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SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface and the volume. Good examples for such processes are processes governed by the heat equation, [1] that is, diffusion and heat transfer by thermal conduction. [2]
For example, some authors use s, indicating species. [ 2 ] x is used here to match the state space notation used in control theory but either notation is acceptable. N {\displaystyle {\bf {N}}} is the stoichiometry matrix which is an m {\displaystyle m} by n {\displaystyle n} matrix of stoichiometry coefficient.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.
Metabolic rate scales with the mass of an organism of a given species according to Kleiber's law where B is whole organism metabolic rate (in watts or other unit of power), M is organism mass (in kg), and B o is a mass-independent normalization constant (given in a unit of power divided by a unit of mass. In this case, watts per kilogram):
In biochemistry and pharmacology, the Hill equation refers to two closely related equations that reflect the binding of ligands to macromolecules, as a function of the ligand concentration. A ligand is "a substance that forms a complex with a biomolecule to serve a biological purpose", and a macromolecule is a very large molecule, such as a ...
The velocities in the differential equations above - and - are dependent on the reaction rates of the underlying equations. The velocities are generally taken from the Michaelis–Menten kinetic theory , which involves the kinetic parameters of the enzymes catalyzing the reactions and the concentration of the metabolites themselves.
For example, the most widely studied bacterium, E. coli strain K-12, is able to produce about 2,338 metabolic enzymes. [1] These enzymes collectively form a complex web of reactions comprising pathways by which substrates (including nutients and intermediates) are converted to products (other intermediates and end-products).