# IGEM:IMPERIAL/2006/project/parts/BBa J37022

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## Contents |

### J37022 Testing Protocol

## Motivation & Design

AiiA forms an integral part of the biological oscillator acting as our predator in the Lotka-Volterra Predator-Prey Model. By testing and characterising this part individually, we can find the rate at which AiiA converts N-acyl homoserine lactone (AHL) into it's inactive form by cleaving the lactone ring (AHL-lactonase activity) at the ester bond.

Parameters to explore:

- Activity of AiiA
- Half-life of AiiA

Michaelis-menten kinetics would determine the activity of the enzyme, thus if we can characterise AiiA based upon it's activity (turnover rate) and half-life, the AiiA construct (part J37025) can be placed anywhere and easily integrated into more complex systems given it's transfer function defined by the enzyme parameters.

Part J37022 is comprised of an AiiA protein coding region with a FLAG immunotag on the 5’ end and a LVA degradation tag on the 3’ end of the sequence. This AiiA protein coding region is ligated to both an RBS and a terminator. The transcription of the entire sequence is controlled by IPTG inducible LacI promoter.

The actual construct that will be placed into the predator cell will be the test construct without the LacI promoter.

Ideally, we would like to be able to characterise AiiA before we implement it into our predator cell and actually build the biological oscillator construct. We strive to measure the half-life of our AiiA as well as Vmax and Km, as defined by Michaelis-Menten enzyme kinetics.

## Creating the Part

We first begin by constructing part J37023 by adding the FLAG immunotag onto C0060, an AiiA construct already with an LVA tag (C0060 is available for us to use). We then ligate this part onto the B0015 terminator (available and working) sequence forming part J37024. Once we complete J37024, we can further ligate this part with either B0034 (RBS) to form the actual oscillator construct, or J04500 (pLacI + RBS) to form J37022 to form J37022 test construct

Individual Parts Contributing to J37022:

- J04500 - LacI promoter with RBS (R0010 + B0034)
- FLAG - Antibody tag (commercially available)
- C0060 - AiiA LVA tagged protein coding region (available)
- B0015 - Terminator (available and working)

__Description__:

IPTG or lactose will induce transcription of the AiiA gene with both the Flag and LVA tags. Flag tag will enable quantitative determination of concentration of AiiA, whilst LVA enhances degradation of the protein. Enhanced degradation for AiiA (C0060) was desired for our project so as not to destroy the oscillations. The terminator and RBS were chosen due to their efficiency values. LacI promoter was chosen due to it's quick response to IPTG versus a pBad promoter in response to arabinose.

__Input__:

- IPTG

__Output__:

- AiiA with LVA and Flag Antibody tags

## Modelling

A simple model can be created for part J37022. We have assumed that the transcription of AiiA is activated by IPTG, so quasi-michaelis-menten kinetics can be applied for this model with ITPG acting as an activator. The only input we have is the concentration of IPTG. At higher values of IPTG, we expect more production of AiiA.

Assumptions:

- IPTG degradation is much longer in magnitude than AiiA degradation, so we can neglect it
- IPTG activates transcription of the gene in michaelis-menten type kinetics with IPTG being the substrate (in high supply)

Input:

- IPTG

Output:

- AiiA concentration

Parameters:

- Vmax and Km values for IPTG activated transcription (both unknown)

Other comments:

- We don't need to know about the Vmax and Km values of the IPTG activated transcription, as we will be more focused on the steady state concentration of AiiA and not the time period from initiation to reaching stead state
- We need to continually monitor the concentration of AiiA to ensure that we have reached steady state
- Our output desired is to compare IPTG concentration with final steady state AiiA concentration
- We will use the FLAG (TM) tag to determine the half-life (as further discussed in the implementation section)
- We will use the AHL assay construct to determine the activity of AiiA (as further discussed in the implementation section)

Below you can see an image of the model that we used in CellDesigner to model the part. Following our assumptions and input/output, we have modelled IPTG activated transcription of AiiA from gene and subsequent degradation.

Below you can see the output simulation. As expected, with zero concentration of IPTG, no expression of AiiA occurs.

Depending upon the concentration of IPTG, the final steady state concentration of AiiA will change, as seen in the figure below.

### Calculation of the Halflife from the raw data

Assuming we already have AiiA within the cell and no IPTG inducing the production of more AiiA, then we can model the degradation of AiiA as normal first order kinetics, similar to radioactive decay. As a differential equation, we can easily write down:

The equation above can be solved and written in a linear form so that we can analyse a straight line graph as such:

Thus, if we plot ln[AiiA] vs. time, then the slope of the graph will yield the decay constant, kdeg. From this, it is easy to obtain the halflife of AiiA.

Part 2 of the halflife protocol deals with this kind of kinetics and we can easily obtain the value of the halflife by solving for kdeg, the decay constant. Intuitively, this is the easiest way of obtaining the halflife value of AiiA. However, if one analyses the production of AiiA, it might also be possible (thanks to Jimmy's observation) to calculate the halflife of AiiA simultaneously with the production of AiiA within the cell (part 1 of the halflife protocol). This will save a lot of time in testing, but ideally, we will test both to ensure we get similar results for the half-life.

So, if we consider the production of AiiA by transcription/translation within the cell as well as degradation of AiiA by cellular processes, we can express the rate of change of AiiA as a differential equation as shown below.

We can make some initial assumptions which will simplify our analysis. These are:

Since the concentration of mRNA is kept at a constant (we are assuming this will happen at steady state), we can rationalise the equations above to form a nice linear equation which can easily be obtained as per the equation below:

The slope will yield the decay constant from which the half-life can be obtained. The y-intercept will give the h value, and we can check to see if our assumption that

is true by making several trials of the experiment.

### Calculation of the Activity from the raw data

As AiiA is an enzyme, we are able to use the Michaelis-Menten equation to define the activity.

We can then rearrange the Michaelis-Menten equation into the standard Lineweaver-Burk equation as shown below:

Thus, if we are able to plot a graph of 1/v vs. 1/[S], then we can linearlise the Michaelis-Menten equation and easily calculate the value for the Km and Vmax. From our raw data, we will get several plots of AHL concentration over time with varying amounts of initial AHL concentrations. We can find the initial rates of reaction by obtaining the slope of the graph at t = 0 sec. We know the starting AHL concentration which is our substrate. By plotting several of these values (i.e. several AHL concentrations), we will be able to spread out the plot and have a more accurate linear line whose slope and y-intercept will yield the activity.

In deriving the Michaelis-Menten equation, we can also derive that:

This means that the value of Vmax will vary for every concentration of AiiA we use. The Michaelis-Menten derivation assumes that the concentration of enzyme is fixed, but in our oscillating system, the concentration of AiiA will be varying continuously. So, if we can decouple the AiiA concentration from the Michaelis-Menten equation, we can easily find the value of k2, the rate constant for the converstion of the enzyme-substrate complex to separate enzyme and product. This can easily be done by inducing the system with varying amounts of IPTG and seeing the final steady state concentration of AiiA within the system. (Done as one of the experiments) Once we have decoupled IPTG concentration to Aiia concentration, we can induce the test construct at varying levels of IPTG and repeat the entire experiment to obtain another value of Vmax (Km values should be the same...so this is also a reality check). We can then use the equation above to find the value of k2, which should be constant for any system regardless of enzyme concentration or substrate concentration.

## Implementation

See the J37022 Testing Protocol page for implementation.