Transcriptome

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Transcriptome 

The transcriptome is the set of all RNA transcripts, including coding and non-coding, in an individual or a population of cells. The term can also sometimes be used to refer to all RNAs, or just mRNA, depending on the particular experiment. The term transcriptome is a portmanteau of the words transcript and genome; it is associated with the process of transcript production during the biological process of transcription.

The early stages of transcriptome annotations began with cDNA libraries published in the 1980s. Subsequently, the advent of high-throughput technology led to faster and more efficient ways of obtaining data about the transcriptome. Two biological techniques are used to study the transcriptome, namely DNA microarray, a hybridization-based technique and RNA-seq, a sequence-based approach. RNA-seq is the preferred method and has been the dominant transcriptomics technique since the 2010s. Single-cell transcriptomics allows tracking of transcript changes over time within individual cells.

Data obtained from the transcriptome is used in research to gain insight into processes such as cellular differentiation, carcinogenesis, transcription regulation and biomarker discovery among others. Transcriptome-obtained data also finds applications in establishing phylogenetic relationships during the process of evolution and in in vitro fertilization. The transcriptome is closely related to other -ome based biological fields of study; it is complementary to the proteome and the metabolome and encompasses the translatome, exome, meiome and thanatotranscriptome which can be seen as ome fields studying specific types of RNA transcripts. The are quantifiable and conserved relationships between the Transcriptome and other -omes, and Transcriptomics data can be used effectively to predict other molecular species, such as metabolites. There are numerous publicly available transcriptome databases.

Etymology and history

The word transcriptome is a portmanteau of the words transcript and genome. It appeared along with other neologisms formed using the suffixes -ome and -omics to denote all studies conducted on a genome-wide scale in the fields of life sciences and technology. As such, transcriptome and transcriptomics were one of the first words to emerge along with genome and proteome. The first study to present a case of a collection of a cDNA library for silk moth mRNA was published in 1979. The first seminal study to mention and investigate the transcriptome of an organism was published in 1997 and it described 60,633 transcripts expressed in S. cerevisiae using serial analysis of gene expression (SAGE). With the rise of high-throughput technologies and bioinformatics and the subsequent increased computational power, it became increasingly efficient and easy to characterize and analyze enormous amount of data. Attempts to characterize the transcriptome became more prominent with the advent of automated DNA sequencing during the 1980s. During the 1990s, expressed sequence tag sequencing was used to identify genes and their fragments. This was followed by techniques such as serial analysis of gene expression (SAGE), cap analysis of gene expression (CAGE), and massively parallel signature sequencing (MPSS).

Transcription

See also: Transcription (biology)

The transcriptome encompasses all the ribonucleic acid (RNA) transcripts present in a given organism or experimental sample. RNA is the main carrier of genetic information that is responsible for the process of converting DNA into an organism's phenotype. A gene can give rise to a single-stranded messenger RNA (mRNA) through a molecular process known as transcription; this mRNA is complementary to the strand of DNA it originated from. The enzyme RNA polymerase II attaches to the template DNA strand and catalyzes the addition of ribonucleotides to the 3' end of the growing sequence of the mRNA transcript.

In order to initiate its function, RNA polymerase II needs to recognize a promoter sequence, located upstream (5') of the gene. In eukaryotes, this process is mediated by transcription factors, most notably Transcription factor II D (TFIID) which recognizes the TATA box and aids in the positioning of RNA polymerase at the appropriate start site. To finish the production of the RNA transcript, termination takes place usually several hundred nuclecotides away from the termination sequence and cleavage takes place. This process occurs in the nucleus of a cell along with RNA processing by which mRNA molecules are capped, spliced and polyadenylated to increase their stability before being subsequently taken to the cytoplasm. The mRNA gives rise to proteins through the process of translation that takes place in ribosomes.

Types of RNA transcripts

In accordance with the central dogma of molecular biology, the transcriptome initially encompassed only protein-coding mRNA transcripts. Nevertheless, several RNA subtypes with distinct functions exist. Many RNA transcripts do not code for protein or have different regulatory functions in the process of gene transcription and translation. RNA types which do not fall within the scope of the central dogma of molecular biology are non-coding RNAs which can be divided into two groups of long non-coding RNA and short non-coding RNA.

Long non-coding RNA includes all non-coding RNA transcripts that are more than 200 nucleotides long. Members of this group comprise the largest fraction of the non-coding transcriptome. Short non-coding RNA includes the following members:

• • transfer RNA (tRNA)
  • micro RNA (miRNA): 19-24 nucleotides (nt) long. Micro RNAs up- or downregulate expression levels of mRNAs by the process of RNA interference at the post-transcriptional level.
  • small interfering RNA (siRNA): 20-24 nt
  • small nucleolar RNA (snoRNA)
  • Piwi-interacting RNA (piRNA): 24-31 nt. They interact with Piwi proteins of the Argonaute family and have a function in targeting and cleaving transposons.
  • enhancer RNA (eRNA)

Scope of study

In the human genome, about 5% of all genes get transcribed into RNA. The transcriptome consists of coding mRNA which comprise around 1-4% of its entirety and non-coding RNAs which comprise the rest of the genome and do not give rise to proteins. The number of non-protein-coding sequences increases in more complex organisms.

Several factors render the content of the transcriptome difficult to establish. These include alternative splicing, RNA editing and alternative transcription among others. Additionally, transcriptome techniques are capable of capturing transcription occurring in a sample at a specific time point, although the content of the transcriptome can change during differentiation. The main aims of transcriptomics are the following: "catalogue all species of transcript, including mRNAs, non-coding RNAs and small RNAs; to determine the transcriptional structure of genes, in terms of their start sites, 5′ and 3′ ends, splicing patterns and other post-transcriptional modifications; and to quantify the changing expression levels of each transcript during development and under different conditions".

The term can be applied to the total set of transcripts in a given organism, or to the specific subset of transcripts present in a particular cell type. Unlike the genome, which is roughly fixed for a given cell line (excluding mutations), the transcriptome can vary with external environmental conditions. Because it includes all mRNA transcripts in the cell, the transcriptome reflects the genes that are being actively expressed at any given time, with the exception of mRNA degradation phenomena such as transcriptional attenuation. The study of transcriptomics, (which includes expression profiling, splice variant analysis etc.), examines the expression level of RNAs in a given cell population, often focusing on mRNA, but sometimes including others such as tRNAs and sRNAs.

Methods of construction

Main article: Transcriptomics technologies

Transcriptomics is the quantitative science that encompasses the assignment of a list of strings ("reads") to the object ("transcripts" in the genome). To calculate the expression strength, the density of reads corresponding to each object is counted. Initially, transcriptomes were analyzed and studied using expressed sequence tags libraries and serial and cap analysis of gene expression (SAGE).

Currently, the two main transcriptomics techniques include DNA microarrays and RNA-Seq. Both techniques require RNA isolation through RNA extraction techniques, followed by its separation from other cellular components and enrichment of mRNA.

There are two general methods of inferring transcriptome sequences. One approach maps sequence reads onto a reference genome, either of the organism itself (whose transcriptome is being studied) or of a closely related species. The other approach, de novo transcriptome assembly, uses software to infer transcripts directly from short sequence reads and is used in organisms with genomes that are not sequenced.

DNA microarrays

Main article: DNA microarray

 

DNA microarray used to detect gene expression in human (left) and mouse (right) samples

The first transcriptome studies were based on microarray techniques (also known as DNA chips). Microarrays consist of thin glass layers with spots on which oligonucleotides, known as "probes" are arrayed; each spot contains a known DNA sequence.

When performing microarray analyses, mRNA is collected from a control and an experimental sample, the latter usually representative of a disease. The RNA of interest is converted to cDNA to increase its stability and marked with fluorophores of two colors, usually green and red, for the two groups. The cDNA is spread onto the surface of the microarray where it hybridizes with oligonucleotides on the chip and a laser is used to scan. The fluorescence intensity on each spot of the microarray corresponds to the level of gene expression and based on the color of the fluorophores selected, it can be determined which of the samples exhibits higher levels of the mRNA of interest.

One microarray usually contains enough oligonucleotides to represent all known genes; however, data obtained using microarrays does not provide information about unknown genes. During the 2010s, microarrays were almost completely replaced by next-generation techniques that are based on DNA sequencing.

RNA sequencing

Main article: RNA-Seq

RNA sequencing is a next-generation sequencing technology; as such it requires only a small amount of RNA and no previous knowledge of the genome. It allows for both qualitative and quantitative analysis of RNA transcripts, the former allowing discovery of new transcripts and the latter a measure of relative quantities for transcripts in a sample.

The three main steps of sequencing transcriptomes of any biological samples include RNA purification, the synthesis of an RNA or cDNA library and sequencing the library. The RNA purification process is different for short and long RNAs. This step is usually followed by an assessment of RNA quality, with the purpose of avoiding contaminants such as DNA or technical contaminants related to sample processing. RNA quality is measured using UV spectrometry with an absorbance peak of 260 nm. RNA integrity can also be analyzed quantitatively comparing the ratio and intensity of 28S RNA to 18S RNA reported in the RNA Integrity Number (RIN) score. Since mRNA is the species of interest and it represents only 3% of its total content, the RNA sample should be treated to remove rRNA and tRNA and tissue-specific RNA transcripts.

The step of library preparation with the aim of producing short cDNA fragments, begins with RNA fragmentation to transcripts in length between 50 and 300 base pairs. Fragmentation can be enzymatic (RNA endonucleases), chemical (trismagnesium salt buffer, chemical hydrolysis) or mechanical (sonication, nebulisation). Reverse transcription is used to convert the RNA templates into cDNA and three priming methods can be used to achieve it, including oligo-DT, using random primers or ligating special adaptor oligos.

Single-cell transcriptomics

Main article: Single-cell transcriptomics

Transcription can also be studied at the level of individual cells by single-cell transcriptomics. Single-cell RNA sequencing (scRNA-seq) is a recently developed technique that allows the analysis of the transcriptome of single cells. With single-cell transcriptomics, subpopulations of cell types that constitute the tissue of interest are also taken into consideration. This approach allows to identify whether changes in experimental samples are due to phenotypic cellular changes as opposed to proliferation, with which a specific cell type might be overexpressed in the sample. Additionally, when assessing cellular progression through differentiation, average expression profiles are only able to order cells by time rather than their stage of development and are consequently unable to show trends in gene expression levels specific to certain stages. Single-cell trarnscriptomic techniques have been used to characterize rare cell populations such as circulating tumor cells, cancer stem cells in solid tumors, and embryonic stem cells (ESCs) in mammalian blastocysts.

Although there are no standardized techniques for single-cell transcriptomics, several steps need to be undertaken. The first step includes cell isolation, which can be performed using low- and high-throughput techniques. This is followed by a qPCR step and then single-cell RNAseq where the RNA of interest is converted into cDNA. Newer developments in single-cell transcriptomics allow for tissue and sub-cellular localization preservation through cryo-sectioning thin slices of tissues and sequencing the transcriptome in each slice. Another technique allows the visualization of single transcripts under a microscope while preserving the spatial information of each individual cell where they are expressed.

Analysis

A number of organism-specific transcriptome databases have been constructed and annotated to aid in the identification of genes that are differentially expressed in distinct cell populations.

RNA-seq is emerging (2013) as the method of choice for measuring transcriptomes of organisms, though the older technique of DNA microarrays is still used. RNA-seq measures the transcription of a specific gene by converting long RNAs into a library of cDNA fragments. The cDNA fragments are then sequenced using high-throughput sequencing technology and aligned to a reference genome or transcriptome which is then used to create an expression profile of the genes.

Applications

Mammals

The transcriptomes of stem cells and cancer cells are of particular interest to researchers who seek to understand the processes of cellular differentiation and carcinogenesis. A pipeline using RNA-seq or gene array data can be used to track genetic changes occurring in stem and precursor cells and requires at least three independent gene expression data from the former cell type and mature cells.

Analysis of the transcriptomes of human oocytes and embryos is used to understand the molecular mechanisms and signaling pathways controlling early embryonic development, and could theoretically be a powerful tool in making proper embryo selection in in vitro fertilisation. Analyses of the transcriptome content of the placenta in the first-trimester of pregnancy in in vitro fertilization and embryo transfer (IVT-ET) revealed differences in genetic expression which are associated with higher frequency of adverse perinatal outcomes. Such insight can be used to optimize the practice. Transcriptome analyses can also be used to optimize cryopreservation of oocytes, by lowering injuries associated with the process.

Transcriptomics is an emerging and continually growing field in biomarker discovery for use in assessing the safety of drugs or chemical risk assessment.

Transcriptomes may also be used to infer phylogenetic relationships among individuals or to detect evolutionary patterns of transcriptome conservation.

Transcriptome analyses were used to discover the incidence of antisense transcription, their role in gene expression through interaction with surrounding genes and their abundance in different chromosomes. RNA-seq was also used to show how RNA isoforms, transcripts stemming from the same gene but with different structures, can produce complex phenotypes from limited genomes.

Plants

Transcriptome analysis have been used to study the evolution and diversification process of plant species. In 2014, the 1000 Plant Genomes Project was completed in which the transcriptomes of 1,124 plant species from the families viridiplantae, glaucophyta and rhodophyta were sequenced. The protein coding sequences were subsequently compared to infer phylogenetic relationships between plants and to characterize the time of their diversification in the process of evolution. Transcriptome studies have been used to characterize and quantify gene expression in mature pollen. Genes involved in cell wall metabolism and cytoskeleton were found to be overexpressed. Transcriptome approaches also allowed to track changes in gene expression through different developmental stages of pollen, ranging from microspore to mature pollen grains; additionally such stages could be compared across species of different plants including Arabidopsis, rice and tobacco.

Relation to other ome fields

General schema showing the relationships of the genome, transcriptome, proteome, and metabolome (lipidome).

Similar to other -ome based technologies, analysis of the transcriptome allows for an unbiased approach when validating hypotheses experimentally. This approach also allows for the discovery of novel mediators in signaling pathways. As with other -omics based technologies, the transcriptome can be analyzed within the scope of a multiomics approach. It is complementary to metabolomics but contrary to proteomics, a direct association between a transcript and metabolite cannot be established.

There are several -ome fields that can be seen as subcategories of the transcriptome. The exome differs from the transcriptome in that it includes only those RNA molecules found in a specified cell population, and usually includes the amount or concentration of each RNA molecule in addition to the molecular identities. Additionally, the transcritpome also differs from the translatome, which is the set of RNAs undergoing translation.

The term meiome is used in functional genomics to describe the meiotic transcriptome or the set of RNA transcripts produced during the process of meiosis. Meiosis is a key feature of sexually reproducing eukaryotes, and involves the pairing of homologous chromosome, synapse and recombination. Since meiosis in most organisms occurs in a short time period, meiotic transcript profiling is difficult due to the challenge of isolation (or enrichment) of meiotic cells (meiocytes). As with transcriptome analyses, the meiome can be studied at a whole-genome level using large-scale transcriptomic techniques. The meiome has been well-characterized in mammal and yeast systems and somewhat less extensively characterized in plants.

The thanatotranscriptome consists of all RNA transcripts that continue to be expressed or that start getting re-expressed in internal organs of a dead body 24–48 hours following death. Some genes include those that are inhibited after fetal development. If the thanatotranscriptome is related to the process of programmed cell death (apoptosis), it can be referred to as the apoptotic thanatotranscriptome. Analyses of the thanatotranscriptome are used in forensic medicine.

eQTL mapping can be used to complement genomics with transcriptomics; genetic variants at DNA level and gene expression measures at RNA level.

Relation to proteome

Further information: Proteome

The transcriptome can be seen as a subset of the proteome, that is, the entire set of proteins expressed by a genome.

However, the analysis of relative mRNA expression levels can be complicated by the fact that relatively small changes in mRNA expression can produce large changes in the total amount of the corresponding protein present in the cell. One analysis method, known as gene set enrichment analysis, identifies coregulated gene networks rather than individual genes that are up- or down-regulated in different cell populations.

Although microarray studies can reveal the relative amounts of different mRNAs in the cell, levels of mRNA are not directly proportional to the expression level of the proteins they code for. The number of protein molecules synthesized using a given mRNA molecule as a template is highly dependent on translation-initiation features of the mRNA sequence; in particular, the ability of the translation initiation sequence is a key determinant in the recruiting of ribosomes for protein translation.

Beta decay

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Beta_decay 

β⁻
 decay in an atomic nucleus (the accompanying antineutrino is omitted). The inset shows beta decay of a free neutron. Neither of these depictions shows the intermediate virtual
W⁻
boson.

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

Beta decay is a consequence of the weak force, which is characterized by relatively lengthy decay times. Nucleons are composed of up quarks and down quarks, and the weak force allows a quark to change its flavour by emission of a W boson leading to creation of an electron/antineutrino or positron/neutrino pair. For example, a neutron, composed of two down quarks and an up quark, decays to a proton composed of a down quark and two up quarks.

Electron capture is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak force, is the same. In electron capture, an inner atomic electron is captured by a proton in the nucleus, transforming it into a neutron, and an electron neutrino is released.

Description

The two types of beta decay are known as beta minus and beta plus. In beta minus (β⁻) decay, a neutron is converted to a proton, and the process creates an electron and an electron antineutrino; while in beta plus (β⁺) decay, a proton is converted to a neutron and the process creates a positron and an electron neutrino. β⁺ decay is also known as positron emission.

Beta decay conserves a quantum number known as the lepton number, or the number of electrons and their associated neutrinos (other leptons are the muon and tau particles). These particles have lepton number +1, while their antiparticles have lepton number −1. Since a proton or neutron has lepton number zero, β⁺ decay (a positron, or antielectron) must be accompanied with an electron neutrino, while β⁻ decay (an electron) must be accompanied by an electron antineutrino.

An example of electron emission (β⁻ decay) is the decay of carbon-14 into nitrogen-14 with a half-life of about 5,730 years:

¹⁴
₆C
→ ¹⁴
₇N
+
e⁻
+
ν
_e

In this form of decay, the original element becomes a new chemical element in a process known as nuclear transmutation. This new element has an unchanged mass number A, but an atomic number Z that is increased by one. As in all nuclear decays, the decaying element (in this case ¹⁴
₆C
) is known as the parent nuclide while the resulting element (in this case ¹⁴
₇N
) is known as the daughter nuclide.

Another example is the decay of hydrogen-3 (tritium) into helium-3 with a half-life of about 12.3 years:

³
₁H
→ ³
₂He
+
e⁻
+
ν
_e

An example of positron emission (β⁺ decay) is the decay of magnesium-23 into sodium-23 with a half-life of about 11.3 s:

²³
₁₂Mg
→ ²³
₁₁Na
+
e⁺
+
ν
_e

β⁺ decay also results in nuclear transmutation, with the resulting element having an atomic number that is decreased by one.

A beta spectrum, showing a typical division of energy between electron and antineutrino

The beta spectrum, or distribution of energy values for the beta particles, is continuous. The total energy of the decay process is divided between the electron, the antineutrino, and the recoiling nuclide. In the figure to the right, an example of an electron with 0.40 MeV energy from the beta decay of ²¹⁰Bi is shown. In this example, the total decay energy is 1.16 MeV, so the antineutrino has the remaining energy: 1.16 MeV − 0.40 MeV = 0.76 MeV. An electron at the far right of the curve would have the maximum possible kinetic energy, leaving the energy of the neutrino to be only its small rest mass.

History

Discovery and initial characterization

Radioactivity was discovered in 1896 by Henri Becquerel in uranium, and subsequently observed by Marie and Pierre Curie in thorium and in the new elements polonium and radium. In 1899, Ernest Rutherford separated radioactive emissions into two types: alpha and beta (now beta minus), based on penetration of objects and ability to cause ionization. Alpha rays could be stopped by thin sheets of paper or aluminium, whereas beta rays could penetrate several millimetres of aluminium. In 1900, Paul Villard identified a still more penetrating type of radiation, which Rutherford identified as a fundamentally new type in 1903 and termed gamma rays. Alpha, beta, and gamma are the first three letters of the Greek alphabet.

In 1900, Becquerel measured the mass-to-charge ratio (m/e) for beta particles by the method of J.J. Thomson used to study cathode rays and identify the electron. He found that m/e for a beta particle is the same as for Thomson's electron, and therefore suggested that the beta particle is in fact an electron.

In 1901, Rutherford and Frederick Soddy showed that alpha and beta radioactivity involves the transmutation of atoms into atoms of other chemical elements. In 1913, after the products of more radioactive decays were known, Soddy and Kazimierz Fajans independently proposed their radioactive displacement law, which states that beta (i.e.,
β⁻
) emission from one element produces another element one place to the right in the periodic table, while alpha emission produces an element two places to the left.

Neutrinos

The study of beta decay provided the first physical evidence for the existence of the neutrino. In both alpha and gamma decay, the resulting alpha or gamma particle has a narrow energy distribution, since the particle carries the energy from the difference between the initial and final nuclear states. However, the kinetic energy distribution, or spectrum, of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background. These measurements offered the first hint that beta particles have a continuous spectrum. In 1914, James Chadwick used a magnetic spectrometer with one of Hans Geiger's new counters to make more accurate measurements which showed that the spectrum was continuous. The distribution of beta particle energies was in apparent contradiction to the law of conservation of energy. If beta decay were simply electron emission as assumed at the time, then the energy of the emitted electron should have a particular, well-defined value. For beta decay, however, the observed broad distribution of energies suggested that energy is lost in the beta decay process. This spectrum was puzzling for many years.

A second problem is related to the conservation of angular momentum. Molecular band spectra showed that the nuclear spin of nitrogen-14 is 1 (i.e., equal to the reduced Planck constant) and more generally that the spin is integral for nuclei of even mass number and half-integral for nuclei of odd mass number. This was later explained by the proton-neutron model of the nucleus. Beta decay leaves the mass number unchanged, so the change of nuclear spin must be an integer. However, the electron spin is 1/2, hence angular momentum would not be conserved if beta decay were simply electron emission.

From 1920 to 1927, Charles Drummond Ellis (along with Chadwick and colleagues) further established that the beta decay spectrum is continuous. In 1933, Ellis and Nevill Mott obtained strong evidence that the beta spectrum has an effective upper bound in energy. Niels Bohr had suggested that the beta spectrum could be explained if conservation of energy was true only in a statistical sense, thus this principle might be violated in any given decay. However, the upper bound in beta energies determined by Ellis and Mott ruled out that notion. Now, the problem of how to account for the variability of energy in known beta decay products, as well as for conservation of momentum and angular momentum in the process, became acute.

In a famous letter written in 1930, Wolfgang Pauli attempted to resolve the beta-particle energy conundrum by suggesting that, in addition to electrons and protons, atomic nuclei also contained an extremely light neutral particle, which he called the neutron. He suggested that this "neutron" was also emitted during beta decay (thus accounting for the known missing energy, momentum, and angular momentum), but it had simply not yet been observed. In 1931, Enrico Fermi renamed Pauli's "neutron" the "neutrino" ('little neutral one' in Italian). In 1933, Fermi published his landmark theory for beta decay, where he applied the principles of quantum mechanics to matter particles, supposing that they can be created and annihilated, just as the light quanta in atomic transitions. Thus, according to Fermi, neutrinos are created in the beta-decay process, rather than contained in the nucleus; the same happens to electrons. The neutrino interaction with matter was so weak that detecting it proved a severe experimental challenge. Further indirect evidence of the existence of the neutrino was obtained by observing the recoil of nuclei that emitted such a particle after absorbing an electron. Neutrinos were finally detected directly in 1956 by Clyde Cowan and Frederick Reines in the Cowan–Reines neutrino experiment. The properties of neutrinos were (with a few minor modifications) as predicted by Pauli and Fermi.

β⁺
 decay and electron capture

In 1934, Frédéric and Irène Joliot-Curie bombarded aluminium with alpha particles to effect the nuclear reaction ⁴
₂He
 + ²⁷
₁₃Al
 → ³⁰
₁₅P
 + ¹
₀n
, and observed that the product isotope ³⁰
₁₅P
emits a positron identical to those found in cosmic rays (discovered by Carl David Anderson in 1932). This was the first example of
β⁺
 decay (positron emission), which they termed artificial radioactivity since ³⁰
₁₅P
is a short-lived nuclide which does not exist in nature. In recognition of their discovery the couple were awarded the Nobel Prize in Chemistry in 1935.

The theory of electron capture was first discussed by Gian-Carlo Wick in a 1934 paper, and then developed by Hideki Yukawa and others. K-electron capture was first observed in 1937 by Luis Alvarez, in the nuclide ⁴⁸V. Alvarez went on to study electron capture in ⁶⁷Ga and other nuclides.

Non-conservation of parity

In 1956, Tsung-Dao Lee and Chen Ning Yang noticed that there was no evidence that parity was conserved in weak interactions, and so they postulated that this symmetry may not be preserved by the weak force. They sketched the design for an experiment for testing conservation of parity in the laboratory. Later that year, Chien-Shiung Wu and coworkers conducted the Wu experiment showing an asymmetrical beta decay of ⁶⁰
Co
at cold temperatures that proved that parity is not conserved in beta decay. This surprising result overturned long-held assumptions about parity and the weak force. In recognition of their theoretical work, Lee and Yang were awarded the Nobel Prize for Physics in 1957. However Wu, who was female, was not awarded the Nobel prize.

β⁻ decay

The leading-order Feynman diagram for
β⁻
 decay of a neutron into a proton, electron, and electron antineutrino via an intermediate
W⁻
boson.

In
β⁻
 decay, the weak interaction converts an atomic nucleus into a nucleus with atomic number increased by one, while emitting an electron (
e⁻
) and an electron antineutrino (
ν
_e).
β⁻
 decay generally occurs in neutron-rich nuclei. The generic equation is:

^A
_ZX
→ ^A
_Z+1X′
+
e⁻
+
ν
_e

where A and Z are the mass number and atomic number of the decaying nucleus, and X and X′ are the initial and final elements, respectively.

Another example is when the free neutron (¹
₀n
) decays by
β⁻
 decay into a proton (
p
):

n
→
p
+
e⁻
+
ν
_e.

At the fundamental level (as depicted in the Feynman diagram on the right), this is caused by the conversion of the negatively charged (−1/3 e) down quark to the positively charged (+2/3 e) up quark by emission of a
W⁻
boson; the
W⁻
boson subsequently decays into an electron and an electron antineutrino:

d
→
u
+
e⁻
+
ν
_e.

β⁺ decay

Main article: Positron emission

 

The leading-order Feynman diagram for
β⁺
 decay of a proton into a neutron, positron, and electron neutrino via an intermediate
W⁺
boson

In
β⁺
 decay, or positron emission, the weak interaction converts an atomic nucleus into a nucleus with atomic number decreased by one, while emitting a positron (
e⁺
) and an electron neutrino (
ν
_e).
β⁺
 decay generally occurs in proton-rich nuclei. The generic equation is:

^A
_ZX
→ ^A
_Z−1X′
+
e⁺
+
ν
_e

This may be considered as the decay of a proton inside the nucleus to a neutron:

p → n +
e⁺
+
ν
_e

However,
β⁺
 decay cannot occur in an isolated proton because it requires energy, due to the mass of the neutron being greater than the mass of the proton.
β⁺
 decay can only happen inside nuclei when the daughter nucleus has a greater binding energy (and therefore a lower total energy) than the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron, and a neutrino and into the kinetic energy of these particles. This process is opposite to negative beta decay, in that the weak interaction converts a proton into a neutron by converting an up quark into a down quark resulting in the emission of a
W⁺
or the absorption of a
W⁻
. When a
W⁺
boson is emitted, it decays into a positron and an electron neutrino:

u
→
d
+
e⁺
+
ν
_e.

Electron capture (K-capture)

Main article: Electron capture

 

The leading-order Feynman diagrams for electron capture decay. An electron interacts with an up quark in the nucleus via a W boson to create a down quark and electron neutrino. Two diagrams comprise the leading (second) order, though as a virtual particle, the type (and charge) of the W-boson is indistinguishable.

In all cases where
β⁺
 decay (positron emission) of a nucleus is allowed energetically, so too is electron capture allowed. This is a process during which a nucleus captures one of its atomic electrons, resulting in the emission of a neutrino:

^A
_ZX
+
e⁻
→ ^A
_Z−1X′
+
ν
_e

An example of electron capture is one of the decay modes of krypton-81 into bromine-81:

⁸¹
₃₆Kr
+
e⁻
→ ⁸¹
₃₅Br
+
ν
_e

All emitted neutrinos are of the same energy. In proton-rich nuclei where the energy difference between the initial and final states is less than 2m_ec²,
β⁺
 decay is not energetically possible, and electron capture is the sole decay mode.

If the captured electron comes from the innermost shell of the atom, the K-shell, which has the highest probability to interact with the nucleus, the process is called K-capture. If it comes from the L-shell, the process is called L-capture, etc.

Electron capture is a competing (simultaneous) decay process for all nuclei that can undergo β⁺ decay. The converse, however, is not true: electron capture is the only type of decay that is allowed in proton-rich nuclides that do not have sufficient energy to emit a positron and neutrino.

Nuclear transmutation

Graph of isotopes by type of nuclear decay. Orange and blue nuclides are unstable, with the black squares between these regions representing stable nuclides. The unbroken line passing below many of the nuclides represents the theoretical position on the graph of nuclides for which proton number is the same as neutron number. The graph shows that elements with more than 20 protons must have more neutrons than protons, in order to be stable.

 

See also: Nuclear drip line

If the proton and neutron are part of an atomic nucleus, the above described decay processes transmute one chemical element into another. For example:

137 55Cs			→	137 56Ba	+	e−	+	ν e	(beta minus decay)
22 11Na			→	22 10Ne	+	e+	+	ν e	(beta plus decay)
22 11Na	+	e−	→	22 10Ne	+	ν e			(electron capture)

Beta decay does not change the number (A) of nucleons in the nucleus, but changes only its charge Z. Thus the set of all nuclides with the same A can be introduced; these isobaric nuclides may turn into each other via beta decay. For a given A there is one that is most stable. It is said to be beta stable, because it presents a local minimum of the mass excess: if such a nucleus has (A, Z) numbers, the neighbour nuclei (A, Z−1) and (A, Z+1) have higher mass excess and can beta decay into (A, Z), but not vice versa. For all odd mass numbers A, there is only one known beta-stable isobar. For even A, there are up to three different beta-stable isobars experimentally known; for example, ¹²⁴
₅₀Sn
, ¹²⁴
₅₂Te
, and ¹²⁴
₅₄Xe
are all beta-stable. There are about 350 known beta-decay stable nuclides.

Competition of beta decay types

Usually unstable nuclides are clearly either "neutron rich" or "proton rich", with the former undergoing beta decay and the latter undergoing electron capture (or more rarely, due to the higher energy requirements, positron decay). However, in a few cases of odd-proton, odd-neutron radionuclides, it may be energetically favorable for the radionuclide to decay to an even-proton, even-neutron isobar either by undergoing beta-positive or beta-negative decay. An often-cited example is the single isotope ⁶⁴
₂₉Cu
(29 protons, 35 neutrons), which illustrates three types of beta decay in competition. Copper-64 has a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay. This particular nuclide (though not all nuclides in this situation) is almost equally likely to decay through proton decay by positron emission (18%) or electron capture (43%) to ⁶⁴
₂₈Ni
, as it is through neutron decay by electron emission (39%) to ⁶⁴
₃₀Zn
.

Stability of naturally occurring nuclides

Most naturally occurring nuclides on earth are beta stable. Nuclides that are not beta stable have half-lives ranging from under a second to periods of time significantly greater than the age of the universe. One common example of a long-lived isotope is the odd-proton odd-neutron nuclide ⁴⁰
₁₉K
, which undergoes all three types of beta decay (
β⁻
,
β⁺
and electron capture) with a half-life of 1.277×10⁹ years.

Conservation rules for beta decay

Baryon number is conserved

$${\displaystyle B={\frac {n_{q}-n_{\bar {q}}}{3}}}$$

where

• ${\displaystyle n_{q}}$ is the number of constituent quarks, and
• ${\displaystyle n_{\overline {q}}}$ is the number of constituent antiquarks.

Beta decay just changes neutron to proton or, in the case of positive beta decay (electron capture) proton to neutron so the number of individual quarks doesn't change. It is only the baryon flavor that changes, here labelled as the isospin.

Up and down quarks have total isospin ${\textstyle I={\frac {1}{2}}}$ and isospin projections

$${\displaystyle I_{\text{z}}={\begin{cases}{\frac {1}{2}}&{\text{up quark}}\\-{\frac {1}{2}}&{\text{down quark}}\end{cases}}}$$

All other quarks have I = 0.

In general

$${\displaystyle I_{\text{z}}={\frac {1}{2}}(n_{\text{u}}-n_{\text{d}})}$$

Lepton number is conserved

$${\displaystyle L\equiv n_{\ell }-n_{\bar {\ell }}}$$

so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0.

$${\displaystyle {\begin{matrix}&{\text{n}}&\rightarrow &{\text{p}}&+&{\text{e}}^{-}&+&{\bar {\nu }}_{\text{e}}\\L:&0&=&0&+&1&-&1\end{matrix}}}$$

Angular momentum

For allowed decays, the net orbital angular momentum is zero, hence only spin quantum numbers are considered.

The electron and antineutrino are fermions, spin-1/2 objects, therefore they may couple to total ${\displaystyle S=1}$ (parallel) or ${\displaystyle S=0}$ (anti-parallel).

For forbidden decays, orbital angular momentum must also be taken into consideration.

Energy release

The Q value is defined as the total energy released in a given nuclear decay. In beta decay, Q is therefore also the sum of the kinetic energies of the emitted beta particle, neutrino, and recoiling nucleus. (Because of the large mass of the nucleus compared to that of the beta particle and neutrino, the kinetic energy of the recoiling nucleus can generally be neglected.) Beta particles can therefore be emitted with any kinetic energy ranging from 0 to Q. A typical Q is around 1 MeV, but can range from a few keV to a few tens of MeV.

Since the rest mass of the electron is 511 keV, the most energetic beta particles are ultrarelativistic, with speeds very close to the speed of light. In the case of ¹⁸⁷Re, the maximum speed of the beta particle is only 9.8% of the speed of light.

The following table gives some examples:

Examples of beta decay energies

Isotope	Energy (keV)	Decay mode	Comments
free Neutron	782.33	β−
3H (Tritium)	18.59	β−	Second lowest known β− energy, being used in the KATRIN experiment.
11C	960.4 1982.4	β+ ε
14C	156.475	β−
20F	5390.86	β−
37K	5125.48 6147.48	β+ ε
163Ho	2.555	ε
187Re	2.467	β−	Lowest known β− energy, being used in the Microcalorimeter Arrays for a Rhenium Experiment experiment
210Bi	1162.2	β−

β⁻ decay

Consider the generic equation for beta decay

^A
_ZX
→ ^A
_Z+1X′
+
e⁻
+
ν
_e.

The Q value for this decay is

${\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)-m_{e}-m_{{\overline {\nu }}_{e}}\right]c^{2}}$,

where ${\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}$ is the mass of the nucleus of the ^A
_ZX
atom, ${\displaystyle m_{e}}$ is the mass of the electron, and ${\displaystyle m_{{\overline {\nu }}_{e}}}$ is the mass of the electron antineutrino. In other words, the total energy released is the mass energy of the initial nucleus, minus the mass energy of the final nucleus, electron, and antineutrino. The mass of the nucleus m_N is related to the standard atomic mass m by

$${\displaystyle m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}=m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)c^{2}+Zm_{e}c^{2}-\sum _{i=1}^{Z}B_{i}.}$$

That is, the total atomic mass is the mass of the nucleus, plus the mass of the electrons, minus the sum of all electron binding energies B_i for the atom. This equation is rearranged to find ${\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)}$, and ${\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)}$ is found similarly. Substituting these nuclear masses into the Q-value equation, while neglecting the nearly-zero antineutrino mass and the difference in electron binding energies, which is very small for high-Z atoms, we have

$${\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}+1}X'}}\right)\right]c^{2}}$$

This energy is carried away as kinetic energy by the electron and antineutrino.

Because the reaction will proceed only when the Q value is positive, β⁻ decay can occur when the mass of atom ^A
_ZX
is greater than the mass of atom ^A
_Z+1X′
.

β⁺ decay

The equations for β⁺ decay are similar, with the generic equation

^A
_ZX
→ ^A
_Z−1X′
+
e⁺
+
ν
_e

giving

$${\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{e}-m_{\nu _{e}}\right]c^{2}.}$$

However, in this equation, the electron masses do not cancel, and we are left with

$${\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-2m_{e}\right]c^{2}.}$$

Because the reaction will proceed only when the Q value is positive, β⁺ decay can occur when the mass of atom ^A
_ZX
exceeds that of ^A
_Z-1X′
by at least twice the mass of the electron.

Electron capture

The analogous calculation for electron capture must take into account the binding energy of the electrons. This is because the atom will be left in an excited state after capturing the electron, and the binding energy of the captured innermost electron is significant. Using the generic equation for electron capture

^A
_ZX
+
e⁻
→ ^A
_Z−1X′
+
ν
_e

we have

$${\displaystyle Q=\left[m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)+m_{e}-m_{N}\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)-m_{\nu _{e}}\right]c^{2},}$$

which simplifies to

$${\displaystyle Q=\left[m\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)-m\left({\ce {^{\mathit {A}}_{{\mathit {Z}}-1}X'}}\right)\right]c^{2}-B_{n},}$$

where B_n is the binding energy of the captured electron.

Because the binding energy of the electron is much less than the mass of the electron, nuclei that can undergo β⁺ decay can always also undergo electron capture, but the reverse is not true.

Beta emission spectrum

Beta spectrum of ²¹⁰Bi. E_max = Q = 1.16 MeV is the maximum energy

Beta decay can be considered as a perturbation as described in quantum mechanics, and thus Fermi's Golden Rule can be applied. This leads to an expression for the kinetic energy spectrum N(T) of emitted betas as follows:

$${\displaystyle N(T)=C_{L}(T)F(Z,T)pE(Q-T)^{2}}$$

where T is the kinetic energy, C_L is a shape function that depends on the forbiddenness of the decay (it is constant for allowed decays), F(Z, T) is the Fermi Function (see below) with Z the charge of the final-state nucleus, E = T + mc² is the total energy, p = √(E/c)² − (mc)² is the momentum, and Q is the Q value of the decay. The kinetic energy of the emitted neutrino is given approximately by Q minus the kinetic energy of the beta.

As an example, the beta decay spectrum of ²¹⁰Bi (originally called RaE) is shown to the right.

Fermi function

The Fermi function that appears in the beta spectrum formula accounts for the Coulomb attraction / repulsion between the emitted beta and the final state nucleus. Approximating the associated wavefunctions to be spherically symmetric, the Fermi function can be analytically calculated to be:

$${\displaystyle F(Z,T)={\frac {2(1+S)}{\Gamma (1+2S)^{2}}}(2p\rho )^{2S-2}e^{\pi \eta }|\Gamma (S+i\eta )|^{2},}$$

where p is the final momentum, Γ the Gamma function, and (if α is the fine-structure constant and r_N the radius of the final state nucleus) S = √1 − α² Z², η = ±Ze²c⁄ℏp (+ for electrons, − for positrons), and ρ = r_N⁄ℏ.

For non-relativistic betas (Q ≪ m_ec²), this expression can be approximated by:

$${\displaystyle F(Z,T)\approx {\frac {2\pi \eta }{1-e^{-2\pi \eta }}}.}$$

Other approximations can be found in the literature.

Kurie plot

A Kurie plot (also known as a Fermi–Kurie plot) is a graph used in studying beta decay developed by Franz N. D. Kurie, in which the square root of the number of beta particles whose momenta (or energy) lie within a certain narrow range, divided by the Fermi function, is plotted against beta-particle energy. It is a straight line for allowed transitions and some forbidden transitions, in accord with the Fermi beta-decay theory. The energy-axis (x-axis) intercept of a Kurie plot corresponds to the maximum energy imparted to the electron/positron (the decay's Q value). With a Kurie plot one can find the limit on the effective mass of a neutrino.

Helicity (polarization) of neutrinos, electrons and positrons emitted in beta decay

After the discovery of parity non-conservation (see History), it was found that, in beta decay, electrons are emitted mostly with negative helicity, i.e., they move, naively speaking, like left-handed screws driven into a material (they have negative longitudinal polarization). Conversely, positrons have mostly positive helicity, i.e., they move like right-handed screws. Neutrinos (emitted in positron decay) have negative helicity, while antineutrinos (emitted in electron decay) have positive helicity.

The higher the energy of the particles, the higher their polarization.

Types of beta decay transitions

Main article: Beta decay transition

Beta decays can be classified according to the angular momentum (L value) and total spin (S value) of the emitted radiation. Since total angular momentum must be conserved, including orbital and spin angular momentum, beta decay occurs by a variety of quantum state transitions to various nuclear angular momentum or spin states, known as "Fermi" or "Gamow–Teller" transitions. When beta decay particles carry no angular momentum (L = 0), the decay is referred to as "allowed", otherwise it is "forbidden".

Other decay modes, which are rare, are known as bound state decay and double beta decay.

Fermi transitions

A Fermi transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin ${\displaystyle S=0}$, leading to an angular momentum change ${\displaystyle \Delta J=0}$ between the initial and final states of the nucleus (assuming an allowed transition). In the non-relativistic limit, the nuclear part of the operator for a Fermi transition is given by

$${\displaystyle {\mathcal {O}}_{F}=G_{V}\sum _{a}{\hat {\tau }}_{a\pm }}$$

with ${\displaystyle G_{V}}$ the weak vector coupling constant, ${\displaystyle \tau _{\pm }}$ the isospin raising and lowering operators, and ${\displaystyle a}$ running over all protons and neutrons in the nucleus.

Gamow–Teller transitions

A Gamow–Teller transition is a beta decay in which the spins of the emitted electron (positron) and anti-neutrino (neutrino) couple to total spin ${\displaystyle S=1}$, leading to an angular momentum change ${\displaystyle \Delta J=0,\pm 1}$ between the initial and final states of the nucleus (assuming an allowed transition). In this case, the nuclear part of the operator is given by

$${\displaystyle {\mathcal {O}}_{GT}=G_{A}\sum _{a}{\hat {\sigma }}_{a}{\hat {\tau }}_{a\pm }}$$

with ${\displaystyle G_{A}}$ the weak axial-vector coupling constant, and ${\displaystyle \sigma }$ the spin Pauli matrices, which can produce a spin-flip in the decaying nucleon.

Forbidden transitions

When L > 0, the decay is referred to as "forbidden". Nuclear selection rules require high L values to be accompanied by changes in nuclear spin (J) and parity (π). The selection rules for the Lth forbidden transitions are:

$${\displaystyle \Delta J=L-1,L,L+1;\Delta \pi =(-1)^{L},}$$

where Δπ = 1 or −1 corresponds to no parity change or parity change, respectively. The special case of a transition between isobaric analogue states, where the structure of the final state is very similar to the structure of the initial state, is referred to as "superallowed" for beta decay, and proceeds very quickly. The following table lists the ΔJ and Δπ values for the first few values of L:

Forbiddenness	ΔJ	Δπ
Superallowed	0	No
Allowed	0, 1	No
First forbidden	0, 1, 2	Yes
Second forbidden	1, 2, 3	No
Third forbidden	2, 3, 4	Yes

Rare decay modes

Bound-state β⁻ decay

A very small minority of free neutron decays (about four per million) are so-called "two-body decays", in which the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral hydrogen atom. In this type of beta decay, in essence all of the neutron decay energy is carried off by the antineutrino.

For fully ionized atoms (bare nuclei), it is possible in likewise manner for electrons to fail to escape the atom, and to be emitted from the nucleus into low-lying atomic bound states (orbitals). This cannot occur for neutral atoms with low-lying bound states which are already filled by electrons.

Bound-state β decays were predicted by Daudel, Jean, and Lecoin in 1947, and the phenomenon in fully ionized atoms was first observed for ¹⁶³Dy⁶⁶⁺ in 1992 by Jung et al. of the Darmstadt Heavy-Ion Research Center. Although neutral ¹⁶³
Dy is a stable isotope, the fully ionized ¹⁶³Dy⁶⁶⁺ undergoes β decay into the K and L shells with a half-life of 47 days. The resulting nucleus - ¹⁶³
Ho - is stable only in the fully ionized state and will decay via electron capture into ¹⁶³
Dy in the neutral state. The half life for the latter is 4750 years.

Another possibility is that a fully ionized atom undergoes greatly accelerated β decay, as observed for ¹⁸⁷Re by Bosch et al., also at Darmstadt. Neutral ¹⁸⁷Re does undergo β decay with a half-life of 41.6×10⁹ years, but for fully ionized ¹⁸⁷Re⁷⁵⁺ this is shortened to only 32.9 years. For comparison the variation of decay rates of other nuclear processes due to chemical environment is less than 1%. Due to the difference in the price of rhenium and osmium and the high share of ¹⁸⁷
Re in rhenium samples found on earth, this could some day be of commercial interest in the synthesis of precious metals.

Double beta decay

Main article: Double beta decay

Some nuclei can undergo double beta decay (ββ decay) where the charge of the nucleus changes by two units. Double beta decay is difficult to study, as the process has an extremely long half-life. In nuclei for which both β decay and ββ decay are possible, the rarer ββ decay process is effectively impossible to observe. However, in nuclei where β decay is forbidden but ββ decay is allowed, the process can be seen and a half-life measured. Thus, ββ decay is usually studied only for beta stable nuclei. Like single beta decay, double beta decay does not change A; thus, at least one of the nuclides with some given A has to be stable with regard to both single and double beta decay.

"Ordinary" double beta decay results in the emission of two electrons and two antineutrinos. If neutrinos are Majorana particles (i.e., they are their own antiparticles), then a decay known as neutrinoless double beta decay will occur. Most neutrino physicists believe that neutrinoless double beta decay has never been observed.