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Cell nucleus

The cell nucleus (: nuclei) is a membrane-bound organelle found in eukaryotic cells. Eukaryotic cells usually have a single nucleus, but a few cell types, such as mammalian red blood cells, have no nuclei, and a few others including osteoclasts have many. The main structures making up the nucleus are the nuclear envelope, a double membrane that encloses the entire organelle and isolates its contents from the cellular cytoplasm; and the nuclear matrix, a network within the nucleus that adds mechanical support.

The cell nucleus contains nearly all of the cell's genome. Nuclear DNA is often organized into multiple chromosomes – long strands of DNA dotted with various proteins, such as histones, that protect and organize the DNA. The genes within these chromosomes are structured in such a way to promote cell function. The nucleus maintains the integrity of genes and controls the activities of the cell by regulating gene expression.

Because the nuclear envelope is impermeable to large molecules, nuclear pores are required to regulate nuclear transport of molecules across the envelope. The pores cross both nuclear membranes, providing a channel through which larger molecules must be actively transported by carrier proteins while allowing free movement of small molecules and ions. Movement of large molecules such as proteins and RNA through the pores is required for both gene expression and the maintenance of chromosomes. Although the interior of the nucleus does not contain any membrane-bound subcompartments, a number of nuclear bodies exist, made up of unique proteins, RNA molecules, and particular parts of the chromosomes. The best-known of these is the nucleolus, involved in the assembly of ribosomes.

Structures

The nucleus contains nearly all of the cell's DNA, surrounded by a network of fibrous intermediate filaments called the nuclear matrix, and is enveloped in a double membrane called the nuclear envelope. The nuclear envelope separates the fluid inside the nucleus, called the nucleoplasm, from the rest of the cell. The size of the nucleus is correlated to the size of the cell, and this ratio is reported across a range of cell types and species. In eukaryotes the nucleus in many cells typically occupies 10% of the cell volume. The nucleus is the largest organelle in animal cells. In human cells, the diameter of the nucleus is approximately six micrometres (μm).

Nuclear envelope and pores

The nuclear envelope consists of two membranes, an inner and an outer nuclear membrane, perforated by nuclear pores. Together, these membranes serve to separate the cell's genetic material from the rest of the cell contents, and allow the nucleus to maintain an environment distinct from the rest of the cell. Despite their close apposition around much of the nucleus, the two membranes differ substantially in shape and contents. The inner membrane surrounds the nuclear content, providing its defining edge. Embedded within the inner membrane, various proteins bind the intermediate filaments that give the nucleus its structure. The outer membrane encloses the inner membrane, and is continuous with the adjacent endoplasmic reticulum membrane. As part of the endoplasmic reticulum membrane, the outer nuclear membrane is studded with ribosomes that are actively translating proteins across membrane. The space between the two membranes is called the perinuclear space, and is continuous with the endoplasmic reticulum lumen.

In a mammalian nuclear envelope there are between 3000 and 4000 nuclear pore complexes (NPCs) perforating the envelope. Each NPC contains an eightfold-symmetric ring-shaped structure at a position where the inner and outer membranes fuse. The number of NPCs can vary considerably across cell types; small glial cells only have about a few hundred, with large Purkinje cells having around 20,000. The NPC provides selective transport of molecules between the nucleoplasm and the cytosol. The nuclear pore complex is composed of approximately thirty different proteins known as nucleoporins. The pores are about 60–80 million daltons in molecular weight and consist of around 50 (in yeast) to several hundred proteins (in vertebrates). The pores are 100 nm in total diameter; however, the gap through which molecules freely diffuse is only about 9 nm wide, due to the presence of regulatory systems within the center of the pore. This size selectively allows the passage of small water-soluble molecules while preventing larger molecules, such as nucleic acids and larger proteins, from inappropriately entering or exiting the nucleus. These large molecules must be actively transported into the nucleus instead. Attached to the ring is a structure called the nuclear basket that extends into the nucleoplasm, and a series of filamentous extensions that reach into the cytoplasm. Both structures serve to mediate binding to nuclear transport proteins.

Most proteins, ribosomal subunits, and some RNAs are transported through the pore complexes in a process mediated by a family of transport factors known as karyopherins. Those karyopherins that mediate movement into the nucleus are also called importins, whereas those that mediate movement out of the nucleus are called exportins. Most karyopherins interact directly with their cargo, although some use adaptor proteins. Steroid hormones such as cortisol and aldosterone, as well as other small lipid-soluble molecules involved in intercellular signaling, can diffuse through the cell membrane and into the cytoplasm, where they bind nuclear receptor proteins that are trafficked into the nucleus. There they serve as transcription factors when bound to their ligand; in the absence of a ligand, many such receptors function as histone deacetylases that repress gene expression.

Nuclear lamina
In animal cells, two networks of intermediate filaments provide the nucleus with mechanical support: The nuclear lamina forms an organized meshwork on the internal face of the envelope, while less organized support is provided on the cytosolic face of the envelope. Both systems provide structural support for the nuclear envelope and anchoring sites for chromosomes and nuclear pores.

The nuclear lamina is composed mostly of lamin proteins. Like all proteins, lamins are synthesized in the cytoplasm and later transported to the nucleus interior, where they are assembled before being incorporated into the existing network of nuclear lamina. Lamins found on the cytosolic face of the membrane, such as emerin and nesprin, bind to the cytoskeleton to provide structural support. Lamins are also found inside the nucleoplasm where they form another regular structure, known as the nucleoplasmic veil, that is visible using fluorescence microscopy. The actual function of the veil is not clear, although it is excluded from the nucleolus and is present during interphase. Lamin structures that make up the veil, such as LEM3, bind chromatin and disrupting their structure inhibits transcription of protein-coding genes.

Like the components of other intermediate filaments, the lamin monomer contains an alpha-helical domain used by two monomers to coil around each other, forming a dimer structure called a coiled coil. Two of these dimer structures then join side by side, in an antiparallel arrangement, to form a tetramer called a protofilament. Eight of these protofilaments form a lateral arrangement that is twisted to form a ropelike filament. These filaments can be assembled or disassembled in a dynamic manner, meaning that changes in the length of the filament depend on the competing rates of filament addition and removal.

Mutations in lamin genes leading to defects in filament assembly cause a group of rare genetic disorders known as laminopathies. The most notable laminopathy is the family of diseases known as progeria, which causes the appearance of premature aging in those with the condition. The exact mechanism by which the associated biochemical changes give rise to the aged phenotype is not well understood.

Chromosomes

The cell nucleus contains the majority of the cell's genetic material in the form of multiple linear DNA molecules organized into structures called chromosomes. Each human cell contains roughly two meters of DNA. During most of the cell cycle these are organized in a DNA-protein complex known as chromatin, and during cell division the chromatin can be seen to form the well-defined chromosomes familiar from a karyotype. A small fraction of the cell's genes are located instead in the mitochondria.

There are two types of chromatin. Euchromatin is the less compact DNA form, and contains genes that are frequently expressed by the cell. The other type, heterochromatin, is the more compact form, and contains DNA that is infrequently transcribed. This structure is further categorized into facultative heterochromatin, consisting of genes that are organized as heterochromatin only in certain cell types or at certain stages of development, and constitutive heterochromatin that consists of chromosome structural components such as telomeres and centromeres. During interphase the chromatin organizes itself into discrete individual patches, called chromosome territories. Active genes, which are generally found in the euchromatic region of the chromosome, tend to be located towards the chromosome's territory boundary.

Antibodies to certain types of chromatin organization, in particular, nucleosomes, have been associated with a number of autoimmune diseases, such as systemic lupus erythematosus. These are known as anti-nuclear antibodies (ANA) and have also been observed in concert with multiple sclerosis as part of general immune system dysfunction.

Nucleolus

The nucleolus is the largest of the discrete densely stained, membraneless structures known as nuclear bodies found in the nucleus. It forms around tandem repeats of rDNA, DNA coding for ribosomal RNA (rRNA). These regions are called nucleolar organizer regions (NOR). The main roles of the nucleolus are to synthesize rRNA and assemble ribosomes. The structural cohesion of the nucleolus depends on its activity, as ribosomal assembly in the nucleolus results in the transient association of nucleolar components, facilitating further ribosomal assembly, and hence further association. This model is supported by observations that inactivation of rDNA results in intermingling of nucleolar structures.

In the first step of ribosome assembly, a protein called RNA polymerase I transcribes rDNA, which forms a large pre-rRNA precursor. This is cleaved into two large rRNA subunits – 5.8S, and 28S, and a small rRNA subunit 18S. The transcription, post-transcriptional processing, and assembly of rRNA occurs in the nucleolus, aided by small nucleolar RNA (snoRNA) molecules, some of which are derived from spliced introns from messenger RNAs encoding genes related to ribosomal function. The assembled ribosomal subunits are the largest structures passed through the nuclear pores.

When observed under the electron microscope, the nucleolus can be seen to consist of three distinguishable regions: the innermost fibrillar centers (FCs), surrounded by the dense fibrillar component (DFC) (that contains fibrillarin and nucleolin), which in turn is bordered by the granular component (GC) (that contains the protein nucleophosmin). Transcription of the rDNA occurs either in the FC or at the FC-DFC boundary, and, therefore, when rDNA transcription in the cell is increased, more FCs are detected. Most of the cleavage and modification of rRNAs occurs in the DFC, while the latter steps involving protein assembly onto the ribosomal subunits occur in the GC.

Other nuclear bodies
Besides the nucleolus, the nucleus contains a number of other nuclear bodies. These include Cajal bodies, gemini of Cajal bodies, polymorphic interphase karyosomal association (PIKA), promyelocytic leukaemia (PML) bodies, paraspeckles, and splicing speckles. Although little is known about a number of these domains, they are significant in that they show that the nucleoplasm is not a uniform mixture, but rather contains organized functional subdomains.

Other subnuclear structures appear as part of abnormal disease processes. For example, the presence of small intranuclear rods has been reported in some cases of nemaline myopathy. This condition typically results from mutations in actin, and the rods themselves consist of mutant actin as well as other cytoskeletal proteins.

Cajal bodies and gems
A nucleus typically contains between one and ten compact structures called Cajal bodies or coiled bodies (CB), whose diameter measures between 0.2 μm and 2.0 μm depending on the cell type and species. When seen under an electron microscope, they resemble balls of tangled thread and are dense foci of distribution for the protein coilin. CBs are involved in a number of different roles relating to RNA processing, specifically small nucleolar RNA (snoRNA) and small nuclear RNA (snRNA) maturation, and histone mRNA modification.

Similar to Cajal bodies are Gemini of Cajal bodies, or gems, whose name is derived from the Gemini constellation in reference to their close "twin" relationship with CBs. Gems are similar in size and shape to CBs, and in fact are virtually indistinguishable under the microscope. Unlike CBs, gems do not contain small nuclear ribonucleoproteins (snRNPs), but do contain a protein called survival of motor neuron (SMN) whose function relates to snRNP biogenesis. Gems are believed to assist CBs in snRNP biogenesis, though it has also been suggested from microscopy evidence that CBs and gems are different manifestations of the same structure. Later ultrastructural studies have shown gems to be twins of Cajal bodies with the difference being in the coilin component; Cajal bodies are SMN positive and coilin positive, and gems are SMN positive and coilin negative.

PIKA and PTF domains
PIKA domains, or polymorphic interphase karyosomal associations, were first described in microscopy studies in 1991. Their function remains unclear, though they were not thought to be associated with active DNA replication, transcription, or RNA processing. They have been found to often associate with discrete domains defined by dense localization of the transcription factor PTF, which promotes transcription of small nuclear RNA (snRNA).

PML-nuclear bodies
Promyelocytic leukemia protein (PML-nuclear bodies) are spherical bodies found scattered throughout the nucleoplasm, measuring around 0.1–1.0 μm. They are known by a number of other names, including nuclear domain 10 (ND10), Kremer bodies, and PML oncogenic domains. PML-nuclear bodies are named after one of their major components, the promyelocytic leukemia protein (PML). They are often seen in the nucleus in association with Cajal bodies and cleavage bodies. Pml-/- mice, which are unable to create PML-nuclear bodies, develop normally without obvious ill effects, showing that PML-nuclear bodies are not required for most essential biological processes.

Splicing speckles
Speckles are subnuclear structures that are enriched in pre-messenger RNA splicing factors and are located in the interchromatin regions of the nucleoplasm of mammalian cells. At the fluorescence-microscope level they appear as irregular, punctate structures, which vary in size and shape, and when examined by electron microscopy they are seen as clusters of interchromatin granules. Speckles are dynamic structures, and both their protein and RNA-protein components can cycle continuously between speckles and other nuclear locations, including active transcription sites. Speckles can work with p53 as enhancers of gene activity to directly enhance the activity of certain genes. Moreover, speckle-associating and non-associating p53 gene targets are functionally distinct.

Studies on the composition, structure and behaviour of speckles have provided a model for understanding the functional compartmentalization of the nucleus and the organization of the gene-expression machinery splicing snRNPs and other splicing proteins necessary for pre-mRNA processing. Because of a cell's changing requirements, the composition and location of these bodies changes according to mRNA transcription and regulation via phosphorylation of specific proteins. The splicing speckles are also known as nuclear speckles (nuclear specks), splicing factor compartments (SF compartments), interchromatin granule clusters (IGCs), and B snurposomes. B snurposomes are found in the amphibian oocyte nuclei and in Drosophila melanogaster embryos. B snurposomes appear alone or attached to the Cajal bodies in the electron micrographs of the amphibian nuclei. IGCs function as storage sites for the splicing factors.

Paraspeckles
Discovered by Fox et al. in 2002, paraspeckles are irregularly shaped compartments in the interchromatin space of the nucleus. First documented in HeLa cells, where there are generally 10–30 per nucleus, paraspeckles are now known to also exist in all human primary cells, transformed cell lines, and tissue sections. Their name is derived from their distribution in the nucleus; the "para" is short for parallel and the "speckles" refers to the splicing speckles to which they are always in close proximity.

Paraspeckles sequester nuclear proteins and RNA and thus appear to function as a molecular sponge that is involved in the regulation of gene expression. Furthermore, paraspeckles are dynamic structures that are altered in response to changes in cellular metabolic activity. They are transcription dependent and in the absence of RNA Pol II transcription, the paraspeckle disappears and all of its associated protein components (PSP1, p54nrb, PSP2, CFI(m)68, and PSF) form a crescent shaped perinucleolar cap in the nucleolus. This phenomenon is demonstrated during the cell cycle. In the cell cycle, paraspeckles are present during interphase and during all of mitosis except for telophase. During telophase, when the two daughter nuclei are formed, there is no RNA Pol II transcription so the protein components instead form a perinucleolar cap.

Perichromatin fibrils
Perichromatin fibrils are visible only under electron microscope. They are located next to the transcriptionally active chromatin and are hypothesized to be the sites of active pre-mRNA processing.

Clastosomes
Clastosomes are small nuclear bodies (0.2–0.5 μm) described as having a thick ring-shape due to the peripheral capsule around these bodies. This name is derived from the Greek klastos, broken and soma, body. Clastosomes are not typically present in normal cells, making them hard to detect. They form under high proteolytic conditions within the nucleus and degrade once there is a decrease in activity or if cells are treated with proteasome inhibitors. The scarcity of clastosomes in cells indicates that they are not required for proteasome function. Osmotic stress has also been shown to cause the formation of clastosomes. These nuclear bodies contain catalytic and regulatory subunits of the proteasome and its substrates, indicating that clastosomes are sites for degrading proteins.

Function
The nucleus provides a site for genetic transcription that is segregated from the location of translation in the cytoplasm, allowing levels of gene regulation that are not available to prokaryotes. The main function of the cell nucleus is to control gene expression and mediate the replication of DNA during the cell cycle.

Cell compartmentalization
The nuclear envelope allows control of the nuclear contents, and separates them from the rest of the cytoplasm where necessary. This is important for controlling processes on either side of the nuclear membrane: In most cases where a cytoplasmic process needs to be restricted, a key participant is removed to the nucleus, where it interacts with transcription factors to downregulate the production of certain enzymes in the pathway. This regulatory mechanism occurs in the case of glycolysis, a cellular pathway for breaking down glucose to produce energy. Hexokinase is an enzyme responsible for the first step of glycolysis, forming glucose-6-phosphate from glucose. At high concentrations of fructose-6-phosphate, a molecule made later from glucose-6-phosphate, a regulator protein removes hexokinase to the nucleus, where it forms a transcriptional repressor complex with nuclear proteins to reduce the expression of genes involved in glycolysis.

In order to control which genes are being transcribed, the cell separates some transcription factor proteins responsible for regulating gene expression from physical access to the DNA until they are activated by other signaling pathways. This prevents even low levels of inappropriate gene expression. For example, in the case of NF-κB-controlled genes, which are involved in most inflammatory responses, transcription is induced in response to a signal pathway such as that initiated by the signaling molecule TNF-α, binds to a cell membrane receptor, resulting in the recruitment of signalling proteins, and eventually activating the transcription factor NF-κB. A nuclear localisation signal on the NF-κB protein allows it to be transported through the nuclear pore and into the nucleus, where it stimulates the transcription of the target genes.

The compartmentalization allows the cell to prevent translation of unspliced mRNA. Eukaryotic mRNA contains introns that must be removed before being translated to produce functional proteins. The splicing is done inside the nucleus before the mRNA can be accessed by ribosomes for translation. Without the nucleus, ribosomes would translate newly transcribed (unprocessed) mRNA, resulting in malformed and nonfunctional proteins.

Replication
The main function of the cell nucleus is to control gene expression and mediate the replication of DNA during the cell cycle. It has been found that replication happens in a localised way in the cell nucleus. In the S phase of interphase of the cell cycle; replication takes place. Contrary to the traditional view of moving replication forks along stagnant DNA, a concept of replication factories emerged, which means replication forks are concentrated towards some immobilised 'factory' regions through which the template DNA strands pass like conveyor belts.

Gene expression

Gene expression first involves transcription, in which DNA is used as a template to produce RNA. In the case of genes encoding proteins, that RNA produced from this process is messenger RNA (mRNA), which then needs to be translated by ribosomes to form a protein. As ribosomes are located outside the nucleus, mRNA produced needs to be exported.

Since the nucleus is the site of transcription, it also contains a variety of proteins that either directly mediate transcription or are involved in regulating the process. These proteins include helicases, which unwind the double-stranded DNA molecule to facilitate access to it, RNA polymerases, which bind to the DNA promoter to synthesize the growing RNA molecule, topoisomerases, which change the amount of supercoiling in DNA, helping it wind and unwind, as well as a large variety of transcription factors that regulate expression.

Processing of pre-mRNA
Newly synthesized mRNA molecules are known as primary transcripts or pre-mRNA. They must undergo post-transcriptional modification in the nucleus before being exported to the cytoplasm; mRNA that appears in the cytoplasm without these modifications is degraded rather than used for protein translation. The three main modifications are 5' capping, 3' polyadenylation, and RNA splicing. While in the nucleus, pre-mRNA is associated with a variety of proteins in complexes known as heterogeneous ribonucleoprotein particles (hnRNPs). Addition of the 5' cap occurs co-transcriptionally and is the first step in post-transcriptional modification. The 3' poly-adenine tail is only added after transcription is complete.

RNA splicing, carried out by a complex called the spliceosome, is the process by which introns, or regions of DNA that do not code for protein, are removed from the pre-mRNA and the remaining exons connected to re-form a single continuous molecule. This process normally occurs after 5' capping and 3' polyadenylation but can begin before synthesis is complete in transcripts with many exons. Many pre-mRNAs can be spliced in multiple ways to produce different mature mRNAs that encode different protein sequences. This process is known as alternative splicing, and allows production of a large variety of proteins from a limited amount of DNA.

Nuclear transport

The entry and exit of large molecules from the nucleus is tightly controlled by the nuclear pore complexes. Although small molecules can enter the nucleus without regulation, macromolecules such as RNA and proteins require association karyopherins called importins to enter the nucleus and exportins to exit. "Cargo" proteins that must be translocated from the cytoplasm to the nucleus contain short amino acid sequences known as nuclear localization signals, which are bound by importins, while those transported from the nucleus to the cytoplasm carry nuclear export signals bound by exportins. The ability of importins and exportins to transport their cargo is regulated by GTPases, enzymes that hydrolyze the molecule guanosine triphosphate (GTP) to release energy. The key GTPase in nuclear transport is Ran, which is bound to either GTP or GDP (guanosine diphosphate), depending on whether it is located in the nucleus or the cytoplasm. Whereas importins depend on RanGTP to dissociate from their cargo, exportins require RanGTP in order to bind to their cargo.

Nuclear import depends on the importin binding its cargo in the cytoplasm and carrying it through the nuclear pore into the nucleus. Inside the nucleus, RanGTP acts to separate the cargo from the importin, allowing the importin to exit the nucleus and be reused. Nuclear export is similar, as the exportin binds the cargo inside the nucleus in a process facilitated by RanGTP, exits through the nuclear pore, and separates from its cargo in the cytoplasm.

Specialized export proteins exist for translocation of mature mRNA and tRNA to the cytoplasm after post-transcriptional modification is complete. This quality-control mechanism is important due to these molecules' central role in protein translation. Mis-expression of a protein due to incomplete excision of exons or mis-incorporation of amino acids could have negative consequences for the cell; thus, incompletely modified RNA that reaches the cytoplasm is degraded rather than used in translation.

Assembly and disassembly

During its lifetime, a nucleus may be broken down or destroyed, either in the process of cell division or as a consequence of apoptosis (the process of programmed cell death). During these events, the structural components of the nucleus — the envelope and lamina — can be systematically degraded. In most cells, the disassembly of the nuclear envelope marks the end of the prophase of mitosis. However, this disassembly of the nucleus is not a universal feature of mitosis and does not occur in all cells. Some unicellular eukaryotes (e.g., yeasts) undergo so-called closed mitosis, in which the nuclear envelope remains intact. In closed mitosis, the daughter chromosomes migrate to opposite poles of the nucleus, which then divides in two. The cells of higher eukaryotes, however, usually undergo open mitosis, which is characterized by breakdown of the nuclear envelope. The daughter chromosomes then migrate to opposite poles of the mitotic spindle, and new nuclei reassemble around them.

At a certain point during the cell cycle in open mitosis, the cell divides to form two cells. In order for this process to be possible, each of the new daughter cells must have a full set of genes, a process requiring replication of the chromosomes as well as segregation of the separate sets. This occurs by the replicated chromosomes, the sister chromatids, attaching to microtubules, which in turn are attached to different centrosomes. The sister chromatids can then be pulled to separate locations in the cell. In many cells, the centrosome is located in the cytoplasm, outside the nucleus; the microtubules would be unable to attach to the chromatids in the presence of the nuclear envelope. Therefore, the early stages in the cell cycle, beginning in prophase and until around prometaphase, the nuclear membrane is dismantled. Likewise, during the same period, the nuclear lamina is also disassembled, a process regulated by phosphorylation of the lamins by protein kinases such as the CDC2 protein kinase. Towards the end of the cell cycle, the nuclear membrane is reformed, and around the same time, the nuclear lamina are reassembled by dephosphorylating the lamins.

However, in dinoflagellates, the nuclear envelope remains intact, the centrosomes are located in the cytoplasm, and the microtubules come in contact with chromosomes, whose centromeric regions are incorporated into the nuclear envelope (the so-called closed mitosis with extranuclear spindle). In many other protists (e.g., ciliates, sporozoans) and fungi, the centrosomes are intranuclear, and their nuclear envelope also does not disassemble during cell division.

Apoptosis is a controlled process in which the cell's structural components are destroyed, resulting in death of the cell. Changes associated with apoptosis directly affect the nucleus and its contents, for example, in the condensation of chromatin and the disintegration of the nuclear envelope and lamina. The destruction of the lamin networks is controlled by specialized apoptotic proteases called caspases, which cleave the lamin proteins and, thus, degrade the nucleus' structural integrity. Lamin cleavage is sometimes used as a laboratory indicator of caspase activity in assays for early apoptotic activity. Cells that express mutant caspase-resistant lamins are deficient in nuclear changes related to apoptosis, suggesting that lamins play a role in initiating the events that lead to apoptotic degradation of the nucleus. Inhibition of lamin assembly itself is an inducer of apoptosis.

The nuclear envelope acts as a barrier that prevents both DNA and RNA viruses from entering the nucleus. Some viruses require access to proteins inside the nucleus in order to replicate and/or assemble. DNA viruses, such as herpesvirus replicate and assemble in the cell nucleus, and exit by budding through the inner nuclear membrane. This process is accompanied by disassembly of the lamina on the nuclear face of the inner membrane.

Disease-related dynamics
Initially, it has been suspected that immunoglobulins in general and autoantibodies in particular do not enter the nucleus. Now there is a body of evidence that under pathological conditions (e.g. lupus erythematosus) IgG can enter the nucleus.

Nuclei per cell
Most eukaryotic cell types usually have a single nucleus, but some have no nuclei, while others have several. This can result from normal development, as in the maturation of mammalian red blood cells, or from faulty cell division.

Anucleated cells

An anucleated cell contains no nucleus and is, therefore, incapable of dividing to produce daughter cells. The best-known anucleated cell is the mammalian red blood cell, or erythrocyte, which also lacks other organelles such as mitochondria, and serves primarily as a transport vessel to ferry oxygen from the lungs to the body's tissues. Erythrocytes mature through erythropoiesis in the bone marrow, where they lose their nuclei, organelles, and ribosomes. The nucleus is expelled during the process of differentiation from an erythroblast to a reticulocyte, which is the immediate precursor of the mature erythrocyte. The presence of mutagens may induce the release of some immature "micronucleated" erythrocytes into the bloodstream. Anucleated cells can also arise from flawed cell division in which one daughter lacks a nucleus and the other has two nuclei.

In flowering plants, this condition occurs in sieve tube elements.

Multinucleated cells
Multinucleated cells contain multiple nuclei. Most acantharean species of protozoa and some fungi in mycorrhizae have naturally multinucleated cells. Other examples include the intestinal parasites in the genus Giardia, which have two nuclei per cell. Ciliates have two kinds of nuclei in a single cell, a somatic macronucleus and a germline micronucleus. In humans, skeletal muscle cells, also called myocytes and syncytium, become multinucleated during development; the resulting arrangement of nuclei near the periphery of the cells allows maximal intracellular space for myofibrils. Other multinucleate cells in the human are osteoclasts a type of bone cell. Multinucleated and binucleated cells can also be abnormal in humans; for example, cells arising from the fusion of monocytes and macrophages, known as giant multinucleated cells, sometimes accompany inflammation and are also implicated in tumor formation.

A number of dinoflagellates are known to have two nuclei. Unlike other multinucleated cells these nuclei contain two distinct lineages of DNA: one from the dinoflagellate and the other from a symbiotic diatom.

Evolution
As the major defining characteristic of the eukaryotic cell, the nucleus's evolutionary origin has been the subject of much speculation. Four major hypotheses have been proposed to explain the existence of the nucleus, although none have yet earned widespread support.

The first model known as the "syntrophic model" proposes that a symbiotic relationship between the archaea and bacteria created the nucleus-containing eukaryotic cell. (Organisms of the Archaea and Bacteria domain have no cell nucleus. ) It is hypothesized that the symbiosis originated when ancient archaea, similar to modern methanogenic archaea, invaded and lived within bacteria similar to modern myxobacteria, eventually forming the early nucleus. This theory is analogous to the accepted theory for the origin of eukaryotic mitochondria and chloroplasts, which are thought to have developed from a similar endosymbiotic relationship between proto-eukaryotes and aerobic bacteria. One possibility is that the nuclear membrane arose as a new membrane system following the origin of mitochondria in an archaebacterial host. The nuclear membrane may have served to protect the genome from damaging reactive oxygen species produced by the protomitochondria. The archaeal origin of the nucleus is supported by observations that archaea and eukarya have similar genes for certain proteins, including histones. Observations that myxobacteria are motile, can form multicellular complexes, and possess kinases and G proteins similar to eukarya, support a bacterial origin for the eukaryotic cell.

A second model proposes that proto-eukaryotic cells evolved from bacteria without an endosymbiotic stage. This model is based on the existence of modern Planctomycetota bacteria that possess a nuclear structure with primitive pores and other compartmentalized membrane structures. A similar proposal states that a eukaryote-like cell, the chronocyte, evolved first and phagocytosed archaea and bacteria to generate the nucleus and the eukaryotic cell.

The most controversial model, known as viral eukaryogenesis, posits that the membrane-bound nucleus, along with other eukaryotic features, originated from the infection of a prokaryote by a virus. The suggestion is based on similarities between eukaryotes and viruses such as linear DNA strands, mRNA capping, and tight binding to proteins (analogizing histones to viral envelopes). One version of the proposal suggests that the nucleus evolved in concert with phagocytosis to form an early cellular "predator". Another variant proposes that eukaryotes originated from early archaea infected by poxviruses, on the basis of observed similarity between the DNA polymerases in modern poxviruses and eukaryotes. It has been suggested that the unresolved question of the evolution of sex could be related to the viral eukaryogenesis hypothesis.

A more recent proposal, the exomembrane hypothesis, suggests that the nucleus instead originated from a single ancestral cell that evolved a second exterior cell membrane; the interior membrane enclosing the original cell then became the nuclear membrane and evolved increasingly elaborate pore structures for passage of internally synthesized cellular components such as ribosomal subunits.

History
The nucleus was the first organelle to be discovered. What is most likely the oldest preserved drawing dates back to the early microscopist Antonie van Leeuwenhoek (1632–1723). He observed a "lumen", the nucleus, in the red blood cells of salmon. Unlike mammalian red blood cells, those of other vertebrates still contain nuclei.

The nucleus was also described by Franz Bauer in 1804 and in more detail in 1831 by Scottish botanist Robert Brown in a talk at the Linnean Society of London. Brown was studying orchids under the microscope when he observed an opaque area, which he called the "areola" or "nucleus", in the cells of the flower's outer layer. He did not suggest a potential function.

In 1838, Matthias Schleiden proposed that the nucleus plays a role in generating cells, thus he introduced the name "cytoblast" ("cell builder"). He believed that he had observed new cells assembling around "cytoblasts". Franz Meyen was a strong opponent of this view, having already described cells multiplying by division and believing that many cells would have no nuclei. The idea that cells can be generated de novo, by the "cytoblast" or otherwise, contradicted work by Robert Remak (1852) and Rudolf Virchow (1855) who decisively propagated the new paradigm that cells are generated solely by cells ("Omnis cellula e cellula"). The function of the nucleus remained unclear.

Between 1877 and 1878, Oscar Hertwig published several studies on the fertilization of sea urchin eggs, showing that the nucleus of the sperm enters the oocyte and fuses with its nucleus. This was the first time it was suggested that an individual develops from a (single) nucleated cell. This was in contradiction to Ernst Haeckel's theory that the complete phylogeny of a species would be repeated during embryonic development, including generation of the first nucleated cell from a "monerula", a structureless mass of primordial protoplasm ("Urschleim"). Therefore, the necessity of the sperm nucleus for fertilization was discussed for quite some time. However, Hertwig confirmed his observation in other animal groups, including amphibians and molluscs. Eduard Strasburger produced the same results for plants in 1884. This paved the way to assign the nucleus an important role in heredity. In 1873, August Weismann postulated the equivalence of the maternal and paternal germ cells for heredity. The function of the nucleus as carrier of genetic information became clear only later, after mitosis was discovered and the Mendelian rules were rediscovered at the beginning of the 20th century; the chromosome theory of heredity was therefore developed.

title: Cell nucleus


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Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people around the world. A feast central to the liturgical year in Christianity, it follows the season of Advent (which begins four Sundays before) or the Nativity Fast, and initiates the season of Christmastide, which historically in the West lasts twelve days and culminates on Twelfth Night. Christmas Day is a public holiday in many countries,  is celebrated religiously by a majority of Christians, as well as culturally by many non-Christians, and forms an integral part of the holiday season surrounding it.

The traditional Christmas narrative recounted in the New Testament, known as the Nativity of Jesus, says that Jesus was born in Bethlehem, in accordance with messianic prophecies. When Joseph and Mary arrived in the city, the inn had no room, and so they were offered a stable where the Christ Child was soon born, with angels proclaiming this news to shepherds, who then spread the word.

There are different hypotheses regarding the date of Jesus's birth, and in the early fourth century, the church fixed the date as December 25. This corresponds to the traditional date of the winter solstice on the Roman calendar. It is exactly nine months after Annunciation on March 25, also the date of the spring equinox. Most Christians celebrate on December 25 in the Gregorian calendar, which has been adopted almost universally in the civil calendars used in countries throughout the world. However, part of the Eastern Christian Churches celebrate Christmas on December 25 of the older Julian calendar, which currently corresponds to January 7 in the Gregorian calendar. For Christians, believing that God came into the world in the form of man to atone for the sins of humanity rather than knowing Jesus's exact birth date is considered to be the primary purpose of celebrating Christmas.

The customs associated with Christmas in various countries have a mix of pre-Christian, Christian, and secular themes and origins. Popular holiday traditions include gift giving; completing an Advent calendar or Advent wreath; Christmas music and caroling; watching Christmas movies; viewing a Nativity play; an exchange of Christmas cards; attending church services; a special meal; and displaying various Christmas decorations, including Christmas trees, Christmas lights, nativity scenes, garlands, wreaths, mistletoe, and holly. Additionally, several related and often interchangeable figures, known as Santa Claus, Father Christmas, Saint Nicholas, and Christkind, are associated with bringing gifts to children during the Christmas season and have their own body of traditions and lore. Because gift-giving and many other aspects of the Christmas festival involve heightened economic activity, the holiday has become a significant event and a key sales period for retailers and businesses. Over the past few centuries, Christmas has had a steadily growing economic effect in many regions of the world.

Etymology
The English word Christmas is a shortened form of 'Christ's Mass'. The word is recorded as Crīstesmæsse in 1038 and Cristes-messe in 1131. Crīst (genitive Crīstes) is from the Greek Χριστός (, 'Christ'), a translation of the Hebrew (, 'Messiah'), meaning 'anointed';  and mæsse is from the Latin missa, the celebration of the Eucharist.

The form Christenmas was also used during some periods, but is now considered archaic and dialectal. The term derives from Middle English Cristenmasse, meaning 'Christian mass'. Xmas is an abbreviation of Christmas found particularly in print, based on the initial letter chi (Χ) in the Greek Χριστός, although some style guides discourage its use. This abbreviation has precedent in Middle English Χρ̄es masse (where Χρ̄ is another abbreviation of the Greek word).

Other names
The holiday has had various other English names throughout its history. The Anglo-Saxons referred to the feast as "midwinter", or, more rarely, as Nātiuiteð (from the Latin nātīvitās below). Nativity, meaning 'birth', is from the Latin nātīvitās. In Old English, Gēola ('Yule') referred to the period corresponding to December and January, which was eventually equated with Christian Christmas. 'Noel' (also 'Nowel' or 'Nowell', as in "The First Nowell") entered English in the late 14th century and is from the Old French noël or naël, itself ultimately from the Latin nātālis (diēs) meaning 'birth (day)'.

Koleda is the traditional Slavic name for Christmas and the period from Christmas to Epiphany or, more generally, to Slavic Christmas-related rituals, some dating to pre-Christian times.

Nativity

The gospels of Luke and Matthew describe Jesus as being born in Bethlehem to the Virgin Mary. In the Gospel of Luke, Joseph and Mary travel from Nazareth to Bethlehem in order to be counted for a census, and Jesus is born there and placed in a manger. Angels proclaim him a savior for all people, and three shepherds come to adore him. In the Gospel of Matthew, by contrast, three magi follow a star to Bethlehem to bring gifts to Jesus, born the king of the Jews. King Herod orders the massacre of all the boys less than two years old in Bethlehem, but the family flees to Egypt and later returns to Nazareth.

Early and medieval era
In the 2nd century, the "earliest church records" indicate that "Christians were remembering and celebrating the birth of the Lord", an "observance [that] sprang up organically from the authentic devotion of ordinary believers"; although "they did not agree upon a set date". The earliest evidence of Christ's birth being marked on December 25 is a sentence in the Chronograph of 354. Liturgical historians generally agree that this part of the text was written in Rome in AD 336. Though Christmas did not appear on the lists of festivals given by the early Christian writers Irenaeus and Tertullian, the early Church Fathers John Chrysostom, Augustine of Hippo, and Jerome attested to December 25 as the date of Christmas toward the end of the fourth century. December 25 was the traditional date of the winter solstice in the Roman Empire, where most Christians lived, and the Roman festival Dies Natalis Solis Invicti (birthday of Sol Invictus, the 'Invincible Sun') had been held on this date since 274 AD.

In the East, the birth of Jesus was celebrated in connection with the Epiphany on January 6. This holiday was not primarily about Christ's birth, but rather his baptism. Christmas was promoted in the East as part of the revival of Orthodox Christianity that followed the death of the pro-Arian Emperor Valens at the Battle of Adrianople in 378. The feast was introduced in Constantinople in 379, in Antioch by John Chrysostom towards the end of the fourth century, probably in 388, and in Alexandria in the following century. The Georgian Iadgari demonstrates that Christmas was celebrated in Jerusalem by the sixth century.

In the Early Middle Ages, Christmas Day was overshadowed by Epiphany, which in western Christianity focused on the visit of the magi. However, the medieval calendar was dominated by Christmas-related holidays. The forty days before Christmas became the "forty days of St. Martin" (which began on November 11, the feast of St. Martin of Tours), now known as Advent. In Italy, former Saturnalian traditions were attached to Advent. Around the 12th century, these traditions transferred again to the Twelve Days of Christmas (December 25 – January 5); a time that appears in the liturgical calendars as Christmastide or Twelve Holy Days.

In 567, the Council of Tours put in place the season of Christmastide, proclaiming "the twelve days from Christmas to Epiphany as a sacred and festive season, and established the duty of Advent fasting in preparation for the feast." This was done in order to solve the "administrative problem for the Roman Empire as it tried to coordinate the solar Julian calendar with the lunar calendars of its provinces in the east."

The prominence of Christmas Day increased gradually after Charlemagne was crowned Emperor on Christmas Day in 800. King Edmund the Martyr was anointed on Christmas in 855 and King William I of England was crowned on Christmas Day 1066.

By the High Middle Ages, the holiday had become so prominent that chroniclers routinely noted where various magnates celebrated Christmas. King Richard II of England hosted a Christmas feast in 1377 at which 28 oxen and 300 sheep were eaten. The Yule boar was a common feature of medieval Christmas feasts. Caroling also became popular, and was originally performed by a group of dancers who sang. The group was composed of a lead singer and a ring of dancers that provided the chorus. Various writers of the time condemned caroling as lewd, indicating that the unruly traditions of Saturnalia and Yule may have continued in this form. "Misrule"—drunkenness, promiscuity, gambling—was also an important aspect of the festival. In England, gifts were exchanged on New Year's Day, and there was special Christmas ale.

Christmas during the Middle Ages was a public festival that incorporated ivy, holly, and other evergreens. Christmas gift-giving during the Middle Ages was usually between people with legal relationships, such as tenant and landlord. The annual indulgence in eating, dancing, singing, sporting, and card playing escalated in England, and by the 17th century the Christmas season featured lavish dinners, elaborate masques, and pageants. In 1607, King James I insisted that a play be acted on Christmas night and that the court indulge in games. It was during the Reformation in 16th–17th-century Europe that many Protestants changed the gift bringer to the Christ Child or Christkindl, and the date of giving gifts changed from December 6 to Christmas Eve.

17th and 18th centuries
Following the Protestant Reformation, many of the new denominations, including the Anglican Church and Lutheran Church, continued to celebrate Christmas. In 1629, the Anglican poet John Milton penned On the Morning of Christ's Nativity, a poem that has since been read by many during Christmastide. Donald Heinz, a professor at California State University, states that Martin Luther "inaugurated a period in which Germany would produce a unique culture of Christmas, much copied in North America." Among the congregations of the Dutch Reformed Church, Christmas was celebrated as one of the principal evangelical feasts.

However, in 17th century England, some groups such as the Puritans strongly condemned the celebration of Christmas, considering it a Catholic invention and the "trappings of popery" or the "rags of the Beast". In contrast, the established Anglican Church "pressed for a more elaborate observance of feasts, penitential seasons, and saints' days. The calendar reform became a major point of tension between the Anglican party and the Puritan party." The Catholic Church also responded, promoting the festival in a more religiously oriented form. King Charles I of England directed his noblemen and gentry to return to their landed estates in midwinter to keep up their old-style Christmas generosity. Following the Parliamentarian victory over Charles I during the English Civil War, England's Puritan rulers banned Christmas in 1647.

Protests followed as pro-Christmas rioting broke out in several cities and for weeks Canterbury was controlled by the rioters, who decorated doorways with holly and shouted royalist slogans. Football, among the sports the Puritans banned on a Sunday, was also used as a rebellious force: when Puritans outlawed Christmas in England in December 1647 the crowd brought out footballs as a symbol of festive misrule. The book, The Vindication of Christmas (London, 1652), argued against the Puritans, and makes note of Old English Christmas traditions, dinner, roast apples on the fire, card playing, dances with "plow-boys" and "maidservants", old Father Christmas and carol singing. During the ban, semi-clandestine religious services marking Christ's birth continued to be held, and people sang carols in secret.

It was restored as a legal holiday in England with the Restoration of King Charles II in 1660 when Puritan legislation was declared null and void, with Christmas again freely celebrated in England. Many Calvinist clergymen disapproved of Christmas celebration. As such, in Scotland, the Presbyterian Church of Scotland discouraged the observance of Christmas, and though James VI commanded its celebration in 1618, attendance at church was scant. The Parliament of Scotland officially abolished the observance of Christmas in 1640, claiming that the church had been "purged of all superstitious observation of days". Whereas in England, Wales and Ireland Christmas Day is a common law holiday, having been a customary holiday since time immemorial, it was not until 1871 that it was designated a bank holiday in Scotland. Following the Restoration of Charles II, Poor Robin's Almanack contained the lines: "Now thanks to God for Charles return, / Whose absence made old Christmas mourn. / For then we scarcely did it know, / Whether it Christmas were or no." The diary of James Woodforde, from the latter half of the 18th century, details the observance of Christmas and celebrations associated with the season over a number of years.

As in England, Puritans in Colonial America staunchly opposed the observation of Christmas. The Pilgrims of New England pointedly spent their first December 25 in the New World working normally. Puritans such as Cotton Mather condemned Christmas both because scripture did not mention its observance and because Christmas celebrations of the day often involved boisterous behavior. Many non-Puritans in New England deplored the loss of the holidays enjoyed by the laboring classes in England. Christmas observance was outlawed in Boston in 1659. The ban on Christmas observance was revoked in 1681 by English governor Edmund Andros, but it was not until the mid-19th century that celebrating Christmas became fashionable in the Boston region.

At the same time, Christian residents of Virginia and New York observed the holiday freely. Pennsylvania Dutch settlers, predominantly Moravian settlers of Bethlehem, Nazareth, and Lititz in Pennsylvania and the Wachovia settlements in North Carolina, were enthusiastic celebrators of Christmas. The Moravians in Bethlehem had the first Christmas trees in America as well as the first Nativity Scenes. Christmas fell out of favor in the United States after the American Revolution, when it was considered an English custom. George Washington attacked Hessian (German) mercenaries on the day after Christmas during the Battle of Trenton on December 26, 1776, Christmas being much more popular in Germany than in America at this time.

With the atheistic Cult of Reason in power during the era of Revolutionary France, Christian Christmas religious services were banned and the three kings cake was renamed the "equality cake" under anticlerical government policies.

19th century

In the early 19th century, Christmas festivities and services became widespread with the rise of the Oxford Movement in the Church of England that emphasized the centrality of Christmas in Christianity and charity to the poor, along with Washington Irving, Charles Dickens, and other authors emphasizing family, children, kind-heartedness, gift-giving, and Santa Claus (for Irving), or Father Christmas (for Dickens).

In the early-19th century, writers imagined Tudor-period Christmas as a time of heartfelt celebration. In 1843, Charles Dickens wrote the novel A Christmas Carol, which helped revive the "spirit" of Christmas and seasonal merriment. Its instant popularity played a major role in portraying Christmas as a holiday emphasizing family, goodwill, and compassion.

Dickens sought to construct Christmas as a family-centered festival of generosity, linking "worship and feasting, within a context of social reconciliation." Superimposing his humanitarian vision of the holiday, in what has been termed "Carol Philosophy", Dickens influenced many aspects of Christmas that are celebrated today in Western culture, such as family gatherings, seasonal food and drink, dancing, games, and a festive generosity of spirit. A prominent phrase from the tale, "Merry Christmas", was popularized following the appearance of the story. This coincided with the appearance of the Oxford Movement and the growth of Anglo-Catholicism, which led a revival in traditional rituals and religious observances.

The term Scrooge became a synonym for miser, with the phrase "Bah! Humbug!" becoming emblematic of a dismissive attitude of the festive spirit. In 1843, the first commercial Christmas card was produced by Sir Henry Cole. The revival of the Christmas Carol began with William Sandys's Christmas Carols Ancient and Modern (1833), with the first appearance in print of "The First Noel", "I Saw Three Ships", "Hark the Herald Angels Sing" and "God Rest Ye Merry, Gentlemen", popularized in Dickens's A Christmas Carol.

In Britain, the Christmas tree was introduced in the early 19th century by the German-born Queen Charlotte. In 1832, the future Queen Victoria wrote about her delight at having a Christmas tree, hung with lights, ornaments, and presents placed round it. After her marriage to her German cousin Prince Albert, by 1841 the custom became more widespread throughout Britain. An image of the British royal family with their Christmas tree at Windsor Castle created a sensation when it was published in the Illustrated London News in 1848. A modified version of this image was published in Godey's Lady's Book, Philadelphia in 1850. By the 1870s, putting up a Christmas tree had become common in America.

In America, interest in Christmas had been revived in the 1820s by several short stories by Washington Irving which appear in his The Sketch Book of Geoffrey Crayon, Gent. and "Old Christmas". Irving's stories depicted harmonious warm-hearted English Christmas festivities he experienced while staying in Aston Hall, Birmingham, England, that had largely been abandoned, and he used the tract Vindication of Christmas (1652) of Old English Christmas traditions, that he had transcribed into his journal as a format for his stories.

In 1822, Clement Clarke Moore wrote the poem A Visit From St. Nicholas (popularly known by its first line: Twas the Night Before Christmas). The poem helped popularize the tradition of exchanging gifts, and seasonal Christmas shopping began to assume economic importance. This also started the cultural conflict between the holiday's spiritual significance and its associated commercialism that some see as corrupting the holiday. In her 1850 book The First Christmas in New England, Harriet Beecher Stowe includes a character who complains that the true meaning of Christmas was lost in a shopping spree.

While the celebration of Christmas was not yet customary in some regions in the U.S., Henry Wadsworth Longfellow detected "a transition state about Christmas here in New England" in 1856. "The old puritan feeling prevents it from being a cheerful, hearty holiday; though every year makes it more so." In Reading, Pennsylvania, a newspaper remarked in 1861, "Even our presbyterian friends who have hitherto steadfastly ignored Christmas—threw open their church doors and assembled in force to celebrate the anniversary of the Savior's birth."

The First Congregational Church of Rockford, Illinois, "although of genuine Puritan stock", was 'preparing for a grand Christmas jubilee', a news correspondent reported in 1864. By 1860, fourteen states including several from New England had adopted Christmas as a legal holiday. In 1875, Louis Prang introduced the Christmas card to Americans. He has been called the "father of the American Christmas card". On June 28, 1870, Christmas was formally declared a United States federal holiday.

20th and 21st centuries
During the First World War and particularly (but not exclusively) in 1914, a series of informal truces took place for Christmas between opposing armies. The truces, which were organised spontaneously by fighting men, ranged from promises not to shoot (shouted at a distance in order to ease the pressure of war for the day) to friendly socializing, gift giving and even sport between enemies. These incidents became a well known and semi-mythologised part of popular memory. They have been described as a symbol of common humanity even in the darkest of situations and used to demonstrate to children the ideals of Christmas.

Up to the 1950s in the UK, many Christmas customs were restricted to the upper and middle classes. Most of the population had not yet adopted many Christmas rituals that later became popular, including Christmas trees. Christmas dinner would normally include beef or goose, not turkey as would later be common. Children would get fruit and sweets in their stocking rather than elaborate gifts. Full celebration of a family Christmas with all the trimmings only became widespread with increased prosperity from the 1950s. National papers were published on Christmas Day until 1912. Post was still delivered on Christmas Day until 1961. League football matches continued in Scotland until the 1970s while in England they ceased at the end of the 1950s.

Under the state atheism of the Soviet Union, after its foundation in 1917, Christmas celebrations—along with other Christian holidays—were prohibited in public. During the 1920s, 1930s, and 1940s, the League of Militant Atheists encouraged school pupils to campaign against Christmas traditions, such as the Christmas tree, as well as other Christian holidays, including Easter; the League established an antireligious holiday to be the 31st of each month as a replacement. At the height of this persecution, in 1929, on Christmas Day, children in Moscow were encouraged to spit on crucifixes as a protest against the holiday. Instead, the importance of the holiday and all its trappings, such as the Christmas tree and gift-giving, was transferred to the New Year. It was not until the dissolution of the Soviet Union in 1991 that the persecution ended and Orthodox Christmas became a state holiday again for the first time in Russia after seven decades.

European History Professor Joseph Perry wrote that likewise, in Nazi Germany, "because Nazi ideologues saw organized religion as an enemy of the totalitarian state, propagandists sought to deemphasize—or eliminate altogether—the Christian aspects of the holiday" and that "Propagandists tirelessly promoted numerous Nazified Christmas songs, which replaced Christian themes with the regime's racial ideologies."

As Christmas celebrations began to spread globally even outside traditional Christian cultures, several Muslim-majority countries began to ban the observance of Christmas, claiming it undermined Islam. In 2023, public Christmas celebrations were cancelled in Bethlehem, the city synonymous with the birth of Jesus. Palestinian leaders of various Christian denominations cited the ongoing Israel–Hamas war in their unanimous decision to cancel celebrations.

Observance and traditions

Christmas Day is celebrated as a major festival and public holiday in countries around the world, including many whose populations are mostly non-Christian. In some non-Christian areas, periods of former colonial rule introduced the celebration (e.g. Hong Kong); in others, Christian minorities or foreign cultural influences have led populations to observe the holiday. Countries such as Japan, where Christmas is popular despite there being only a small number of Christians, have adopted many of the cultural aspects of Christmas, such as gift-giving, decorations, and Christmas trees. A similar example is in Turkey, being Muslim-majority and with a small number of Christians, where Christmas trees and decorations tend to line public streets during the festival.

Many popular customs associated with Christmas developed independently of the commemoration of Jesus's birth, with some claiming that certain elements are Christianized and have origins in pre-Christian festivals that were celebrated by pagan populations who were later converted to Christianity; other scholars reject these claims and affirm that Christmas customs largely developed in a Christian context. The prevailing atmosphere of Christmas has also continually evolved since the holiday's inception, ranging from a sometimes raucous, drunken, carnival-like state in the Middle Ages, to a tamer family-oriented and children-centered theme introduced in a 19th-century transformation. The celebration of Christmas was banned on more than one occasion within certain groups, such as the Puritans and Jehovah's Witnesses (who do not celebrate birthdays in general), due to concerns that it was too unbiblical.

Prior to and through the early Christian centuries, winter festivals were the most popular of the year in many European pagan cultures. Reasons included the fact that less agricultural work needed to be done during the winter, as well as an expectation of better weather as spring approached. Celtic winter herbs such as mistletoe and ivy, and the custom of kissing under a mistletoe, are common in modern Christmas celebrations in the English-speaking countries.

The pre-Christian Germanic peoples—including the Anglo-Saxons and the Norse—celebrated a winter festival called Yule, held in the late December to early January period, yielding modern English yule, today used as a synonym for Christmas. In Germanic language-speaking areas, numerous elements of modern Christmas folk custom and iconography may have originated from Yule, including the Yule log, Yule boar, and the Yule goat. Often leading a ghostly procession through the sky (the Wild Hunt), the long-bearded god Odin is referred to as "the Yule one" and "Yule father" in Old Norse texts, while other gods are referred to as "Yule beings". On the other hand, as there are no reliable existing references to a Christmas log prior to the 16th century, the burning of the Christmas block may have been an early modern invention by Christians unrelated to the pagan practice.

Among countries with a strong Christian tradition, a variety of Christmas celebrations have developed that incorporate regional and local cultures. For example, in eastern Europe Christmas celebrations incorporated pre-Christian traditions such as the Koleda, which shares parallels with the Christmas carol.

Church attendance
Christmas Day (inclusive of its vigil, Christmas Eve), is a Festival in the Lutheran Churches, a solemnity in the Roman Catholic Church, and a Principal Feast of the Anglican Communion. Other Christian denominations do not rank their feast days but nevertheless place importance on Christmas Eve/Christmas Day, as with other Christian feasts like Easter, Ascension Day, and Pentecost. As such, for Christians, attending a Christmas Eve or Christmas Day church service plays an important part in the recognition of the Christmas season. Christmas, along with Easter, is the period of highest annual church attendance. A 2010 survey by LifeWay Christian Resources found that six in ten Americans attend church services during this time. In the United Kingdom, the Church of England reported an estimated attendance of 2.5million people at Christmas services in 2015.

Decorations

Nativity scenes are known from 10th-century Rome. They were popularised by Saint Francis of Assisi from 1223, quickly spreading across Europe. Different types of decorations developed across the Christian world, dependent on local tradition and available resources, and can vary from simple representations of the crib to far more elaborate sets – renowned manger scene traditions include the colourful Kraków szopka in Poland, which imitate Kraków's historical buildings as settings, the elaborate Italian presepi (Presepe napoletano, Presepe genovese and Presepe bolognese),   or the Provençal crèches in southern France, using hand-painted terracotta figurines called santons. In certain parts of the world, notably Sicily, living nativity scenes following the tradition of Saint Francis are a popular alternative to static crèches. The first commercially produced decorations appeared in Germany in the 1860s, inspired by paper chains made by children. In countries where a representation of the Nativity scene is very popular, people are encouraged to compete and create the most original or realistic ones. Within some families, the pieces used to make the representation are considered a valuable family heirloom.

The traditional colors of Christmas decorations are red, green, and gold. Red symbolizes the blood of Jesus, which was shed in his crucifixion; green symbolizes eternal life, and in particular the evergreen tree, which does not lose its leaves in the winter; and gold is the first color associated with Christmas, as one of the three gifts of the Magi, symbolizing royalty.

The Christmas tree was first used by German Lutherans in the 16th century, with records indicating that a Christmas tree was placed in the Cathedral of Strassburg in 1539, under the leadership of the Protestant Reformer, Martin Bucer. In the United States, these "German Lutherans brought the decorated Christmas tree with them; the Moravians put lighted candles on those trees." When decorating the Christmas tree, many individuals place a star at the top of the tree symbolizing the Star of Bethlehem, a fact recorded by The School Journal in 1897. Professor David Albert Jones of Oxford University writes that in the 19th century, it became popular for people to also use an angel to top the Christmas tree in order to symbolize the angels mentioned in the accounts of the Nativity of Jesus. Additionally, in the context of a Christian celebration of Christmas, the Christmas tree, being evergreen in colour, is symbolic of Christ, who offers eternal life; the candles or lights on the tree represent the Light of the World—Jesus—born in Bethlehem. Christian services for family use and public worship have been published for the blessing of a Christmas tree, after it has been erected. The Christmas tree is considered by some as Christianisation of pagan tradition and ritual surrounding the Winter Solstice, which included the use of evergreen boughs, and an adaptation of pagan tree worship; according to eighth-century biographer Æddi Stephanus, Saint Boniface (634–709), who was a missionary in Germany, took an ax to an oak tree dedicated to Thor and pointed out a fir tree, which he stated was a more fitting object of reverence because it pointed to heaven and it had a triangular shape, which he said was symbolic of the Trinity. The English language phrase "Christmas tree" is first recorded in 1835 and represents an importation from the German language.

Since the 16th century, the poinsettia, a native plant from Mexico, has been associated with Christmas carrying the Christian symbolism of the Star of Bethlehem; in that country it is known in Spanish as the Flower of the Holy Night. Other popular holiday plants include holly, mistletoe, red amaryllis, and Christmas cactus.

Other traditional decorations include bells, candles, candy canes, stockings, wreaths, and angels. Both the displaying of wreaths and candles in each window are a more traditional Christmas display. The concentric assortment of leaves, usually from an evergreen, make up Christmas wreaths and are designed to prepare Christians for the Advent season. Candles in each window are meant to demonstrate the fact that Christians believe that Jesus Christ is the ultimate light of the world.

Christmas lights and banners may be hung along streets, music played from speakers, and Christmas trees placed in prominent places. It is common in many parts of the world for town squares and consumer shopping areas to sponsor and display decorations. Rolls of brightly colored paper with secular or religious Christmas motifs are manufactured for the purpose of wrapping gifts. In some countries, Christmas decorations are traditionally taken down on Twelfth Night.

Nativity play
For the Christian celebration of Christmas, the viewing of the Nativity play is one of the oldest Christmastime traditions, with the first reenactment of the Nativity of Jesus taking place in 1223 AD in the Italian town of Greccio. In that year, Francis of Assisi assembled a Nativity scene outside of his church in Italy and children sung Christmas carols celebrating the birth of Jesus. Each year, this grew larger and people travelled from afar to see Francis's depiction of the Nativity of Jesus that came to feature drama and music. Nativity plays eventually spread throughout all of Europe, where they remain popular. Christmas Eve and Christmas Day church services often came to feature Nativity plays, as did schools and theatres. In France, Germany, Mexico and Spain, Nativity plays are often reenacted outdoors in the streets.

Music and carols

The earliest extant specifically Christmas hymns appear in fourth-century Rome. Latin hymns such as "Veni redemptor gentium", written by Ambrose, Archbishop of Milan, were austere statements of the theological doctrine of the Incarnation in opposition to Arianism. "Corde natus ex Parentis" ("Of the Father's love begotten") by the Spanish poet Prudentius (died 413) is still sung in some churches today. In the 9th and 10th centuries, the Christmas "Sequence" or "Prose" was introduced in North European monasteries, developing under Bernard of Clairvaux into a sequence of rhymed stanzas. In the 12th century the Parisian monk Adam of St. Victor began to derive music from popular songs, introducing something closer to the traditional Christmas carol. Christmas carols in English appear in a 1426 work of John Awdlay who lists twenty five "caroles of Cristemas", probably sung by groups of 'wassailers', who went from house to house.

The songs now known specifically as carols were originally communal folk songs sung during celebrations such as "harvest tide" as well as Christmas. It was only later that carols began to be sung in church. Traditionally, carols have often been based on medieval chord patterns, and it is this that gives them their uniquely characteristic musical sound. Some carols like "Personent hodie", "Good King Wenceslas", and "In dulci jubilo" can be traced directly back to the Middle Ages. They are among the oldest musical compositions still regularly sung. "Adeste Fideles" (O Come all ye faithful) appeared in its current form in the mid-18th century.

The singing of carols increased in popularity after the Protestant Reformation in the Lutheran areas of Europe, as the Reformer Martin Luther wrote carols and encouraged their use in worship, in addition to spearheading the practice of caroling outside the Mass. The 18th-century English reformer Charles Wesley, a founder of Methodism, understood the importance of music to Christian worship. In addition to setting many psalms to melodies, he wrote texts for at least three Christmas carols. The best known was originally entitled "Hark! How All the Welkin Rings", later renamed "Hark! The Herald Angels Sing".

Christmas seasonal songs of a secular nature emerged in the late 18th century. The Welsh melody for "Deck the Halls" dates from 1794, with the lyrics added by Scottish musician Thomas Oliphant in 1862, and the American "Jingle Bells" was copyrighted in 1857. Other popular carols include "The First Noel", "God Rest You Merry, Gentlemen", "The Holly and the Ivy", "I Saw Three Ships", "In the Bleak Midwinter", "Joy to the World", "Once in Royal David's City" and "While Shepherds Watched Their Flocks". In the 19th and 20th centuries, African American spirituals and songs about Christmas, based in their tradition of spirituals, became more widely known. An increasing number of seasonal holiday songs were commercially produced in the 20th century, including jazz and blues variations. In addition, there was a revival of interest in early music, from groups singing folk music, such as The Revels, to performers of early medieval and classical music.

One of the most ubiquitous festive songs is "We Wish You a Merry Christmas", which originates from the West Country of England in the 1930s. Radio has covered Christmas music from variety shows from the 1940s and 1950s, as well as modern-day stations that exclusively play Christmas music from late November through December 25. Hollywood movies have featured new Christmas music, such as "White Christmas" in Holiday Inn and Rudolph the Red-Nosed Reindeer. Traditional carols have also been included in Hollywood films, such as "Hark! The Herald Angels Sing" in It's a Wonderful Life (1946), and "Silent Night" in A Christmas Story.

Traditional cuisine

A special Christmas family meal is traditionally an important part of the holiday's celebration, and the food that is served varies greatly from country to country. Some regions have special meals for Christmas Eve, such as Sicily, where twelve kinds of fish are served. In the United Kingdom and countries influenced by its traditions, a standard Christmas meal includes turkey, goose or other large bird, gravy, potatoes, vegetables, sometimes bread and cider. Special desserts are also prepared, such as Christmas pudding, mince pies, Christmas cake, and latterly Panettone and Yule log. A traditional Christmas meal in Central Europe features fried carp or other fish.

Cards

Christmas cards are illustrated messages of greeting exchanged between friends and family members during the weeks preceding Christmas Day. The traditional greeting reads "wishing you a Merry Christmas and a Happy New Year", much like that of the first commercial Christmas card, produced by Sir Henry Cole in London in 1843. The custom of sending them has become popular among a wide cross-section of people with the emergence of the modern trend towards exchanging E-cards.

Christmas cards are purchased in considerable quantities and feature artwork, commercially designed and relevant to the season. The content of the design might relate directly to the Christmas narrative, with depictions of the Nativity of Jesus, or Christian symbols such as the Star of Bethlehem, or a white dove, which can represent both the Holy Spirit and Peace on Earth. Other Christmas cards are more secular and can depict Christmas traditions, mythical figures such as Santa Claus, objects directly associated with Christmas such as candles, holly, and baubles, or a variety of images associated with the season, such as Christmastide activities, snow scenes, and the wildlife of the northern winter.

Some prefer cards with a poem, prayer, or Biblical verse; while others distance themselves from religion with an all-inclusive "Season's greetings".

Commemorative stamps
A number of nations have issued commemorative stamps at Christmastide. Postal customers will often use these stamps to mail Christmas cards, and they are popular with philatelists. These stamps are regular postage stamps, unlike Christmas seals, and are valid for postage year-round. They usually go on sale sometime between early October and early December and are printed in considerable quantities.

Christmas seals
Christmas seals were first issued to raise funding to fight and bring awareness to tuberculosis. The first Christmas seal was issued in Denmark in 1904, and since then other countries have issued their own Christmas seals.

Gift giving

The exchanging of gifts is one of the core aspects of the modern Christmas celebration, making it the most profitable time of year for retailers and businesses throughout the world. On Christmas, people exchange gifts based on the Christian tradition associated with Saint Nicholas, and the gifts of gold, frankincense, and myrrh which were given to the baby Jesus by the Magi. The practice of gift giving in the Roman celebration of Saturnalia may have influenced Christian customs, but on the other hand the Christian "core dogma of the Incarnation, however, solidly established the giving and receiving of gifts as the structural principle of that recurrent yet unique event", because it was the Biblical Magi, "together with all their fellow men, who received the gift of God through man's renewed participation in the divine life." However, Thomas J. Talley holds that the Roman Emperor Aurelian placed the alternate festival on December 25 in order to compete with the growing rate of the Christian Church, which had already been celebrating Christmas on that date first.

Gift-bearing figures
A number of figures are associated with Christmas and the seasonal giving of gifts. Among these are Father Christmas, also known as Santa Claus (derived from the Dutch for Saint Nicholas), Père Noël, and the Weihnachtsmann; Saint Nicholas or Sinterklaas; the Christkind; Kris Kringle; Joulupukki; tomte/nisse; Babbo Natale; Saint Basil; and Ded Moroz. The Scandinavian tomte (also called nisse) is sometimes depicted as a gnome instead of Santa Claus.

The best known of these figures today is red-dressed Santa Claus, of diverse origins. The name 'Santa Claus' can be traced back to the Dutch Sinterklaas ('Saint Nicholas'). Nicholas was a 4th-century Greek bishop of Myra, a city in the Roman province of Lycia, whose ruins are 3 km from modern Demre in southwest Turkey. Among other saintly attributes, he was noted for the care of children, generosity, and the giving of gifts. His feast day, December 6, came to be celebrated in many countries with the giving of gifts.

Saint Nicholas traditionally appeared in bishop's attire, accompanied by helpers, inquiring about the behaviour of children during the past year before deciding whether they deserved a gift or not. By the 13th century, Saint Nicholas was well known in the Netherlands, and the practice of gift-giving in his name spread to other parts of central and southern Europe. At the Reformation in 16th- and 17th-century Europe, many Protestants changed the gift bringer to the Christ Child or Christkindl, corrupted in English to 'Kris Kringle', and the date of giving gifts changed from December 6 to Christmas Eve.

The modern popular image of Santa Claus, however, was created in the United States, and in particular in New York. The transformation was accomplished with the aid of notable contributors including Washington Irving and the German-American cartoonist Thomas Nast (1840–1902). Following the American Revolutionary War, some of the inhabitants of New York City sought out symbols of the city's non-English past. New York had originally been established as the Dutch colonial town of New Amsterdam and the Dutch Sinterklaas tradition was reinvented as Saint Nicholas.

Current tradition in several Latin American countries (such as Venezuela and Colombia) holds that while Santa makes the toys, he then gives them to the Baby Jesus, who is the one who actually delivers them to the children's homes, a reconciliation between traditional religious beliefs and the iconography of Santa Claus imported from the United States.

In Italy's South Tyrol, Austria, the Czech Republic, Southern Germany, Hungary, Liechtenstein, Slovakia, and Switzerland, the Christkind (Ježíšek in Czech, Jézuska in Hungarian and Ježiško in Slovak) brings the presents. Greek children get their presents from Saint Basil on New Year's Eve, the eve of that saint's liturgical feast. The German St. Nikolaus is not identical with the Weihnachtsmann (who is the German version of Santa Claus / Father Christmas). St. Nikolaus wears a bishop's dress and still brings small gifts (usually candies, nuts, and fruits) on December 6 and is accompanied by Knecht Ruprecht. Although many parents around the world routinely teach their children about Santa Claus and other gift bringers, some have come to reject this practice, considering it deceptive.

Multiple gift-giver figures exist in Poland, varying between regions and individual families. St Nicholas (Święty Mikołaj) dominates Central and North-East areas, the Starman (Gwiazdor) is most common in Greater Poland, Baby Jesus (Dzieciątko) is unique to Upper Silesia, with the Little Star (Gwiazdka) and the Little Angel (Aniołek) being common in the South and the South-East. Grandfather Frost (Dziadek Mróz) is less commonly accepted in some areas of Eastern Poland. It is worth noting that across all of Poland, St Nicholas is the gift giver on Saint Nicholas Day on December 6.

Sport
Christmas during the Middle Ages was a public festival with annual indulgences included the sporting. When Puritans outlawed Christmas in England in December 1647 the crowd brought out footballs as a symbol of festive misrule. The Orkney Christmas Day Ba' tradition continues. In the former top tier of English football, home and away Christmas Day and Boxing Day double headers were often played guaranteeing football clubs large crowds by allowing many working people their only chance to watch a game. Champions Preston North End faced Aston Villa on Christmas Day 1889 and the last December 25 fixture was in 1965 in England, Blackpool beating Blackburn Rovers 4–2. One of the most memorable images of the Christmas truce during World War I was the games of football played between the opposing sides on Christmas Day 1914.

More recently, in the United States, both NFL and NBA have held fixtures on Christmas Day.

Choice of date

There are two main theories behind December 25 becoming the traditional date for Christmas, although Theology professor Susan Roll says that "No liturgical historian[...] goes so far as to deny that it has any sort of relation with the sun, the winter solstice and the popularity of solar worship in the later Roman Empire". December 25 was the date of the winter solstice in the Roman calendar. Some early Christian writers noted the solar symbolism in placing Jesus's birthday at the winter solstice and John's birthday at the summer solstice.

The 'history of religions' theory suggests the Church chose December 25 as Christ's birthday (dies Natalis Christi) to appropriate the Roman winter solstice festival dies Natalis Solis Invicti (birthday of Sol Invictus, the 'Invincible Sun'), held on this date since 274 AD. The early Church linked Jesus Christ to the Sun and referred to him as the 'Sun of Righteousness' (Sol Justitiae) prophesied by Malachi. Gary Forsythe, Professor of Ancient History, says that the Natalis Solis Invicti followed "the seven-day period of the Saturnalia (December 17–23), Rome's most joyous holiday season since Republican times, characterized by parties, banquets, and exchanges of gifts".

Another theory, the 'computation hypothesis' or 'calculation theory', notes that December 25 is nine months after March 25, a date chosen as Jesus's conception (the Annunciation) and the date of the spring equinox on the Roman calendar.

Date according to Julian calendar
Some jurisdictions of the Eastern Orthodox Church, including those of Russia, Georgia, Macedonia, Montenegro, Serbia, and Jerusalem, mark feasts using the older Julian calendar. As of 2024, there is a difference of 13 days between the Julian calendar and the modern Gregorian calendar, which is used internationally for most secular purposes. As a result, December 25 on the Julian calendar currently corresponds to January 7 on the calendar used by most governments and people in everyday life. Therefore, the aforementioned Orthodox Christians mark December 25 (and thus Christmas) on the day that is internationally considered to be January 7.

However, following the Council of Constantinople in 1923, other Orthodox Christians, such as those belonging to the jurisdictions of Constantinople, Bulgaria, Greece, Romania, Antioch, Alexandria, Albania, Cyprus, Finland, and the Orthodox Church in America, among others, began using the Revised Julian calendar, which at present corresponds exactly to the Gregorian calendar. Therefore, these Orthodox Christians mark December 25 (and thus Christmas) on the same day that is internationally considered to be December 25.

A further complication is added by the fact that the Armenian Apostolic Church continues the original ancient Eastern Christian practice of celebrating the birth of Christ not as a separate holiday, but on the same day as the celebration of his baptism (Theophany), which is on January 6. This is a public holiday in Armenia, and it is held on the same day that is internationally considered to be January 6, because since 1923 the Armenian Church in Armenia has used the Gregorian calendar.

However, there is also a small Armenian Patriarchate of Jerusalem, which maintains the traditional Armenian custom of celebrating the birth of Christ on the same day as Theophany (January 6), but uses the Julian calendar for the determination of that date. As a result, this church celebrates "Christmas" (more properly called Theophany) on the day that is considered January 19 on the Gregorian calendar in use by the majority of the world.

Following the 2022 invasion of its territory by Russia, Ukraine officially moved its Christmas date from January 7 to December 25, to distance itself from the Russian Orthodox Church that had supported Russia's invasion. This followed the Orthodox Church of Ukraine formally adopting the Revised Julian calendar for fixed feasts and solemnities.

Table of dates
There are four different dates used by different Christian groups to mark the birth of Christ, given in the table below.

Economy

Christmas is typically a peak selling season for retailers in many nations around the world since sales increase dramatically during this time as people purchase gifts, decorations, and supplies to celebrate. In the United States, the "Christmas shopping season" starts as early as October. In Canada, merchants begin advertising campaigns just before Halloween (October 31), and step up their marketing following Remembrance Day on November 11. In the UK and Ireland, the Christmas shopping season starts from mid-November, around the time when high street Christmas lights are turned on. A concept devised by retail entrepreneur David Lewis, the first Christmas grotto opened in Lewis's department store in Liverpool, England in 1879. In the United States, it has been calculated that a quarter of all personal spending takes place during the Christmas/holiday shopping season. Figures from the US Census Bureau reveal that expenditure in department stores nationwide rose from $20.8billion in November 2004 to $31.9billion in December 2004, an increase of 54 percent. In other sectors, the pre-Christmas increase in spending was even greater, there being a November–December buying surge of 100 percent in bookstores and 170 percent in jewelry stores. In the same year employment in American retail stores rose from 1.6million to 1.8million in the two months leading up to Christmas. Industries completely dependent on Christmas include Christmas cards, of which 1.9billion are sent in the United States each year, and live Christmas trees, of which 20.8million were cut in the US in 2002. For 2019, the average US adult was projected to spend $920 on gifts alone. In the UK in 2010, up to £8billion was expected to be spent online at Christmas, approximately a quarter of total retail festive sales.

In most Western nations, Christmas Day is the least active day of the year for business and commerce; almost all retail, commercial and institutional businesses are closed, and almost all industries cease activity (more than any other day of the year), whether laws require such or not. In England and Wales, the Christmas Day (Trading) Act 2004 prevents all large shops from trading on Christmas Day. Similar legislation was approved in Scotland in 2007. Film studios release many high-budget movies during the holiday season, including Christmas films, fantasy movies or high-tone dramas with high production values to hopes of maximizing the chance of nominations for the Academy Awards.

One economist's analysis calculates that, despite increased overall spending, Christmas is a deadweight loss under orthodox microeconomic theory, because of the effect of gift-giving. This loss is calculated as the difference between what the gift giver spent on the item and what the gift receiver would have paid for the item. It is estimated that in 2001, Christmas resulted in a $4billion deadweight loss in the US alone. Because of complicating factors, this analysis is sometimes used to discuss possible flaws in current microeconomic theory. Other deadweight losses include the effects of Christmas on the environment and the fact that material gifts are often perceived as white elephants, imposing cost for upkeep and storage and contributing to clutter.

Controversies

Christmas has at times been the subject of controversy and attacks from various sources, both Christian and non-Christian. Historically, it was prohibited by Puritans during their ascendency in the Commonwealth of England (1647–1660), and in Colonial New England where the Puritans outlawed the celebration of Christmas in 1659 on the grounds that Christmas was not mentioned in Scripture and therefore violated the Reformed regulative principle of worship. The Parliament of Scotland, which was dominated by Presbyterians, passed a series of acts outlawing the observance of Christmas between 1637 and 1690; Christmas Day did not become a public holiday in Scotland until 1871. Today, some conservative Reformed denominations such as the Free Presbyterian Church of Scotland and the Reformed Presbyterian Church of North America likewise reject the celebration of Christmas based on the regulative principle and what they see as its non-Scriptural origin. Christmas celebrations have also been prohibited by atheist states such as the Soviet Union and more recently majority Muslim states such as Somalia, Tajikistan and Brunei.

Some Christians and organizations such as Pat Robertson's American Center for Law and Justice cite alleged attacks on Christmas (dubbing them a "war on Christmas"). Such groups claim that any specific mention of the term "Christmas" or its religious aspects is being increasingly censored, avoided, or discouraged by a number of advertisers, retailers, government (prominently schools), and other public and private organizations. One controversy is the occurrence of Christmas trees being renamed Holiday trees. In the U.S. there has been a tendency to replace the greeting Merry Christmas with Happy Holidays, which is considered inclusive at the time of the Jewish celebration of Hanukkah. In the U.S. and Canada, where the use of the term "Holidays" is most prevalent, opponents have denounced its usage and avoidance of using the term "Christmas" as being politically correct. In 1984, the U.S. Supreme Court ruled in Lynch v. Donnelly that a Christmas display (which included a Nativity scene) owned and displayed by the city of Pawtucket, Rhode Island, did not violate the First Amendment. American Muslim scholar Abdul Malik Mujahid has said that Muslims must treat Christmas with respect, even if they disagree with it.

The government of the People's Republic of China officially espouses state atheism, and has conducted antireligious campaigns to this end. In December 2018, officials raided Christian churches prior to Christmastide and coerced them to close; Christmas trees and Santa Clauses were also forcibly removed.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Christmas


text:
Contraction mapping

In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number $$0 \leq k < 1$$ such that for all x and y in M,

 * $$d(f(x),f(y)) \leq k\,d(x,y).$$

The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps. If the above condition is instead satisfied for k ≤ 1, then the mapping is said to be a non-expansive map.

More generally, the idea of a contractive mapping can be defined for maps between metric spaces. Thus, if (M, d) and (N, d') are two metric spaces, then $$f:M \rightarrow N$$ is a contractive mapping if there is a constant $$0 \leq k < 1$$ such that
 * $$d'(f(x),f(y)) \leq k\,d(x,y)$$

for all x and y in M.

Every contraction mapping is Lipschitz continuous and hence uniformly continuous (for a Lipschitz continuous function, the constant k is no longer necessarily less than 1).

A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f (x), f (f (x)), f (f (f (x))), ... converges to the fixed point. This concept is very useful for iterated function systems where contraction mappings are often used. Banach's fixed-point theorem is also applied in proving the existence of solutions of ordinary differential equations, and is used in one proof of the inverse function theorem.

Contraction mappings play an important role in dynamic programming problems.

Firmly non-expansive mapping
A non-expansive mapping with $$k=1$$ can be generalized to a firmly non-expansive mapping in a Hilbert space $$\mathcal{H}$$ if the following holds for all x and y in $$\mathcal{H}$$:
 * $$\|f(x)-f(y) \|^2 \leq \, \langle x-y, f(x) - f(y) \rangle.$$

where
 * $$d(x,y) = \|x-y\|$$.

This is a special case of $$\alpha$$ averaged nonexpansive operators with $$\alpha = 1/2$$. A firmly non-expansive mapping is always non-expansive, via the Cauchy–Schwarz inequality.

The class of firmly non-expansive maps is closed under convex combinations, but not compositions. This class includes proximal mappings of proper, convex, lower-semicontinuous functions, hence it also includes orthogonal projections onto non-empty closed convex sets. The class of firmly nonexpansive operators is equal to the set of resolvents of maximally monotone operators. Surprisingly, while iterating non-expansive maps has no guarantee to find a fixed point (e.g. multiplication by -1), firm non-expansiveness is sufficient to guarantee global convergence to a fixed point, provided a fixed point exists. More precisely, if $$\text{Fix}f := \{x \in \mathcal{H} \ | \ f(x) = x\} \neq \varnothing$$, then for any initial point $$x_0 \in \mathcal{H}$$, iterating

$$ (\forall n \in \mathbb{N})\quad x_{n+1} = f(x_n) $$

yields convergence to a fixed point $$ x_n \to z \in \text{Fix} f$$. This convergence might be weak in an infinite-dimensional setting.

Subcontraction map
A subcontraction map or subcontractor is a map f on a metric space (M, d) such that

 * $$ d(f(x), f(y)) \leq d(x,y);$$
 * $$ d(f(f(x)),f(x)) < d(f(x),x) \quad \text{unless} \quad x = f(x).$$

If the image of a subcontractor f is compact, then f has a fixed point.

Locally convex spaces
In a locally convex space (E, P) with topology given by a set P of seminorms, one can define for any p ∈ P a p-contraction as a map f such that there is some kp < 1 such that p(f(x) − f(y)) ≤ kp p(x − y). If f is a p-contraction for all p ∈ P and (E, P) is sequentially complete, then f has a fixed point, given as limit of any sequence xn+1 = f(xn), and if (E, P) is Hausdorff, then the fixed point is unique.

title: Contraction mapping