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Modeling Scenario


Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: DNA\kinetis plasma rat pharmacokinetis

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Resource Image We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process.


Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Course Level
Key Scientific Process Skills
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level


Then we seek to compare the results of the final model with estimated parameters (as best we can) with our ``estimated" or ``rough" data to that in the paper.

A major obstacle in gene delivery is the transport of intact plasmid DNA (pDNA) to target sites.

We sought to investigate the kinetic processes underlying the degradation of pDNA in a rat plasma model, as this is one of the main components responsible for the clearance of pDNA after intravenous administration. We further sought to construct a complete kinetic model to describe the degradation of all three topoforms (supercoiled, open circular, and linear) of pDNA in a rat plasma model. Supercoiled pDNA was incubated in isolated rat plasma at 37oC in vitro.

At various time points, the plasma was assayed by electrophoresis for the amounts of supercoiled, open circular, and full-length linear pDNA remaining. The calculated amounts remaining were fit to linear differential equations describing this process.

In this model, pDNA degradation is considered to be a unidirectional process, with supercoiled degrading to open circular and then to the linear topoform.

The calculated kinetic parameters suggested that supercoiled pDNA degrades in rat plasma with a half-life of 1.2 minutes, open circular pDNA degrades with a half-life of 21 minutes, and linear pDNA degrades with a half-life of 11 minutes.

Complexation of pDNA with liposomes resulted in a portion of the supercoiled plasmid remaining detectable through 5.5 hours.

Article Files


Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations



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