Basis set (chemistry)

From Wikipedia, the free encyclopedia

In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.

The use of basis sets is equivalent to the use of an approximate resolution of the identity: the orbitals ${\displaystyle |{\psi }_i⟩}$ are expanded within the basis set as a linear combination of the basis functions $|{\psi }_i⟩\approx \sum _{\mu }{c}_{\mu i}|\mu ⟩$, where the expansion coefficients ${\displaystyle c_{\mu i}}$ are given by $c_{\mu i}=\sum _{\nu }⟨\mu |\nu {⟩}^{-1}⟨\nu |{\psi }_i⟩$.

The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the quantum chemistry community; plane waves which are typically used within the solid state community, or real-space approaches. Several types of atomic orbitals can be used: Gaussian-type orbitals, Slater-type orbitals, or numerical atomic orbitals. Out of the three, Gaussian-type orbitals are by far the most often used, as they allow efficient implementations of post-Hartree–Fock methods.

Introduction

In modern computational chemistry, quantum chemical calculations are performed using a finite set of basis functions. When the finite basis is expanded towards an (infinite) complete set of functions, calculations using such a basis set are said to approach the complete basis set (CBS) limit. In this context, basis function and atomic orbital are sometimes used interchangeably, although the basis functions are usually not true atomic orbitals.

Within the basis set, the wavefunction is represented as a vector, the components of which correspond to coefficients of the basis functions in the linear expansion. In such a basis, one-electron operators correspond to matrices (a.k.a. rank two tensors), whereas two-electron operators are rank four tensors.

When molecular calculations are performed, it is common to use a basis composed of atomic orbitals, centered at each nucleus within the molecule (linear combination of atomic orbitals ansatz). The physically best motivated basis set are Slater-type orbitals (STOs), which are solutions to the Schrödinger equation of hydrogen-like atoms, and decay exponentially far away from the nucleus. It can be shown that the molecular orbitals of Hartree–Fock and density-functional theory also exhibit exponential decay. Furthermore, S-type STOs also satisfy Kato's cusp condition at the nucleus, meaning that they are able to accurately describe electron density near the nucleus. However, hydrogen-like atoms lack many-electron interactions, thus the orbitals do not accurately describe electron state correlations.

Unfortunately, calculating integrals with STOs is computationally difficult and it was later realized by Frank Boys that STOs could be approximated as linear combinations of Gaussian-type orbitals (GTOs) instead. Because the product of two GTOs can be written as a linear combination of GTOs, integrals with Gaussian basis functions can be written in closed form, which leads to huge computational savings (see John Pople).

Dozens of Gaussian-type orbital basis sets have been published in the literature. Basis sets typically come in hierarchies of increasing size, giving a controlled way to obtain more accurate solutions, however at a higher cost.

The smallest basis sets are called minimal basis sets. A minimal basis set is one in which, on each atom in the molecule, a single basis function is used for each orbital in a Hartree–Fock calculation on the free atom. For atoms such as lithium, basis functions of p type are also added to the basis functions that correspond to the 1s and 2s orbitals of the free atom, because lithium also has a 1s2p bound state. For example, each atom in the second period of the periodic system (Li – Ne) would have a basis set of five functions (two s functions and three p functions).

A d-polarization function added to a p orbital

A minimal basis set may already be exact for the gas-phase atom at the self-consistent field level of theory. In the next level, additional functions are added to describe polarization of the electron density of the atom in molecules. These are called polarization functions. For example, while the minimal basis set for hydrogen is one function approximating the 1s atomic orbital, a simple polarized basis set typically has two s- and one p-function (which consists of three basis functions: px, py and pz). This adds flexibility to the basis set, effectively allowing molecular orbitals involving the hydrogen atom to be more asymmetric about the hydrogen nucleus. This is very important for modeling chemical bonding, because the bonds are often polarized. Similarly, d-type functions can be added to a basis set with valence p orbitals, and f-functions to a basis set with d-type orbitals, and so on.

Another common addition to basis sets is the addition of diffuse functions. These are extended Gaussian basis functions with a small exponent, which give flexibility to the "tail" portion of the atomic orbitals, far away from the nucleus. Diffuse basis functions are important for describing anions or dipole moments, but they can also be important for accurate modeling of intra- and inter-molecular bonding.

STO hierarchy

The most common minimal basis set is STO-nG, where n is an integer. The STO-nG basis sets are derived from a minimal Slater-type orbital basis set, with n representing the number of Gaussian primitive functions used to represent each Slater-type orbital. Minimal basis sets typically give rough results that are insufficient for research-quality publication, but are much cheaper than their larger counterparts. Commonly used minimal basis sets of this type are:

• STO-3G
• STO-4G
• STO-6G
• STO-3G* – Polarized version of STO-3G

There are several other minimum basis sets that have been used such as the MidiX basis sets.

Split-valence basis sets

During most molecular bonding, it is the valence electrons which principally take part in the bonding. In recognition of this fact, it is common to represent valence orbitals by more than one basis function (each of which can in turn be composed of a fixed linear combination of primitive Gaussian functions). Basis sets in which there are multiple basis functions corresponding to each valence atomic orbital are called valence double, triple, quadruple-zeta, and so on, basis sets (zeta, ζ, was commonly used to represent the exponent of an STO basis function). Since the different orbitals of the split have different spatial extents, the combination allows the electron density to adjust its spatial extent appropriate to the particular molecular environment. In contrast, minimal basis sets lack the flexibility to adjust to different molecular environments.

Pople basis sets

The notation for the split-valence basis sets arising from the group of John Pople is typically X-YZg. In this case, X represents the number of primitive Gaussians comprising each core atomic orbital basis function. The Y and Z indicate that the valence orbitals are composed of two basis functions each, the first one composed of a linear combination of Y primitive Gaussian functions, the other composed of a linear combination of Z primitive Gaussian functions. In this case, the presence of two numbers after the hyphens implies that this basis set is a split-valence double-zeta basis set. Split-valence triple- and quadruple-zeta basis sets are also used, denoted as X-YZWg, X-YZWVg, etc.

Polarization functions are denoted by two different notations. The original Pople notation added "*" to indicate that all "heavy" atoms (everything but H and He) have a small set of polarization functions added to the basis (in the case of carbon, a set of 3d orbital functions). The "**" notation indicates that all "light" atoms also receive polarization functions (this adds a set of 2p orbitals to the basis for each hydrogen atom). Eventually it became desirable to add more polarization to the basis sets, and a new notation was developed in which the number and types of polarization functions are given explicitly in parentheses in the order (heavy,light) but with the principal quantum numbers of the orbitals implicit. For example, the * notation becomes (d) and the ** notation is now given as (d,p). If instead 3d and 4f functions were added to each heavy atom and 2p, 3p, 3d functions were added to each light atom, the notation would become (df,2pd).

In all cases, diffuse functions are indicated by either adding a + before the letter G (diffuse functions on heavy atoms only) or ++ (diffuse functions are added to all atoms).

Here is a list of commonly used split-valence basis sets of this type:

• 3-21G
• 3-21G* – Polarization functions on heavy atoms
• 3-21G** – Polarization functions on heavy atoms and hydrogen
• 3-21+G – Diffuse functions on heavy atoms
• 3-21++G – Diffuse functions on heavy atoms and hydrogen
• 3-21+G* – Polarization and diffuse functions on heavy atoms only
• 3-21+G** – Polarization functions on heavy atoms and hydrogen, as well as diffuse functions on heavy atoms
• 4-21G
• 4-31G
• 6-21G
• 6-31G
• 6-31G*
• 6-31+G*
• 6-31G(3df,3pd) – 3 sets of d functions and 1 set of f functions on heavy atoms and 3 sets of p functions and 1 set of d functions on hydrogen
• 6-311G
• 6-311G*
• 6-311+G*
• 6-311+G(2df,2p)

In summary; the 6-31G* basis set (defined for the atoms H through Zn) is a split-valence double-zeta polarized basis set that adds to the 6-31G set five d-type Cartesian-Gaussian polarization functions on each of the atoms Li through Ca and ten f-type Cartesian Gaussian polarization functions on each of the atoms Sc through Zn.

The Pople basis sets were originally developed for use in Hartree-Fock calculations. Since then, correlation-consistent or polarization-consistent basis sets (see below) have been developed which are usually more appropriate for correlated wave function calculations. For Hartree–Fock or density functional theory, however, Pople basis sets are more efficient (per unit basis function) as compared to other alternatives, provided that the electronic structure program can take advantage of combined sp shells, and are still widely used for molecular structure determination of large molecules and as components of quantum chemistry composite methods.

Correlation-consistent basis sets

Some of the most widely used basis sets are those developed by Dunning and coworkers, since they are designed for converging post-Hartree–Fock calculations systematically to the complete basis set limit using empirical extrapolation techniques.

For first- and second-row atoms, the basis sets are cc-pVNZ where N = D,T,Q,5,6,... (D = double, T = triple, etc.). The 'cc-p', stands for 'correlation-consistent polarized' and the 'V' indicates that only basis sets for the valence orbitals are of multiple-zeta quality. (Like the Pople basis sets, the core orbitals are of single-zeta quality.) They include successively larger shells of polarization (correlating) functions (d, f, g, etc.). More recently these 'correlation-consistent polarized' basis sets have become widely used and are the current state of the art for correlated or post-Hartree–Fock calculations. The aug- prefix is added if diffuse functions are included in the basis. Examples of these are:

• cc-pVDZ – Double-zeta
• cc-pVTZ – Triple-zeta
• cc-pVQZ – Quadruple-zeta
• cc-pV5Z – Quintuple-zeta, etc.
• aug-cc-pVDZ, etc. – Augmented versions of the preceding basis sets with added diffuse functions.
• cc-pCVDZ – Double-zeta with core correlation

For period-3 atoms (Al–Ar), additional functions have turned out to be necessary; these are the cc-pV(N+d)Z basis sets. Even larger atoms may employ pseudopotential basis sets, cc-pVNZ-PP, or relativistic-contracted Douglas-Kroll basis sets, cc-pVNZ-DK.

While the usual Dunning basis sets are for valence-only calculations, the sets can be augmented with further functions that describe core electron correlation. These core-valence sets (cc-pCVXZ) can be used to approach the exact solution to the all-electron problem, and they are necessary for accurate geometric and nuclear property calculations.

Weighted core-valence sets (cc-pwCVXZ) have also been recently suggested. The weighted sets aim to capture core-valence correlation, while neglecting most of core-core correlation, in order to yield accurate geometries with smaller cost than the cc-pCVXZ sets.

Diffuse functions can also be added for describing anions and long-range interactions such as Van der Waals forces, or to perform electronic excited-state calculations, electric field property calculations. A recipe for constructing additional augmented functions exists; as many as five augmented functions have been used in second hyperpolarizability calculations in the literature. Because of the rigorous construction of these basis sets, extrapolation can be done for almost any energetic property. However, care must be taken when extrapolating energy differences as the individual energy components converge at different rates: the Hartree–Fock energy converges exponentially, whereas the correlation energy converges only polynomially.

	H-He	Li-Ne	Na-Ar
cc-pVDZ	[2s1p] → 5 func.	[3s2p1d] → 14 func.	[4s3p1d] → 18 func.
cc-pVTZ	[3s2p1d] → 14 func.	[4s3p2d1f] → 30 func.	[5s4p2d1f] → 34 func.
cc-pVQZ	[4s3p2d1f] → 30 func.	[5s4p3d2f1g] → 55 func.	[6s5p3d2f1g] → 59 func.
aug-cc-pVDZ	[3s2p] → 9 func.	[4s3p2d] → 23 func.	[5s4p2d] → 27 func.
aug-cc-pVTZ	[4s3p2d] → 23 func.	[5s4p3d2f] → 46 func.	[6s5p3d2f] → 50 func.
aug-cc-pVQZ	[5s4p3d2f] → 46 func.	[6s5p4d3f2g] → 80 func.	[7s6p4d3f2g] → 84 func.

To understand how to get the number of functions, consider the cc-pVDZ basis set for H: There are two s (L = 0) orbitals and one p (L = 1) orbital that has 3 components along the z-axis (m_L = −1,0,1) corresponding to p_x, p_y and p_z. Thus, there are five spatial orbitals in total. Note that each orbital can hold two electrons of opposite spin.

As another example, Ar [1s, 2s, 2p, 3s, 3p] has 3 s orbitals (L = 0) and 2 sets of p orbitals (L = 1). Using cc-pVDZ, orbitals are [1s, 2s, 2p, 3s, 3s, 3p, 3p, 3d'] (where ' represents the added in polarisation orbitals), with 4 s orbitals (4 basis functions), 3 sets of p orbitals (3 × 3 = 9 basis functions), and 1 set of d orbitals (5 basis functions). Adding up the basis functions gives a total of 18 functions for Ar with the cc-pVDZ basis-set.

Polarization-consistent basis sets

Density-functional theory has recently become widely used in computational chemistry. However, the correlation-consistent basis sets described above are suboptimal for density-functional theory, because the correlation-consistent sets have been designed for post-Hartree–Fock, while density-functional theory exhibits much more rapid basis set convergence than wave function methods.

Adopting a similar methodology to the correlation-consistent series, Frank Jensen introduced polarization-consistent (pc-n) basis sets as a way to quickly converge density functional theory calculations to the complete basis set limit. Like the Dunning sets, the pc-n sets can be combined with basis set extrapolation techniques to obtain CBS values.

The pc-n sets can be augmented with diffuse functions to obtain augpc-n sets.

Karlsruhe basis sets

Some of the various valence adaptations of Karlsruhe basis sets are briefly described below.

• def2-SV(P) – Split valence with polarization functions on heavy atoms (not hydrogen)
• def2-SVP – Split valence polarization
• def2-SVPD – Split valence polarization with diffuse functions
• def2-TZVP – Valence triple-zeta polarization
• def2-TZVPD – Valence triple-zeta polarization with diffuse functions
• def2-TZVPP – Valence triple-zeta with two sets of polarization functions
• def2-TZVPPD – Valence triple-zeta with two sets of polarization functions and a set of diffuse functions
• def2-QZVP – Valence quadruple-zeta polarization
• def2-QZVPD – Valence quadruple-zeta polarization with diffuse functions
• def2-QZVPP – Valence quadruple-zeta with two sets of polarization functions
• def2-QZVPPD – Valence quadruple-zeta with two sets of polarization functions and a set of diffuse functions

Completeness-optimized basis sets

Gaussian-type orbital basis sets are typically optimized to reproduce the lowest possible energy for the systems used to train the basis set. However, the convergence of the energy does not imply convergence of other properties, such as nuclear magnetic shieldings, the dipole moment, or the electron momentum density, which probe different aspects of the electronic wave function.

Manninen and Vaara have proposed completeness-optimized basis sets, where the exponents are obtained by maximization of the one-electron completeness profile instead of minimization of the energy. Completeness-optimized basis sets are a way to easily approach the complete basis set limit of any property at any level of theory, and the procedure is simple to automatize.

Completeness-optimized basis sets are tailored to a specific property. This way, the flexibility of the basis set can be focused on the computational demands of the chosen property, typically yielding much faster convergence to the complete basis set limit than is achievable with energy-optimized basis sets.

Even-tempered basis sets

s-type Gaussian functions using six different exponent values obtained from an even-tempered scheme starting with α = 0.1 and β = sqrt(10). Plot generated with Gnuplot.

In 1974 Bardo and Ruedenberg  proposed a simple scheme to generate the exponents of a basis set that spans the Hilbert space evenly  by following a geometric progression of the form: $${\displaystyle {\alpha }_{i,l}={\alpha }_l{\beta }_l^{i-1},{\alpha }_l,{\beta }_l>0,{\beta }_l\ne 1i=1,2,\dots ,N_l}$$ for each angular momentum ${\displaystyle l}$, where ${\displaystyle N_l}$ is the number of primitives functions. Here, only the two parameters ${\displaystyle {\alpha }_l}$ and ${\displaystyle {\beta }_l}$ must be optimized, significantly reducing the dimension of the search space or even avoiding the exponent optimization problem. In order to properly describe electronic delocalized states, a previously optimized standard basis set can be complemented with additional delocalized Gaussian functions with small exponent values, generated by the even-tempered scheme. This approach has also been employed to generate basis sets for other types of quantum particles rather than electrons, like quantum nuclei, negative muons or positrons.

Plane-wave basis sets

In addition to localized basis sets, plane-wave basis sets can also be used in quantum-chemical simulations. Typically, the choice of the plane wave basis set is based on a cutoff energy. The plane waves in the simulation cell that fit below the energy criterion are then included in the calculation. These basis sets are popular in calculations involving three-dimensional periodic boundary conditions.

The main advantage of a plane-wave basis is that it is guaranteed to converge in a smooth, monotonic manner to the target wavefunction. In contrast, when localized basis sets are used, monotonic convergence to the basis set limit may be difficult due to problems with over-completeness: in a large basis set, functions on different atoms start to look alike, and many eigenvalues of the overlap matrix approach zero.

In addition, certain integrals and operations are much easier to program and carry out with plane-wave basis functions than with their localized counterparts. For example, the kinetic energy operator is diagonal in the reciprocal space. Integrals over real-space operators can be efficiently carried out using fast Fourier transforms. The properties of the Fourier Transform allow a vector representing the gradient of the total energy with respect to the plane-wave coefficients to be calculated with a computational effort that scales as NPW*ln(NPW) where NPW is the number of plane-waves. When this property is combined with separable pseudopotentials of the Kleinman-Bylander type and pre-conditioned conjugate gradient solution techniques, the dynamic simulation of periodic problems containing hundreds of atoms becomes possible.

In practice, plane-wave basis sets are often used in combination with an 'effective core potential' or pseudopotential, so that the plane waves are only used to describe the valence charge density. This is because core electrons tend to be concentrated very close to the atomic nuclei, resulting in large wavefunction and density gradients near the nuclei which are not easily described by a plane-wave basis set unless a very high energy cutoff, and therefore small wavelength, is used. This combined method of a plane-wave basis set with a core pseudopotential is often abbreviated as a PSPW calculation.

Furthermore, as all functions in the basis are mutually orthogonal and are not associated with any particular atom, plane-wave basis sets do not exhibit basis-set superposition error. However, the plane-wave basis set is dependent on the size of the simulation cell, complicating cell size optimization.

Due to the assumption of periodic boundary conditions, plane-wave basis sets are less well suited to gas-phase calculations than localized basis sets. Large regions of vacuum need to be added on all sides of the gas-phase molecule in order to avoid interactions with the molecule and its periodic copies. However, the plane waves use a similar accuracy to describe the vacuum region as the region where the molecule is, meaning that obtaining the truly noninteracting limit may be computationally costly.

Linearized augmented-plane-wave basis sets

A combination of some of the properties of localized basis sets and plane-wave approaches is achieved by linearized augmented-plane-wave (LAPW) basis sets. These are based on a partitioning of space into nonoverlapping spheres around each atom and an interstitial region in between the spheres. An LAPW basis function is a plane wave in the interstitial region, which is augmented by numerical atomic functions in each sphere. The numerical atomic functions hereby provide a linearized representation of wave functions for arbitrary energies around automatically determined energy parameters.

Similarly to plane-wave basis sets an LAPW basis set is mainly determined by a cutoff parameter for the plane-wave representation in the interstitial region. In the spheres the variational degrees of freedom can be extended by adding local orbitals to the basis set. This allows representations of wavefunctions beyond the linearized description.

The plane waves in the interstitial region imply three-dimensional periodic boundary conditions, though it is possible to introduce additional augmentation regions to reduce this to one or two dimensions, e.g., for the description of chain-like structures or thin films. The atomic-like representation in the spheres allows to treat each atom with its potential singularity at the nucleus and to not rely on a pseudopotential approximation.

The disadvantage of LAPW basis sets is its complex definition, which comes with many parameters that have to be controlled either by the user or an automatic recipe. Another consequence of the form of the basis set are complex mathematical expressions, e.g., for the calculation of a Hamiltonian matrix or atomic forces.

Real-space basis sets

Real-space approaches offer powerful methods to solve electronic structure problems thanks to their controllable accuracy. Real-space basis sets can be thought to arise from the theory of interpolation, as the central idea is to represent the (unknown) orbitals in terms of some set of interpolation functions.

Various methods have been proposed for constructing the solution in real space, including finite elements, basis splines, Lagrange sinc-functions, and wavelets. Finite difference algorithms are also often included in this category, even though precisely speaking, they do not form a proper basis set and are not variational unlike e.g. finite element methods.

A common feature of all real-space methods is that the accuracy of the numerical basis set is improvable, so that the complete basis set limit can be reached in a systematical manner. Moreover, in the case of wavelets and finite elements, it is easy to use different levels of accuracy in different parts of the system, so that more points are used close to the nuclei where the wave function undergoes rapid changes and where most of the total energies lie, whereas a coarser representation is sufficient far away from nuclei; this feature is extremely important as it can be used to make all-electron calculations tractable.

For example, in finite element methods (FEMs), the wave function is represented as a linear combination of a set of piecewise polynomials. Lagrange interpolating polynomials (LIPs) are a commonly used basis for FEM calculations. The local interpolation error in LIP basis of order ${\displaystyle n}$ is of the form ${\displaystyle h^{n+1}max{f}^{(n+1)}(\xi )}$. The complete basis set can thereby be reached either by going to smaller and smaller elements (i.e. dividing space in smaller and smaller subdivisions; ${\displaystyle h}$-adaptive FEM), by switching to the use of higher and higher order polynomials (${\displaystyle p}$-adaptive FEM), or by a combination of both strategies (${\displaystyle hp}$-adaptive FEM). The use of high-order LIPs has been shown to be highly beneficial for accuracy.

Gland

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Gland 

Gland
Human submandibular gland. At the right is a group of mucous acini, at the left a group of serous acini.

A gland is a cell or an organ in an animal's body that produces and secretes different substances that the organism needs, either into the bloodstream or into a body cavity or outer surface. A gland may also function to remove unwanted substances such as urine from the body.

There are two types of gland, each with a different method of secretion. Endocrine glands are ductless and secrete their products, hormones, directly into interstitial spaces to be taken up into the bloodstream. Exocrine glands secrete their products through a duct into a body cavity or outer surface.

Glands are mostly composed of epithelial tissue, and typically have a supporting framework of connective tissue, and a capsule.

Structure

See also: List of glands of the human body

Development

This image shows some of the various possible glandular arrangements. These are the simple tubular, simple branched tubular, simple coiled tubular, simple acinar, and simple branched acinar glands.

This image shows some of the various possible glandular arrangements. These are the compound tubular, compound acinar, and compound tubulo-acinar glands.

Every gland is formed by an ingrowth from an epithelial surface. This ingrowth may in the beginning possess a tubular structure, but in other instances glands may start as a solid column of cells which subsequently becomes tubulated.

As growth proceeds, the column of cells may split or give off offshoots, in which case a compound gland is formed. In many glands, the number of branches is limited, in others (salivary, pancreas) a very large structure is finally formed by repeated growth and sub-division. As a rule, the branches do not unite with one another. One exception to this rule is the liver; this occurs when a reticulated compound gland is produced. In compound glands the more typical or secretory epithelium is found forming the terminal portion of each branch, and the uniting portions form ducts and are lined with a less modified type of epithelial cell.

Glands are classified according to their shape.

• If the gland retains its shape as a tube throughout it is termed a tubular gland.
• In the second main variety of gland the secretory portion is enlarged and the lumens variously increased in size. These are termed alveolar or saccular glands.

Types of glands

Glands are divided based on their function into two groups:

This diagram shows the differences between endocrine and exocrine glands. The major difference is that exocrine glands secrete substances out of the body and endocrine glands secrete substances into capillaries and blood vessels.

Endocrine glands

Main article: Endocrine gland

Endocrine glands secrete substances that circulate through the bloodstream. The glands secrete their products through basal lamina into the bloodstream. Basal lamina typically can be seen as a layer around the glands to which more than a million tiny blood vessels are attached. These glands often secrete hormones which play an important role in maintaining homeostasis. The pineal gland, thymus gland, pituitary gland, thyroid gland, and the two adrenal glands are all endocrine glands.

Exocrine glands

Main article: Exocrine gland

Exocrine glands secrete their products through a duct onto an outer or inner surface of the body, such as the skin or the gastrointestinal tract. Secretion is directly onto the apical surface. The glands in this group can be divided into three groups:

• Merocrine glands – cells secrete their substances by exocytosis. (e.g. mucous and serous glands; also called "eccrine", e.g. major sweat glands of humans, goblet cells, salivary gland, tear gland and intestinal glands)
• Apocrine glands – a portion of the secreting cell's body is lost during secretion. The term Apocrine gland is often used to refer to the apocrine sweat glands, however it is thought that apocrine sweat glands may not be true apocrine glands as they may not use the apocrine method of secretion. (e.g. mammary gland, sweat gland of arm pit, pubic region, skin around anus, lips and nipples)
• Holocrine glands – the entire cell disintegrates to secrete its substances. (e.g. sebaceous glands: meibomian and zeis glands)

Exocrine glands can further be categorized by their product:

• Serous glands secrete a watery, often protein-rich, fluid-like product, e.g. sweat glands.
• Mucous glands secrete a viscous product, rich in carbohydrates (such as glycoproteins), e.g. goblet cells.
• Sebaceous glands secrete a lipid product. These glands are also known as oil glands, e.g. Fordyce spots and meibomian glands.

Encephalization quotient

From Wikipedia, the free encyclopedia

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

Encephalization quotient (EQ), encephalization level (EL), or just encephalization is a relative brain size measure that is defined as the ratio between observed and predicted brain mass for an animal of a given size, based on nonlinear regression on a range of reference species. It has been used as a proxy for intelligence and thus as a possible way of comparing the intelligence levels of different species. For this purpose, it is a more refined measurement than the raw brain-to-body mass ratio, as it takes into account allometric effects. Expressed as a formula, the relationship has been developed for mammals and may not yield relevant results when applied outside this group.

Perspective on intelligence measures

Encephalization quotient was developed in an attempt to provide a way of correlating an animal's physical characteristics with perceived intelligence. It improved on the previous attempt, brain-to-body mass ratio, so it has persisted. Subsequent work, notably Roth, found EQ to be flawed and suggested brain size was a better predictor, but that has problems as well.

Currently the best predictor for intelligence across all animals is forebrain neuron count. This was not seen earlier because neuron counts were previously inaccurate for most animals. For example, human brain neuron count was given as 100 billion for decades before Herculano-Houzel found a more reliable method of counting brain cells.

It could have been anticipated that EQ might be superseded because of both the number of exceptions and the growing complexity of the formulae it used. (See the rest of this article.) The simplicity of counting neurons has replaced it. The concept in EQ of comparing the brain capacity exceeding that required for body sense and motor activity may yet live on to provide an even better prediction of intelligence, but that work has not been done yet.

Variance in brain sizes

Body size accounts for 80–90% of the variance in brain size, between species, and a relationship described by an allometric equation: the regression of the logarithms of brain size on body size. The distance of a species from the regression line is a measure of its encephalization. The scales are logarithmic, distance, or residual, is an encephalization quotient (EQ), the ratio of actual brain size to expected brain size. Encephalization is a characteristic of a species.

Rules for brain size relates to the number brain neurons have varied in evolution, then not all mammalian brains are necessarily built as larger or smaller versions of a same plan, with proportionately larger or smaller numbers of neurons. Similarly sized brains, such as a cow or chimpanzee, might in that scenario contain very different numbers of neurons, just as a very large cetacean brain might contain fewer neurons than a gorilla brain. Size comparison between the human brain and non-primate brains, larger or smaller, might simply be inadequate and uninformative – and our view of the human brain as outlier, a special oddity, may have been based on the mistaken assumption that all brains are made the same (Herculano-Houzel, 2012).

Limitations and possible improvements over EQ

There is a distinction between brain parts that are necessary for the maintenance of the body and those that are associated with improved cognitive functions. These brain parts, although functionally different, all contribute to the overall weight of the brain. Jerison (1973) has for this reason considered 'extra neurons', neurons that contribute strictly to cognitive capacities, as more important indicators of intelligence than pure EQ. Gibson et al. (2001) reasoned that bigger brains generally contain more 'extra neurons' and thus are better predictors of cognitive abilities than pure EQ among primates.

Factors such as the recent evolution of the cerebral cortex and different degrees of brain folding (gyrification), which increases the surface area (and volume) of the cortex, are positively correlated to intelligence in humans.

In a meta-analysis, Deaner et al. (2007) tested absolute brain size (ABS), cortex size, cortex-to-brain ratio, EQ, and corrected relative brain size (cRBS) against global cognitive capacities. They have found that, after normalization, only ABS and neocortex size showed significant correlation to cognitive abilities. In primates, ABS, neocortex size, and Nc (the number of cortical neurons) correlated fairly well with cognitive abilities. However, there were inconsistencies found for Nc. According to the authors, these inconsistencies were the result of the faulty assumption that Nc increases linearly with the size of the cortical surface. This notion is incorrect because the assumption does not take into account the variability in cortical thickness and cortical neuron density, which should influence Nc.

According to Cairo (2011), EQ has flaws to its design when considering individual data points rather than a species as a whole. It is inherently biased given that the cranial volume of an obese and underweight individual would be roughly similar, but their body masses would be drastically different. Another difference of this nature is a lack of accounting for sexual dimorphism. For example, the female human generally has smaller cranial volume than the male; however, this does not mean that a female and male of the same body mass would have different cognitive abilities. Considering all of these flaws, EQ should not be viewed as a valid metric for intraspecies comparison.

The notion that encephalization quotient corresponds to intelligence has been disputed by Roth and Dicke (2012). They consider the absolute number of cortical neurons and neural connections as better correlates of cognitive ability. According to Roth and Dicke (2012), mammals with relatively high cortex volume and neuron packing density (NPD) are more intelligent than mammals with the same brain size. The human brain stands out from the rest of the mammalian and vertebrate taxa because of its large cortical volume and high NPD, conduction velocity, and cortical parcellation. All aspects of human intelligence are found, at least in its primitive form, in other nonhuman primates, mammals, or vertebrates, with the exception of syntactical language. Roth and Dicke consider syntactical language an "intelligence amplifier".

Brain-body size relationship

Species	Simple brain-to-body ratio (E/S)
Treeshrew	1/10
Small birds	1/12
Human	1/40
Mouse	1/40
Dolphin	1/50
Cat	1/100
Chimpanzee	1/113
Dog	1/125
Frog	1/172
Lion	1/550
Elephant	1/560
Horse	1/600
Shark	1/2496
Hippopotamus	1/2789

Brain size usually increases with body size in animals (is positively correlated), i.e. large animals usually have larger brains than smaller animals. The relationship is not linear, however. Generally, small mammals have relatively larger brains than big ones. Mice have a direct brain/body size ratio similar to humans (1/40), while elephants have a comparatively small brain/body size (1/560), despite being quite intelligent animals. Treeshrews have a brain/body mass ratio of (1/10).

Several reasons for this trend are possible, one of which is that neural cells have a relative constant size. Some brain functions, like the brain pathway responsible for a basic task like drawing breath, are basically similar in a mouse and an elephant. Thus, the same amount of brain matter can govern breathing in a large or a small body. While not all control functions are independent of body size, some are, and hence large animals need comparatively less brain than small animals. This phenomenon can be described by an equation ${\displaystyle C=E/S^{2/3},}$ where ${\displaystyle E}$ and ${\displaystyle S}$ are brain and body weights respectively, and ${\displaystyle C}$ is called the cephalization factor. To determine the value of this factor, the brain and body weights of various mammals were plotted against each other, and the curve of such formula chosen as the best fit to that data.

The cephalization factor and the subsequent encephalization quotient was developed by H. J. Jerison in the late 1960s. The formula for the curve varies, but an empirical fitting of the formula to a sample of mammals gives $${\displaystyle \frac{w(\text{brain})}{1\text{g}}=0.12{\left(\frac{w(\text{body})}{1\text{g}}\right)}^{\frac{2}{3}}=12{\left(\frac{w(\text{body})}{1\text{kg}}\right)}^{\frac{2}{3}}.}$$ As this formula is based on data from mammals, it should be applied to other animals with caution. For some of the other vertebrate classes the power of 3/4 rather than 2/3 is sometimes used, and for many groups of invertebrates the formula may give no meaningful results at all.

Calculation

Snell's equation of simple allometry is

${\displaystyle E=C{S}^r,}$

were ${\displaystyle E}$ is the weight of the brain, ${\displaystyle C}$ is the cephalization factor, ${\displaystyle S}$ is body weight, and ${\displaystyle r}$ is the exponential constant.

The "encephalization quotient" (EQ) is the coefficient ${\displaystyle C}$ in Snell's allometry equation, usually normalized with respect to a reference species. In the following table, the coefficients have been normalized with respect to the value for the cat, which is therefore attributed an EQ of 1.

Another way to calculate encephalization quotient is by dividing the actual weight of an animal's brain with its predicted weight according to Jerison's formula.

Species	Encephalization quotient (EQ)
Human	7.4–7.8
Northern right whale dolphin	5.55
Bottlenose dolphin	5.26
Orca	2.57–3.3
Chimpanzee	2.2–2.5
Raven	2.49
Domestic Pig (newborn)	2.42
Rhesus macaque	2.1
Red fox	1.92
Elephant	1.75–2.36
Raccoon	1.62
Gorilla	1.39
California sea lion	1.39
Chinchilla	1.34
Dog	1.2
Squirrel	1.1
Cat	1.00
Hyena	0.92
Horse	0.92
Elephant shrew	0.82
Brown bear	0.82
Sheep	0.8
Taurine cattle	0.52–0.59
Mouse	0.5
Rat	0.4
Rabbit	0.4
Domestic Pig (adult)	0.38
Hippopotamus	0.37
Opossum	0.2

This measurement of approximate intelligence is more accurate for mammals than for other classes and phyla of Animalia.

EQ and intelligence in mammals

Intelligence in animals is hard to establish, but the larger the brain is relative to the body, the more brain weight might be available for more complex cognitive tasks. The EQ formula, as opposed to the method of simply measuring raw brain weight or brain weight to body weight, makes for a ranking of animals that coincides better with observed complexity of behaviour. A primary reason for the use of EQ instead of a simple brain to body mass ratio is that smaller animals tend to have a higher proportional brain mass, but do not show the same indications of higher cognition as animals with a high EQ.

Grey floor

The driving theorization behind the development of EQ is that an animal of a certain size requires a minimum number of neurons for basic functioning, sometimes referred to as a grey floor. There is also a limit to how large an animal's brain can grow given its body size – due to limitations like gestation period, energetics, and the need to physically support the encephalized region throughout maturation. When normalizing a standard brain size for a group of animals, a slope can be determined to show what a species' expected brain to body mass ratio would be. Species with brain to body mass ratios below this standard are nearing the grey floor, and do not need extra grey matter. Species which fall above this standard have more grey matter than is necessary for basic functions. Presumably these extra neurons are used for higher cognitive processes.

Taxonomic trends

Mean EQ for mammals is around 1, with carnivorans, cetaceans and primates above 1, and insectivores and herbivores below. Large mammals tend to have the highest EQs of all animals, while small mammals and avians have similar EQs. This reflects two major trends. One is that brain matter is extremely costly in terms of energy needed to sustain it. Animals with nutrient rich diets tend to have higher EQs, which is necessary for the energetically costly tissue of brain matter. Not only is it metabolically demanding to grow throughout embryonic and postnatal development, it is costly to maintain as well.

Arguments have been made that some carnivores may have higher EQ's due to their relatively enriched diets, as well as the cognitive capacity required for effectively hunting prey. One example of this is brain size of a wolf; about 30% larger than a similarly sized domestic dog, potentially derivative of different needs in their respective way of life.

Dietary trends

Of the animals demonstrating the highest EQ's (see associated table), many are primarily frugivores, including apes, macaques, and proboscideans. This dietary categorization is significant to inferring the pressures which drive higher EQ's. Specifically, frugivores must utilize a complex, trichromatic map of visual space to locate and pick ripe fruits and are able to provide for the high energetic demands of increased brain mass.

Trophic level—"height" on the food chain—is yet another factor that has been correlated with EQ in mammals. Eutheria with either high AB (absolute brain-mass) or high EQ occupy positions at high trophic levels. Eutheria low on the network of food chains can only develop a high RB (relative brain-mass) so long as they have small body masses. This presents an interesting conundrum for intelligent small animals, who have behaviors radically different from intelligent large animals.

According to Steinhausen et al.(2016):

Animals with high RB [relative brain-mass] usually have (1) a short life span, (2) reach sexual maturity early, and (3) have short and frequent gestations. Moreover, males of species with high RB also have few potential sexual partners. In contrast, animals with high EQs have (1) a high number of potential sexual partners, (2) delayed sexual maturity, and (3) rare gestations with small litter sizes.

Sociality

Another factor previously thought to have great impact on brain size is sociality and flock size. This was a long-standing theory until the correlation between frugivory and EQ was shown to be more statistically significant. While no longer the predominant inference as to selection pressure for high EQ, the social brain hypothesis still has some support. For example, dogs (a social species) have a higher EQ than cats (a mostly solitary species). Animals with very large flock size and/or complex social systems consistently score high EQ, with dolphins and orcas having the highest EQ of all cetaceans, and humans with their extremely large societies and complex social life topping the list by a good margin.

Comparisons with non-mammalian animals

Birds generally have lower EQ than mammals, but parrots and particularly the corvids show remarkable complex behaviour and high learning ability. Their brains are at the high end of the bird spectrum, but low compared to mammals. Bird cell size is on the other hand generally smaller than that of mammals, which may mean more brain cells and hence synapses per volume, allowing for more complex behaviour from a smaller brain. Both bird intelligence and brain anatomy are however very different from those of mammals, making direct comparison difficult.

Manta rays have the highest EQ among fish, and either octopuses or jumping spiders have the highest among invertebrates. Despite the jumping spider having a huge brain for its size, it is minuscule in absolute terms, and humans have a much higher EQ despite having a lower raw brain-to-body weight ratio. Mean EQs for reptiles are about one tenth of those of mammals. EQ in birds (and estimated EQ in other dinosaurs) generally also falls below that of mammals, possibly due to lower thermoregulation and/or motor control demands. Estimation of brain size in Archaeopteryx (one of the oldest known ancestors of birds), shows it had an EQ well above the reptilian range, and just below that of living birds.

Biologist Stephen Jay Gould has noted that if one looks at vertebrates with very low encephalization quotients, their brains are slightly less massive than their spinal cords. Theoretically, intelligence might correlate with the absolute amount of brain an animal has after subtracting the weight of the spinal cord from the brain. This formula is useless for invertebrates because they do not have spinal cords or, in some cases, central nervous systems.

EQ in paleoneurology

Behavioral complexity in living animals can to some degree be observed directly, making the predictive power of the encephalization quotient less relevant. It is however central in paleoneurology, where the endocast of the brain cavity and estimated body weight of an animal is all one has to work from. The behavior of extinct mammals and dinosaurs is typically investigated using EQ formulas.

Encephalization quotient is also used in estimating evolution of intelligent behavior in human ancestors. This technique can help in mapping the development of behavioral complexities during human evolution. However, this technique is only limited to when there are both cranial and post-cranial remains associated with individual fossils, to allow for brain to body size comparisons. For example, remains of one Middle Pleistocene human fossil from Jinniushan province in northern China has allowed scientists to study the relationship between brain and body size using the Encephalization Quotient. Researchers obtained an EQ of 4.150 for the Jinniushan fossil, and then compared this value with preceding Middle Pleistocene estimates of EQ at 3.7770. The difference in EQ estimates has been associated with a rapid increase in encephalization in Middle Pleistocene hominins. Paleo-neurological comparisons between Neanderthals and anatomically modern Homo sapiens (AMHS) via Encephalization quotient often rely on the use of endocasts, but this method has many drawbacks. For example, endocasts do not provide any information regarding the internal organization of the brain. Furthermore, endocasts are often unclear in terms of the preservation of their boundaries, and it becomes hard to measure where exactly a certain structure starts and ends. If endocasts themselves are not reliable, then the value for brain size used to calculate the EQ could also be unreliable. Additionally, previous studies have suggested that Neanderthals have the same encephalization quotient as modern humans, although their post-crania suggests that they weighed more than modern humans. Because EQ relies on values from both postcrania and crania, the margin for error increases in relying on this proxy in paleo-neurology because of the inherent difficulty in obtaining accurate brain and body mass measurements from the fossil record.

EQ of livestock animals

The EQ of livestock farm animals such as the domestic pig may be significantly lower than would suggest for their apparent intelligence. According to Minervini et al (2016) the brain of the domestic pig is a rather small size compared to the mass of the animal. The tremendous increase in body weight imposed by industrial farming significantly influences brain-to-body weight measures, including the EQ. The EQ of the domestic adult pig is just 0.38, yet pigs can use visual information seen in a mirror to find food, show evidence of self-recognition when presented with their reflections and there is evidence suggesting that pigs are as socially complex as many other highly intelligent animals, possibly sharing a number of cognitive capacities related to social complexity.

History

The concept of encephalization has been a key evolutionary trend throughout human evolution, and consequently an important area of study. Over the course of hominin evolution, brain size has seen an overall increase from 400 cm³ to 1400 cm³. Furthermore, the genus Homo is specifically defined by a significant increase in brain size. The earliest Homo species were larger in brain size as compared to contemporary Australopithecus counterparts, with which they co-inhabited parts of Eastern and Southern Africa.

Throughout modern history, humans have been fascinated by the large relative size of our brains, trying to connect brain sizes to overall levels of intelligence. Early brain studies were focused in the field of phrenology, which was pioneered by Franz Joseph Gall in 1796 and remained a prevalent discipline throughout the early 19th century. Specifically, phrenologists paid attention to the external morphology of the skull, trying to relate certain lumps to corresponding aspects of personality. They further measured physical brain size in order to equate larger brain sizes to greater levels of intelligence. Today, however, phrenology is considered a pseudoscience.

Among ancient Greek philosophers, Aristotle in particular believed that after the heart, the brain was the second most important organ of the body. He also focused on the size of the human brain, writing in 335 BCE that "of all the animals, man has the brain largest in proportion to his size." In 1861, French neurologist Paul Broca tried to make a connection between brain size and intelligence. Through observational studies, he noticed that people working in what he deemed to be more complex fields had larger brains than people working in less complex fields. Also, in 1871, Charles Darwin wrote in his book The Descent of Man: "No one, I presume, doubts that the large proportion which the size of man's brain bears to his body, compared to the same proportion in the gorilla or orang, is closely connected with his mental powers." The concept of quantifying encephalization is also not a recent phenomenon. In 1889, Sir Francis Galton, through a study on college students, attempted to quantify the relationship between brain size and intelligence.

Due to the Nazi's racial policies before and during World War II, studies on brain size and intelligence temporarily gained a negative reputation, as they resemble the "Ubermensch" school of thought that enable the Holocaust. However, with the rise of neofascism and the advent of imaging techniques such as the fMRI and PET scan, several scientific studies were launched to suggest a relationship between encephalization and advanced cognitive abilities. Harry J. Jerison, who invented the formula for encephalization quotient, believed that brain size was proportional to the ability of humans to process information. With this belief, a higher level of encephalization equated to a higher ability to process information. A larger brain could mean a number of different things, including a larger cerebral cortex, a greater number of neuronal associations, or a greater number of neurons overall.

Epithelium

From Wikipedia, the free encyclopedia

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

Epithelium

Types of epithelium Epithelium or epithelial tissue is a thin, continuous, protective layer of cells with little extracellular matrix. An example is the epidermis, the outermost layer of the skin. Epithelial (mesothelial) tissues line the outer surfaces of many internal organs, the corresponding inner surfaces of body cavities, and the inner surfaces of blood vessels. Epithelial tissue is one of the four basic types of animal tissue, along with connective tissue, muscle tissue and nervous tissue. These tissues also lack blood or lymph supply. The tissue is supplied by nerves.

There are three principal shapes of epithelial cell: squamous (scaly), columnar, and cuboidal. These can be arranged in a singular layer of cells as simple epithelium, either simple squamous, simple columnar, or simple cuboidal, or in layers of two or more cells deep as stratified (layered), or compound, either squamous, columnar or cuboidal. In some tissues, a layer of columnar cells may appear to be stratified due to the placement of the nuclei. This sort of tissue is called pseudostratified. All glands are made up of epithelial cells. Functions of epithelial cells include diffusion, filtration, secretion, selective absorption, germination, and transcellular transport. Compound epithelium has protective functions.

Epithelial layers contain no blood vessels (avascular), so they must receive nourishment via diffusion of substances from the underlying connective tissue, through the basement membrane. Cell junctions are especially abundant in epithelial tissues.

Classification

Simple epithelium

Simple epithelium is a single layer of cells with every cell in direct contact with the basement membrane that separates it from the underlying connective tissue. In general, it is found where absorption and filtration occur. The thinness of the epithelial barrier facilitates these processes.

In general, epithelial tissues are classified by the number of their layers and by the shape and function of the cells. The basic cell types are squamous, cuboidal, and columnar, classed by their shape.

Type	Description
Squamous	Squamous cells have the appearance of thin, flat plates that can look polygonal when viewed from above. Their name comes from squāma, Latin for "scale" – as on fish or snake skin. The cells fit closely together in tissues, providing a smooth, low-friction surface over which fluids can move easily. The shape of the nucleus usually corresponds to the cell form and helps to identify the type of epithelium. Squamous cells tend to have horizontally flattened, nearly oval-shaped nuclei because of the thin, flattened form of the cell. Squamous epithelium is found lining surfaces such as skin or alveoli in the lung, enabling simple passive diffusion as also found in the alveolar epithelium in the lungs. Specialized squamous epithelium also forms the lining of cavities such as in blood vessels (as endothelium), in the pericardium (as mesothelium), and in other body cavities.
Cuboidal	Cuboidal epithelial cells have a cube-like shape and appear square in cross-section. The cell nucleus is large, spherical and is in the center of the cell. Cuboidal epithelium is commonly found in secretive tissue such as the exocrine glands, or in absorptive tissue such as the pancreas, the lining of the kidney tubules as well as in the ducts of the glands. The germinal epithelium that covers the female ovary, and the germinal epithelium that lines the walls of the seminferous tubules in the testes are also of the cuboidal type. Cuboidal cells provide protection and may be active in pumping material in or out of the lumen, or passive depending on their location and specialisation. Simple cuboidal epithelium commonly differentiates to form the secretory and duct portions of glands. Stratified cuboidal epithelium protects areas such as the ducts of sweat glands, mammary glands, and salivary glands.
Columnar	Columnar epithelial cells are elongated and column-shaped and have a height of at least four times their width. Their nuclei are elongated and are usually located near the base of the cells. Columnar epithelium forms the lining of the stomach and intestines. The cells here may possess microvilli for maximizing the surface area for absorption, and these microvilli may form a brush border. Other cells may be ciliated to move mucus in the function of mucociliary clearance. Other ciliated cells are found in the fallopian tubes, the uterus and central canal of the spinal cord. Some columnar cells are specialized for sensory reception such as in the nose, ears and the taste buds. Hair cells in the inner ears have stereocilia which are similar to microvilli. Goblet cells are modified columnar cells and are found between the columnar epithelial cells of the duodenum. They secrete mucus, which acts as a lubricant. Single-layered non-ciliated columnar epithelium tends to indicate an absorptive function. Stratified columnar epithelium is rare but is found in lobar ducts in the salivary glands, the eye, the pharynx, and sex organs. This consists of a layer of cells resting on at least one other layer of epithelial cells, which can be squamous, cuboidal, or columnar.
Pseudostratified	These are simple columnar epithelial cells whose nuclei appear at different heights, giving the misleading (hence "pseudo") impression that the epithelium is stratified when the cells are viewed in cross section. Ciliated pseudostratified epithelial cells have cilia. Cilia are capable of energy-dependent pulsatile beating in a certain direction through interaction of cytoskeletal microtubules and connecting structural proteins and enzymes. In the respiratory tract, the wafting effect produced causes mucus secreted locally by the goblet cells (to lubricate and to trap pathogens and particles) to flow in that direction (typically out of the body). Ciliated epithelium is found in the airways (nose, bronchi), but is also found in the uterus and fallopian tubes, where the cilia propel the ovum to the uterus.

Summary showing different epithelial cells/tissues and their characteristics.

By layer, epithelium is classed as either simple epithelium, only one cell thick (unilayered), or stratified epithelium having two or more cells in thickness, or multi-layered – as stratified squamous epithelium, stratified cuboidal epithelium, and stratified columnar epithelium, and both types of layering can be made up of any of the cell shapes. However, when taller simple columnar epithelial cells are viewed in cross section showing several nuclei appearing at different heights, they can be confused with stratified epithelia. This kind of epithelium is therefore described as pseudostratified columnar epithelium.

Transitional epithelium has cells that can change from squamous to cuboidal, depending on the amount of tension on the epithelium.

Stratified epithelium

Stratified or compound epithelium differs from simple epithelium in that it is multilayered. It is therefore found where body linings have to withstand mechanical or chemical insult such that layers can be abraded and lost without exposing subepithelial layers. Cells flatten as the layers become more apical, though in their most basal layers, the cells can be squamous, cuboidal, or columnar.

Stratified epithelia (of columnar, cuboidal, or squamous type) can have the following specializations:

Specialization	Description
Keratinized	In this particular case, the most apical layers (exterior) of cells are dead and lose their nucleus and cytoplasm, instead contain a tough, resistant protein called keratin. This specialization makes the epithelium somewhat water-resistant, so is found in the mammalian skin. The lining of the oesophagus is an example of a non-keratinized or "moist" stratified epithelium.
Parakeratinized	In this case, the most apical layers of cells are filled with keratin, but they still retain their nuclei. These nuclei are pyknotic, meaning that they are highly condensed. Parakeratinized epithelium is sometimes found in the oral mucosa and in the upper regions of the oesophagus.
Transitional	Transitional epithelia are found in tissues that stretch, and it can appear to be stratified cuboidal when the tissue is relaxed, or stratified squamous when the organ is distended and the tissue stretches. It is sometimes called urothelium since it is almost exclusively found in the bladder, ureters and urethra.

Structure

Epithelial tissue cells can adopt shapes of varying complexity from polyhedral to scutoidal to punakoidal. They are tightly packed and form a continuous sheet with almost no intercellular spaces. All epithelia is usually separated from underlying tissues by an extracellular fibrous basement membrane. The lining of the mouth, lung alveoli and kidney tubules are all made of epithelial tissue. The lining of the blood and lymphatic vessels are of a specialised form of epithelium called endothelium.

Location

Normal histology of the breast, with luminal epithelial cells annotated near bottom right.

See also: Table of epithelia of human organs

Epithelium lines both the outside (skin) and the inside cavities and lumina of bodies. The outermost layer of human skin is composed of dead stratified squamous, keratinized epithelial cells.

Tissues that line the inside of the mouth, the esophagus, the vagina, and part of the rectum are composed of nonkeratinized stratified squamous epithelium. Other surfaces that separate body cavities from the outside environment are lined by simple squamous, columnar, or pseudostratified epithelial cells. Other epithelial cells line the insides of the lungs, the gastrointestinal tract, the reproductive and urinary tracts, and make up the exocrine and endocrine glands. The outer surface of the cornea is covered with fast-growing, easily regenerated epithelial cells. A specialised form of epithelium, endothelium, forms the inner lining of blood vessels and the heart, and is known as vascular endothelium, and lining lymphatic vessels as lymphatic endothelium. Another type, mesothelium, forms the walls of the pericardium, pleurae, and peritoneum.

In arthropods, the integument, or external "skin", consists of a single layer of epithelial ectoderm from which arises the cuticle, an outer covering of chitin, the rigidity of which varies as per its chemical composition.

Basement membrane

The basal surface of epithelial tissue rests on a basement membrane and the free/apical surface faces body fluid or outside. The basement membrane acts as a scaffolding on which epithelium can grow and regenerate after injuries. Epithelial tissue has a nerve supply, but no blood supply and must be nourished by substances diffusing from the blood vessels in the underlying tissue. The basement membrane acts as a selectively permeable membrane that determines which substances will be able to enter the epithelium.

The basal lamina is made up of laminin (glycoproteins) secreted by epithelial cells. The reticular lamina beneath the basal lamina is made up of collagen proteins secreted by connective tissue.

Cell junctions

Cell junctions are especially abundant in epithelial tissues. They consist of protein complexes and provide contact between neighbouring cells, between a cell and the extracellular matrix, or they build up the paracellular barrier of epithelia and control the paracellular transport.

Cell junctions are the contact points between plasma membrane and tissue cells. There are mainly 5 different types of cell junctions: tight junctions, adherens junctions, desmosomes, hemidesmosomes, and gap junctions. Tight junctions are a pair of trans-membrane protein fused on outer plasma membrane. Adherens junctions are a plaque (protein layer on the inside plasma membrane) which attaches both cells' microfilaments. Desmosomes attach to the microfilaments of cytoskeleton made up of keratin protein. Hemidesmosomes resemble desmosomes on a section. They are made up of the integrin (a transmembrane protein) instead of cadherin. They attach the epithelial cell to the basement membrane. Gap junctions connect the cytoplasm of two cells and are made up of proteins called connexins (six of which come together to make a connexion).

Development

Epithelial tissues are derived from all of the embryological germ layers:

• from ectoderm (e.g., the epidermis);
• from endoderm (e.g., the lining of the gastrointestinal tract);
• from mesoderm (e.g., the inner linings of body cavities).

However, pathologists do not consider endothelium and mesothelium (both derived from mesoderm) to be true epithelium. This is because such tissues present very different pathology. For that reason, pathologists label cancers in endothelium and mesothelium sarcomas, whereas true epithelial cancers are called carcinomas. Additionally, the filaments that support these mesoderm-derived tissues are very distinct. Outside of the field of pathology, it is generally accepted that the epithelium arises from all three germ layers.

Cell turnover

Epithelia turn over at some of the fastest rates in the body. For epithelial layers to maintain constant cell numbers essential to their functions, the number of cells that divide must match those that die. They do this mechanically. If there are too few of the cells, the stretch that they experience rapidly activates cell division. Alternatively, when too many cells accumulate, crowding triggers their death by activation epithelial cell extrusion. Here, cells fated for elimination are seamlessly squeezed out by contracting a band of actin and myosin around and below the cell, preventing any gaps from forming that could disrupt their barriers. Failure to do so can result in aggressive tumors and their invasion by aberrant basal cell extrusion.

Functions

Forms of secretion in glandular tissue

Different characteristics of glands of the body

Epithelial tissues have as their primary functions:

1. to protect the tissues that lie beneath from radiation, desiccation, toxins, invasion by pathogens, and physical trauma
2. the regulation and exchange of chemicals between the underlying tissues and a body cavity
3. the secretion of hormones into the circulatory system, as well as the secretion of sweat, mucus, enzymes, and other products that are delivered by ducts
4. to provide sensation
5. Absorb water and digested food in the lining of digestive canal.

Glandular tissue

Glandular tissue is the type of epithelium that forms the glands from the infolding of epithelium and subsequent growth in the underlying connective tissue. They may be specialized columnar or cuboidal tissues consisting of goblet cells, which secrete mucus. There are two major classifications of glands: endocrine glands and exocrine glands:

• Endocrine glands secrete their product into the extracellular space where it is rapidly taken up by the circulatory system.
• Exocrine glands secrete their products into a duct that then delivers the product to the lumen of an organ or onto the free surface of the epithelium. Their secretions include tears, saliva, oil (sebum), enzyme, digestive juices, sweat, etc.

Sensing the extracellular environment

Some epithelial cells are ciliated, especially in respiratory epithelium, and they commonly exist as a sheet of polarised cells forming a tube or tubule with cilia projecting into the lumen." Primary cilia on epithelial cells provide chemosensation, thermoception, and mechanosensation of the extracellular environment by playing "a sensory role mediating specific signalling cues, including soluble factors in the external cell environment, a secretory role in which a soluble protein is released to have an effect downstream of the fluid flow, and mediation of fluid flow if the cilia are motile.

Host immune response

Epithelial cells express many genes that encode immune mediators and proteins involved in cell-cell communication with hematopoietic immune cells. The resulting immune functions of these non-hematopoietic, structural cells contribute to the mammalian immune system ("structural immunity"). Relevant aspects of the epithelial cell response to infections are encoded in the epigenome of these cells, which enables a rapid response to immunological challenges.

Clinical significance

Epithelial cell infected with Chlamydia pneumoniae

The slide shows at (1) an epithelial cell infected by Chlamydia pneumoniae; their inclusion bodies shown at (3); an uninfected cell shown at (2) and (4) showing the difference between an infected cell nucleus and an uninfected cell nucleus.

Epithelium grown in culture can be identified by examining its morphological characteristics. Epithelial cells tend to cluster together, and have a "characteristic tight pavement-like appearance". But this is not always the case, such as when the cells are derived from a tumor. In these cases, it is often necessary to use certain biochemical markers to make a positive identification. The intermediate filament proteins in the cytokeratin group are almost exclusively found in epithelial cells, so they are often used for this purpose.

Cancers originating from the epithelium are classified as carcinomas. In contrast, sarcomas develop in connective tissue.

When epithelial cells or tissues are damaged from cystic fibrosis, sweat glands are also damaged, causing a frosty coating of the skin.

Etymology and pronunciation

The word epithelium uses the Greek roots ἐπί (epi), "on" or "upon", and θηλή (thēlē), "nipple". Epithelium is so called because the name was originally used to describe the translucent covering of small "nipples" of tissue on the lip. The word has both mass and count senses; the plural form is epithelia.