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Kinetic Models in Biology and Chemistry
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| Organization: | Merck Research Laboratories |
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2006 Wolfram Technology Conference
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Champaign IL
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Dynamically changing systems in biology and chemistry are often modeled as a system of ordinary differential equations (ODEs). Biologists and chemists often represent these systems as a network of entities connected by arrows. For example, the Michaelis-Menten enzyme catalyzed reaction is written thus a The model for absorption and distribution of a drug is often drawn pictorially, as shown on the left, and can also be represented mechanistically, as on the right. illustration We will describe the package ChemicalKinetics.m that facilitates the use of these mechanistic representations for constructing the system of ODEs for both mass-action and Michaelis-Menten models. We have also developed two other packages: UnitsTools.m and ODEDerivatives.m. The functions in the former help the user verify that the dimensional units of the parameters of the model are self-consistent (and thereby avoid problems with transferability), and make it easy to use units with numerical functions such as NDSolve, NMinimize, and NonlinearRegress. The functions in the latter package define the rules by which Mathematica can automatically take derivatives with respect to parameters of the system of ODEs so that the user can perform sensitivity analyses and use gradient-based methods for parameter fitting.
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kinetic models, biology, chemistry
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| Kinetic Models in Biology and Chemistry.nb (3 MB) - Mathematica Notebook [for Mathematica 5.2] |
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