Moiety conservation is the conservation of a subgroup in a
chemical species, which is cyclically transferred from one molecule to another. In biochemistry, moiety conservation can have profound effects on the system's dynamics.
Moiety-conserved cycles in biochemistry
A typical example of a conserved moiety in biochemistry is the
Adenosine diphosphate
Adenosine diphosphate (ADP), also known as adenosine pyrophosphate (APP), is an important organic compound in metabolism and is essential to the flow of energy in living cells. ADP consists of three important structural components: a sugar backbon ...
(ADP) subgroup that remains unchanged when it is
phosphorylated
In chemistry, phosphorylation is the attachment of a phosphate group to a molecule or an ion. This process and its inverse, dephosphorylation, are common in biology and could be driven by natural selection. Text was copied from this source, whi ...
to create
adenosine triphosphate
Adenosine triphosphate (ATP) is an organic compound that provides energy to drive many processes in living cells, such as muscle contraction, nerve impulse propagation, condensate dissolution, and chemical synthesis. Found in all known forms of ...
(ATP) and then dephosphorylated back to ADP forming a conserved cycle.
Moiety
Moiety may refer to:
Chemistry
* Moiety (chemistry), a part or functional group of a molecule
** Moiety conservation, conservation of a subgroup in a chemical species
Anthropology
* Moiety (kinship), either of two groups into which a society is ...
-conserved cycles in nature exhibit unique network control features which can be elucidated using techniques such as
metabolic control analysis Metabolic control analysis (MCA) is a mathematical framework for describing
metabolic, signaling, and genetic pathways. MCA quantifies how variables,elastsuch as fluxes and species concentrations, depend on network parameters.
In particular, it is ...
. Other examples in metabolism include NAD/NADH, NADP/NADPH, CoA/Acetyl-CoA. Conserved cycles also exist in large numbers in protein signaling networks when proteins get phosphorylated and phosphorylated.
Most, if not all, of these cycles, are time-scale-dependent. For example, although a protein in a phosphorylation cycle is conserved during the interconversion, over a longer time scale, there will be low levels of protein synthesis and degradation, which change the level of protein moiety. The same applies to cycles involving ATP, NAD, etc. Thus, although the concept of a moiety-conserved cycle in biochemistry is a useful approximation, over time scales that include significant net synthesis and degradation of the moiety, the approximation is no longer valid. When invoking the conserved-moiety assumption on a particular moiety, we are, in effect, assuming the system is closed to that moiety.
Identifying conserved cycles
Conserved cycles in a biochemical network can be identified by examination of the
stoichiometry matrix,
The stoichiometry matrix for a simple cycle with species A and AP is given by:
The rates of change of A and AP can be written using the equation:
Expanding the expression leads to:
Note that
. This means that
, where
is the total mass of moiety
.
Given an arbitrary system:
elementary row operations In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GL''n''(F) when F is a field. Left multiplication (pre-multipli ...
can be applied to both sides such that the stoichiometric matrix is reduced to its
echelon form
In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination.
A matrix being in row echelon form means that Gaussian elimination has operated on the rows, and
column echelon form means that Gaussian el ...
,
giving:
The elementary operations are captured in the
matrix. We can partition
to match the echelon matrix where the zero rows begin such that:
By multiplying out the lower partition, we obtain:
The
matrix will contain entries corresponding to the conserved cycle participants.
Conserved cycles and computer models
The presence of conserved moieties can affect how computer simulation models are constructed. Moiety-conserved cycles will reduce the number of differential equations required to solve a system. For example, a simple cycle has only one independent variable. The other variable can be computed using the difference between the total mass and the independent variable. The set of differential equations for the two-cycle is given by:
These can be reduced to one differential equation and one linear algebraic equation:
References
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Mathematical and theoretical biology
Systems biology
Biochemistry