Difference between revisions of "Team:Michigan/Modeling"

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<p>The action of thrombin switch 2.0 can be modeled as the system of chemical reactions below:
 
<p>The action of thrombin switch 2.0 can be modeled as the system of chemical reactions below:
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This allows us to treat transcription and translation as first order chemical reactions (assuming an excess of ribosomes, tRNA’s, and dNTP’s. The activation of the RNA switch by thrombin can be treated as a second order chemical reaction because it requires a bimolecular collision. Dissociation of thrombin and the RNA switch is omitted from this model for simplicity (K<sub>d</sub> of aptamers produced by SELEX is typically in the nanomolar to picomolar range). This yields the following system of differential equations where [Thrombin] indicates the concentration of thrombin in micromolar, [DNA] indicates the concentration of DNA in micromolar, etc.:
 
This allows us to treat transcription and translation as first order chemical reactions (assuming an excess of ribosomes, tRNA’s, and dNTP’s. The activation of the RNA switch by thrombin can be treated as a second order chemical reaction because it requires a bimolecular collision. Dissociation of thrombin and the RNA switch is omitted from this model for simplicity (K<sub>d</sub> of aptamers produced by SELEX is typically in the nanomolar to picomolar range). This yields the following system of differential equations where [Thrombin] indicates the concentration of thrombin in micromolar, [DNA] indicates the concentration of DNA in micromolar, etc.:
 
<br>image2<br>
 
<br>image2<br>

Revision as of 00:34, 19 September 2015

Modeling

The action of thrombin switch 2.0 can be modeled as the system of chemical reactions below:

Modeling1
This allows us to treat transcription and translation as first order chemical reactions (assuming an excess of ribosomes, tRNA’s, and dNTP’s. The activation of the RNA switch by thrombin can be treated as a second order chemical reaction because it requires a bimolecular collision. Dissociation of thrombin and the RNA switch is omitted from this model for simplicity (Kd of aptamers produced by SELEX is typically in the nanomolar to picomolar range). This yields the following system of differential equations where [Thrombin] indicates the concentration of thrombin in micromolar, [DNA] indicates the concentration of DNA in micromolar, etc.:
image2
In-vitro transcription of this type is expected to achieve a maximum rate of approximately 20ug of RNA per hour from 84 ng of template DNA. This gives a K1 of approximately .3776s-1. The amount of protein produced from active RNA per second (K3) varies depending on promoter strength, codon optimization, and other factors; however, a rough estimate for K3 might fall between 0.05s-1 and .5s-1 (.278s-1 was used in this model, but the exact value has not yet been determined, see future plans section). K2 must be determined experimentally. Solving the above system of differential equations gives:
image3
Where T0 is the initial concentration of thrombin (micromolar), and t is the time in seconds. As expected, this gives a [GFP] curve which is concave upward initially and then linearizes after all thrombin is bound to an RNA molecule (at this point a fixed concentration of active RNA is available for translation). As t increases to infinity, [GFP] approaches the expression .278T0t. Therefore, because the fluorescence of GFP is proportional to its concentration, the fluorescence output (RFU) observed is expected to be proportional to T0t as the reaction time approaches infinity; however, limitations such as the finite supply of tRNA in the reaction mixture cause the fluorescence to plateau after a time.

As expected, our experimental results for thrombin switch 2.0 contain a linear portion (r squared > .98 for all curves) between 25 minutes and 85 minutes (marked as 20 and 80 minutes on graph in results section due to differences between reaction start time and measurement start time). Interestingly, the slope of the regression varied by up to a factor of 2.3, with higher slopes observed at lower concentrations of thrombin. This suggests that K3 may actually vary significantly depending on the initial thrombin concentration present, possibly a result of ribosome saturation at higher levels of thrombin.

Note

In order to be considered for the Best Model award, you must fill out this page.

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.

Here are a few examples from previous teams: