Team:LCG-UNAM-Mexico/Notebook/2008-August

MODELING:
Hill cooperativity 5th Reaction Reminder:

A + B <--> AB
Ka=Keq=[AB]/[A][B]=1/Kd
θ=[AB]/([AB]+[A])=[B]/([B]+Kd)

MWC Model (Cooperativity)
A + nB <--> ABn
Ka=Keq=[ABn]/[A][B]n=1/Kd
θ=[B]n/([B]n+Kd)
log(θ/(1- θ))=nlog(B)-log(kd) …Hill's equation

Suppression mediated by cI:
ρ + nCI <--> ρ:CIn (k+, k-)
Keq=Ka=[ρ:CIn]/[ρ][CI]n
Si ρ0=[ρ]+[ρ:CIn]
… ρ0=[ρ]+Keq[ρ][CI]n
=> ρ= (ρ0/Keq)/((1/keq)+[CI]n)

Flow= k+[ρ][CI]n = K+((ρ0/Keq)/((1/Keq)+[CI]n))[CI]n

Flow= k+([ρ0]/Keq) [CI]n / ((1/Keq)+[CI]n)

=> Vm= k+([ρ0]/Keq) & Kp=1/Keq=Kd

Therefore:
Keq = exp( -ΔG / R T )
k+ = (KB/h) T exp( -ΔG / R T ) = (KB/h) T Keq

MODELING:
Hill Cooperativity

5th Reaction, conflict

If we consider that:

  - Keq = exp (-ΔG / R T)

  - k + = (KB / h) T exp (-ΔG / R T) = (KB / h) T Keq

and given that the flow is (k + / Keq) [ρ0] [CI] n / ((1/Keq) + [CI] n), the value of the maximum speed of the flow loses its meaning.

The speed limit is being determined by (k + / Keq) [ρ0], but k + / Keq = (KB / h) * T, and we know that [ρ0] is arbitrary, i.e., Vmax is no longer based on the reaction as such, which does not make sense.

For example: Take the same reaction that we are considering, the maximum speed of the flow of the reaction would be the same with the promoter that has the operators of CI, that if you used one with a random sequence, so, whether we repeated the experiment, with the same temperature and the same concentration of DNA and an equal number of copies of the sequence, the maximum speed reached by the flow would be the same for the real promoter as for for any sequence, without taking any consideration with their affinity for their substrates... That does not makes sense!

The proposed explanation is that the equation used to determine k + does not fit our model. We should explore other possibilities.

MODELING:
Hill Cooperativity:
5th Reaction, solving the problem:

The error in the previous approach was that we were considering ΔG to be the same for both equations (for Keq & k+).

We know that the equilibrium depends solely on the difference in the free energy of Gibbs between the substrate and the product (ΔG 'th). The one with less energy will be favored in the balance, while the rate of reaction depends on the activation energy needed for the conversion (ΔG ‡). A reaction reaches equilibrium faster or slower depending on the rate of reaction (depending on the magnitude of its ΔG ‡), but the balance itself does not change.

Thus:
Keq = exp (- ΔG 'º / R T)
k + = (KB / h) T exp (- ΔG ‡ / RT) ≠ (KB / h) T Keq

GROUP MEETING
Wet Lab Statusk

Objectives:
- Build the bioparts.
- Transform the bacteria with the construction that we have.
- Design the experiments to test our construction.
- Build the system.
- Collaborate with the modeling group.

To do:
- Extract DNA from the wild type strain to obtain RcnA.
- Get the bioparts catalog.
- Obtain a large amount of plasmid that we can use, and amplify the bioparts.
- Transformation of the bacteria with bioparts.

Currently:
- There are plasmids.
- There are parts already amplified and in a plasmid.

Problems:
- The DNA that we needed was not in the registry.
- The oligos were delayed 2 weeks and a half.
- Issues to extract the plasmid from the colonies.
- Make a PCR ligation with the three parts and amplify with the ends (it did not work).
- With the enzyme used the frequency of spontaneous mutation was increased to about an error every thousand base pairs.
- There is a problem with tetracycline. You get false positives.

What can be done:
- The biopart with RcnA can already be linked to the plasmid.
- For the other construction we will have to link two parts and digest them, then link them with the third part and digest once more, then insert into the final plasmid.
- HindIII can be used with the large biopart to verify the sequence.

Electrodes:
- Will they be specific for Nickel?

We received an e-mail from the Mexico-UNAM-IPN with several questions in regards to our project, here is our reply:

Hello,
We apologize for the late reply, but we had to discuss carefully our answer.
First of all, we think you are confused about what our project really is. We want to make bacteria to modify the extracellular nickel concentration in response to an external signal (AHL in this case), and of course, be able to predict to what extent the concentration of the input signal will affect the amount of nickel in the medium. To achieve this, it is true we have to synchronize our cell population at the beginning. This is easy to do and doesn't represent any technical problems.
We are very conscious of the facts you tell us, first: we know the half-life of the lactones is relatively long (24 hrs as you say). That's why we are including AiiA under a constitutive promoter in our model, which degrades AHL very efficiently. This will ensure AHL does not saturate the medium. Second, we know AiiA does not diffuse freely through the cell membrane. However, we don't need that to happen, as each cell will degrade its own AHL (yes, we are assuming that all AHL will enter a cell within a window of time).
In other words, we do not need to synchronize the bacterial population more than in the first step. We are considering that some cells may respond earlier than others. However, we are assuming that, as we are not changing the physical nor chemical conditions, the proportion of cells responding "earlier" will remain constant, thus allowing us to draw some conclusions of the behaviour of the population as a whole. We hope you see why the synchrony is no longer important for our project.

To summarize what we plan to do, AHL will enter the cell and form a dimer with LuxR (which is under a constitutive promoter, so AHL is the only limiting step). This will start the transcription of cI*, which will repress the expression of RcnA. RcnA is the nickel efflux pump, and thus we are aiming to predict the amount of AHL necessary to get the desired extracellular nickel concentration.
We are doing small moves. At first, we only want to make one successful assay. We hope that in the near future we will be able to use the response time of the system to generate a succession of desired nickel concentrations, thus generating a song.
We hope this letter answers your questions,

LCG-UNAM-Mexico Team
Cuernavaca, Morelos

MODELING:
Reaction 3, AHL:LuxR
Conflict: k3 (ON) <k3 (OFF)?
Reference: Goryachev et al. (2006)

The references they cite for obtaining their parameters were not specific for that kind of parameters, in fact, one mentions the rate of RNA polymerase in HUMAN!
- Check whether the article mentions how they transformed the parameters.

They seem to explain why in their model, the k3(ON) is "so small" to start with:
<<common to all models considered here, is that the stability of the state "off" defined by the constitutive Transcription levels of I and R comes at a price of high value for the critical self Extracellular concentration.>>

This explains the criteria they used to determine their parameters:
<<For each layout we attempted to identify a set of parameters that optimize the functional fitness of the network. The search in the parameter space is constrained by requesting that the kinetic parameters must remain in the biologically realistic range and the resulting network should demonstrate the behavior compatible with our present understanding of the phenomenon quorum sensing.>>

MODELING:

Reaction 4: Natural degradation of cI*

Today we sent an e-mail to Dr. Peter Chivers, an expert in RcnR, to ask him for information in regards to RcnA.

Our mail to Dr. Peter Chivers:
Dr. Peter Chivers,

Hi! My name is Carlos and I'm a student of the Undergraduate Program in Genomic Sciences of the National Autonomous University of Mexico and currently I'm on the fourth year.

The main reason of this e-mail is to get in contact with you, I'll explain you why as briefly as I can. Several students of the program decided to participate in a systems biology competition known as iGEM, and our project focuses on regulating nickel efflux in e. coli. We have to both build the circuit and design a mathematical model to accurately predict the behaviour of our system.

Taking several issues in consideration we decided to regulate RcnA.
Here is the page of our team in case you're interested in reading more about our project:

https://2008.igem.org/Team:LCG-UNAM-Mexico

However we've been having some trouble in finding parameters for our model (such as RcnA's half-life, efficiency, synthesis rate among others). Therefore, having exhausted (or so we believe) the literary resources and having found your name in many of the papers regarding RcnA we decided to contact you. I'll try to explain with more detail the parameters we still lack in case you're interested in providing us with information.

I greatly thank you for taking the time to read this e-mail and await your answer.

Carlos Vargas


Dr. Peter Chivers' reply

Dear Carlos,

Thank you for your e-mail. From what I read on your website, it looks like your team is tackling an interesting project. Unfortunately, there are very few papers on RcnA itself, and none of them have examined the parameters that you need for your model. As far as I know, the groups that have published in the RcnR/RcnA area don't typically do those sorts of measurements so they are unlikely that have the data you need. We have no plans to do these experiments as my lab focuses on the nickel responsive regulators, RcnR and NikR.

I'm sorry that I can't be of more assistance. Good luck with your project, I hope it is well received at the iGEM competition.

Best regards,

Peter

MODELING:
Checking parameters:

Reaction 6
The value that had been found before for k6 (Pl) = 0.20mM / h is in reality the flow of the reaction (which is why the units are mM/h). That is, how many mRNA molecules are being produced per unit of time. The system in which they measured this parameter is a derivative of the plasmid pBR322, pTrc99A. It has the same origin of replication and the number of copies is estimated at 15-20 but under certain conditions where replication is limited it appears to be between 3-5 copies.

Using the previous information we can calculate the value of k+ of the reaction in our system if we consider that each promoter acts independently and we multiply by the ratio between the number of copies of our plasmid and those of their plasmid.

MODELING:

To-do List 1. Find Missing Parameters.
- cI Dimerization.
- Nickel efflux . (Estimate?).
- RcnA degradation.
- Nickel Internalization (Experimentally,?).
- Initial concentrations (aiiA, LuxR? (Define arbitrary medium), ? (by number of copies of the plasmid; change to molar), Ni-ext (experimental)).
2. Review tools in SimBiology (sensitivity analysis, parameter estimation, moiety conservation).
3. Stationary states of the system (whether there is multistationarity).
4. Jacobian.
5. Analysis of the stechiometric matrix (also analyze the null space and its transpose).
6. Electrochemical theory (the relationship between electric potential and the concentration of nickel).
7. Electrodes.
->We need to check for advances in the construction of the measurement device we will use.
->Take into account the possibility of asking for support to Dr. Peña.