Cooperativity is a phenomenon displayed by systems involving identical or near-identical elements, which act dependently of each other, relative to a hypothetical standard non-interacting system in which the individual elements are acting independently.
One manifestation of this is
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...
s or
receptor
Receptor may refer to:
*Sensory receptor, in physiology, any structure which, on receiving environmental stimuli, produces an informative nerve impulse
*Receptor (biochemistry), in biochemistry, a protein molecule that receives and responds to a n ...
s that have multiple
binding sites where the affinity of the binding sites for a ligand is ''apparently'' increased, positive cooperativity, or decreased, negative cooperativity, upon the binding of a ligand to a binding site.
For example, when an oxygen atom binds to one of hemoglobin's four binding sites, the affinity to oxygen of the three remaining available binding sites increases; i.e. oxygen is more likely to bind to a hemoglobin bound to one oxygen than to an unbound hemoglobin. This is referred to as
cooperative binding
Molecular binding is an interaction between molecules that results in a stable physical association between those molecules. Cooperative binding occurs in binding systems containing more than one type, or species, of molecule and in which one of t ...
.
We also see cooperativity in large chain molecules made of many identical (or nearly identical) subunits (such as
DNA,
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, res ...
s, and
phospholipid
Phospholipids, are a class of lipids whose molecule has a hydrophilic "head" containing a phosphate group and two hydrophobic "tails" derived from fatty acids, joined by an alcohol residue (usually a glycerol molecule). Marine phospholipids typ ...
s), when such molecules undergo phase transitions such as melting, unfolding or unwinding. This is referred to as subunit cooperativity. However, the definition of cooperativity based on apparent increase or decrease in affinity to successive ligand binding steps is problematic, as the concept of "energy" must always be defined relative to a standard state. When we say that the affinity is increased upon binding of one ligand, it is empirically unclear what we mean since a non-cooperative binding curve is required to rigorously define binding energy and hence also affinity. A much more general and useful definition of positive cooperativity is: A process involving multiple identical incremental steps, in which intermediate states are statistically ''underrepresented'' relative to a hypothetical standard system (null hypothesis) where the steps occur independently of each other.
Likewise, a definition of negative cooperativity would be a process involving multiple identical incremental steps, in which the intermediate states are ''overrepresented'' relative to a hypothetical standard state in which individual steps occur independently. These latter definitions for positive and negative cooperativity easily encompass all processes which we call "cooperative", including conformational transitions in large molecules (such as proteins) and even psychological phenomena of large numbers of people (which can act independently of each other, or in a co-operative fashion).
Cooperative binding
When a substrate binds to one enzymatic subunit, the rest of the subunits are stimulated and become active.
Ligands
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 ...
can either have positive cooperativity, negative cooperativity, or non-cooperativity.
An example of positive cooperativity is the binding of
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
to
hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythroc ...
. One
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
molecule can bind to the
ferrous iron
In chemistry, iron(II) refers to the element iron in its +2 oxidation state. In ionic compounds (salts), such an atom may occur as a separate cation (positive ion) denoted by Fe2+.
The adjective ferrous or the prefix ferro- is often used to sp ...
of a heme molecule in each of the four chains of a
hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythroc ...
molecule. Deoxy-hemoglobin has a relatively low affinity for
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
, but when one molecule binds to a single heme, the
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
affinity increases, allowing the second molecule to bind more easily, and the third and fourth even more easily. The
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
affinity of 3-oxy-hemoglobin is ~300 times greater than that of deoxy-hemoglobin. This behavior leads the affinity curve of
hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythroc ...
to be
sigmoidal, rather than
hyperbolic as with the monomeric
myoglobin
Myoglobin (symbol Mb or MB) is an iron- and oxygen-binding protein found in the cardiac and skeletal muscle tissue of vertebrates in general and in almost all mammals. Myoglobin is distantly related to hemoglobin. Compared to hemoglobin, myoglob ...
. By the same process, the ability for
hemoglobin
Hemoglobin (haemoglobin BrE) (from the Greek word αἷμα, ''haîma'' 'blood' + Latin ''globus'' 'ball, sphere' + ''-in'') (), abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein present in red blood cells (erythroc ...
to lose
oxygen
Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
increases as fewer oxygen molecules are bound.
''See also
Oxygen-hemoglobin dissociation curve.
Negative cooperativity means that the opposite will be true; as
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 elect ...
s bind to the
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, res ...
, the
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, res ...
's affinity for the ligand will decrease, i.e. it becomes less likely for the ligand to bind to the protein. An example of this occurring is the relationship between
glyceraldehyde-3-phosphate
Glyceraldehyde 3-phosphate, also known as triose phosphate or 3-phosphoglyceraldehyde and abbreviated as G3P, GA3P, GADP, GAP, TP, GALP or PGAL, is a metabolite that occurs as an intermediate in several central pathways of all organisms.Nelson, D ...
and the
enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...
glyceraldehyde-3-phosphate dehydrogenase.
Homotropic cooperativity refers to the fact that the molecule causing the cooperativity is the one that will be affected by it.
Heterotropic cooperativity is where a third party substance causes the change in affinity. Homotropic or heterotropic cooperativity could be of both positives as well as negative types depend upon whether it support or oppose further binding of the ligand molecules to the enzymes.
Subunit cooperativity
Cooperativity is not only a phenomenon of ligand binding, but also applies anytime energetic interactions make it easier or more difficult for something to happen involving multiple units as opposed to with single units. (That is, easier or more difficult compared with what is expected when only accounting for the addition of multiple units). For example, unwinding of
DNA involves cooperativity: Portions of DNA must unwind in order for DNA to carry out
replication,
transcription and
recombination. Positive cooperativity among adjacent DNA
nucleotide
Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecu ...
s makes it easier to unwind a whole group of adjacent nucleotides than it is to unwind the same number of nucleotides spread out along the DNA chain. The
cooperative unit size is the number of adjacent bases that tend to unwind as a single unit due to the effects of positive cooperativity. This phenomenon applies to other types of chain molecules as well, such as the folding and unfolding of proteins and in the "melting" of
phospholipid
Phospholipids, are a class of lipids whose molecule has a hydrophilic "head" containing a phosphate group and two hydrophobic "tails" derived from fatty acids, joined by an alcohol residue (usually a glycerol molecule). Marine phospholipids typ ...
chains that make up the
membranes of cells. Subunit cooperativity is measured on the relative scale known as Hill's Constant.
Hill equation
A simple and widely used model for molecular interactions is the
Hill equation, which provides a way to quantify cooperative binding by describing the fraction of saturated ligand binding sites as a function of the ligand concentration.
Hill coefficient
The Hill coefficient is a measure of
ultrasensitivity
In molecular biology, ultrasensitivity describes an output response that is more sensitive to stimulus change than the hyperbolic Michaelis-Menten response. Ultrasensitivity is one of the biochemical switches in the cell cycle and has been implic ...
(i.e. how steep is the response curve).
From an operational point of view the Hill coefficient can be calculated as:
:
.
where
EC90 and
EC10 are the input values needed to produce the 10% and 90% of the maximal response, respectively.
Response coefficient
Global sensitivity measure such as Hill coefficient do not characterise the local behaviours of the s-shaped curves. Instead, these features are well captured by the response coefficient measure
defined as:
:
Link between Hill coefficient and response coefficient
Altszyler et al. (2017) have shown that these ultrasensitivity measures can be linked by the following equation:
:
where
denoted the mean value of the variable x over the range
,b
Ultrasensitivity in function composition
Consider two coupled ultrasensitive modules, disregarding effects of sequestration of molecular components between layers. In this case, the expression for the system's dose-response curve, , results from the mathematical composition of the functions,
, which describe the input/output relationship of isolated modules
:
:
Brown et al. (1997)
[ This article contains quotations from this source, which is available under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.] have shown that the local ultrasensitivity of the different layers combines multiplicatively:
:
.
In connection with this result, Ferrell et al. (1997)
showed, for Hill-type modules, that the overall cascade global ultrasensitivity had to be less than or equal to the product of the global ultrasensitivity estimations of each cascade's layer,
:
,
where
and
are the Hill coefficient of modules 1 and 2 respectively.
Altszyler et al. (2017)
have shown that the cascade's global ultrasensitivity can be analytically calculated:
:
where
and
delimited the Hill input's working range of the composite system, i.e. the input values for the i-layer so that the last layer (corresponding to
in this case) reached the 10% and 90% of it maximal output level. It followed this equation that the system's Hill coefficient could be written as the product of two factors,
and
, which characterized local average sensitivities over the relevant input region for each layer: