Dissociation Constant
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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
,
biochemistry Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and ...
, and
pharmacology Pharmacology is a branch of medicine, biology and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemica ...
, a dissociation constant (K_D) is a specific type of
equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
falls apart into its component
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s, or when a
salt Salt is a mineral composed primarily of sodium chloride (NaCl), a chemical compound belonging to the larger class of salts; salt in the form of a natural crystalline mineral is known as rock salt or halite. Salt is present in vast quantitie ...
splits up into its component
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s. The dissociation constant is the inverse of the
association constant The binding constant, or affinity constant/association constant, is a special case of the equilibrium constant ''K'', and is the inverse of the dissociation constant. It is associated with the binding and unbinding reaction of receptor (R) and li ...
. In the special case of salts, the dissociation constant can also be called an
ionization constant In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction :HA ...
. For a general reaction: : A_\mathit B_\mathit <=> \mathit A + \mathit B in which a complex \ce_x \ce_y breaks down into ''x'' A subunits and ''y'' B subunits, the dissociation constant is defined as : K_D = \frac where and ''x'' B''y''are the equilibrium concentrations of A, B, and the complex A''x'' B''y'', 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 ce A= K_D, then ce B= ce /math> or equivalently \tfrac = \tfrac. 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. It is useful as a quick description of the binding of a substance, in the same way that
EC50 ] Half maximal effective concentration (EC50) is a measure of the concentration of a drug, antibody or toxicant which induces a Stimulus%E2%80%93response_model, response halfway between the baseline and maximum after a specified exposure time. Mo ...
and
IC50 The half maximal inhibitory concentration (IC50) is a measure of the potency of a substance in inhibiting a specific biological or biochemical function. IC50 is a quantitative measure that indicates how much of a particular inhibitory substance ...
describe the biological activities of substances.


Concentration of bound molecules


Molecules with one binding site

Experimentally, the concentration of the molecule complex Bis obtained indirectly from the measurement of the concentration of a free molecules, either or In principle, the total amounts of molecule sub>0 and sub>0 added to the reaction are known. They separate into free and bound components according to the mass conservation principle: :\begin \ce &= \ce \\ \ce &= \ce \end To track the concentration of the complex B one substitutes the concentration of the free molecules ( or , of the respective conservation equations, by the definition of the dissociation constant, : ce A0 = K_D \frac + ce This yields the concentration of the complex related to the concentration of either one of the free molecules : \ce = \frac\ce = \frac\ce


Macromolecules with identical independent binding sites

Many biological proteins and enzymes can possess more than one binding site. Usually, when a
ligand In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...
binds with a macromolecule , it can influence binding kinetics of other ligands 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 subunits are identical, symmetric and that they possess only one single binding site. Then, the concentration of bound ligands becomes : \ce_\text = \frac In this case, \ce_\text \neq \ce, but comprises all partially saturated forms of the macromolecule: : \ce_\text = \ce + \ce + \ce + \ldots + n \ce where the saturation occurs stepwise :\begin \ce &\ce & K'_1 &= \frac\ce & \ce &= \frac\ce \\ \ce &\ce & K'_2 &= \frac\ce & \ce &= \frac\ce \\ \ce &\ce & K'_3 &= \frac\ce & \ce &= \frac\ce \\ & \vdots & & \vdots & & \vdots \\ \ce &\ce & K'_n &= \frac\ce & ce L_n \ce M&= \frac \end For the derivation of the general binding equation a saturation function r is defined as the quotient from the portion of bound ligand to the total amount of the macromolecule: : r = \frac\ce\ce = \frac\ce\ce = \frac Even if all microscopic dissociation constants are identical, they differ from the macroscopic ones and there are differences between each binding step. The general relationship between both types of dissociation constants for ''n'' binding sites is : K_i' = K_D \frac Hence, the ratio of bound ligand to macromolecules becomes : r = \frac = \frac where \binom = \frac is the
binomial coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...
. Then, the first equation is proved by applying the binomial rule : r = \frac = \frac = \frac = \frac\ce\ce


Protein-ligand binding

The dissociation constant is commonly used to describe the
affinity Affinity may refer to: Commerce, finance and law * Affinity (law), kinship by marriage * Affinity analysis, a market research and business management technique * Affinity Credit Union, a Saskatchewan-based credit union * Affinity Equity Par ...
between a
ligand In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...
L (such as a
drug A drug is any chemical substance that causes a change in an organism's physiology or psychology when consumed. Drugs are typically distinguished from food and substances that provide nutritional support. Consumption of drugs can be via insuffla ...
) and a
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
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 bond In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a ...
ing, electrostatic interactions,
hydrophobic In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water (known as a hydrophobe). In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, t ...
and
van der Waals force In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
s. Affinities can also be affected by high concentrations of other macromolecules, which causes
macromolecular crowding The phenomenon of macromolecular crowding alters the properties of molecules in a solution when high concentrations of macromolecules such as proteins are present. Such conditions occur routinely in living cells; for instance, the cytosol of ''Esch ...
. The formation of a ligand-protein complex LP can be described by a two-state process : L + P <=> LP the corresponding dissociation constant is defined : K_D = \frac where /chem> and P/chem> represent
molar concentration Molar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solut ...
s of the protein, ligand and complex, respectively. The dissociation constant has molar units (M) and corresponds to the ligand concentration /chem> at which half of the proteins are occupied at equilibrium, i.e., the concentration of ligand at which the concentration of protein with ligand bound P/chem> equals the concentration of protein with no ligand bound /chem>. 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.
Ribonuclease inhibitor Ribonuclease inhibitor (RI) is a large (~450 residues, ~49 kDa), acidic (pI ~4.7), leucine-rich repeat protein that forms extremely tight complexes with certain ribonucleases. It is a major cellular protein, comprising ~0.1% of all cellular pr ...
proteins may also bind to
ribonuclease Ribonuclease (commonly abbreviated RNase) is a type of nuclease that catalyzes the degradation of RNA into smaller components. Ribonucleases can be divided into endoribonucleases and exoribonucleases, and comprise several sub-classes within ...
with a similar 10−15 M affinity. The dissociation constant for a particular ligand-protein interaction can change significantly with solution conditions (e.g.,
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
, pH and salt concentration). The effect of different solution conditions is to effectively modify the strength of any
intermolecular interactions An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. a ...
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 Studies that are ''in vivo'' (Latin for "within the living"; often not italicized in English) are those in which the effects of various biological entities are tested on whole, living organisms or cells, usually animals, including humans, and pl ...
'' 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 : K_A = \frac = \frac This
chemical equilibrium In a chemical reaction, chemical equilibrium is the state in which both the Reagent, reactants and Product (chemistry), products are present in concentrations which have no further tendency to change with time, so that there is no observable chan ...
is also the ratio of the on-rate (kforward) or (ka) and off-rate (kback) or (kd) 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. : K_A = \frac = \frac


Acid–base reactions

For the
deprotonation Deprotonation (or dehydronation) is the removal (transfer) of a proton (or hydron, or hydrogen cation), (H+) from a Brønsted–Lowry acid in an acid–base reaction.Henry Jakubowski, Biochemistry Online Chapter 2A3, https://employees.csbsju.ed ...
of
acid In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...
s, ''K'' is known as ''K''a, the
acid dissociation constant In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction :HA ...
. Stronger acids, for example sulfuric or
phosphoric acid Phosphoric acid (orthophosphoric acid, monophosphoric acid or phosphoric(V) acid) is a colorless, odorless phosphorus-containing solid, and inorganic compound with the chemical formula . It is commonly encountered as an 85% aqueous solution, w ...
, have larger dissociation constants; weaker acids, like
acetic acid Acetic acid , systematically named ethanoic acid , is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main component ...
, have smaller dissociation constants. (The symbol K_a, used for the acid dissociation constant, can lead to confusion with the
association constant The binding constant, or affinity constant/association constant, is a special case of the equilibrium constant ''K'', and is the inverse of the dissociation constant. It is associated with the binding and unbinding reaction of receptor (R) and li ...
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 pK_a, which is defined as: : \textK_a = -\log_ This \mathrmK notation is seen in other contexts as well; it is mainly used for
covalent A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
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 In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a ...
. The first (e.g., acetic acid or ammonium) have only one dissociable group, the second ( carbonic acid,
bicarbonate In inorganic chemistry, bicarbonate (IUPAC-recommended nomenclature: hydrogencarbonate) is an intermediate form in the deprotonation of carbonic acid. It is a polyatomic anion with the chemical formula . Bicarbonate serves a crucial biochem ...
,
glycine Glycine (symbol Gly or G; ) is an amino acid that has a single hydrogen atom as its side chain. It is the simplest stable amino acid (carbamic acid is unstable), with the chemical formula NH2‐ CH2‐ COOH. Glycine is one of the proteinogeni ...
) have two dissociable groups and the third (e.g., phosphoric acid) have three dissociable groups. In the case of multiple p''K'' values they are designated by indices: p''K''1, p''K''2, p''K''3 and so on. For amino acids, the p''K''1 constant refers to its
carboxyl In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is or , with R referring to the alkyl, alkenyl, aryl, or other group. Carboxylic ...
(-COOH) group, p''K''2 refers to its
amino In chemistry, amines (, ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are formally derivatives of ammonia (), wherein one or more hydrogen atoms have been replaced by a substituent ...
(-NH2) group and the p''K''3 is the p''K'' value of its
side chain In organic chemistry and biochemistry, a side chain is a chemical group that is attached to a core part of the molecule called the "main chain" or backbone. The side chain is a hydrocarbon branching element of a molecule that is attached to a ...
. :\begin \ce &\ce & K_1 &= \ce & \mathrmK_1 &= -\log K_1 \\ \ce &\ce & K_2 &= \ce & \mathrmK_2 &= -\log K_2 \\ \ce &\ce & K_3 &= \ce & \mathrmK_3 &= -\log K_3 \end


Dissociation constant of water

The dissociation constant of
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...
is denoted ''K''w: :K_\mathrm = ce^+ ce^-/math> The concentration of water, 2O is omitted by convention, which means that the value of ''K''w differs from the value of ''K''eq that would be computed using that concentration. The value of ''K''w 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. :


See also

*
Acid In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...
*
Equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
* ''K''i Database *
Competitive inhibition Competitive inhibition is interruption of a chemical pathway owing to one chemical substance inhibiting the effect of another by competing with it for binding or bonding. Any metabolic or chemical messenger system can potentially be affected b ...
* pH *
Scatchard plot The Scatchard equation is an equation used in molecular biology to calculate the affinity and number of binding sites of a receptor for a ligand. It is named after the American chemist George Scatchard. Equation Throughout this article, 'RL''deno ...
*
Ligand binding In biochemistry and pharmacology, a ligand is a substance that forms a complex with a biomolecule to serve a biological purpose. The etymology stems from ''ligare'', which means 'to bind'. In protein-ligand binding, the ligand is usually a mo ...
*
Avidity In biochemistry, avidity refers to the accumulated strength of ''multiple'' affinities of individual non-covalent binding interactions, such as between a protein receptor and its ligand, and is commonly referred to as functional affinity. Avidity di ...


References

{{Authority control Equilibrium chemistry Enzyme kinetics