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Algebraic Models

Some processes are so simple that they can be described in terms of algebraic equations, either explicitly, or implicitly as the solution to a differential equation. Algebraic equations are usually defined by applying some law of physics like conservation of mass or conservation of momentum or a time or space dependent equation describing the temporal movement of something. For example this is an explicit algebraic model:

$\displaystyle \textrm{age} = x - \textrm{date of birth},$    

where $ x$ is today's date. An example of an implicit algebraic equation is the description of the time course of binding of drug to a receptor. The dynamics is best characterized by a differential equation (equating changes in the fraction of bound receptors to the difference between rates of forming and unforming bound receptors) which has a simple algebraic solution:

$\displaystyle b = 1 - e^{-(kD + l)t},$    

where $ b$ is the fraction of bound receptors, $ kD$ is the rate of making bound receptors, $ l$ is the rate of unmaking bound receptors and $ t$ is time.

Algebraic models are usually easy to explore because we can simple generate a sequence of values for the independent variable and plot the resulting values of the model's dependent variable.


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Next: Ordinary Differential Equations Up: How to create a Previous: Reverse Engineering   Index

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Frank Starmer 2004-05-19
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