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150 years of the mass action law.

Voit EO, Martens HA, Omholt SW - PLoS Comput. Biol. (2015)

Bottom Line: The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate.It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases.The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

View Article: PubMed Central - PubMed

Affiliation: Wallace H. Coulter Department of Biomedical Engineering, Georgia Tech and Emory University, Atlanta, Georgia, United States of America.

ABSTRACT
This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been "there" forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

Show MeSH
Generic pathway with one activating and two inhibitory signals.Subscripted X's are metabolites, while subscripted v's are processes.
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pcbi-1004012-g003: Generic pathway with one activating and two inhibitory signals.Subscripted X's are metabolites, while subscripted v's are processes.

Mentions: A significant advantage of this power-law formulation is the fact that biochemical diagrams can immediately be converted into well-structured equations, quasi as a default representation. Specifically, each process is written as a power-law term that contains exactly those variables that directly affect this process, be it as a substrate, modulator, or regulator. As an illustration, it is easy to write down a stoichiometric model of the generic diagram in Fig. 3 where, for instance, the dynamics of X1 is directly given as(12)However, it is not at all evident how to formulate the processes vij. The default in biochemistry might be a Michaelis-Menten model, but it is known that its prerequisites are seldom satisfied in vivo [47]. By contrast, a power-law formulation makes no assumptions beyond positivity of its state variables and is, at the same time, mathematically guaranteed to be correct at an operating point of one's choice, and very accurate close to it, if parameter values are chosen appropriately. Thus, one can immediately formulate the dynamics of X1 as(13)and the problem of choosing a functional format is reduced to a much simpler task of estimating parameter values.


150 years of the mass action law.

Voit EO, Martens HA, Omholt SW - PLoS Comput. Biol. (2015)

Generic pathway with one activating and two inhibitory signals.Subscripted X's are metabolites, while subscripted v's are processes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4288704&req=5

pcbi-1004012-g003: Generic pathway with one activating and two inhibitory signals.Subscripted X's are metabolites, while subscripted v's are processes.
Mentions: A significant advantage of this power-law formulation is the fact that biochemical diagrams can immediately be converted into well-structured equations, quasi as a default representation. Specifically, each process is written as a power-law term that contains exactly those variables that directly affect this process, be it as a substrate, modulator, or regulator. As an illustration, it is easy to write down a stoichiometric model of the generic diagram in Fig. 3 where, for instance, the dynamics of X1 is directly given as(12)However, it is not at all evident how to formulate the processes vij. The default in biochemistry might be a Michaelis-Menten model, but it is known that its prerequisites are seldom satisfied in vivo [47]. By contrast, a power-law formulation makes no assumptions beyond positivity of its state variables and is, at the same time, mathematically guaranteed to be correct at an operating point of one's choice, and very accurate close to it, if parameter values are chosen appropriately. Thus, one can immediately formulate the dynamics of X1 as(13)and the problem of choosing a functional format is reduced to a much simpler task of estimating parameter values.

Bottom Line: The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate.It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases.The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

View Article: PubMed Central - PubMed

Affiliation: Wallace H. Coulter Department of Biomedical Engineering, Georgia Tech and Emory University, Atlanta, Georgia, United States of America.

ABSTRACT
This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been "there" forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

Show MeSH