# All entries for January 2006

## January 30, 2006

### D stability references

Had a chat with Iulian and got some references off him on D-stability

• The $D$-stability problem for $4\times 4$ real matrices
Serkan T. Impram, Russell Johnson, Raffaella Pavani [ PDF ].
• A Simple and Less Conservative Test for ${\Bbb D}$-Stability
Ricardo C. L. F. Oliveira, Pedro L. D. Peres [ DOI ]
• D-Stability from a Numerical Point of View,
Raffaella Pavani, Politecnico di Milano, Italy [ PDF ]
• this document states theorem on D-stability linking it with mixing stability like conditions:
http://cepa.newschool.edu/het/essays/get/local.htm#dynamic

Other notes matrix stabiliy:

• Hurwitz criterion too expensive for high dimentions
• Sign stability: most matrices of biochemical systems are not sign stable, so not a useful criterion
• most promising: find good criteria for D-stabiliy. rumour has it that the commercial LMA toolbox for matlab, which deals with matrix inequalities, might be able to help. orr maybe SciLab as the non-commercial substitute.

And finally we have also books about that, e.g.

• Matrix Diagonal Stability in Systems and Computation (Hardcover)
by Eugenius Kaszkurewicz, Amit Bhaya [ at Amazon ] [ and here ]

## January 25, 2006

### Update on the labwork

Meeting with Isabelle. Labwork will start mid-february. We will fuse a luciferace reporter Lux A/B (I believe) with the glnAP2 promoter to track transcription dynamics of glnG. Steps are:

• Amplify glnAP2 region including the lac1 operator sites with PCR.
• Add resctriction enzyme sites to the sequence to create the sticky ends.
• Insert the promoter region in front of the Lux A/B gene (restriction sites are in front of the gene sequence) which comes on a plasmid.
• Single out plasmid carrying cells by the ampillicin resistance gene Amp which is also on the plasmid.

There were other issues to think about..

• When cultures sit on a plate, they create a local environment by secretion so that they no longer need the ampicillin resistance. The chemostat circumvented that problem by constantly refreshing the medium.
• In liquid culture the clock could be startet by first adding and then removing a certain chemical. On plates its not that easy to manipulate the medium. What to do? Maybe back to liquid culture – there was something about plates with many small cylinders of which luminescence could be measured.

## January 09, 2006

### Paper: PII signal transduction proteins, Ninfa 2000

The Atkinson 2003 synthetic gene circuit relies among others on components of the bacterial nitrogen regulation system, more precisely on

• the glnG gene and its product, the NRI protein
• the glnAp2 promoter (product of glnA gene is GS) (requires NRI-P for activation)
• the glnKp promoter (also requires NRI-P for activation, activation less potent) (prodcut of glnK gene is glnK protein, PII like, see below)

To have a better understanding where these components are coming from I had a look at the above named paper Ninfa 2000 .

Remark:
It seem noteworthy that NRI-P has a inhibiting influence on the glnA transcritption at higher concentrations, and that glnK is only expressed at these higher concentrations. Or so I understand the description of the various levels of the response to nitrogen stress, see below .

Introduction:

• PII proteins, found in bacteria, Archaea and plants, are involved in coordinating carbon and nitrogen assimilation by regulation of correponding signal transduction enzymes. They integrate antagonistic signals of carbon and nitrogen status.
• developmental regulation systems probably eveolved from metabolic regulation systems.
• switching between regulatory cell types depending on carbon-nitrogen condition is reversible, but cell should not flip back and forth to often -> certain constraints.
• PII is direct and indirect sensor of various stimuli that cause the formation of different PII conformations

Nitrogen regulation in E. coli

• if ammonia is present, assimilation of ammonia into glutamine is regulated in response to the intracellular concentration of glutamine (nitrogen signal) and 2-ketoglutarate (2KG) (carbon signal).
• glutamine synthetase (GS) is responsible for most of the ammonia assimilation, closely regulated and limits the rate of nitrogen assimilation to keep it in balance with the rate of caron assimilation.

GS regulation

• GS regulated by a) regulation of its structural gene glnA and b) by regulation of GS activity by reversible covalent adenylylation.
• Adenylylation state of GS is controlled by the bifunctional enzyme adenylyltransferase (ATase)
• transcription of glnA requires transcription factor NRI-P (phosporylated NRI)
• phosphorylation of NRI is controlled by NRII
• So NRII and ATase control level and activity (respectively) and are at least in part controlled by PII

Role of PII

• PII inhibits autophosphorylation of NRII and activates its phophatase activity -> results in decrease in the extent of NRI phosphorylation.
• PII, by binding to ATase, activates GS adenylylation.

Regulation of PII

• PII activity in turn is regulated by small-molecule signals of carbon and nitrogen status:

PII regulation by nitrogen signal

• Glutamine is sensed by ATase and a bifunctional uridylyltransferase-uridylylremoving enzyme UTase-UR, which controls PII activity: it uridylylates PII if glutamine concentration is low and deuridylylates PII when the glutamine concentration is high.
• PII-UMP does not bind to NRII, thus at low glutamine, NRII can phosphorylate NRI, thus turning on nitrogen-regulated gene expresion Ntr including glnA, gene of GS.
• Further PII-UMP binds to ATase, stimulating deadenylylation of GS-AMP, activating GS.

PII regulation by carbon signal

• Carbon signals, mainly 2KG, directly bind to PII, which as a trimer has three binding sites for 2KG and ATP. Synergistic dynamics lead to binding of one 2KG and three ATP at normal concentrations and saturation of PII only at very high 2KG levels.
• 2KG saturated PII cannot interact with NRII or ATase. So carbon signal can counteract the effect of the nitrogen signal.
• Signals are sensed independently since saturation of PII by 2KG does not affect its interaction with UTase-UR.

• Concentration of the components of the signal transduction system must be balanced

Response of the cell to nitrogen stress (starvation)

• Level One: Increase of NRI and NRII expression.
• Level Two: Switching on of Ntr genes.
• Level Three: Switching on of nif genes (in some organisms).

Closer look at switch from first two second level response:

• The transcription factor NRI-P binds upstream enhancers and interacts with sigma RNA polymerase at the target promoters by means of a DNA loop, whose stability is further regulated by other factors.
• Boils down to: Each Ntr promoter becomes activated only when the NRI-P concentration is above a certain threshhold.
• Negative regulation of NRI-P has also been observed. In particular, the expression of glnA first increases and then decreases at high NRI-P concentrations.
• The Ntr genes of the second level require a higher level of NRI-P concentration than the glnA promoter.
• One second level gene is GlnK, which encodes the PII like protein GlnK, which seems to be designed to function under nitrogen starvation conditions. It might serve a role similar to PII or replacing it under these conditions. Not fully understood.

## January 2006

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