Sensitivity analysis: Models... have feelings too!

Vicki and Chinee has put quite an amout of time into tracking down those sensitive ones in our system. Vicki is currently working with the Sensitivity analysis tool in Matlab commandline in order to find the sensitive parameters that influence the GFP output the most. The following graph is the result her sensitivity analysis model has generated so far: (click to enlarge)



The closer the graph gets to 0, the lower the influence this parameter has on the GFP output, and vice versa. According to this graph, the kForward (reaction rates)values 1, 3, and 4 seems the most influential parameters relative to 2 and 5; thus these parameters will be looked at further.

From these results, Vicki performed parameter optimization on them. In parameter optimization function, she was able to play with the individual parameter values in order to come up with a best fit line model to the predicted levels of GFP output. The following is the graphical result of the above function.



Here, the circles represent the made up predicted data, and the colored lines represent each optimized parameters. The optimized rate constants for kForward1, 3, and 4 fit nicely to the pattern of the predicted data; however, the optimized rate constants for kForward 2 and 5 do not, meaning that these parameters do not play a big role in determining the GFP output values.

From these two functions, Vicki would be able to, once we get some lab results, optimize our significant rate constants to fit the behavior of our AI-2 system.

Along with Vicki, Chinee was also working on the parameter sensitivity; however, with a different tool. In Simbiology, Chinee was able to outline the key difference between the initial amount and the reaction rates of the parameter. The following is the graph when all the parameters have a reaction rate value of 1:



The following is the graph when all the parameters have a reaction rate value of 10:



The only difference between the above two graphs are that the lines in the second graph are much more steep than the lines in the first graph. This means that the reaction rate only influences how immediate the reactions happen.

And finally, the graph when all the parameters have an initial amount of 10:



The above graph is very different from the ones above. From this, one can see how initial amounts of parameter play a much bigger role than the rate constants of each parameters.

I, Kevin, and Carol attempted to fix some biological misunderstandings within the reactions, and produce a graph that displays the pattern of each parameters. The following is the graph:



The patterns observed are reasonable and match what was expected. The lab data is needed to get an accurate model of our system; however, from it we can still test the sensitivity of each parameters by changing them one by one and simulating the results.

We hope to get some lab data by this week.

Lab: Some Progress Finally!!!

Hi Everyone! Thanks for reading our lab blog once again! Just a quick lab update for all you readers this week. Emily has finally completed her mutant circuit for
luxOD47E. Congrats to her! Jeremy and Jamie are currently working on several things right now. First, they finally performed a plasmid switch from pSB1AK3 to pSB1AC3 for luxPQOU. Now that they have successfully switched plasmids, they will be constructing luxPQOU into pCS26 (surette vector) by cutting with NotI enzyme. Finally, they are working on verifying cllamda. Unfortunately, after many enzyme digestions, they are unable to verify that the sequence is in the vector. They are currently trying again and hopefully will get results later this week. Kevin is working on the reporter circuit and he is verifying that circuit today with restriction enzymes. He is going to look into how to test the mutant circuits this week as well. Finally I am still stuck with the sigma 70 promoter. Unfortunately, I am still unable to get any colonies. We are currently looking at other ways to optimize the results. Hopefully, I'll have better results to report next week! Thanks for reading!

Modelling: Collaborative Work

Hi Everyone! Not much to update for modelling this week. We had a big meeting with all the teams on friday, and the two modelling teams (Membrane Computing and Mathematical Modelling) will meet every tuesday and thursday for meetings. This will give us time to draw parallel between the two types of modelling. We have also discussed about how to seperate all the experiments to characterize our signalling system. All this detail will be touched tomorrow at the meeting. Other than that, not much to update. Hopefully next week, we have more to add! Peace :)

Modeling: Learning how to write

Hi everyone, its Carol again!
This week for modeling, we focused mainly on writing up several ways to characterize the AI-2 signaling system. The characterization methods that we decided to explore are the following:
1. Static Performance
2. Dynamic Response
3. Response Time
4. Robustness
The robustness part of characterizing the system would be the most interesting. The degree of robustness depends on how sensitive the system is to fluctuations and changes. If this part of the signaling system can be explored in more detail, it will be an advantageous component to our project. We spent the past week summarizing this in paper format. I am currently working on a promoter library, which will play a huge role in exploring the expression of luxPQ. Once the circuits are done, some of these experiments can be done in a few days. We will hopefully by the end this summer have some characterization done. Stay tuned! Signing off now, peace!

Carol Chan Battles LuxCDABE

Hi everyone, it’s Carol again! I won’t re-introduce myself again since I wrote the modelling blog a few days ago. I don’t have much to report since I’ve been having bad luck in the lab lately, actually from the start! I am working with Kevin (the nice individual) to construct the reporter circuit for the project; however, due to my lack of lab skills, I’m delaying the whole project and leaving Kevin with nothing to do! I’m just kidding. I spent a few weeks trying to concentrate DNA plasmids for LuxCDABE sequence in topo vector. After many failed maxi-prep and many mini-preps (with the help of my favourite lab equipment, the vacifuge), I was able to concentrate my sample. As well, before Biobrick construction, I was left with a difficult task of single site mutagenesis. For some reason (with my luck) after one trial I was able to mutate a specific site within the LuxCDABE gene. This past week, I was unable to successfully clone and transform the LuxCDABE into the Biobrick vector. The lab team are trying to think of other ‘innovative’ ways to get this large gene cloned into Biobrick vector. Hopefully, next week, I’ll be able to show some better results, as of now, only time will tell! Talk to you guys on Monday!

Modelling: How Engineers Understand the Social Life of Bacteria...

Hi! My name is Carol and I’m heading into my third year of biomedical and chemical engineering in the fall, and I have completed a degree in biomedical sciences. I love watching sports (especially football and hockey) and I enjoy cooking and reading. I’m part of the laboratory and modelling team, so you’ll be hearing from me lots this summer!

In the past few weeks, the modelling team focused on familiarizing with Matlab and Simbiology. Before I move on, I should introduce you to my team mates that make this team possible! Vicki is a recent graduate from Engineering from the University of Toronto and she has worked with Matlab and its applications extensively throughout her studies. Chinee is also a third year chemical engineering and has some experience with Matlab as well. Finally, Kevin who is going into his second year of Kinesiology is just helping out because he is just a nice individual! With all the skills from each team member, we believe that we can produce a great model for our project. Back to modelling, one of our facilitators (Dr. Nygren) gave us an assignment that helped us understand the program more. We had to model the three gene repressilator in Matlab via two different methods, stochastic and deterministic. I’m going to spend some time now to explain the two methods that we will be using to model our quorum sensing model.

Differential (Deterministic) Model

This model uses equations that involve derivatives to illustrate concentrations of different molecules within a network. In our case, we will be using equations to describe the concentrations of different molecules within the Autoinducer-II (AI-2) cascade. With the ability to solve the differential equations, we can investigate how the concentration of different molecules within the cascade modifies compared with initial conditions. However, this method of modelling is often used with systems with high concentrations of chemicals and we expect that the importance of rare events is low. Furthermore, this type of modelling is often used in smaller networks.

Stochastic Models

The other type of model that can be used to describe our model is through probabilistic equations that can describe the probability that a certain chemical reaction will occur between certain types of molecules at any instant. Furthermore, these equations can also be used to calculate the quantities of all species at the end of a small time step. Therefore, it is plausible to evaluate how the molecules within the cascade change over time by repeating this process over many steps. Since random variable input is involved with this type of modelling, each simulation run can produce varying results. By using averages through numerous simulation runs, a trend can be predicted. This type of modelling is used for small numbers of molecules because they take more computing power. This is because of the random nature of molecular interaction and it accounts for the probability of rare events occurring.

Our goal for this week is to successfully build the AI-2 system in Simbiology. We’ve been busy the last few weeks reading up on literature and we were able to successfully find some phosphorylation rates that can be incorporated into our model. Next week, we will show you what we’ve built in Simbiology and give you a tour of Simbiology and Matlab! Stay Tuned!