Difference between revisions of "Template:CLSB-UK Model MAK"
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=== Results fitting and analysis === | === Results fitting and analysis === | ||
| − | Having collected our results | + | Having collected our [[Team:CLSB-UK/Results|experimental results]] we reevaluated our model. We scaled the results to fit them on the graph, as they were in arbitrary units of fluorescence. We can plot this fluorescence is proportional to GFP concentration (specifically EGFP in our system).<ref>Furtado, A., & Henry, R. (2002). Measurement of green fluorescent protein concentration in single cells by image analysis. Analytical biochemistry, 310(1), 84-92.</ref> |
Revision as of 22:58, 28 October 2017
Contents
Mass-action kinetics
Mass-action kinetics is the assumption that the rate of reaction is proportional to concentration of the reactants. We chose to create a mass-action kinetics model as we could use relatively few parameters. Reducing the number of parameters, whilst keeping the model representative of the system, made it easier to understand the effect of varying each parameter. We built the model in MATLAB first, and later ported it to JavaScript to make it a better design tool for the biologists and better communicate how the model works.
Graph interactivity
We spent a long time reviewing previous teams models. A problem we found was that most models weren’t communicated in a way that was engaging and easy to understand. We’ve tried to explain our model in a way that someone with no experience in modelling could understand.
We’ve used interactive graphs on this page - when you get to them you can drag the sliders to change parameters and see how they affect the system.
We initially ported our model to a webpage so the design team could try out new stuff when they were designing our toehold switches. This turned out to be very useful for both of us. We decided to make it look a lot nicer and improve its compatibility with different browsers so we could put it on the wiki.
As a webpage it’s much more accessible - anyone (even on a phone) could use it without having to install any custom programs which would take both time to install and might require a license.
As far as we’re aware, we’re the first iGEM team to ever put up something like this. The closest was Pretoria UP 2016, but our graphs also contained our entire mass action kinetics model, instead of just a visualization.
It was built in JavaScript and therefore not limited by proprietary license agreements, and doesn’t require Java applets to be enabled (which modern browsers no longer support due to stability and security issues).[1]
JavaScript follows ECMA’s open standard so it can run on purely open-source tools. This helps acheive “iGEM’s goal of making everything in the competition open source”.[2] There are also a lot more open source libraries available for JavaScript which means other teams can build upon our work easier. These include Chart.js, the library we are using to draw the graphs.
Finally, our JavaScript code ran faster than our MATLAB code, which we attribute to both our greater experience in JavaScript and the aggressive optimisation that’s been done by vendors trying to compete for the fastest browsers.[3]
Initial mass-action kinetics model
We created our first model following a meeting with Thomas Ouldridge at Imperial, who recently coauthored a paper about mathematically modelling toehold-mediated strand displacement. In the meeting we agreed that we’d need to model the different states of the toehold switch. We also discussed modelling the miRNA binding and unbinding to and from the toehold base-by-base. We later decided against this, as whilst it may have been useful for learning about the kinetics of toehold switches it would not have given us useful information to put into our design process and would have overcomplicated our model.
We first modelled a simple system of 4 substances with reversible reactions as follows:
Where CTS, PBTS and OTS represent the toehold switch in closed, partially bound and open states respectively. At this point we didn’t know the value of the rate constants so we used placeholders.
This was useful as it gave us experience programming in MATLAB, which we hadn’t done before, as well as forced us to learn the foundations for the maths we’d need later; mainly ODEs. Khan Academy was very helpful with this.
With all three reactions being reversible, MATLABs dsolve function was not able to solve our differential equations. We tried them by hand but were not able to solve them analystically. We had to solve numerically and chose the Euler method. This involves iterating with short time intervals (here we used dt ≈ 1s) between each calculation using a loop to keep a record of how the substances changed over time. We then graphed these values as follows:
We’ve recreated this model so it’s actually running in the browser - try dragging the sliders above the graph to modify the rate constants.
Mass-action kinetics model with transcription and translation
The first simple model neglected transcription and translation completely, which meant it was an excessive simplification and consequently was not that useful. To address these shortcomings, we created a second model, derived from parts of Tobias Stögbauer’s PhD, with many more species.[4]
Following correspondence with Oxford’s modelling team, we changed the values of some of our parameters. Oxford recommended we used Karzburn’s 2011 paper, ‘Coarse grained dynamics of a cell free system’ for the translation constant. They also pointed out that we had forgotten to change some of the parameters’ units so our model was not dimensionally consistent, and we updated the model to fix those.
| Parameter name | Where we got it | Value |
|---|---|---|
| ktranscription | Used Tobias Stoegbauer’s PhD for this value, as it is equivalent to his kts value of 2.2NtPs-1 | 1.1×10-3s-1 |
| ktranslation | Karzburn’s 2011 paper gave 4 amino acids s-1[5]. As the GFP sequence we used was 239 amino acids long,[6] we simply did 4aa s-1 ÷ 239 aa. | 1.7×10-2s-1 |
| kopen | When we met Thomas Ouldridge at Imperial he suggested a range of 105 to 106 for this value, given his experience modelling toehold switches. | 6×105 M-1s-1 |
| kdecay | Estimate of messenger RNA decay rate in our cell free extract.[7] | 1.28×10-3 |
One of the biggest potential problems we identified was that if enough translation of closed switches occurred, it would be difficult to see any meaningful results. The kleakage parameter represents the ratio of translation rate on the closed and the open switch. We concluded that would not get any observable difference if translation on the closed switch was above a ten thousandth of the rate on the open switch, something we would never have been able to quantify easily without the model.
Without the model we wouldn’t have realised quite how crucial reducing leakage was. We spent a lot of time designing our switches to minimize leakage.
The lab team also asked us to find the optimal concentration DNA for both output variation and overall output. By varying ktranslation and the concentration of DNA we found that a higher concentration was better in general, however it would plateau eventually as miRNA consumption became the limiting factor. In the specific case of miRNA degradation being 2 orders of magnitude lower than the rate of degradation of the other RNAs the GFP concentration plateaued around 5×10-9 mol dm-3.
Try out the model for yourself and see if you can see our conclusions by changing the parameters to see the final output of GFP here:
Results fitting and analysis
Having collected our experimental results we reevaluated our model. We scaled the results to fit them on the graph, as they were in arbitrary units of fluorescence. We can plot this fluorescence is proportional to GFP concentration (specifically EGFP in our system).[8]
The major differences between the results and our theoretical values was the later maximum GFP concentration and the difference between the measured maximum and the theoretical maximum for 9×10-9moles/dm-3 of miRNA. In order to delay the peak in GFP concentration the rate of RNA decay had to be decreased. We also introduced a term for GFP degradation, to account for the peak in fluorescence. We then tried to fit the data by changing the parameters with these ideas in mind. The new values for these parameters were:
- kdecay ≈ 3×10-4
- GFPdecay ≈ 1×10-5
The other the parameters were varied within our uncertainties and we found to reduce the gap between the lowest miRNA concentration we should decrease kopen</open> to 105, the lowest possible value in our range.
Another way of solving this problem could be increase the decay rate of miRNA. We assumed it decayed at the same rate as the other RNAs in our system although if it decayed faster, and the other RNAs decayed slower, it had similar effect to changing kopen.
With our initial parameters our model was a poor representation of our system. Once we updated our parameters, it was able to represent our results relatively well. We found RNA decay had been significantly overestimated.
- ↑ Chrome Developers (2013, September 23). Saying Goodbye to Our Old Friend NPAPI. Chromium Blog. Retrieved October 9, 2017, from https://blog.chromium.org/2013/09/saying-goodbye-to-our-old-friend-npapi.html
- ↑ (2017). Competition/Deliverables/Wiki - 2017.igem.org. Retrieved October 1, 2017, from https://2017.igem.org/Competition/Deliverables/Wiki
- ↑ CreativeJS (2013, June 3). The race for speed part 1: The JavaScript engine family tree. Retrieved October 8, 2017, from http://creativejs.com/2013/06/the-race-for-speed-part-1-the-javascript-engine-family-tree/index.html
- ↑ Stögbauer, S. (2012) Experiment and quantitative modeling of cell-free gene expression dynamics. Ludwig Maximilian University of Munich, Germany
- ↑ Karzbrun, E., Shin, J., Bar-Ziv, R. H., & Noireaux, V. (2011). Coarse-grained dynamics of protein synthesis in a cell-free system. Physical review letters, 106(4), 048104.
- ↑ SnapGene (n.d.). eGFP Sequence and Map. Retrieved October 8, 2017, from http://www.snapgene.com/resources/plasmid_files/fluorescent_protein_genes_and_plasmids/EGFP/
- ↑ Shin, J., & Noireaux, V. (2010). Study of messenger RNA inactivation and protein degradation in an Escherichia coli cell-free expression system. Journal of biological engineering, 4(1), 9.
- ↑ Furtado, A., & Henry, R. (2002). Measurement of green fluorescent protein concentration in single cells by image analysis. Analytical biochemistry, 310(1), 84-92.
