Degradation of DNA in Plasma

Gene therapy is one biotechnology example of a clinical application where it is possible to produce proteins in vivo, using the body’s own mechanisms for protein production. Major issues in gene delivery involve the transport of plasmid DNA (pDNA) to target sites and the conversion between different forms of pDNA.

This example uses the Parameter Estimation feature with the Reaction Engineering interface to find the rate constants of three consecutive reactions involved in a DNA degradation process.

This application requires the Optimization Module.

Model Description

pDNA can be used to express proteins in the human body, proteins that can have therapeutic effects. pDNA exists in three forms — a supercoiled form (SC), an open-circular form (OC), and a linear form (L) — each with varying protein-expression rates. These pDNA-forms interconvert and degrade with time, which means a patient’s therapy benefits from knowledge about the distribution of pDNA-forms over time.

The protein expression rate for the SC form is greater than the one for the OC form, which in turn is significantly greater than that for the L form. The kinetic model in this study assumes that the pDNA-forms interconvert and decompose according to the mechanism in Figure 1.

Figure 1: Kinetic model of plasmid DNA interconversion and decomposition. Supercoiled pDNA (SC) converts to an open-circular form (OC), which in turn converts to a linear form (L). The linear pDNA decomposes to form linear fragments (F).

This example proposes a set of irreversible reactions in which an SC-form pDNA converts to the OC form and then to the L form. Then the L-form decomposes into a number of linear fragments, collectively denoted as F.

The three irreversible reactions in Figure 1 translate into these reaction rate expressions:

The rate constants k1 through k3 are found by parameter estimation, making use of the experimental data summarized in the table:

Table 1: Experimental Concentration Data.
Time (s)	cSC (ng/μl)	cOC (ng/μl)	cL (ng/μl)
5	9.3	0.5	0
60	5.0	4.1	0.1
120	3.5	6.5	0.3
180	1.1	7.0	0.5
300	0.5	8.1	0.8
420	0.1	8.0	1.2
600	0	7.8	1.7
900	0	7.1	2.4
1200	0	6.3	2.5
1800	0	4.5	2.6
2400	0	3.0	2.0
3000	0	2.1	1.8
3600	0	1.5	1.2

The unit of the experimental data in the table above is ng/μl (= 1·10-3 kg/m3). For consistent units the model variable, used in the optimization, is defined as the molar concentration (mol/m3) times the molar mass (kg/mol).

Results and Discussion

The following rate constants are calculated from the experimental data and proposed reaction mechanism: k1 = 9.6·10-3 (1/s), k2 = 4.8·10-4 (1/s), and k3 = 9.6·10-4 (1/s). In addition, the initial concentration of the SC species is estimated to 9.7 ng/μl.

Figure 2 shows the experimental values in the same plot as the simulation results. Clearly, the assumptions of the kinetic model are in agreement with the experimental findings.

Figure 2: A plot resulting from reading in experimental data and comparing it to simulation results.

The estimated rate constants show that the supercoiled pDNA rapidly transforms into the open-circular form with a half-life of approximately 1.2 minutes:

The open-circular and linear pDNA decay with half-lives of 24.1 and 12.0 minutes, respectively. As mentioned, the supercoiled pDNA has the highest protein-expression rate of the three forms. However, because the SC form has a half-life of only 1.2 minutes, it is likely that it decomposes during transport to the therapeutic target sites. These findings imply that you have to find ways to hinder the relatively fast decay of SC.

Reference

1. B.E. Houk, G. Hochhaus, and J.A. Hughes, “Kinetic modeling of plasmid DNA degradation in rat plasma,” AAPS Pharmsci, vol. 1, no. 3, pp. 15–20, 1999.

Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/dna_degradation

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Read model parameters from a text file.

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file dna_degradation_parameters.txt.

Read variable definitions from a text file.

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file dna_degradation_variables.txt.

The variable expressions are shown in yellow since the model variables re.c_SC, re.c_SC and re.c_SC are not created yet.

Start by entering the reaction properties in the interface.

Reaction Engineering (re)

The main fluid for DNA degradation in plasma consists of water. Set the to the "Liquid".

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

Reaction 1

In the toolbar, click

In the window for , locate the section.

In the text field, type SC=>OC.

Locate the section. In the kf text field, type k1.

Species: SC

In the window, click .

In the window for , locate the section.

Clear the check box.

Species: OC

In the window, click .

In the window for , locate the section.

Clear the check box.

Reaction 2

In the toolbar, click

In the window for , locate the section.

In the text field, type OC=>L.

Locate the section. In the kf text field, type k2.

Reaction 3

In the toolbar, click

In the window for , locate the section.

In the text field, type L=>F.

Locate the section. In the kf text field, type k3.

Species: F

In the window, click .

In the window for , locate the section.

Clear the check box.

Species 1

The species are dissolved in water. Add water as a solvent (the solvent water does not affect the final result).

In the toolbar, click

In the window for , locate the section.

In the text field, type H2O.

Locate the section. From the list, choose .

Parameter Estimation 1

Choose a feature to optimize the three reaction rate constants in the reactions entered in the interface.

In the toolbar, click

Select the parameters to be estimated and provide an initial guess. The parameter c_SC_init will be used to estimate the initial concentration of the species SC.

In the window for , locate the section.

In the table, enter the following settings:


Parameter	Initial value	Scale	Lower bound	Upper bound
k1	1e-3	1e-3

Click

In the table, enter the following settings:


Parameter	Initial value	Scale	Lower bound	Upper bound
k2	1e-3	1e-3

Click

In the table, enter the following settings:


Parameter	Initial value	Scale	Lower bound	Upper bound
k3	1e-3	1e-3

Click

In the table, enter the following settings:


Parameter	Initial value	Scale	Lower bound	Upper bound
c_SC_init	10[ng/ul]/M_pDNA	10[ng/ul]/M_pDNA

Prescribing scales for the estimation parameters increases the efficiency of the optimization procedure. A good starting point is to use scales of the same order as the initial values.

Experiment 1

Select an feature to import experimental data to which the simulation will be optimized.

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file dna_degradation_experiment1.csv.

Click

Note that the concentration unit in the imported data file is ng/μl, while the unit of concentration variable in is mol/m^3. To specify the unit, enter ng/ul in the column of the section. The mass concentrations equal the molar concentrations multiplied by the molar mass (M_pDNA), as defined in the node above. Enter these variables in the column .

In the table, enter the following settings:


Data column	Use	Model variables	Unit	Weight
Time	√	t	1	1
Conc. SC	√	m_SC	ng/ul	1
Conc. OC	√	m_OC	ng/ul	1
Conc. L	√	m_L	ng/ul	1

Initial Values 1

The default unit in feature is mol/m^3. For water, the density is 1000 [kg/m^3], its molar concentration (mol/m^3) is c_H2O_init = 1000 [kg/m^3]/18 [g/mol].