BME494s2013 Project Team2: Difference between revisions
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[[Image:Food_Screening.jpg|thumb|140px||left|Effective food testing represents a very large portion of the culinary economy.]] | [[Image:Food_Screening.jpg|thumb|140px||left|Effective food testing represents a very large portion of the culinary economy.]] | ||
<!-- This is where you can get creative. Think of a practical application for a genetic input/ output switch that is based on the Lac switch you designed. Perhaps it can generate some useful compound instead of RFP/ GFP? Perhaps you could replace the Lac Repressor/ promoter part with something that binds to a different compound to make a sensor? Type a "10,000 foot" overview of your project below this comment line. What is your project's impact on the world? --> | <!-- This is where you can get creative. Think of a practical application for a genetic input/ output switch that is based on the Lac switch you designed. Perhaps it can generate some sort of useful compound instead of RFP/ GFP? Perhaps you could replace the Lac Repressor/ promoter part with something that binds to a different compound to make a sensor? Type a "10,000 foot" overview of your project below this comment line. What is your project's impact on the world? --> | ||
<!-- In the next paragraph, explain how the IPTG-input/ fluorescent protein-output Lac switch you proposed to build (in Unit 2) serves as a roof-of-concept for the practical application you just described --> | <!-- In the next paragraph, explain how the IPTG-input/ fluorescent protein-output Lac switch you proposed to build (in Unit 2) serves as a roof-of-concept for the practical application you just described --> | ||
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. | 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. Furthermore, food waste equates 1.3 billion tons annually. Lack of effective processing results in greater environmental damage through waste and economic damage through business scandals. | ||
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. | 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 | Our project is a proof-of-concept of this potential assay through an IPTG inducible modified Lac switch. When exposed to IPTG, a lactose mimic, GFP instead of β-galactosidase is produced, therefore indicating that various input substrates can yield fluorescent outputs. Future applications of the switch could be modified to incorporate a promoter that detects allergens such as gluten or even bacterial contaminants to help mitigate overall health risks. | ||
One such promoter might be the AHL sensor BBa_F2620 to detect quorum sensing (a form of cellular communication) in bacteria. This would allow for detection of the presence of bacteria by detecting various cellular signals. | |||
<br> | |||
<!-- These are lines breaks for spacing purposes. You can add or delete these as needed --> | <!-- These are lines breaks for spacing purposes. You can add or delete these as needed --> | ||
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<!-- Background information on the natural Lac operon. This should be based on Group Presentation 2 --> | <!-- Background information on the natural Lac operon. This should be based on Group Presentation 2 --> | ||
The 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. | The 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. | ||
<br> | <br><br> | ||
[[Image: Lac-operon-1.gif |thumb|400px||left|Structure of the Lac Operon [1]]] | [[Image: Lac-operon-1.gif |thumb|400px||left|Structure of the Lac Operon [1]]] | ||
'''STRUCTURE'''<br> | '''STRUCTURE'''<br> | ||
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==Design: Our genetic circuit== | ==Design: Our genetic circuit== | ||
'''OUR GENE SWITCH''': | '''OUR GENE SWITCH''': <br> | ||
<!-- Show a network/ circuit diagram of your team's Lac switch. Include a paragraph to explain how it works (i.e., how to switch the system from on to off and vice versa, and what happens to each component as the system switches between states) --> | <!-- Show a network/ circuit diagram of your team's Lac switch. Include a paragraph to explain how it works (i.e., how to switch the system from on to off and vice versa, and what happens to each component as the system switches between states) --> | ||
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 | 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 also chose to use IPTG instead of lactose as the system's input; we were able to do this because IPTG acts as a lactose mimic due to its similar structure and active regions. (Note: IPTG is frequently used as a synthetic replacement for lactose in systems created in laboratory settings.) Therefore, our switch turns "on" in the presence of IPTG (our input) and produces a green fluorescent color (GFP) as its output. | ||
<br><br> | <br><br> | ||
Also, we chose a promoter that was not sensitive to the CAP-cAMP complex so that our switch would not be influenced by the presence of glucose. Therefore, IPTG would be the only input affecting our system, as it would not be positively regulated by glucose intake. | Also, we chose a promoter that was not sensitive to the CAP-cAMP complex so that our switch would not be influenced by the presence of glucose. Therefore, IPTG would be the only input affecting our system, as it would not be positively regulated by glucose intake. | ||
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* The <b>GFP gene:</b> This is the gene that will be transcribed to produce GFP. <br> | * The <b>GFP gene:</b> This is the gene that will be transcribed to produce GFP. <br> | ||
* <b>Terminators</b>: These signal the end of the transcription process. <br><br> | * <b>Terminators</b>: These signal the end of the transcription process. <br><br> | ||
''' | '''HOW IT WORKS: THE ROLE OF IPTG AND LACI'''<br> | ||
The switch response of this device is due to the relationships it creates between IPTG, the LacI protein, and the GFP output. Transcription of the GFP output depends on the activity of the stage 2 promoter, the Lac-I regulated promoter. If this promoter is active, GFP will be produced. This promoter is regulated by the LacI repressor protein. Presence of the LacI protein inhibits the promoter, which turns off GFP production. The LacI protein is created in stage 1 of the genetic circuit. In its default state, the mechanism would operate as follows: <br> | The switch response of this device is due to the relationships it creates between IPTG, the LacI protein, and the GFP output. Transcription of the GFP output depends on the activity of the stage 2 promoter, the Lac-I regulated promoter. If this promoter is active, GFP will be produced. This promoter is regulated by the LacI repressor protein. Presence of the LacI protein inhibits the promoter, which turns off GFP production. The LacI protein is created in stage 1 of the genetic circuit. In its default state, the mechanism would operate as follows: <br> | ||
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==Testing: Modeling and GFP Imaging== | ==Testing: Modeling and GFP Imaging== | ||
'''A LAC SWITCH MODEL'''<br> | |||
'''A LAC SWITCH MODEL''' | |||
<br> | |||
[[Image:Another_Example_of_a_Mathematical_Model.gif |thumb|noframe|300px|right|Another example of a (very complex) mathematical model. [6]]] | [[Image:Another_Example_of_a_Mathematical_Model.gif |thumb|noframe|300px|right|Another example of a (very complex) mathematical model. [6]]] | ||
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* <b>a<sup>M</sup><sub>G</sub></b> - GFP transcription rate<br> | * <b>a<sup>M</sup><sub>G</sub></b> - GFP transcription rate<br> | ||
* <b>a<sup>M</sup><sub>L</sub></b> - LacI transcription rate<br> | * <b>a<sup>M</sup><sub>L</sub></b> - LacI transcription rate<br> | ||
<br> | <br><br> | ||
'''AN INTERACTIVE MODEL''' | '''AN INTERACTIVE MODEL''' | ||
<br> | <br> | ||
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* <b>Alpha<sub>B</sub></b> - Represents the production rate of Bgal (β-galactosidase), or the rate at which β-galactosidase is translated from mRNA. | * <b>Alpha<sub>B</sub></b> - Represents the production rate of Bgal (β-galactosidase), or the rate at which β-galactosidase is translated from mRNA. | ||
* <b>Cell = 1</b> - "Cell" represents the bacterial cell volume. This statement sets this volume to an arbitrary value 1.<br><br> | * <b>Cell = 1</b> - "Cell" represents the bacterial cell volume. This statement sets this volume to an arbitrary value 1.<br><br> | ||
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 | 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 graphs of mRNA concentration over time (Figure 1) and IPTG concentration over time (Figure 2) as shown. The concentration of β-galactosidase over time for this input concentration is the top blue curve in Figure 3. <br> | ||
[[Image:MRNAconc.jpg |thumb|noframe|300px| | [[Image:MRNAconc.jpg |thumb|noframe|300px|left|Figure 1: mRNA Concentration vs. Time]] | ||
[[Image:IPTG.jpg |thumb|noframe|300px| | [[Image:IPTG.jpg |thumb|noframe|300px|center|Figure 2: IPTG Concentration vs. Time]] | ||
<br> | <br> | ||
As we can see from these graphs, 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 (blue curve in 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<sub>B</sub>) must reach the degradation rate of β-galactosidase (Gamma<sub>B</sub>), 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.<br><br> | |||
[[Image:I6.jpg |thumb|noframe|520px|right|Figure 3: β-galactosidase Concentration vs. Time]] | |||
To further analyze how IPTG concentration affects the concentration of β-galactosidase, we thought we would change the initial value for the concentration of IPTG. We set the concentration of IPTG to the arbitrary value of 0.25 and produced the | To further analyze how IPTG concentration affects the concentration of β-galactosidase, we thought we would change the initial value for the concentration of IPTG. We set the concentration of IPTG to the arbitrary value of 0.25 and produced the second curve in Figure 3. | ||
From this curve we can see that when the IPTG concentration is 0.25, the maximum output of β-galactosidase seems to be about 3.0x10^-4. This value is significantly lower than the value procured from Figure 3; thus, we can infer that as the system input of IPTG concentration decreases, so does the system output of β-galactosidase. <br><br> | |||
Changing the input parameters and observing the simulated response would allow us to decide what levels of input concentration would be beneficial for Bgal output. Therefore, we varied the parameters in search of a cutoff input concentration level, above which would produce a sustained Bgal output, and below which would produce a declining output over time. After simulating several different initial concentrations, we found that the turning point occurred at about I = 0.063. | Changing the input parameters and observing the simulated response would allow us to decide what levels of input concentration would be beneficial for Bgal output. Therefore, we varied the parameters in search of a cutoff input concentration level, above which would produce a sustained Bgal output, and below which would produce a declining output over time. After simulating several different initial concentrations, we found that the turning point occurred at about I = 0.063. Figure 4 shows the resultant mRNA concentration in this case. The Bgal concentration over time was also graphed for this input concentration and appears as the bottom red curve in Figure 3. Therefore, transcription and the output Bgal decrease over time for an input concentration of I = 0.06, below the threshold we found. | ||
[[Image:mRNA06.jpg |thumb|noframe|300px|left|Figure 4: mRNA Concentration vs. Time, I = 0.06]] | |||
<br><br><br><br><br><br><br><br><br><br><br><br><br><br><br> | |||
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ImageJ software was used to track output data of one cell at a time across the 24 time points. The average intensity of the image across the chosen cell was recorded for each frame, since this brightness would correspond to GFP output level. Data of this nature was recorded for 8 different cells, allowing for the calculation of an average brightness or GFP production level at each frame or time point. This average production over time was then graphed using MatLab. Using MatLab's native fitting tools, a 6th order polynomial was fit to the plot and the equation for this polynomial was generated, as shown below. <br> | ImageJ software was used to track output data of one cell at a time across the 24 time points. The average intensity of the image across the chosen cell was recorded for each frame, since this brightness would correspond to GFP output level. Data of this nature was recorded for 8 different cells, allowing for the calculation of an average brightness or GFP production level at each frame or time point. This average production over time was then graphed using MatLab. Using MatLab's native fitting tools, a 6th order polynomial was fit to the plot and the equation for this polynomial was generated, as shown below. <br> | ||
[[Image:SyntheticFitting.jpg |thumb|noframe|800px| | [[Image:SyntheticFitting.jpg |thumb|noframe|800px|center|'''6th degree polynomial fit to the raw GFP output data; K value and Hill Coefficient, n, shown.''']] | ||
<br> | <br> | ||
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 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. The inflection point of the curve corresponds to the maximum of the derivative of the curve. Therefore, the maximum rate of GFP output production would occur at the maximum of the derivative curve of the polynomial fit equation. To find the maximum rate of GFP production relative to changing input concentration, this derivative was graphed and its maximum was found. | 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 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. The inflection point of the curve corresponds to the maximum of the derivative of the curve. Therefore, the maximum rate of GFP output production would occur at the maximum of the derivative curve of the polynomial fit equation. To find the maximum rate of GFP production relative to changing input concentration, this derivative was graphed and its maximum was found. | ||
[[Image:SyntheticFitDeriv.jpg |thumb|noframe|800px| | [[Image:SyntheticFitDeriv.jpg |thumb|noframe|800px|center|'''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 the GFP transcription rate, a<sup>M</sup><sub>G</sub> in the Ceroni et al. model. | Ideally, the GFP production rate measured by this method could be entered as a value for the GFP transcription rate, a<sup>M</sup><sub>G</sub> in the Ceroni et al. model. | ||
<br><br><br><br><br> | |||
==Human Practices== | ==Human Practices== | ||
<br> | |||
[[Image:GapAnalysis2.png|thumb|900px|center|'''Gap Analysis of the GFP Assay''']] | [[Image:GapAnalysis2.png|thumb|900px|center|'''Gap Analysis of the GFP Assay''']] <br> | ||
<!--Wait until Unit 3 to fill this in. Demonstrate that you have considered the societal aspects of your project - what could go wrong? Is it implementable? Etc.--> | <!--Wait until Unit 3 to fill this in. Demonstrate that you have considered the societal aspects of your project - what could go wrong? Is it implementable? Etc.--> | ||
'''Food Waste'''<br> | |||
1.3 billion tons of food thrown away yearly. This creates massive wastes ranging from environmental problems to simple affluence. Use of a faster colorimetric assay would be effective in mitigating the overall waste generated by food. This problem goes beyond economic incentives for the businesses. It also supports the consumer--individuals who are exposed to various contaminants and allergens that should not be found otherwise. The impact of reducing food waste would encourage a healthier ecosystem of effective resource stewardship, less landfills, and less health complications on both corporate and social levels. | |||
<br><br> | |||
==Our Team== | ==Our Team== | ||
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<div style="color: #808080; background-color: #ffffff; width: 600px; padding: 5px"> | <div style="color: #808080; background-color: #ffffff; width: 600px; padding: 5px"> | ||
[[Image: | [[Image:JoePhoto.JPG |thumb|noframe|130px|left|'''Kwanho Yun''']] | ||
Latest revision as of 16:39, 30 April 2013
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Overview & Purpose
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. Furthermore, food waste equates 1.3 billion tons annually. Lack of effective processing results in greater environmental damage through waste and economic damage through business scandals. 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 modified Lac switch. When exposed to IPTG, a lactose mimic, GFP instead of β-galactosidase is produced, therefore indicating that various input substrates can yield fluorescent outputs. Future applications of the switch could be modified to incorporate a promoter that detects allergens such as gluten or even bacterial contaminants to help mitigate overall health risks. One such promoter might be the AHL sensor BBa_F2620 to detect quorum sensing (a form of cellular communication) in bacteria. This would allow for detection of the presence of bacteria by detecting various cellular signals.
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: 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: As stated above, the device circuit is made out of 3 parts: The IPTG inducible Lac promoter cassette, the GFP brick and the vector. Listed below, are all the details and specifics for each part. IPTG Inducible Lac promoter cassette:
GFP brick (includes RBS, GFP gene, and terminator):
Vector:
Type IIS Assembly is used to assemble all the DNA parts to form the final device. Type IIS Assembly is protocol that is used to seamlessly assemble DNA parts through the use of a Type IIS restriction enzyme. Key features of Type IIS Assembly:
Before the parts can be assembled, PCR must be used to amplify the parts and to add the necessary primers. The copied DNA parts are then purified and ligated using the BsmBI/T4 ligase mediated assembly. To ensure a successful ligation step, the DNA parts were screened for BsmBI sites using APE. If any of the DNA parts contain the BsmBI sequence anywhere other then at their restriction sites, a separate primer is made to modify the sequence.
PRIMERS: The assembly also requires the design and use of custom primers. The purpose of the primers is to add BsmBI sites to the ends of all the DNA parts. The following custom primers are used for this device: 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 ImagingA LAC SWITCH MODEL 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.
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 graphs of mRNA concentration over time (Figure 1) and IPTG concentration over time (Figure 2) as shown. The concentration of β-galactosidase over time for this input concentration is the top blue curve in Figure 3.
To further analyze how IPTG concentration affects the concentration of β-galactosidase, we thought we would change the initial value for the concentration of IPTG. We set the concentration of IPTG to the arbitrary value of 0.25 and produced the second curve in Figure 3. From this curve we can see that when the IPTG concentration is 0.25, the maximum output of β-galactosidase seems to be about 3.0x10^-4. This value is significantly lower than the value procured from Figure 3; thus, we can infer that as the system input of IPTG concentration decreases, so does the system output of β-galactosidase. Changing the input parameters and observing the simulated response would allow us to decide what levels of input concentration would be beneficial for Bgal output. Therefore, we varied the parameters in search of a cutoff input concentration level, above which would produce a sustained Bgal output, and below which would produce a declining output over time. After simulating several different initial concentrations, we found that the turning point occurred at about I = 0.063. Figure 4 shows the resultant mRNA concentration in this case. The Bgal concentration over time was also graphed for this input concentration and appears as the bottom red curve in Figure 3. Therefore, transcription and the output Bgal decrease over time for an input concentration of I = 0.06, below the threshold we found.
COLLECTING IMPERICAL VALUES TO IMPROVE THE MODEL
Images of GFP producing cells were taken over time in order to track GFP output. There were 24 frames of images sorted chronologically.
ImageJ software was used to track output data of one cell at a time across the 24 time points. The average intensity of the image across the chosen cell was recorded for each frame, since this brightness would correspond to GFP output level. Data of this nature was recorded for 8 different cells, allowing for the calculation of an average brightness or GFP production level at each frame or time point. This average production over time was then graphed using MatLab. Using MatLab's native fitting tools, a 6th order polynomial was fit to the plot and the equation for this polynomial was generated, as shown below.
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 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. The inflection point of the curve corresponds to the maximum of the derivative of the curve. Therefore, the maximum rate of GFP output production would occur at the maximum of the derivative curve of the polynomial fit equation. To find the maximum rate of GFP production relative to changing input concentration, this derivative was graphed and its maximum was found.
Human Practices
Food Waste
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 |