Planckian locus

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

 

Planckian locus in the CIE 1931 chromaticity diagram

In physics and color science, the Planckian locus or black body locus is the path or locus that the color of an incandescent black body would take in a particular chromaticity space as the blackbody temperature changes. It goes from deep red at low temperatures through orange, yellowish white, white, and finally bluish white at very high temperatures.

A color space is a three-dimensional space; that is, a color is specified by a set of three numbers (the CIE coordinates X, Y, and Z, for example, or other values such as hue, colorfulness, and luminance) which specify the color and brightness of a particular homogeneous visual stimulus. A chromaticity is a color projected into a two-dimensional space that ignores brightness. For example, the standard CIE XYZ color space projects directly to the corresponding chromaticity space specified by the two chromaticity coordinates known as x and y, making the familiar chromaticity diagram shown in the figure. The Planckian locus, the path that the color of a black body takes as the blackbody temperature changes, is often shown in this standard chromaticity space.

The Planckian locus in the XYZ color space

CIE 1931 Standard Colorimetric Observer functions used to map blackbody spectra to XYZ coordinates

In the CIE XYZ color space, the three coordinates defining a color are given by X, Y, and Z:

${\displaystyle X_T={\int }_0^{\mathrm{\infty }}X(\lambda )M(\lambda ,T)d\lambda }$

${\displaystyle Y_T={\int }_0^{\mathrm{\infty }}Y(\lambda )M(\lambda ,T)d\lambda }$

${\displaystyle Z_T={\int }_0^{\mathrm{\infty }}Z(\lambda )M(\lambda ,T)d\lambda }$

where M(λ,T) is the spectral radiant exitance of the light being viewed, and X(λ), Y(λ) and Z(λ) are the color matching functions of the CIE standard colorimetric observer, shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting into the above equations the black body spectral radiant exitance, which is given by Planck's law:

${\displaystyle M(\lambda ,T)=\frac{c_1}{{\lambda }^5}\frac{1}{\exp \left(\frac{c_2}{\lambda T}\right)-1}}$

where:

c₁ = 2πhc² is the first radiation constant

c₂ = hc/k is the second radiation constant

and:

M is the black body spectral radiant exitance (power per unit area per unit wavelength: watt per square meter per meter (W/m³))

T is the temperature of the black body

h is Planck's constant

c is the speed of light

k is Boltzmann's constant

This will give the Planckian locus in CIE XYZ color space. If these coordinates are X_T, Y_T, Z_T where T is the temperature, then the CIE chromaticity coordinates will be

${\displaystyle x_T=\frac{X_T}{X_T+Y_T+Z_T}}$

${\displaystyle y_T=\frac{Y_T}{X_T+Y_T+Z_T}}$

Note that in the above formula for Planck’s Law, you might as well use c_1L = 2hc² (the first radiation constant for spectral radiance) instead of c₁ (the “regular” first radiation constant), in which case the formula would give the spectral radiance L(λ,T) of the black body instead of the spectral radiant exitance M(λ,T). However, this change only affects the absolute values of X_T, Y_T and Z_T, not the values relative to each other. Since X_T, Y_T and Z_T are usually normalized to Y_T = 1 (or Y_T = 100) and are normalized when x_T and y_T are calculated, the absolute values of X_T, Y_T and Z_T do not matter. For practical reasons, c₁ might therefore simply be replaced by 1.

Approximation

The Planckian locus in xy space is depicted as a curve in the chromaticity diagram above. While it is possible to compute the CIE xy co-ordinates exactly given the above formulas, it is faster to use approximations. Since the mired scale changes more evenly along the locus than the temperature itself, it is common for such approximations to be functions of the reciprocal temperature. Kim et al. uses a cubic spline:

${\displaystyle x_c=\{\begin{array}{ll}-0.2661239\frac{{10}^9}{T^3}-0.2343589\frac{{10}^6}{T^2}+0.8776956\frac{{10}^3}{T}+0.179910& 1667\text{K}\le T\le 4000\text{K}\\ -3.0258469\frac{{10}^9}{T^3}+2.1070379\frac{{10}^6}{T^2}+0.2226347\frac{{10}^3}{T}+0.240390& 4000\text{K}\le T\le 25000\text{K}\end{array}}$

${\displaystyle y_c=\{\begin{array}{ll}-1.1063814x_c^3-1.34811020x_c^2+2.18555832x_c-0.20219683& 1667\text{K}\le T\le 2222\text{K}\\ -0.9549476x_c^3-1.37418593x_c^2+2.09137015x_c-0.16748867& 2222\text{K}\le T\le 4000\text{K}\\ +3.0817580x_c^3-5.87338670x_c^2+3.75112997x_c-0.37001483& 4000\text{K}\le T\le 25000\text{K}\end{array}}$

Kim et al.'s approximation to the Planckian locus (shown in red). The notches demarcate the three splines (shown in blue).

 

Animation showing an approximation of the color of the Planckian Locus through the visible spectrum

The Planckian locus can also be approximated in the CIE 1960 color space, which is used to compute CCT and CRI, using the following expressions:

${\displaystyle \overline{u}(T)=\frac{0.860117757+1.54118254\times {10}^{-4}T+1.28641212\times {10}^{-7}{T}^2}{1+8.42420235\times {10}^{-4}T+7.08145163\times {10}^{-7}{T}^2}}$

${\displaystyle \overline{v}(T)=\frac{0.317398726+4.22806245\times {10}^{-5}T+4.20481691\times {10}^{-8}{T}^2}{1-2.89741816\times {10}^{-5}T+1.61456053\times {10}^{-7}{T}^2}}$

This approximation is accurate to within ${\displaystyle \left|u-\overline{u}\right|<8\times {10}^{-5}}$ and ${\displaystyle \left|v-\overline{v}\right|<9\times {10}^{-5}}$ for ${\displaystyle 1000K<T<15,000K}$. Alternatively, one can use the chromaticity (x, y) coordinates estimated from above to derive the corresponding (u, v), if a larger range of temperatures is required.

The inverse calculation, from chromaticity co-ordinates (x,y) on or near the Planckian locus to correlated color temperature, is discussed in Color temperature § Approximation.

Correlated color temperature

The correlated color temperature (T_cp) is the temperature of the Planckian radiator whose perceived colour most closely resembles that of a given stimulus at the same brightness and under specified viewing conditions

— CIE/IEC 17.4:1987, International Lighting Vocabulary (ISBN 3900734070)

The mathematical procedure for determining the correlated color temperature involves finding the closest point to the light source's white point on the Planckian locus. Since the CIE's 1959 meeting in Brussels, the Planckian locus has been computed using the CIE 1960 color space, also known as MacAdam's (u,v) diagram. Today, the CIE 1960 color space is deprecated for other purposes:

The 1960 UCS diagram and 1964 Uniform Space are declared obsolete recommendation in CIE 15.2 (1986), but have been retained for the time being for calculating colour rendering indices and correlated colour temperature.

— CIE 13.3 (1995), Method of Measuring and Specifying Colour Rendering Properties of Light Sources

Owing to the perceptual inaccuracy inherent to the concept, it suffices to calculate to within 2K at lower CCTs and 10K at higher CCTs to reach the threshold of imperceptibility.

Close up of the CIE 1960 UCS. The isotherms are perpendicular to the Planckian locus, and are drawn to indicate the maximum distance from the locus that the CIE considers the correlated color temperature to be meaningful: ${\displaystyle {\mathrm{\Delta }}_{uv}=\pm 0.05}$

International Temperature Scale

The Planckian locus is derived by the determining the chromaticity values of a Planckian radiator using the standard colorimetric observer. The relative spectral power distribution (SPD) of a Planckian radiator follows Planck's law, and depends on the second radiation constant, ${\displaystyle c_2=hc/k}$. As measuring techniques have improved, the General Conference on Weights and Measures has revised its estimate of this constant, with the International Temperature Scale (and briefly, the International Practical Temperature Scale). These successive revisions caused a shift in the Planckian locus and, as a result, the correlated color temperature scale. Before ceasing publication of standard illuminants, the CIE worked around this problem by explicitly specifying the form of the SPD, rather than making references to black bodies and a color temperature. Nevertheless, it is useful to be aware of previous revisions in order to be able to verify calculations made in older texts:

• ${\displaystyle c_2=1.432\times {10}^{-2}\text{m·K}}$ (ITS-27). Note: Was in effect during the standardization of Illuminants A, B, C (1931), however the CIE used the value recommended by the U.S. National Bureau of Standards, 1.435 × 10⁻²
• ${\displaystyle c_2=1.4380\times {10}^{-2}\text{m·K}}$ (IPTS-48). In effect for Illuminant series D (formalized in 1967).
• ${\displaystyle c_2=1.4388\times {10}^{-2}\text{m·K}}$ (ITS-68), (ITS-90). Often used in recent papers.
• ${\displaystyle c_2=1.4387770(13)\times {10}^{-2}\text{m·K}}$ (CODATA, 2010)
• ${\displaystyle c_2=1.43877736(83)\times {10}^{-2}\text{m·K}}$ (CODATA, 2014)
• ${\displaystyle c_2=\mathrm{1.438776877...}\times {10}^{-2}\text{m·K}}$ (CODATA, 2018). Current value, as of 2020. The 2019 redefinition of the SI base units fixed the Boltzmann constant to an exact value. Since the Planck constant and the speed of light were already fixed to exact values, that means that c₂ is now an exact value as well. Note that ... doesn't indicate a repeating fraction; it merely means that of this exact value only the first ten digits are shown.

Black body

From Wikipedia, the free encyclopedia

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

A black body radiator used in CARLO laboratory in Poland. It is an approximation of a model described by Planck's law utilized as a spectral irradiance standard.

 

As the temperature of a black body decreases, its intensity also decreases and its peak moves to longer wavelengths. Shown for comparison is the classical Rayleigh–Jeans law and its ultraviolet catastrophe.

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by a black body in thermal equilibrium with its environment is called black-body radiation. The name "black body" is given because it absorbs all colors of light. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions."

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition.

An ideal black body in thermal equilibrium has two main properties:

1. It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature.
2. It is a diffuse emitter: measured per unit area perpendicular to the direction, the energy is radiated isotropically, independent of direction.

Real materials emit energy at a fraction—called the emissivity—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity ε = 1. A source with a lower emissivity, independent of frequency, is often referred to as a gray body. Constructing black bodies with an emissivity as close to 1 as possible remains a topic of current interest.

In astronomy, the radiation from stars and planets is sometimes characterized in terms of an effective temperature, the temperature of a black body that would emit the same total flux of electromagnetic energy.

Definition

The idea of a black body originally was introduced by Gustav Kirchhoff in 1860 as follows:

...the supposition that bodies can be imagined which, for infinitely small thicknesses, completely absorb all incident rays, and neither reflect nor transmit any. I shall call such bodies perfectly black, or, more briefly, black bodies.

A more modern definition drops the reference to "infinitely small thicknesses":

An ideal body is now defined, called a blackbody. A blackbody allows all incident radiation to pass into it (no reflected energy) and internally absorbs all the incident radiation (no energy transmitted through the body). This is true for radiation of all wavelengths and for all angles of incidence. Hence the blackbody is a perfect absorber for all incident radiation.

Idealizations

This section describes some concepts developed in connection with black bodies.

An approximate realization of a black body as a tiny hole in an insulated enclosure

Cavity with a hole

A widely used model of a black surface is a small hole in a cavity with walls that are opaque to radiation. Radiation incident on the hole will pass into the cavity, and is very unlikely to be re-emitted if the cavity is large. The hole is not quite a perfect black surface—in particular, if the wavelength of the incident radiation is greater than the diameter of the hole, part will be reflected. Similarly, even in perfect thermal equilibrium, the radiation inside a finite-sized cavity will not have an ideal Planck spectrum for wavelengths comparable to or larger than the size of the cavity.

Suppose the cavity is held at a fixed temperature T and the radiation trapped inside the enclosure is at thermal equilibrium with the enclosure. The hole in the enclosure will allow some radiation to escape. If the hole is small, radiation passing in and out of the hole has negligible effect upon the equilibrium of the radiation inside the cavity. This escaping radiation will approximate black-body radiation that exhibits a distribution in energy characteristic of the temperature T and does not depend upon the properties of the cavity or the hole, at least for wavelengths smaller than the size of the hole. See the figure in the Introduction for the spectrum as a function of the frequency of the radiation, which is related to the energy of the radiation by the equation E = hf, with E = energy, h = Planck's constant, f = frequency.

At any given time the radiation in the cavity may not be in thermal equilibrium, but the second law of thermodynamics states that if left undisturbed it will eventually reach equilibrium, although the time it takes to do so may be very long. Typically, equilibrium is reached by continual absorption and emission of radiation by material in the cavity or its walls. Radiation entering the cavity will be "thermalized" by this mechanism: the energy will be redistributed until the ensemble of photons achieves a Planck distribution. The time taken for thermalization is much faster with condensed matter present than with rarefied matter such as a dilute gas. At temperatures below billions of Kelvin, direct photon–photon interactions are usually negligible compared to interactions with matter. Photons are an example of an interacting boson gas, and as described by the H-theorem, under very general conditions any interacting boson gas will approach thermal equilibrium.

Transmission, absorption, and reflection

A body's behavior with regard to thermal radiation is characterized by its transmission τ, absorption α, and reflection ρ.

The boundary of a body forms an interface with its surroundings, and this interface may be rough or smooth. A nonreflecting interface separating regions with different refractive indices must be rough, because the laws of reflection and refraction governed by the Fresnel equations for a smooth interface require a reflected ray when the refractive indices of the material and its surroundings differ. A few idealized types of behavior are given particular names:

An opaque body is one that transmits none of the radiation that reaches it, although some may be reflected. That is, τ = 0 and α + ρ = 1.

A transparent body is one that transmits all the radiation that reaches it. That is, τ = 1 and α = ρ = 0.

A grey body is one where α, ρ and τ are constant for all wavelengths; this term also is used to mean a body for which α is temperature- and wavelength-independent.

A white body is one for which all incident radiation is reflected uniformly in all directions: τ = 0, α = 0, and ρ = 1.

For a black body, τ = 0, α = 1, and ρ = 0. Planck offers a theoretical model for perfectly black bodies, which he noted do not exist in nature: besides their opaque interior, they have interfaces that are perfectly transmitting and non-reflective.

Kirchhoff's perfect black bodies

Kirchhoff in 1860 introduced the theoretical concept of a perfect black body with a completely absorbing surface layer of infinitely small thickness, but Planck noted some severe restrictions upon this idea. Planck noted three requirements upon a black body: the body must (i) allow radiation to enter but not reflect; (ii) possess a minimum thickness adequate to absorb the incident radiation and prevent its re-emission; (iii) satisfy severe limitations upon scattering to prevent radiation from entering and bouncing back out. As a consequence, Kirchhoff's perfect black bodies that absorb all the radiation that falls on them cannot be realized in an infinitely thin surface layer, and impose conditions upon scattering of the light within the black body that are difficult to satisfy.

Realizations

A realization of a black body refers to a real world, physical embodiment. Here are a few.

Cavity with a hole

In 1898, Otto Lummer and Ferdinand Kurlbaum published an account of their cavity radiation source. Their design has been used largely unchanged for radiation measurements to the present day. It was a hole in the wall of a platinum box, divided by diaphragms, with its interior blackened with iron oxide. It was an important ingredient for the progressively improved measurements that led to the discovery of Planck's law. A version described in 1901 had its interior blackened with a mixture of chromium, nickel, and cobalt oxides. See also Hohlraum.

Near-black materials

There is interest in blackbody-like materials for camouflage and radar-absorbent materials for radar invisibility. They also have application as solar energy collectors, and infrared thermal detectors. As a perfect emitter of radiation, a hot material with black body behavior would create an efficient infrared heater, particularly in space or in a vacuum where convective heating is unavailable. They are also useful in telescopes and cameras as anti-reflection surfaces to reduce stray light, and to gather information about objects in high-contrast areas (for example, observation of planets in orbit around their stars), where blackbody-like materials absorb light that comes from the wrong sources.

It has long been known that a lamp-black coating will make a body nearly black. An improvement on lamp-black is found in manufactured carbon nanotubes. Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%. In 2009, a team of Japanese scientists created a material called nanoblack which is close to an ideal black body, based on vertically aligned single-walled carbon nanotubes. This absorbs between 98% and 99% of the incoming light in the spectral range from the ultra-violet to the far-infrared regions.

Other examples of nearly perfect black materials are super black, prepared by chemically etching a nickel–phosphorus alloy, vertically aligned carbon nanotube arrays (like VantaBlack) and flower carbon nanostructures; all absorb 99.9% of light or more.

Stars and planets

For more about the UBV color index, see Photometric system.

 

An idealized view of the cross-section of a star. The photosphere contains photons of light nearly in thermal equilibrium, and some escape into space as near-black-body radiation.

A star or planet often is modeled as a black body, and electromagnetic radiation emitted from these bodies as black-body radiation. The figure shows a highly schematic cross-section to illustrate the idea. The photosphere of the star, where the emitted light is generated, is idealized as a layer within which the photons of light interact with the material in the photosphere and achieve a common temperature T that is maintained over a long period of time. Some photons escape and are emitted into space, but the energy they carry away is replaced by energy from within the star, so that the temperature of the photosphere is nearly steady. Changes in the core lead to changes in the supply of energy to the photosphere, but such changes are slow on the time scale of interest here. Assuming these circumstances can be realized, the outer layer of the star is somewhat analogous to the example of an enclosure with a small hole in it, with the hole replaced by the limited transmission into space at the outside of the photosphere. With all these assumptions in place, the star emits black-body radiation at the temperature of the photosphere.

Effective temperature of a black body compared with the B-V and U-B color index of main sequence and super giant stars in what is called a color-color diagram.

Using this model the effective temperature of stars is estimated, defined as the temperature of a black body that yields the same surface flux of energy as the star. If a star were a black body, the same effective temperature would result from any region of the spectrum. For example, comparisons in the B (blue) or V (visible) range lead to the so-called B-V color index, which increases the redder the star, with the Sun having an index of +0.648 ± 0.006. Combining the U (ultraviolet) and the B indices leads to the U-B index, which becomes more negative the hotter the star and the more the UV radiation. Assuming the Sun is a type G2 V star, its U-B index is +0.12. The two indices for two types of most common star sequences are compared in the figure (diagram) with the effective surface temperature of the stars if they were perfect black bodies. There is a rough correlation. For example, for a given B-V index measurement, the curves of both most common sequences of star (the main sequence and the supergiants) lie below the corresponding black-body U-B index that includes the ultraviolet spectrum, showing that both groupings of star emit less ultraviolet light than a black body with the same B-V index. It is perhaps surprising that they fit a black body curve as well as they do, considering that stars have greatly different temperatures at different depths. For example, the Sun has an effective temperature of 5780 K, which can be compared to the temperature of its photosphere (the region generating the light), which ranges from about 5000 K at its outer boundary with the chromosphere to about 9500 K at its inner boundary with the convection zone approximately 500 km (310 mi) deep.

Black holes

See also: Hawking radiation

A black hole is a region of spacetime from which nothing escapes. Around a black hole there is a mathematically defined surface called an event horizon that marks the point of no return. It is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, making it almost an ideal black body (radiation with a wavelength equal to or larger than the diameter of the hole may not be absorbed, so black holes are not perfect black bodies). Physicists believe that to an outside observer, black holes have a non-zero temperature and emit black-body radiation, radiation with a nearly perfect black-body spectrum, ultimately evaporating. The mechanism for this emission is related to vacuum fluctuations in which a virtual pair of particles is separated by the gravity of the hole, one member being sucked into the hole, and the other being emitted. The energy distribution of emission is described by Planck's law with a temperature T:

${\displaystyle T=\frac{\hslash c^3}{8\pi G{k}_{\text{B}}M},}$

where c is the speed of light, ℏ is the reduced Planck constant, k_B is the Boltzmann constant, G is the gravitational constant and M is the mass of the black hole. These predictions have not yet been tested either observationally or experimentally.

Cosmic microwave background radiation

See also: Big Bang and Cosmic microwave background radiation

The Big Bang theory is based upon the cosmological principle, which states that on large scales the Universe is homogeneous and isotropic. According to theory, the Universe approximately a second after its formation was a near-ideal black body in thermal equilibrium at a temperature above 10¹⁰ K. The temperature decreased as the Universe expanded and the matter and radiation in it cooled. The cosmic microwave background radiation observed today is "the most perfect black body ever measured in nature". It has a nearly ideal Planck spectrum at a temperature of about 2.7 K. It departs from the perfect isotropy of true black-body radiation by an observed anisotropy that varies with angle on the sky only to about one part in 100,000.

Radiative cooling

Log-log graphs of peak emission wavelength and radiant exitance vs black-body temperature – red arrows show that 5780 K black bodies have 501 nm peak wavelength and 63.3 MW/m²; radiant exitance

 

See also: Radiative cooling and Radiosity (heat transfer)

The integration of Planck's law over all frequencies provides the total energy per unit of time per unit of surface area radiated by a black body maintained at a temperature T, and is known as the Stefan–Boltzmann law:

${\displaystyle P/A=\sigma T^4,}$

where σ is the Stefan–Boltzmann constant, σ ≈ 5.67×10⁻⁸ W⋅m⁻²⋅K⁻⁴ To remain in thermal equilibrium at constant temperature T, the black body must absorb or internally generate this amount of power P over the given area A.

The cooling of a body due to thermal radiation is often approximated using the Stefan–Boltzmann law supplemented with a "gray body" emissivity ε ≤ 1 (P/A = εσT⁴). The rate of decrease of the temperature of the emitting body can be estimated from the power radiated and the body's heat capacity. This approach is a simplification that ignores details of the mechanisms behind heat redistribution (which may include changing composition, phase transitions or restructuring of the body) that occur within the body while it cools, and assumes that at each moment in time the body is characterized by a single temperature. It also ignores other possible complications, such as changes in the emissivity with temperature, and the role of other accompanying forms of energy emission, for example, emission of particles like neutrinos.

If a hot emitting body is assumed to follow the Stefan–Boltzmann law and its power emission P and temperature T are known, this law can be used to estimate the dimensions of the emitting object, because the total emitted power is proportional to the area of the emitting surface. In this way it was found that X-ray bursts observed by astronomers originated in neutron stars with a radius of about 10 km, rather than black holes as originally conjectured. An accurate estimate of size requires some knowledge of the emissivity, particularly its spectral and angular dependence.

Receptor antagonist

From Wikipedia, the free encyclopedia

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

 

Antagonists will block the binding of an agonist at a receptor molecule, inhibiting the signal produced by a receptor–agonist coupling.

A receptor antagonist is a type of receptor ligand or drug that blocks or dampens a biological response by binding to and blocking a receptor rather than activating it like an agonist. Antagonist drugs interfere in the natural operation of receptor proteins. They are sometimes called blockers; examples include alpha blockers, beta blockers, and calcium channel blockers. In pharmacology, antagonists have affinity but no efficacy for their cognate receptors, and binding will disrupt the interaction and inhibit the function of an agonist or inverse agonist at receptors. Antagonists mediate their effects by binding to the active site or to the allosteric site on a receptor, or they may interact at unique binding sites not normally involved in the biological regulation of the receptor's activity. Antagonist activity may be reversible or irreversible depending on the longevity of the antagonist–receptor complex, which, in turn, depends on the nature of antagonist–receptor binding. The majority of drug antagonists achieve their potency by competing with endogenous ligands or substrates at structurally defined binding sites on receptors.

Etymology

The English word antagonist in pharmaceutical terms comes from the Greek ἀνταγωνιστής – antagonistēs, "opponent, competitor, villain, enemy, rival", which is derived from anti- ("against") and agonizesthai ("to contend for a prize"). Antagonists were discovered in the 20th century by American biologist Bailey Edgren.

Receptors

Main article: Receptor (biochemistry)

Biochemical receptors are large protein molecules that can be activated by the binding of a ligand such as a hormone or a drug. Receptors can be membrane-bound, as cell surface receptors, or inside the cell as intracellular receptors, such as nuclear receptors including those of the mitochondrion. Binding occurs as a result of non-covalent interactions between the receptor and its ligand, at locations called the binding site on the receptor. A receptor may contain one or more binding sites for different ligands. Binding to the active site on the receptor regulates receptor activation directly. The activity of receptors can also be regulated by the binding of a ligand to other sites on the receptor, as in allosteric binding sites. Antagonists mediate their effects through receptor interactions by preventing agonist-induced responses. This may be accomplished by binding to the active site or the allosteric site. In addition, antagonists may interact at unique binding sites not normally involved in the biological regulation of the receptor's activity to exert their effects.

The term antagonist was originally coined to describe different profiles of drug effects. The biochemical definition of a receptor antagonist was introduced by Ariens and Stephenson in the 1950s. The current accepted definition of receptor antagonist is based on the receptor occupancy model. It narrows the definition of antagonism to consider only those compounds with opposing activities at a single receptor. Agonists were thought to turn "on" a single cellular response by binding to the receptor, thus initiating a biochemical mechanism for change within a cell. Antagonists were thought to turn "off" that response by 'blocking' the receptor from the agonist. This definition also remains in use for physiological antagonists, substances that have opposing physiological actions, but act at different receptors. For example, histamine lowers arterial pressure through vasodilation at the histamine H₁ receptor, while adrenaline raises arterial pressure through vasoconstriction mediated by alpha-adrenergic receptor activation.

Our understanding of the mechanism of drug-induced receptor activation and receptor theory and the biochemical definition of a receptor antagonist continues to evolve. The two-state model of receptor activation has given way to multistate models with intermediate conformational states. The discovery of functional selectivity and that ligand-specific receptor conformations occur and can affect interaction of receptors with different second messenger systems may mean that drugs can be designed to activate some of the downstream functions of a receptor but not others. This means efficacy may actually depend on where that receptor is expressed, altering the view that efficacy at a receptor is receptor-independent property of a drug.

Pharmacodynamics

Main article: Pharmacodynamics

Efficacy and potency

Agonists require higher dose/concentration to achieve the same effect when in the presence of a reversible competitive antagonist.

By definition, antagonists display no efficacy to activate the receptors they bind. Antagonists do not maintain the ability to activate a receptor. Once bound, however, antagonists inhibit the function of agonists, inverse agonists, and partial agonists. In functional antagonist assays, a dose-response curve measures the effect of the ability of a range of concentrations of antagonists to reverse the activity of an agonist. The potency of an antagonist is usually defined by its half maximal inhibitory concentration (i.e., IC₅₀ value). This can be calculated for a given antagonist by determining the concentration of antagonist needed to elicit half inhibition of the maximum biological response of an agonist. Elucidating an IC₅₀ value is useful for comparing the potency of drugs with similar efficacies, however the dose-response curves produced by both drug antagonists must be similar. The lower the IC₅₀ the greater the potency of the antagonist, and the lower the concentration of drug that is required to inhibit the maximum biological response. Lower concentrations of drugs may be associated with fewer side-effects.

Agonists get its maximum effect reduced when in the presence of an Irreversible Competitive Antagonist or a Reversible Non-Competitive Antagonist.

Affinity

The affinity of an antagonist for its binding site (K_i), i.e. its ability to bind to a receptor, will determine the duration of inhibition of agonist activity. The affinity of an antagonist can be determined experimentally using Schild regression or for competitive antagonists in radioligand binding studies using the Cheng-Prusoff equation. Schild regression can be used to determine the nature of antagonism as beginning either competitive or non-competitive and K_i determination is independent of the affinity, efficacy or concentration of the agonist used. However, it is important that equilibrium has been reached. The effects of receptor desensitization on reaching equilibrium must also be taken into account. The affinity constant of antagonists exhibiting two or more effects, such as in competitive neuromuscular-blocking agents that also block ion channels as well as antagonising agonist binding, cannot be analyzed using Schild regression. Schild regression involves comparing the change in the dose ratio, the ratio of the EC₅₀ of an agonist alone compared to the EC₅₀ in the presence of a competitive antagonist as determined on a dose response curve. Altering the amount of antagonist used in the assay can alter the dose ratio. In Schild regression, a plot is made of the log (dose ratio-1) versus the log concentration of antagonist for a range of antagonist concentrations. The affinity or K_i is where the line cuts the x-axis on the regression plot. Whereas, with Schild regression, antagonist concentration is varied in experiments used to derive K_i values from the Cheng-Prusoff equation, agonist concentrations are varied. Affinity for competitive agonists and antagonists is related by the Cheng-Prusoff factor used to calculate the K_i (affinity constant for an antagonist) from the shift in IC₅₀ that occurs during competitive inhibition. The Cheng-Prusoff factor takes into account the effect of altering agonist concentration and agonist affinity for the receptor on inhibition produced by competitive antagonists.

Types

See also: Enzyme inhibitor § Types of reversible inhibitors

Competitive

Further information: Competitive inhibition

Competitive antagonists bind to receptors at the same binding site (active site) as the endogenous ligand or agonist, but without activating the receptor. Agonists and antagonists "compete" for the same binding site on the receptor. Once bound, an antagonist will block agonist binding. Sufficient concentrations of an antagonist will displace the agonist from the binding sites, resulting in a lower frequency of receptor activation. The level of activity of the receptor will be determined by the relative affinity of each molecule for the site and their relative concentrations. High concentrations of a competitive agonist will increase the proportion of receptors that the agonist occupies, higher concentrations of the antagonist will be required to obtain the same degree of binding site occupancy. In functional assays using competitive antagonists, a parallel rightward shift of agonist dose–response curves with no alteration of the maximal response is observed.

Competitive antagonists are used to prevent the activity of drugs, and to reverse the effects of drugs that have already been consumed. Naloxone (also known as Narcan) is used to reverse opioid overdose caused by drugs such as heroin or morphine. Similarly, Ro15-4513 is an antidote to alcohol and flumazenil is an antidote to benzodiazepines.

Competitive antagonists are sub-classified as reversible (surmountable) or irreversible (insurmountable) competitive antagonists, depending on how they interact with their receptor protein targets. Reversible antagonists, which bind via noncovalent intermolecular forces, will eventually dissociate from the receptor, freeing the receptor to be bound again. Irreversible antagonists bind via covalent intermolecular forces. Because there is not enough free energy to break covalent bonds in the local environment, the bond is essentially "permanent", meaning the receptor-antagonist complex will never dissociate. The receptor will thereby remain permanently antagonized until it is ubiquitinated and thus destroyed.

Non-competitive

A non-competitive antagonist is a type of insurmountable antagonist that may act in one of two ways: by binding to an allosteric site of the receptor, or by irreversibly binding to the active site of the receptor. The former meaning has been standardised by the IUPHAR, and is equivalent to the antagonist being called an allosteric antagonist. While the mechanism of antagonism is different in both of these phenomena, they are both called "non-competitive" because the end-results of each are functionally very similar. Unlike competitive antagonists, which affect the amount of agonist necessary to achieve a maximal response but do not affect the magnitude of that maximal response, non-competitive antagonists reduce the magnitude of the maximum response that can be attained by any amount of agonist. This property earns them the name "non-competitive" because their effects cannot be negated, no matter how much agonist is present. In functional assays of non-competitive antagonists, depression of the maximal response of agonist dose-response curves, and in some cases, rightward shifts, is produced. The rightward shift will occur as a result of a receptor reserve (also known as spare receptors) and inhibition of the agonist response will only occur when this reserve is depleted.

An antagonist that binds to the active site of a receptor is said to be "non-competitive" if the bond between the active site and the antagonist is irreversible or nearly so. This usage of the term "non-competitive" may not be ideal, however, since the term "irreversible competitive antagonism" may also be used to describe the same phenomenon without the potential for confusion with the second meaning of "non-competitive antagonism" discussed below.

The second form of "non-competitive antagonists" act at an allosteric site. These antagonists bind to a distinctly separate binding site from the agonist, exerting their action to that receptor via the other binding site. They do not compete with agonists for binding at the active site. The bound antagonists may prevent conformational changes in the receptor required for receptor activation after the agonist binds. Cyclothiazide has been shown to act as a reversible non-competitive antagonist of mGluR1 receptor.

Uncompetitive

Uncompetitive antagonists differ from non-competitive antagonists in that they require receptor activation by an agonist before they can bind to a separate allosteric binding site. This type of antagonism produces a kinetic profile in which "the same amount of antagonist blocks higher concentrations of agonist better than lower concentrations of agonist". Memantine, used in the treatment of Alzheimer's disease, is an uncompetitive antagonist of the NMDA receptor.

Silent antagonists

Chart demonstrating the difference between agonists, silent antagonists, and inverse agonists.

Silent antagonists are competitive receptor antagonists that have zero intrinsic activity for activating a receptor. They are true antagonists, so to speak. The term was created to distinguish fully inactive antagonists from weak partial agonists or inverse agonists.

Partial agonists

Partial agonists are defined as drugs that, at a given receptor, might differ in the amplitude of the functional response that they elicit after maximal receptor occupancy. Although they are agonists, partial agonists can act as a competitive antagonist in the presence of a full agonist, as it competes with the full agonist for receptor occupancy, thereby producing a net decrease in the receptor activation as compared to that observed with the full agonist alone. Clinically, their usefulness is derived from their ability to enhance deficient systems while simultaneously blocking excessive activity. Exposing a receptor to a high level of a partial agonist will ensure that it has a constant, weak level of activity, whether its normal agonist is present at high or low levels. In addition, it has been suggested that partial agonism prevents the adaptive regulatory mechanisms that frequently develop after repeated exposure to potent full agonists or antagonists. E.g. Buprenorphine, a partial agonist of the μ-opioid receptor, binds with weak morphine-like activity and is used clinically as an analgesic in pain management and as an alternative to methadone in the treatment of opioid dependence.

Inverse agonists

An inverse agonist can have effects similar to those of an antagonist, but causes a distinct set of downstream biological responses. Constitutively active receptors that exhibit intrinsic or basal activity can have inverse agonists, which not only block the effects of binding agonists like a classical antagonist but also inhibit the basal activity of the receptor. Many drugs previously classified as antagonists are now beginning to be reclassified as inverse agonists because of the discovery of constitutive active receptors. Antihistamines, originally classified as antagonists of histamine H₁ receptors have been reclassified as inverse agonists.

Reversibility

Many antagonists are reversible antagonists that, like most agonists, will bind and unbind a receptor at rates determined by receptor-ligand kinetics.

Irreversible antagonists covalently bind to the receptor target and, in general, cannot be removed; inactivating the receptor for the duration of the antagonist effects is determined by the rate of receptor turnover, the rate of synthesis of new receptors. Phenoxybenzamine is an example of an irreversible alpha blocker—it permanently binds to α adrenergic receptors, preventing adrenaline and noradrenaline from binding. Inactivation of receptors normally results in a depression of the maximal response of agonist dose-response curves and a right shift in the curve occurs where there is a receptor reserve similar to non-competitive antagonists. A washout step in the assay will usually distinguish between non-competitive and irreversible antagonist drugs, as effects of non-competitive antagonists are reversible and activity of agonist will be restored.

Irreversible competitive antagonists also involve competition between the agonist and antagonist of the receptor, but the rate of covalent bonding differs and depends on affinity and reactivity of the antagonist. For some antagonists, there may be a distinct period during which they behave competitively (regardless of basal efficacy), and freely associate to and dissociate from the receptor, determined by receptor-ligand kinetics. But, once irreversible bonding has taken place, the receptor is deactivated and degraded. As for non-competitive antagonists and irreversible antagonists in functional assays with irreversible competitive antagonist drugs, there may be a shift in the log concentration–effect curve to the right, but, in general, both a decrease in slope and a reduced maximum are obtained.