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Chuck Norris facts:

smolen oscillator


Deterministic model - overview

As already mentioned, deterministic model is based on a system of ordinary differential equations, which needs to be solved. Deterministic model was implemented in the MATLABs toolkit SimBiology. The following differential equations were used (pT7* denotes the activated promoter, while pT7' is repressed promoter):

1. plasmid (T7 RNA polymerase under the control of T7 promoter and T7 RNA polymerase under the control of constitutive cytomegalovirus promoter):

Osci dif enacbe plasmid1.png

2. plasmid (transcriptional repressor NICTAL under the control of T7 promoter):

Osci dif enacbe plasmid2.png

3. plasmid (yellow flourescent protein Venus under the control of T7 promoter):

Osci dif enacbe plasmid3.png

MATLAB SimBiology project file (SBML) for this model can be found here. You can find how to set up the simulation in simbiology here.

Deterministic model - results

The following initial parameters were used for the simulation. Values represent relative concentration units, ratios were considered in later biological experiments:

[pT7_rnapt7] = 1 [pT7_ZNF] = 20 [pT7_gfp] = 2000 [pCMV] = 1

All other initial concentrations were set to 0.

Figure 1: Deterministic simulation of Smolen-type oscillator based on T7RNAP and artificial repressor. In deterministic simulation the first oscillation is higher - the so called starting impulse. After the starting impulse the result of deterministic simulation are steady and constant oscillations.

The base period of this simulation is around 2700 seconds, which is approximately 45 minutes. Model shows that longer periods (meaning lower frequency) can be achieved by adjusting the concentration of ZNF or T7 RNA polymerase under the control of T7 promoter. The first higher peak is due to the ramp-up of oscillator and it appeared in every simulation we ran. Note that these graphs show the concentration of the actual product of the reporter and not the repressed or activated promoters.

Stochastic model - Overview

Same chemical equations, constants and kinetic rates were used as in deterministic model. The script for MATLAB can be found here, while the input file for SGN Sim can be found here. Detailed explanation of what these two files contain is here.

Stochastic model - Results

Several different initial parameter values were used in order to see what happens with the system if we were able to adjust the degradation of repressors or if we adjust the amount of the initial promoter concentration. Figure 1 bellow presents the results obtained using parameter values that were the same as in our deterministic simulations.

Figure 2: Stochastic simulation of Smolen oscillator. The oscillation period is similar to the one from deterministic simulation.

Results are in accordance with our deterministic simulation, however stochastic simulation is a better approximation of the real system as it  include the 'random' nature factor. The period from stochastic simulation is little over 3000 seconds, which is approximately 50 minutes.

Figure 3: Eukaryonic versus prokaryotic cell oscillations based on the same initial parameter values - the oscillation period is expected to be longer in eukaryotic cells, because of the delay between transcription and translation.

The period of oscillation in eukaryotic cells is longer due to the delay between transcription and translation.

Both deterministic and stochastic simulations give similar results. Because Smolen oscillator is quite simple, the period length is shorter compared to repressilator.