene expression Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. The ...
data from
microarray A microarray is a multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of genes from a sample (e.g. from a tissue). It is a two-dimensional array on a solid substrate—usually a glass slide or silico ...
and
RNA-Seq RNA-Seq (named as an abbreviation of RNA sequencing) is a sequencing technique which uses next-generation sequencing (NGS) to reveal the presence and quantity of RNA in a biological sample at a given moment, analyzing the continuously changing c ...
experiments for measuring change in the expression level of a gene. A disadvantage and serious risk of using fold change in this setting is that it is biased and may misclassify differentially expressed genes with large differences (''B'' − ''A'') but small ratios (''B''/''A''), leading to poor identification of changes at high expression levels. Furthermore, when the
denominator A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
is close to zero, the ratio is not stable, and the fold change value can be disproportionately affected by measurement noise.


Alternative definition

There is an alternative definition of fold change, although this has generally fallen out of use. Here, fold change is defined as the ratio of the difference between final value and the initial value divided by the initial value. For quantities ''A'' and ''B'', the fold change is given as (''B'' − ''A'')/''A'', or equivalently ''B''/''A'' − 1. This formulation has appealing properties such as no change being equal to zero, a 100% increase is equal to 1, and a 100% decrease is equal to −1. However, verbally referring to a doubling as a one-fold change and tripling as a two-fold change is counter-intuitive, and so this formulation is rarely used. This formulation is sometimes called the
relative change In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' va ...
and is labeled as ''fractional difference'' in the software package Prism.


Fold changes in genomics and bioinformatics

In the field of
genomics Genomics is an interdisciplinary field of biology focusing on the structure, function, evolution, mapping, and editing of genomes. A genome is an organism's complete set of DNA, including all of its genes as well as its hierarchical, three-dim ...
(and more generally in
bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combine ...
), the modern usage is to define fold change in terms of ratios, and not by the alternative definition. However, log-ratios are often used for analysis and visualization of fold changes. The logarithm to base 2 is most commonly used, as it is easy to interpret, e.g. a doubling in the original scaling is equal to a log2 fold change of 1, a quadrupling is equal to a log2 fold change of 2 and so on. Conversely, the measure is symmetric when the change decreases by an equivalent amount e.g. a halving is equal to a log2 fold change of −1, a quartering is equal to a log2 fold change of −2 and so on. This leads to more aesthetically pleasing plots, as exponential changes are displayed as linear and so the dynamic range is increased. For example, on a plot axis showing log2 fold changes, an 8-fold increase will be displayed at an axis value of 3 (since 23 = 8). However, there is no mathematical reason to only use logarithm to base 2, and due to many discrepancies in describing the log2 fold changes in gene/protein
expression Expression may refer to: Linguistics * Expression (linguistics), a word, phrase, or sentence * Fixed expression, a form of words with a specific meaning * Idiom, a type of fixed expression * Metaphorical expression, a particular word, phrase, ...
, a new term " loget" has been proposed.


See also

*
Ratio In mathematics, a ratio shows how many times one number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in lan ...
*
Relative change In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' va ...
*
Replicate (biology) In the biological sciences, a replicate is an exact copy of a sample that is being analyzed, such as a cell, organism or molecule, on which exactly the same procedure is done. This is often done in order to check for experimental or procedural erro ...


Notes

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External links


A comparison of fold-change and the t-statistic for microarray data analysis
Measurement