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	link
d_{mRNA_RIBOKEY}	0.00462 s^-1		link
d_{closed_mRNA_T7}	0.00462 s^-1		link
d_{open_mRNA_T7}	0.00231 s^-1		link
d_{open_mRNA_T7_complex}	0.00231 s^-1		link
Equilibrium constants
K_{eq_1}	0,015 [M]	between closed and open T7 mRNA, experimental	link
K_{eq_2}	0.0212 [M]	between closed T7 mRNA and key unlocked mRNA complex, experimental	link
Rate constants
k_dis	100 s^-1	derived from experimental values
k_complex	57 s^-1	derived from experimental values
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

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 66: / Line 66: @@
 | K<sub>eq_1</sub>
 | 0,015 [M]
-| closed and open mRNA, derived from experiments
+| between closed and open T7 mRNA, experimental
 | [http://parts2.mit.edu/wiki/index.php/Berkeley2006-RiboregulatorsMain link]
 |-
 | K<sub>eq_2</sub>
 | 0.0212 [M]
-| closed and key unlocked mRNA complex, derived from experiments
+| between closed T7 mRNA and key unlocked mRNA complex, experimental
 | [http://parts2.mit.edu/wiki/index.php/Berkeley2006-RiboregulatorsMain link]
 |-