Team:KULeuven/Model/Filter

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Filter

Position in the system

The filter is positioned immediately after the input, because its job is to filter out possible noise signals or background signals that aren't caused by the "desease". It is the starting piece of the whole system, situated before the invertimer- and the reset-subsystem.

Describing the system

ODE's

Parameters

*Parameter values Filter*
Name	Value	Comments	Reference
Degradation rates
d_{pT7 tag}	0.00155 s^-1	UmuD tag added to speed up degradation of otherwise too stable T7 polymerase	[http://www.openwetware.org/wiki/IGEM:Tsinghua/2007/Projects/RAP#Model_and_simulation link]
d_{mRNA RIBOKEY}	0.00462 s^-1	estimate: because this RNA isn't translated, it degrades faster	[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=124983&blobtype=pdf link]
d_{closed mRNA T7}	0.00462 s^-1	estimate: because this mRNA isn't translated, it degrades faster	[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=124983&blobtype=pdf link]
d_{open mRNA T7}	0.00231 s^-1		[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=124983&blobtype=pdf link]
d_{open mRNA T7 complex}	0.00231 s^-1		[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=124983&blobtype=pdf link]
Equilibrium constants
K_{eq 1}	0,015 [M]	between closed and open T7 mRNA, experimental	[http://parts2.mit.edu/wiki/index.php/Berkeley2006-RiboregulatorsMain link]
K_{eq 2}	0.0212 [M]	between closed T7 mRNA and key unlocked mRNA complex, experimental	[http://parts2.mit.edu/wiki/index.php/Berkeley2006-RiboregulatorsMain link]
Rate constants
k_dis	100 s^-1	derived from experimental values
k_complex	57 s^-1	derived from experimental values
k_closed	100 s^-1	derived from experimental values
k_open	1.5 s^-1	derived from experimental values
k_translation	0.167 s^-1	translation rate for B0032 RBS (0.3 relative efficiency)	[http://partsregistry.org/Part:BBa_B0032 link]
Transcription rates
TetR_var_transcr_rate	p(TetR) dependent	(RiboKey) between 5E-5 and 0.0125 s^-1 ~ [aTc]
k_{mRNA T7}	0,0011 s^-1	weak constitutive promoter J23109	[http://partsregistry.org/Part:BBa_J23109 link]

Remark: The key-lock system has been enhanced to 0.3%-14% (todo: new parameters will be added in a new overview)

Models

CellDesigner (SBML file)

Matlab (SBML file)

Simulations

1. AND gate of the filter

In the simulation we can clearly see this series of events:

when dark blue(ribokey) starts to increase, red (T7) also starts to increase, giving rise to an increasing amount of lactonase (blue) = AND-GATE.
when dark blue(ribokey) starts to decrease, red (T7) also starts to decrease, but much slower. The lactonase also starts to decrease, as it should be.

The short lifetime of the ribokey compared to the lifetime of the T7-protein, guarantees that the AND-GATE always works perfectly fine: when there's no more input, the ribokey will rapidly decrease (and disappear) and makes sure that the AND-GATE is not activated anymore, even when the T7-protein is slowly decreasing.

2. Filtering in practice

In the simulation three kinds of inputpulses have been used:

First pulse: 300s
- small peak of lactonase
- no influence on the timer

Second pulse: 1000s
- medium peak of lactonase
- influences the timer by levelling the timing capabilities, but it doesn't reset the timer

Third pulse: 5000s
- huge peak of lactonase
- reset of the timer: amount of complex goes to zero

Sensitivity Analysis

@@ Line 95: / Line 95: @@
 | derived from experimental values
 |
+|-
+| k<sub>translation</sub>
+| 0.167 s<sup>-1</sup>
+| translation rate for B0032 RBS (0.3 relative efficiency)
+| [http://partsregistry.org/Part:BBa_B0032 link]
 |-
 ! colspan="4" style="border-bottom: 1px solid #003E81;" | Transcription rates