Dissociation constant




In chemistry, biochemistry, and pharmacology, a dissociation constant (Kd{displaystyle K_{d}}K_{d}) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is the inverse of the association constant. In the special case of salts, the dissociation constant can also be called an ionization constant.[citation needed]


For a general reaction:


AxBy↽−−⇀xA+yB{displaystyle {ce {A_{mathit {x}}B_{mathit {y}}<=>{mathit {x}}A{}+{mathit {y}}B}}}{displaystyle {ce {A_{mathit {x}}B_{mathit {y}}<=>{mathit {x}}A{}+{mathit {y}}B}}}

in which a complex AxBy{displaystyle {ce {A}}_{x}{ce {B}}_{y}}{displaystyle {ce {A}}_{x}{ce {B}}_{y}} breaks down into x A subunits and y B subunits, the dissociation constant is defined


Kd=[A]x[B]y[AxBy]{displaystyle K_{d}={frac {[{ce {A}}]^{x}[{ce {B}}]^{y}}{[{ce {A}}_{x}{ce {B}}_{y}]}}}{displaystyle K_{d}={frac {[{ce {A}}]^{x}[{ce {B}}]^{y}}{[{ce {A}}_{x}{ce {B}}_{y}]}}}

where [A], [B], and [AxBy] are the equilibrium concentrations of A, B, and the complex AxBy, respectively.


One reason for the popularity of the dissociation constant in biochemistry and pharmacology is that in the frequently encountered case where x=y=1, Kd has a simple physical interpretation: when [A]=Kd{displaystyle [{ce {A}}]=K_{d}}{displaystyle [{ce {A}}]=K_{d}}, [B]=[AB]{displaystyle [{ce {B}}]=[{ce {AB}}]}{displaystyle [{ce {B}}]=[{ce {AB}}]} or equivalently [AB][B]+[AB]=12{displaystyle {tfrac {[{ce {AB}}]}{{[{ce {B}}]}+[{ce {AB}}]}}={tfrac {1}{2}}}{displaystyle {tfrac {[{ce {AB}}]}{{[{ce {B}}]}+[{ce {AB}}]}}={tfrac {1}{2}}}. That is, Kd, which has the dimensions of concentration, equals the concentration of free A at which half of the total molecules of B are associated with A. This simple interpretation does not apply for higher values of x or y. It also presumes the absence of competing reactions, though the derivation can be extended to explicitly allow for and describe competitive binding.[citation needed] It is useful as a quick description of the binding of a substance, in the same way that EC50 and IC50 describe the biological activities of substances.




Contents






  • 1 Concentration of bound molecules


    • 1.1 Molecules with one binding site


    • 1.2 Macromolecules with identical independent binding sites




  • 2 Protein-ligand binding


    • 2.1 Antibodies




  • 3 Acid–base reactions


  • 4 Dissociation constant of water


  • 5 See also


  • 6 References





Concentration of bound molecules



Molecules with one binding site


Experimentally, the concentration of the molecule complex [AB] is obtained indirectly from the measurement of the concentration of a free molecules, either [A] or [B].[1]
In principle, the total amounts of molecule [A]0 and [B]0 added to the reaction are known.
They separate into free and bound components according to the mass conservation principle:


[A]0=[A]+[AB][B]0=[B]+[AB]{displaystyle {begin{aligned}{ce {[A]_0}}&={ce {{[A]}+ [AB]}}\{ce {[B]_0}}&={ce {{[B]}+ [AB]}}end{aligned}}}{displaystyle {begin{aligned}{ce {[A]_0}}&={ce {{[A]}+ [AB]}}\{ce {[B]_0}}&={ce {{[B]}+ [AB]}}end{aligned}}}

To track the concentration of the complex [AB], one substitutes the concentration of the free molecules ([A] or [B]), of the respective conservation equations, by the definition of the dissociation constant,


[A]0=Kd[AB][B]+[AB]{displaystyle [{{ce {A}}}]_{0}=K_{d}{frac {[{{ce {AB}}}]}{[{{ce {B}}}]}}+[{{ce {AB}}}]}{displaystyle [{ce {A}}]_{0}=K_{d}{frac {[{ce {AB}}]}{[{ce {B}}]}}+[{ce {AB}}]}

This yields the concentration of the complex related to the concentration of either one of the free molecules


[AB]=[A]0[B]Kd+[B]=[B]0[A]Kd+[A]{displaystyle {{ce {[AB]}}}={frac {{ce {[A]_{0}[B]}}}{K_{d}+[{{ce {B}}}]}}={frac {{ce {[B]_{0}[A]}}}{K_{d}+[{{ce {A}}}]}}}{displaystyle {ce {[AB]}}={frac {ce {[A]_{0}[B]}}{K_{d}+[{ce {B}}]}}={frac {ce {[B]_{0}[A]}}{K_{d}+[{ce {A}}]}}}


Macromolecules with identical independent binding sites


Many biological proteins and enzymes can possess more than one binding site.[1]
Usually, when a ligand L binds with a macromolecule M, it can influence binding kinetics of other ligands L binding to the macromolecule.
A simplified mechanism can be formulated if the affinity of all binding sites can be considered independent of the number of ligands bound to the macromolecule.
This is valid for macromolecules composed of more than one, mostly identical, subunits. It can be then assumed that each of these n subunits are identical, symmetric and that they possess only one single binding site. Then, the concentration of bound ligands [L]bound{displaystyle {{ce {[L]_{bound}}}}}{displaystyle {ce {[L]_{bound}}}} becomes


[L]bound=n[M]0[L]Kd+[L]{displaystyle {ce {[L]}}_{text{bound}}={frac {n{ce {[M]}}_{0}{ce {[L]}}}{K_{d}+{ce {[L]}}}}}{displaystyle {ce {[L]}}_{text{bound}}={frac {n{ce {[M]}}_{0}{ce {[L]}}}{K_{d}+{ce {[L]}}}}}

In this case, [L]bound≠[LM]{displaystyle {ce {[L]}}_{text{bound}}neq {ce {[LM]}}}{displaystyle {ce {[L]}}_{text{bound}}neq {ce {[LM]}}}, but comprises all partially saturated forms of the macromolecule:


[L]bound=[LM]+2[L2M]+3[L3M]+…+n[LnM]{displaystyle {ce {[L]}}_{text{bound}}={ce {[LM]}}+{ce {2[L_{2}M]}}+{ce {3[L_{3}M]}}+ldots +n{ce {[L_{mathit {n}}M]}}}{displaystyle {ce {[L]}}_{text{bound}}={ce {[LM]}}+{ce {2[L_{2}M]}}+{ce {3[L_{3}M]}}+ldots +n{ce {[L_{mathit {n}}M]}}}

where the saturation occurs stepwise


[L]+[M]↽−−⇀[LM]K1′=[L][M][LM][LM]=[L][M]K1′[L]+[LM]↽−−⇀[L2M]K2′=[L][LM][L2M][L2M]=[L]2[M]K1′K2′[L]+[L2M]↽−−⇀[L3M]K3′=[L][L2M][L3M][L3M]=[L]3[M]K1′K2′K3′⋮⋮⋮[L]+[Ln−1M]↽−−⇀[LnM]Kn′=[L][Ln−1M][LnM][LnM]=[L]n[M]K1′K2′K3′⋯Kn′{displaystyle {begin{aligned}{ce {{[L]}+[M]}}&{ce {{}<=>{[LM]}}}&K'_{1}&={frac {ce {[L][M]}}{[LM]}}&{ce {[LM]}}&={frac {ce {[L][M]}}{K'_{1}}}\{ce {{[L]}+[LM]}}&{ce {{}<=>{[L2M]}}}&K'_{2}&={frac {ce {[L][LM]}}{[L_{2}M]}}&{ce {[L_{2}M]}}&={frac {ce {[L]^{2}[M]}}{K'_{1}K'_{2}}}\{ce {{[L]}+[L2M]}}&{ce {{}<=>{[L3M]}}}&K'_{3}&={frac {ce {[L][L_{2}M]}}{[L_{3}M]}}&{ce {[L_{3}M]}}&={frac {ce {[L]^{3}[M]}}{K'_{1}K'_{2}K'_{3}}}\&vdots &&vdots &&vdots \{ce {{[L]}+[L_{mathit {n-1}}M]}}&{ce {{}<=>{[L_{mathit {n}}M]}}}&K'_{n}&={frac {ce {[L][L_{n-1}M]}}{[L_{n}M]}}&[{ce {L}}_{n}{ce {M}}]&={frac {[{ce {L}}]^{n}[{ce {M}}]}{K'_{1}K'_{2}K'_{3}cdots K'_{n}}}end{aligned}}}{displaystyle {begin{aligned}{ce {{[L]}+[M]}}&{ce {{}<=>{[LM]}}}&K'_{1}&={frac {ce {[L][M]}}{[LM]}}&{ce {[LM]}}&={frac {ce {[L][M]}}{K'_{1}}}\{ce {{[L]}+[LM]}}&{ce {{}<=>{[L2M]}}}&K'_{2}&={frac {ce {[L][LM]}}{[L_{2}M]}}&{ce {[L_{2}M]}}&={frac {ce {[L]^{2}[M]}}{K'_{1}K'_{2}}}\{ce {{[L]}+[L2M]}}&{ce {{}<=>{[L3M]}}}&K'_{3}&={frac {ce {[L][L_{2}M]}}{[L_{3}M]}}&{ce {[L_{3}M]}}&={frac {ce {[L]^{3}[M]}}{K'_{1}K'_{2}K'_{3}}}\&vdots &&vdots &&vdots \{ce {{[L]}+[L_{mathit {n-1}}M]}}&{ce {{}<=>{[L_{mathit {n}}M]}}}&K'_{n}&={frac {ce {[L][L_{n-1}M]}}{[L_{n}M]}}&[{ce {L}}_{n}{ce {M}}]&={frac {[{ce {L}}]^{n}[{ce {M}}]}{K'_{1}K'_{2}K'_{3}cdots K'_{n}}}end{aligned}}}

For the derivation of the general binding equation a saturation function r{displaystyle r}r is defined as the quotient from the portion of bound ligand to the total
amount of the macromolecule:


r=[L]bound[M]0=[LM]+2[L2M]+3[L3M]+⋅⋅⋅+n[LnM][M]+[LM]+[L2M]+[L3M]+⋅⋅⋅+[LnM]=∑i=1n(i[L]i∏j=1iKj′)1+∑i=1n([L]i∏j=1iKj′){displaystyle r={frac {ce {[L]_{bound}}}{ce {[M]_{0}}}}={frac {ce {{[LM]}+{2[L_{2}M]}+{3[L_{3}M]}+...+{mathit {n}}[L_{mathit {n}}M]}}{ce {{[M]}+{[LM]}+{[L_{2}M]}+{[L_{3}M]}+...+[L_{mathit {n}}M]}}}={frac {sum _{i=1}^{n}left({frac {i[{ce {L}}]^{i}}{prod _{j=1}^{i}K_{j}'}}right)}{1+sum _{i=1}^{n}left({frac {[{ce {L}}]^{i}}{prod _{j=1}^{i}K_{j}'}}right)}}}{displaystyle r={frac {ce {[L]_{bound}}}{ce {[M]_{0}}}}={frac {ce {{[LM]}+{2[L_{2}M]}+{3[L_{3}M]}+...+{mathit {n}}[L_{mathit {n}}M]}}{ce {{[M]}+{[LM]}+{[L_{2}M]}+{[L_{3}M]}+...+[L_{mathit {n}}M]}}}={frac {sum _{i=1}^{n}left({frac {i[{ce {L}}]^{i}}{prod _{j=1}^{i}K_{j}'}}right)}{1+sum _{i=1}^{n}left({frac {[{ce {L}}]^{i}}{prod _{j=1}^{i}K_{j}'}}right)}}}

Even if all microscopic dissociation constants[clarification needed] are identical, they differ from the macroscopic ones and there are differences between each binding step.[clarification needed]
The general relationship between both types of dissociation constants for n binding sites is


Ki′=Kdin−i+1{displaystyle K_{i}'=K_{d}{frac {i}{n-i+1}}}{displaystyle K_{i}'=K_{d}{frac {i}{n-i+1}}}

Hence, the ratio of bound ligand to macromolecules becomes


r=∑i=1ni(∏j=1in−j+1j)([L]Kd)i1+∑i=1n(∏j=1in−j+1j)([L]Kd)i=∑i=1ni(ni)([L]Kd)i1+∑i=1n(ni)([L]Kd)i{displaystyle r={frac {sum _{i=1}^{n}ileft(prod _{j=1}^{i}{frac {n-j+1}{j}}right)left({frac {{ce {[L]}}}{K_{d}}}right)^{i}}{1+sum _{i=1}^{n}left(prod _{j=1}^{i}{frac {n-j+1}{j}}right)left({frac {[L]}{K_{d}}}right)^{i}}}={frac {sum _{i=1}^{n}i{binom {n}{i}}left({frac {[L]}{K_{d}}}right)^{i}}{1+sum _{i=1}^{n}{binom {n}{i}}left({frac {{ce {[L]}}}{K_{d}}}right)^{i}}}}{displaystyle r={frac {sum _{i=1}^{n}ileft(prod _{j=1}^{i}{frac {n-j+1}{j}}right)left({frac {{ce {[L]}}}{K_{d}}}right)^{i}}{1+sum _{i=1}^{n}left(prod _{j=1}^{i}{frac {n-j+1}{j}}right)left({frac {[L]}{K_{d}}}right)^{i}}}={frac {sum _{i=1}^{n}i{binom {n}{i}}left({frac {[L]}{K_{d}}}right)^{i}}{1+sum _{i=1}^{n}{binom {n}{i}}left({frac {{ce {[L]}}}{K_{d}}}right)^{i}}}}

where (ni)=n!(n−i)!i!{displaystyle {binom {n}{i}}={frac {n!}{(n-i)!i!}}}{displaystyle {binom {n}{i}}={frac {n!}{(n-i)!i!}}} is the binomial coefficient.
Then, the first equation is proved by applying the binomial rule


r=n([L]Kd)(1+[L]Kd)n−1(1+[L]Kd)n=n([L]Kd)(1+[L]Kd)=n[L]Kd+[L]=[L]bound[M]0{displaystyle r={frac {nleft({frac {{ce {[L]}}}{K_{d}}}right)left(1+{frac {{ce {[L]}}}{K_{d}}}right)^{n-1}}{left(1+{frac {{ce {[L]}}}{K_{d}}}right)^{n}}}={frac {nleft({frac {{ce {[L]}}}{K_{d}}}right)}{left(1+{frac {{ce {[L]}}}{K_{d}}}right)}}={frac {n[{{ce {L}}}]}{K_{d}+[{{ce {L}}}]}}={frac {{ce {[L]_{bound}}}}{{ce {[M]_{0}}}}}}{displaystyle r={frac {nleft({frac {ce {[L]}}{K_{d}}}right)left(1+{frac {ce {[L]}}{K_{d}}}right)^{n-1}}{left(1+{frac {ce {[L]}}{K_{d}}}right)^{n}}}={frac {nleft({frac {ce {[L]}}{K_{d}}}right)}{left(1+{frac {ce {[L]}}{K_{d}}}right)}}={frac {n[{ce {L}}]}{K_{d}+[{ce {L}}]}}={frac {ce {[L]_{bound}}}{ce {[M]_{0}}}}}


Protein-ligand binding


The dissociation constant is commonly used to describe the affinity between a ligand L{displaystyle {{ce {L}}}}{displaystyle {ce {L}}} (such as a drug) and a protein P{displaystyle {ce {P}}}{displaystyle {ce {P}}}; i.e., how tightly a ligand binds to a particular protein. Ligand-protein affinities are influenced by non-covalent intermolecular interactions between the two molecules such as hydrogen bonding, electrostatic interactions, hydrophobic and van der Waals forces. Affinities can also be affected by high concentrations of other macromolecules, which causes macromolecular crowding.[2][3]


The formation of a ligand-protein complex LP{displaystyle {{ce {LP}}}}{displaystyle {ce {LP}}} can be described by a two-state process


L+P↽−−⇀LP{displaystyle {ce {L + P <=> LP}}}{displaystyle {ce {L + P <=> LP}}}

the corresponding dissociation constant is defined


Kd=[L][P][LP]{displaystyle K_{d}={frac {left[{{ce {L}}}right]left[{{ce {P}}}right]}{left[{{ce {LP}}}right]}}}{displaystyle K_{d}={frac {left[{ce {L}}right]left[{ce {P}}right]}{left[{ce {LP}}right]}}}

where [P],[L]{displaystyle {ce {[P], [L]}}}{displaystyle {ce {[P], [L]}}} and [LP]{displaystyle {{ce {[LP]}}}}{displaystyle {ce {[LP]}}} represent molar concentrations of the protein, ligand and complex, respectively.


The dissociation constant has molar units (M) and corresponds to the ligand concentration [L]{displaystyle {{ce {[L]}}}}{displaystyle {ce {[L]}}} at which half of the proteins are occupied at equilibrium [4], i.e., the concentration of ligand at which the concentration of protein with ligand bound [LP]{displaystyle {{ce {[LP]}}}}{displaystyle {ce {[LP]}}} equals the concentration of protein with no ligand bound [P]{displaystyle {ce {[P]}}}{displaystyle {ce {[P]}}}. The smaller the dissociation constant, the more tightly bound the ligand is, or the higher the affinity between ligand and protein. For example, a ligand with a nanomolar (nM) dissociation constant binds more tightly to a particular protein than a ligand with a micromolar (μM) dissociation constant.


Sub-picomolar dissociation constants as a result of non-covalent binding interactions between two molecules are rare. Nevertheless, there are some important exceptions. Biotin and avidin bind with a dissociation constant of roughly 10−15 M = 1 fM = 0.000001 nM.[5]Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10−15 M affinity.[6]
The dissociation constant for a particular ligand-protein interaction can change significantly with solution conditions (e.g., temperature, pH and salt concentration). The effect of different solution conditions is to effectively modify the strength of any intermolecular interactions holding a particular ligand-protein complex together.


Drugs can produce harmful side effects through interactions with proteins for which they were not meant to or designed to interact. Therefore, much pharmaceutical research is aimed at designing drugs that bind to only their target proteins (Negative Design) with high affinity (typically 0.1-10 nM) or at improving the affinity between a particular drug and its in-vivo protein target (Positive Design).



Antibodies


In the specific case of antibodies (Ab) binding to antigen (Ag), usually the term affinity constant refers to the association constant.


Ab+Ag↽−−⇀AbAg{displaystyle {ce {Ab + Ag <=> AbAg}}}{displaystyle {ce {Ab + Ag <=> AbAg}}}

Ka=[AbAg][Ab][Ag]=1Kd{displaystyle K_{a}={frac {left[{{ce {AbAg}}}right]}{left[{{ce {Ab}}}right]left[{{ce {Ag}}}right]}}={frac {1}{K_{d}}}}{displaystyle K_{a}={frac {left[{ce {AbAg}}right]}{left[{ce {Ab}}right]left[{ce {Ag}}right]}}={frac {1}{K_{d}}}}

This chemical equilibrium is also the ratio of the on-rate (kforward) and off-rate (kback) constants. Two antibodies can have the same affinity, but one may have both a high on- and off-rate constant, while the other may have both a low on- and off-rate constant.


Ka=kforwardkback=on-rateoff-rate{displaystyle K_{a}={frac {k_{text{forward}}}{k_{text{back}}}}={frac {mbox{on-rate}}{mbox{off-rate}}}}{displaystyle K_{a}={frac {k_{text{forward}}}{k_{text{back}}}}={frac {mbox{on-rate}}{mbox{off-rate}}}}


Acid–base reactions
















Acids and Bases


  • Acid

  • Acid–base reaction

  • Acid strength

  • Acidity function

  • Amphoterism

  • Base

  • Buffer solutions

  • Dissociation constant

  • Equilibrium chemistry

  • Extraction

  • Hammett acidity function

  • pH

  • Proton affinity

  • Self-ionization of water

  • Titration

  • Lewis acid catalysis

  • Frustrated Lewis pair

  • Chiral Lewis acid

Acid types


  • Brønsted

  • Lewis

  • Acceptor

  • Mineral

  • Organic

  • Strong

  • Superacids

  • Weak

  • Solid

Base types


  • Brønsted

  • Lewis

  • Donor

  • Organic

  • Strong

  • Superbases

  • Non-nucleophilic

  • Weak

  • v

  • t

  • e


Main article: Acid dissociation constant

For the deprotonation of acids, K is known as Ka, the acid dissociation constant. Stronger acids, for example sulfuric or phosphoric acid, have larger dissociation constants; weaker acids, like acetic acid, have smaller dissociation constants.


(The symbol Ka{displaystyle K_{a}}K_{a}, used for the acid dissociation constant, can lead to confusion with the association constant and it may be necessary to see the reaction or the equilibrium expression to know which is meant.)


Acid dissociation constants are sometimes expressed by pKa{displaystyle pK_{a}}{displaystyle pK_{a}}, which is defined as:


pKa=−log10⁡Ka{displaystyle {text{p}}K_{a}=-log _{10}{K_{a}}}{displaystyle {text{p}}K_{a}=-log _{10}{K_{a}}}

This pK{displaystyle mathrm {p} K}mathrm{p}K notation is seen in other contexts as well; it is mainly used for covalent dissociations (i.e., reactions in which chemical bonds are made or broken) since such dissociation constants can vary greatly.


A molecule can have several acid dissociation constants. In this regard, that is depending on the number of the protons they can give up, we define monoprotic, diprotic and triprotic acids. The first (e.g., acetic acid or ammonium) have only one dissociable group, the second (carbonic acid, bicarbonate, glycine) have two dissociable groups and the third (e.g., phosphoric acid) have three dissociable groups. In the case of multiple pK values they are designated by indices: pK1, pK2, pK3 and so on. For amino acids, the pK1 constant refers to its carboxyl (-COOH) group, pK2 refers to its amino (-NH3) group and the pK3 is the pK value of its side chain.


H3B↽−−⇀H++H2B−K1=[H+]⋅[H2B−][H3B]pK1=−log⁡K1H2B−↽−−⇀H++HB−2K2=[H+]⋅[HB−2][H2B−]pK2=−log⁡K2HB−2↽−−⇀H++B−3K3=[H+]⋅[B−3][HB−2]pK3=−log⁡K3{displaystyle {begin{aligned}{ce {H3B}}&{ce {{}<=>{H+}+{H2B^{-}}}}&K_{1}&={ce {[H+].[H2B^{-}] over [H3B]}}&mathrm {p} K_{1}&=-log K_{1}\{ce {H2B^{-}}}&{ce {{}<=>{H+}+{HB^{-2}}}}&K_{2}&={ce {[H+].[HB^{-2}] over [H2B^{-}]}}&mathrm {p} K_{2}&=-log K_{2}\{ce {HB^{-2}}}&{ce {{}<=>{H+}+{B^{-3}}}}&K_{3}&={ce {[H+].[B^{-3}] over [HB^{-2}]}}&mathrm {p} K_{3}&=-log K_{3}end{aligned}}}{displaystyle {begin{aligned}{ce {H3B}}&{ce {{}<=>{H+}+{H2B^{-}}}}&K_{1}&={ce {[H+].[H2B^{-}] over [H3B]}}&mathrm {p} K_{1}&=-log K_{1}\{ce {H2B^{-}}}&{ce {{}<=>{H+}+{HB^{-2}}}}&K_{2}&={ce {[H+].[HB^{-2}] over [H2B^{-}]}}&mathrm {p} K_{2}&=-log K_{2}\{ce {HB^{-2}}}&{ce {{}<=>{H+}+{B^{-3}}}}&K_{3}&={ce {[H+].[B^{-3}] over [HB^{-2}]}}&mathrm {p} K_{3}&=-log K_{3}end{aligned}}}


Dissociation constant of water


Main article: Self-ionization of water

The dissociation constant of water is denoted Kw:


Kw=[H+][OH−]{displaystyle K_{w}=[{{ce {H}}}^{+}][{{ce {OH}}}^{-}]}{displaystyle K_{w}=[{ce {H}}^{+}][{ce {OH}}^{-}]}

The concentration of water H2O{displaystyle {ce {H2O}}}{displaystyle {ce {H2O}}} is omitted by convention, which means that the value of Kw differs from the value of Keq that would be computed using that concentration.


The value of Kw varies with temperature, as shown in the table below. This variation must be taken into account when making precise measurements of quantities such as pH.

































Water temperature
 Kw / 10−14
 pKw[7]
0 °C
 0.112
 14.95
25 °C
 1.023
 13.99
50 °C
 5.495
 13.26
75 °C
 19.95
 12.70
100 °C
 56.23
 12.25


See also



  • Acid

  • Equilibrium constant


  • Ki Database

  • Competitive inhibition

  • pH

  • Scatchard plot

  • Ligand binding



References





  1. ^ ab Bisswanger, Hans (2008). Enzyme Kinetics: Principles and Methods (PDF). Weinheim: Wiley-VCH. p. 302. ISBN 978-3-527-31957-2..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}


  2. ^ Zhou, H.; Rivas, G.; Minton, A. (2008). "Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences". Annual Review of Biophysics. 37: 375–397. doi:10.1146/annurev.biophys.37.032807.125817. PMC 2826134. PMID 18573087.


  3. ^ Minton, A. P. (2001). "The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media" (PDF). The Journal of Biological Chemistry. 276 (14): 10577–10580. doi:10.1074/jbc.R100005200. PMID 11279227.


  4. ^ Björkelund, Hanna; Gedda, Lars; Andersson, Karl (2011-01-31). "Comparing the Epidermal Growth Factor Interaction with Four Different Cell Lines: Intriguing Effects Imply Strong Dependency of Cellular Context". PLOS ONE. 6 (1): e16536. Bibcode:2011PLoSO...616536B. doi:10.1371/journal.pone.0016536. ISSN 1932-6203.


  5. ^ Livnah, O.; Bayer, E.; Wilchek, M.; Sussman, J. (1993). "Three-dimensional structures of avidin and the avidin-biotin complex". Proceedings of the National Academy of Sciences of the United States of America. 90 (11): 5076–5080. Bibcode:1993PNAS...90.5076L. doi:10.1073/pnas.90.11.5076. PMC 46657. PMID 8506353.


  6. ^ Johnson, R.; Mccoy, J.; Bingman, C.; Phillips Gn, J.; Raines, R. (2007). "Inhibition of human pancreatic ribonuclease by the human ribonuclease inhibitor protein". Journal of Molecular Biology. 368 (2): 434–449. doi:10.1016/j.jmb.2007.02.005. PMC 1993901. PMID 17350650.


  7. ^ Bandura, Andrei V.; Lvov, Serguei N. (2006). "The Ionization Constant of Water over Wide Ranges of Temperature and Density" (PDF). Journal of Physical and Chemical Reference Data. 35 (1): 15–30. Bibcode:2006JPCRD..35...15B. doi:10.1063/1.1928231.











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Bressuire

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Subprefecture and commune in Nouvelle-Aquitaine, France Bressuire Subprefecture and commune Chateau de Bressuire and the Eglise Notre-Dame Coat of arms Location of Bressuire Bressuire Show map of France Bressuire Show map of Nouvelle-Aquitaine Coordinates: 46°50′27″N 0°29′14″W  /  46.8408°N 0.4872°W  / 46.8408; -0.4872 Coordinates: 46°50′27″N 0°29′14″W  /  46.8408°N 0.4872°W  / 46.8408; -0.4872 Country France Region Nouvelle-Aquitaine Department Deux-Sèvres Arrondissement Bressuire Canton Bressuire Government  • Mayor .mw-parser-output .nobold{font-weight:normal} (2014–20) Jean Michel Bernier Area 1 180.59 km 2 (69.73 sq mi) Population (2014) 2 19,300  • Density 110/km 2 (280/sq mi) Time zone UTC+01:00 (CET)  • Summer (DST) UTC+02:00 (CEST) INSEE/Postal code 79049 /79300 Elevation 98–236 m (322–774 ft) (avg. 173 m or 568 ft) 1 French Land Register data, which exclude...
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Vorschmack

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Vorschmack Ukrainian Jewish-style vorschmack served on rye bread Course Hors d'oeuvre Region or state Eastern Europe Associated national cuisine Ashkenazi Jewish, Finnish, German, Ukrainian, Polish, Russian Main ingredients Ground meat and/or fish Cookbook: Vorschmack   Media: Vorschmack Vorschmack or forshmak (Yiddish: פֿאָרשמאַק ‎, from archaic German Vorschmack , "foretaste" [1] or "appetizer" [2] ) is an originally East European dish made of salty minced fish or meat. Different variants of this dish are especially common in Ashkenazi Jewish and Finnish cuisine. Some varieties are also known in Russian and Polish cuisine. Contents 1 In Jewish cuisine 2 In Russian cuisine 3 In Polish cuisine 4 In Finnish cuisine 5 See also 6 References In Jewish cuisine According to Gil Marks, the German name points to the possible Germanic origin of this dish. [1] William Pokhlyobkin descr...
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Quarantine

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For other uses, see Quarantine (disambiguation). Signal flag "Lima" called the "Yellow Jack" which when flown in harbor means ship is under quarantine. A simple yellow flag (also called the "Yellow Jack") had historically been used to signal quarantine (it stands for Q among signal flags), but now indicates the opposite, as a signal of a ship free of disease that requests boarding and inspection. A quarantine is used to separate and restrict the movement of people; it is 'a restraint upon the activities or communication of persons or the transport of goods designed to prevent the spread of disease or pests', for a certain period of time. [1] This is often used in connection to disease and illness, such as those who may possibly have been exposed to a communicable disease. [2] The term is often erroneously used to mean medical isolation, which is "to separate ill persons who have a communicable disease from those who are healthy...
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