Team:Bologna/Modeling

From 2008.igem.org

(Difference between revisions)
(The genetic Flip-Flop)
Line 34: Line 34:
<br>
<br>
LacI-ON represents the stable state in which LacI gene is active and LacI protein represses the TetR gene expression, with a positive feedback.<br> Therefore, the LacI-ON state coincides with the TetR-OFF condition. On the contrary, the TetR-ON represents the state with the TetR gene active and the LacI gene silenced (LacI-OFF). Owing to the coexistence of two stable states (bistability), this circuit is capable of serving as a binary of memory. We denominated it Flip-Flop since it works as a SR Latch: LacI state is the  output and TetR state is the  output. Uvc is the set signal and IPTG is the reset signal. Indeed, IPTG stimulation inhibits LacI repressor, thus can cause the transition from the LacI-ON state to the TetR-ON, whereas UVc radiation inactiving LexA  repressor through the SOS response (Friedberg et al., 1995) can cause the opposite transition from LacI-ON to TetR-ON.
LacI-ON represents the stable state in which LacI gene is active and LacI protein represses the TetR gene expression, with a positive feedback.<br> Therefore, the LacI-ON state coincides with the TetR-OFF condition. On the contrary, the TetR-ON represents the state with the TetR gene active and the LacI gene silenced (LacI-OFF). Owing to the coexistence of two stable states (bistability), this circuit is capable of serving as a binary of memory. We denominated it Flip-Flop since it works as a SR Latch: LacI state is the  output and TetR state is the  output. Uvc is the set signal and IPTG is the reset signal. Indeed, IPTG stimulation inhibits LacI repressor, thus can cause the transition from the LacI-ON state to the TetR-ON, whereas UVc radiation inactiving LexA  repressor through the SOS response (Friedberg et al., 1995) can cause the opposite transition from LacI-ON to TetR-ON.
 +
 +
== Mathematical model ==
[[Image:tab.jpg|center]]
[[Image:tab.jpg|center]]

Revision as of 14:05, 27 October 2008

Logo1a.gifTestata dx.jpg
HOME TEAM PROJECT MODELING WET-LAB SOFTWARE SUBMITTED PARTS BIOSAFETY AND PROTOCOLS


Contents

Model-based analysis of the genetic Flip-Flop


The genetic Flip-Flop


The molecular circuit in Figure 1 works as a Flip-Flop (SR Latch), which can switch between two different states according to the external stimuli (UVc and IPTG).

Figure 1: Scheme of the genetic Flip-Flop


LacI-ON represents the stable state in which LacI gene is active and LacI protein represses the TetR gene expression, with a positive feedback.
Therefore, the LacI-ON state coincides with the TetR-OFF condition. On the contrary, the TetR-ON represents the state with the TetR gene active and the LacI gene silenced (LacI-OFF). Owing to the coexistence of two stable states (bistability), this circuit is capable of serving as a binary of memory. We denominated it Flip-Flop since it works as a SR Latch: LacI state is the output and TetR state is the output. Uvc is the set signal and IPTG is the reset signal. Indeed, IPTG stimulation inhibits LacI repressor, thus can cause the transition from the LacI-ON state to the TetR-ON, whereas UVc radiation inactiving LexA repressor through the SOS response (Friedberg et al., 1995) can cause the opposite transition from LacI-ON to TetR-ON.

Mathematical model

Tab.jpg
  • A common motif in repressor proteins is the presence of a dimeric nucleotide binding site. In accordance to this general structure the cooperativity coefficients () were assumed equal to 2.


In the model we distinguish between LacI protein binded to repressor IPTG F001.jpg and protein free F002.jpg.

Since F003.jpg and considering the law of mass action F004.jpg we can write:


F005new.jpg


Up

Adimensional equations


The equations (1.1) and (1.2) were modified to an adimensional form:


Equa2new.jpg

where:


F006.jpg
F007.jpg



Up

Equibrium conditions

At equilibrium and in absence of stimuli, the adimensional concentrations of LacI (i) and TetR (r) are related by the equation:

Equa3new.jpg

To obtain these equations the second term in equation (1.5)was ignored (). This is justified by the high binding constant of LexA for its operator, and the consequent low production of LacI (see Figure 1).


Up

Stability analysis

Assuming as starting condition the LacION state (Figure 1) its stability is guaranteed if the adimensional concentration of LacI is higher than 1 (Figure 2).
In the limit of (), equation (1.7) simplifies:

Experimental identification

The MAVs were identified comparing the experimental response of the genetic circuits in Figure

Numerical simulation

Bibliography

Up