BME494s2013 Project Team2: Difference between revisions
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As described above, fitting this data to a mathematical equation allows us to solve for parameter values of the system, from which we can infer information about production of the output. The Hill Coefficient, n, can be found from this fit. The Hill Coefficient occurs at the inflection point of the rising output curve, meaning it represents the maximum rate of GFP production. The inflection point is also the maximum of the curve of the derivative of the polynomial fit equation, so n will also appear there. The parameter K described above is related to the Hill Coefficient, n. K represents the input concentration at which n occurs. In our mathematical model, K and n are the x and y values at which the inflection point of the GFP production curve occurs, and at which the maximum of the derivative of the fit curve occurs. To find the maximum rate of GFP production relative to input concentration, the derivative of the polynomial fit equation was graphed, and its maximum was found. The input concentration, or x-axis, value was found at this maximum. This value is K, the input concentration at which the maximum rate of GFP production occurs. The output level, or y-axis, value at this maximum was found. This value would be n, the Hill Coefficient, which is the maximum GFP production rate. | As described above, fitting this data to a mathematical equation allows us to solve for parameter values of the system, from which we can infer information about production of the output. The Hill Coefficient, n, can be found from this fit. The Hill Coefficient occurs at the inflection point of the rising output curve, meaning it represents the maximum rate of GFP production. The inflection point is also the maximum of the curve of the derivative of the polynomial fit equation, so n will also appear there. The parameter K described above is related to the Hill Coefficient, n. K represents the input concentration at which n occurs. In our mathematical model, K and n are the x and y values at which the inflection point of the GFP production curve occurs, and at which the maximum of the derivative of the fit curve occurs. To find the maximum rate of GFP production relative to input concentration, the derivative of the polynomial fit equation was graphed, and its maximum was found. The input concentration, or x-axis, value was found at this maximum. This value is K, the input concentration at which the maximum rate of GFP production occurs. The output level, or y-axis, value at this maximum was found. This value would be n, the Hill Coefficient, which is the maximum GFP production rate. | ||
[[Image: | [[Image:SyntheticFitDeriv.jpg |thumb|noframe|800px|left|'''5th degree derivative of the polynomial fit; maximum GFP production rate shown.''']] | ||
<br> | <br> | ||
Ideally, the GFP production rate measured by this method could be entered as a value for [which parameter] in the Ceroni et al. model. | Ideally, the GFP production rate measured by this method could be entered as a value for [which parameter] in the Ceroni et al. model. |
Revision as of 01:10, 28 April 2013
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Overview & Purpose
Yo... Joe! And Michael.... too! Yo yo yo, Joe Joe Joe (and Michael) put some shiz here (in the hizzhouse!) The food packaging industry is worth $100 billion dollars annually. Among that, about $77 billion dollars represents that meat packaging industry. Despite representing such a high economic value, the food industry still has recalls and contamination scandals every year. Contaminants often include pathogenic bacteria and allergens such as gluten. Synthetic biology offers a promising solution. A biological assay could be constructed to produce a fluorescent output depending on the presence of various contaminants. This could be done through a modification of the promoter of the GFP to detect a contaminant such as gluten. A quick swab of a food sample could be applied to the bacteria, and if gluten is present, then a green fluorescence could be identified. Our project is a proof-of-concept of this potential assay through an IPTG inducible Lac switch. When exposed to IPTG, GFP is produced, therefore indicating that various input substrates can yield fluorescence outputs.
Background: The Lac OperonThe Lac Operon is a gene specific to E. Coli that controls the cell's digestion of lactose. It consists of a promoter, an operator, three structural genes, and a terminator. It is both positively and negatively regulated, allowing expression to be contingent on the concentrations of glucose and lactose in the cell.
STRUCTURE
In addition to the structural genes, the Lac Operon includes a promoter and an operator region. The promoter region is the area to which the Lac I repressor and the CAP-cAMP complex bind, the mechanics of which will be discussed later (see Positive Regulation and Negative Regulation).
Why does this phenomenon occur? Well, like stated before, lactose is the cell's last resort energy source because it requires more energy from the cell to digest than does glucose. The enzyme that digests lactose is β-galactosidase, which can only be produced by initiating transcription of the Lac Operon. Thus, to be able to digest lactose, the cell needs to initiate transcription of the Lac Operon.
The genes encoding the LacI repressor are actually located upstream of the Lac Operon. The LacI gene is not regulated; therefore, it is produced continuously. It binds to the Lac Operon in the promoter region; however, it does not bind if there is lactose in the cell. Why is this? Well, the cell produces very low levels of β-galactosidase even when not in the presence of lactose. In these very low lactose conditions, β-galactosidase has a different function: it cleaves lactose and recombines it to form allolactose, which acts as an inducer for LacI. It binds to LacI and causes a conformational change, which in turn makes LacI unable to bind to the promoter region of the Lac Operon.
POSITIVE REGULATION: CAP-cAMP Complex
SUMMARY
If we analyze it from a digital logic context, we can describe glucose and lactose as inputs, and the transcription of β-galactosidase as an output. Furthermore, we can build a logic circuit symbolizing the operon's functionality (illustrated in diagram on left). When glucose acts as an input, it produces a NOT gate functionality (See Table 2). When lactose and the NOT gate output of glucose are incorporated as inputs to the system, they produce an AND gate functionality (see Table 3). Furthermore, there are a couple of other other proteins that "mimic" the function of lactose as an input for the natural lac operon. Among these are IPTG (used for our switch), and the previously mentioned allolactose which is an isomer of lactose.
Design: Our genetic circuitOUR GENE SWITCH:
As described above, the structural protein regions of the natural Lac Operon can be replaced by various other protein coding regions to alter the output of the Lac Operon. In the case of our gene switch, we chose to replace β-galactosidase with a gene coding for GFP, or green fluorescent protein. We used the lactose mimic IPTG as our system's input. Therefore, our switch turns "on" in the presence of IPTG, and produces a green fluorescent color as its output.
DEVICE STRUCTURE
Brick 2: GFP Production Brick
How it Works: The Role of IPTG and LacI
On the other hand, when an IPTG input is added to the system, this results in the following:
Building: Assembly SchemeDNA Assembly: IPTG Inducible Lac promoter cassette:
GFP brick (includes RBS, GFP gene, and terminator):
Vector:
PCR was used to amplify the DNA parts and add the primers prior to assembly. The copied DNA parts are purified and then ligated using the BsmBI/ T4 ligase mediated assembly
Forward Lac-I primer: cacaccaCGTCTCaTAGAttgacggctagctc Reverse Lac-I Primer: cacaccaCGTCTCaTAGAtgagctagccgtcaa Forward GFP Brick Primer: cacaccaCGTCTCaaaagaggagaaata Reverse GFP Brick Primer: cacaccaCGTCTCaTAGTtataaacgcagaaag Forward Vector Primer: cacaccaCGTCTCaactagtagcggccgct Reverse Vector Primer: cacaccaCGTCTCatctagatgcggccgcg
Testing: Modeling and GFP Imaging
We used a previously published synthetic switch, developed by Ceroni et al., to understand how our system could potentially be modeled and simulated. A mathematical model is a mathematical representation of system behaviors defined by the relationships between various system parameters. Parameters are simply different values that affect the behavior of the system. One could even use a simple algebraic equation to represent a mathematical model. In the following equation,
the equation "3x - 7" would be a mathematical model of the system y. Because the value of x affects the ultimate value of y, x would be a parameter of this system.
AN INTERACTIVE MODEL
When analyzing this model, we were concerned with three main things: how mRNA concentration changed over time, how IPTG concentration changed over time, and how the concentration of β-galactosidase changed over time. We ran a simulation setting the concentration of IPTG at an arbitrary value of 0.32 and produced the following three graphs: As we can see from the graphs on the right, plotting mRNA concentration over time (Figure 1) results in a curve that oscillates around the value of 6.06x10^-4. Plotting IPTG concentration over time (Figure 2) results in a straight line, which is unsurprising considering that the model assumes that IPTG stays constant over time for simplification purposes, which is of course not true in real life. Plotting the concentration of β-galactosidase over time (Figure 3) results in a curve that seems to max out at a value of 4.5x10^-4. Logically, this makes sense: at some point in time, the rate of production of β-galactosidase (Alpha_B) must reach the degradation rate of β-galactosidase (Gamma_B), meaning that the concentration of β-galactosidase will no longer increase; it will simply stay the same no matter how much more IPTG is added to the system.
As described above, fitting this data to a mathematical equation allows us to solve for parameter values of the system, from which we can infer information about production of the output. The Hill Coefficient, n, can be found from this fit. The Hill Coefficient occurs at the inflection point of the rising output curve, meaning it represents the maximum rate of GFP production. The inflection point is also the maximum of the curve of the derivative of the polynomial fit equation, so n will also appear there. The parameter K described above is related to the Hill Coefficient, n. K represents the input concentration at which n occurs. In our mathematical model, K and n are the x and y values at which the inflection point of the GFP production curve occurs, and at which the maximum of the derivative of the fit curve occurs. To find the maximum rate of GFP production relative to input concentration, the derivative of the polynomial fit equation was graphed, and its maximum was found. The input concentration, or x-axis, value was found at this maximum. This value is K, the input concentration at which the maximum rate of GFP production occurs. The output level, or y-axis, value at this maximum was found. This value would be n, the Hill Coefficient, which is the maximum GFP production rate.
Human Practices
Our Team
Works Cited[1] Heller, H. Craig., David M. Hillis, Gordon H. Orians, William K. Purves, and David Sadava. Life: The Science of Biology. Sunderland, MA,: Sinauer Ass., W.H. Freeman and, 2008. N. pag. Print. [2] Escalante, Ananias. "Regulation I." Class Notes. University of Arizona. 20 February 2013. [3] Registry of Standard Biological Parts. Web. 25 Apr 2013. <partsregistry.org>. [4] Slonczewski, Joan, and John Watkins. Foster. Microbiology: An Evolving Science. New York: W.W. Norton &, 2009. Print. [5] Schmidt, Markus. Synthetic Biology: Industrial and Environmental Applications. Weinheim, Germany: Wiley-Blackwell, 2012. Print. [6] Filho, Ernesto R., Fransisco L. Nunes, Jr., and Sidney O. Nunes. "Synchronus Machine Field Current Calculation Taking Into Account the Magnetic Saturation." SciELO - Scientific Electronic Library Online. N.p., May 2002. Web. 26 Apr. 2013. [7] "Haynes:TypeIIS Assembly." OpenWetWare, . 25 Feb 2013, 18:20 UTC. 18 Mar 2013, 03:49 <http://openwetware.org/index.php?title=Haynes:TypeIIS_Assembly&oldid=679110>. [8] Engler C, Gruetzner R, Kandzia R, Marillonnet S. (2009) Golden Gate Shuffling: A One-Pot DNA Shuffling Method Based on Type IIs Restriction Enzymes. PLoS One. 4 |