Overview & Purpose
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Background: The Lac Operon
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.
Structure of the Lac Operon 
The Lac Operon encodes three structural genes:
- LacZ: The Lac Z structural region, or β-galactosidase, hydrolyzes the disaccharide lactose into glucose and galactose, sugars that are smaller and easier for the cell to digest. However, in low concentrations of lactose, β-galactosidase cleaves and rearranges lactose into allolactose, which acts as an inducer for the LacI repressor (see Negative Regulation).
- LacY: LacY, or lactose permease, is a transmembrane protein that transports lactose into the cell.
- LacA: LacA is a transacetylase. While it has functionality, it has little effect on the output of our design, so it will not be discussed.
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).
Expression of the Lac Operon is determined jointly by the levels of glucose and lactose in the cell. Being a monosaccharide, glucose is easier (i.e., takes less energy) to digest; therefore, if glucose is present, the cell will prefer to use it as an energy source. However, if glucose is not available as an energy source, the cell will use lactose instead. A table describing this relationship is below:
Table 1: Glucose/Lactose Relationship to Lac Operon Transcription (2)
|| CAP-cAMP Complex
|| LacI Repressor
|| RNA Polymerase
|| Transcription of Lac Operon
| + Glucose, + Lactose || Not bound to DNA || Lifted off operator site || Keeps falling off promoter site || Very low transcription
| + Glucose, - Lactose || Not bound to DNA || Bound to operator site || Blocked by repressor || No transcription
| - Glucose, - Lactose || Bound to DNA || Bound to operator site || Blocked by the repressor || No transcription
| - Glucose, + Lactose || Bound to DNA || Lifted off operator site || Sits on promoter site || TRANSCRIPTION
From this table, we can observe a multitude of things:
- Transcription only occurs when lactose, but not glucose, is present.
- When glucose is not present, the CAP-cAMP complex (or the activator protein) is not bound to DNA.
- Thus, the absence of glucose promotes transcription.
- When lactose is not present, the LacI repressor is bound to the operator site. When lactose is absent, the repressor is NOT bound to the operator site.
- Thus, the presence of lactose promotes transcription.
- For the RNA Polymerase to properly attach to the Lac Operon, the CAP-cAMP complex must be <b>attached to the DNA, and the LacI repressor must not be attached to the operator site.
- Therefore, transcription only occurs when lactose, but not glucose, is present.
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.
NEGATIVE REGULATION: The LacI Repressor
Example of negative regulation of the LacI repressor 
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 and negative regulation of the Lac Operon 
POSITIVE REGULATION: CAP-cAMP Complex
Remember from before, the absence of the LacI repressor is not the only factor that allows transcription to occur. There is also a form of positive regulation that occurs via the CAP-cAMP Complex, the formation of which is controlled by the levels of glucose within the cell. As glucose levels in the cell begin to decline, E. Coli responds by beginning to synthesize cyclic adenosine monophosphate, or cAMP. As cAMP concentration increases, it binds to a catabolite activator protein, or CAP. cAMP acts as an inducer for CAP, causing a conformational change that allows CAP to bind to the promoter region of the Lac Operon. This cAMP-CAP complex interacts with the RNA polymerase, increasing its affinity for the Lac promoter. Without attachment of the cAMP-CAP complex, or in high levels of glucose, affinity wouldn't be high enough to cause significant transcription.
A circuit diagram illustrating glucose and lactose as inputs.
So far, what do we know about the natural Lac Operon? Well, we know that it is a gene that produces a number of structural proteins, including β-galactosidase. We also know that it requires lactose to be present and glucose to be absent for transcription to occur. What we haven't discussed is the function of the operon from an engineering perspective.
Table 2: Glucose NOT Gate
| Input (Glucose)
| 1 || 0
| 0 || 1
Table 3: Glucose and Lactose AND Gate
| Input 1 (Table 2 Output)
|| Input 2 (Lactose)
| 0 || 0 || 0
| 0 || 1 || 0
| 1 || 0 || 0
| 1 || 1 || 1
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.
From a genetic engineering perspective, the structural genes encoding for β-galactosidase can be replaced with different genes encoding other proteins, therefore creating a designer system that produces proteins when induced by lactose. A few genetic regions that can be substituted are a gene coding for insulin to produce insulin for people with diabetes, a gene for heparin to use as a coating on implant device, or even a gene that codes for a fluorescent protein, therefore producing an indicator of the presence of lactose. Applications of engineering the Lac Operon are endless, only bounded by the human imagination.
Design: Our genetic circuit
OUR 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.
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.
Device design. Image adapted from
Our design incorporates BioBrick parts from the Registry of Standard Biological Parts (see diagram on left for specific part numbers). There are two main BioBricks used in our system:
Brick 1: IPTG-Inducible Lac Promoter Brick
The first BioBrick includes the genetic region that codes for the LacI repressor protein, as well a promoter adapted from the natural Lac Operon that is negatively regulated by it. This BioBrick consists of:
- A consitutive promoter: Causes transcription to begin.
- A ribosome binding site: Ribosomes will attach here during transcription.
- The gene for the LacI repressor protein: This gene is what will be transcribed to create the protein of interest, the LacI repressor.
- Terminators: These signal the end of the transcription process.
- LacI regulated promoter: This promoter will cause the next stage of transcription to begin, and is negatively regulated (repressed) by the LacI protein. Therefore, transcription will occur only in the absence of the LacI protein.
Brick 2: GFP Production Brick
The second BioBrick includes the parts necessary to produce an output of Green Fluorescence Protein (GFP). This output is regulated by the parts from the previous stage. This BioBrick consists of:
- A ribosome binding site: This stage involves a second round of transcription, so it needs its own site for ribosome binding.
- The GFP gene: This is the gene that will be transcribed to produce GFP.
- Terminators: These signal the end of the transcription process.
How it Works: The Role of IPTG and Lac-I
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:
- LacI protein is created → LacI regulated promoter is inhibited → Transcription of GFP is inhibited → No Output
On the other hand, when an IPTG input is added to the system, results in the following:
- IPTG is added → LacI protein is created → IPTG binds to LacI → Conformational change in LacI protein → LacI can no longer bind to the stage 2 promoter → Transcription of GFP is no longer inhibited → GFP Is Produced
Building: Assembly Scheme
Testing: Modeling and GFP Imaging
A LAC SWITCH MODEL
Another example of a (very complex) mathematical 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,
y = 3x - 7
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
We used a model of the natural Lac operon to understand how changing the parameter values changes the behavior of the system. Some of the parameters that were used to describe its behavior are as follows:
- Mu - Describes the dilution of the system input, or IPTG. A mathematical way of thinking about this would be to take IPTG concentration as a percentage of cell volume, or [IPTG]/cell volume.
- Gamma_M - Every protein in a cell has a limited lifespan; at some point, chemical reactions will occur that degrade it or cause it to lose its functionality. Gamma_M represents the degradation rate of M, M being the concentration of mRNA for Bgal (β-galactosidase) in the cell.
- Gamma_B - Represents the degradation rate of Bgal, or β-galactosidase.
- K - Represents the half-max of the transfer function, or the point at which the output reaches half of its maximum output. It also represents the concentration value of the input at the point where the rate of increase of output is at a maximum.
- Alpha_M - Represents the production rate of M (mRNA), or the rate at which mRNA is transcribed from DNA.
- Alpha_B - Represents the production rate of Bgal (β-galactosidase), or the rate at which β-galactosidase is translated from mRNA.
- Cell = 1 - "Cell" represents the bacterial cell volume. This statement sets this volume to an arbitrary value 1.
YO JOE INSERT YOUR DIAGRAM THINGY HERE
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:
Figure 1: mRNA Concentration vs. Time
Figure 2: IPTG Concentration vs. Time
Figure 3: β-galactosidase Concentration vs. Time (When [IPTG] = 0.32)
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.
To further analyze how IPTG concentration affects the concentration of β-galactosidase, we though 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 following graph (Figure 4).
Figure 3: β-galactosidase Concentration vs. Time (When [IPTG] = 0.25)
In Figure 4, 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.
Things we need to include:
- DONE Which parameters were included in the model
- DONE Figure 1 - mRNA concentration vs. Time
- DONE Figure 3 - IPTG Concentration vs. Time
- DONE Figure 2 with original parameter value (I = 0.32) That's the concentration of IPTG in the system. Determining the threshold of IPTG that produces an "on" state.
- DONE Figure 2 with I = 0.25
- Try different concentrations until to find the two closest concentrations where one produces sustained Bgal output and the other produces none over a long period of time. (I = 0.063)
- The model assumes that IPTG stays constant over time, but that does not happen in reality. Why?
- What happens to Bgal when I = 0.32 and we remove dy(5) = 0? What did we just do?
COLLECTING IMPERICAL VALUES TO IMPROVE THE MODEL
We explored how one technique, imaging via microscopy could be used to determine the production rate of an output protein, in this case GFP in yeast, could be used to determine a "real" value for maximum GFP production rate under our own laboratory conditions.
Ideally, the GFP production rate measured by this method could be entered as a value for [which parameter] in the Ceroni et al. model.
6th degree polynomial fit to the raw GFP output data.
5th degree derivative of the polynomial fit; k value and Hill Coefficient, n, shown.
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- My name is Shay Ravacchioli, and I am a Junior majoring in Biomedical Engineering with minors in Biological Sciences and Psychology. I am taking BME 494 because I think Synthetic Biology is fascinating. An interesting fact about me is that I play piano and guitar.
- My name is Jenessa Lancaster, and I am a Junior majoring in Biomedical Engineering with a minor in Psychology. I am taking BME 494 because I have always wanted to learn more about Synthetic Biology and Genetic Engineering. An interesting fact about me is that I write songs.
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- My name is Kwanho Yun, and I am a Junior majoring in Molecular Biosciences and Biotechnology. I am taking BME 494 because I am a big fan of synthetic biology and hope to learn more about the industry and how the technology works. An interesting fact about me is that I grow red beard hairs.
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 Slonczewski, Joan, and John Watkins. Foster. Microbiology: An Evolving Science. New York: W.W. Norton &, 2009. Print.
 Schmidt, Markus. Synthetic Biology: Industrial and Environmental Applications. Weinheim, Germany: Wiley-Blackwell, 2012. Print.
 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.