Project

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When working in binary, only two digits are used: 0 and 1. A single binary digit is called a '''bit'''. Counting proceeds as:  
When working in binary, only two digits are used: 0 and 1. A single binary digit is called a '''bit'''. Counting proceeds as:  
To add two binary numbers, the process is much the same as adding two decimal (ordinary) numbers, except that instead of carrying when two digits add to ten, carrying must be performed when two digits add to two. In other words, 0 + 1 adds to 1, but 1 + 1 adds to 0 with a carry of 1, which gives 10 (just as in decimal 1 + 9 would add to 0 with a carry of 1, to give 10). A complete list of the possibilities is as follows:
To add two binary numbers, the process is much the same as adding two decimal (ordinary) numbers, except that instead of carrying when two digits add to ten, carrying must be performed when two digits add to two. In other words, 0 + 1 adds to 1, but 1 + 1 adds to 0 with a carry of 1, which gives 10 (just as in decimal 1 + 9 would add to 0 with a carry of 1, to give 10). A complete list of the possibilities is as follows:
 +
 +
[[Image:000.jpg]]
Here is an example of long addition:
Here is an example of long addition:
<div style="float:center;width:225px;">
<div style="float:center;width:225px;">
-
[[Image:000.jpg]][[Image:222.jpg]]<br clear="all" />
+
[[Image:222.jpg]]<br clear="all" />
</div>
</div>
Line 73: Line 75:
For the following explanations, A and B represent statements that can be either true or false.  
For the following explanations, A and B represent statements that can be either true or false.  
 +
<center><table cols="3" style="border: 1px solid gray; border-collapse: collapse; padding:15px; "> 
-
====OR Gate====
+
  <tr style="background-color:#CCCCCC; text-align:left;">
 +
    <th>Operator</th>
 +
    <th>Condition </th>
 +
    <th>Truth Table</th>
 +
  </tr>
 +
  <tr valign="middle" style="border-top: 1px solid gray;border-bottom: 1px solid gray;">
 +
    <td style="padding:2em;">a OR b</td>
 +
    <td style="padding:2em;">If a, b, or both are true</td>
 +
    <td>[[Image:UW_Or_TABLE.jpg]]</td>
 +
  </tr>
 +
  <tr valign="middle" style="border-top: 1px solid gray;border-bottom: 1px solid gray;">
 +
    <td style="padding:2em;">a XOR b</td>
 +
    <td style="padding:2em;">If a and b are different</td>
 +
    <td>[[Image:UW_XOR_TABLE.jpg]]</td>
 +
  </tr>
 +
  <tr valign="middle" style="border-top: 1px solid gray;border-bottom: 1px solid grayk;">
 +
    <td style="padding:2em;">AND</td>
 +
    <td style="padding:2em;">If both are true</td>
 +
    <td>[[Image:UW_And_TABLE.jpg]]</td>
 +
  </tr>
 +
  <tr valign="middle" style="border-top: 1px solid gray;">
 +
    <td style="padding:2em;">NOT a</td>
 +
    <td style="padding:2em;">If a is false</td>
 +
    <td>[[Image:UW_NOT_TABLE.jpg]]</td>
 +
  </tr>
 +
</table></center>
-
Consider the statement "A OR B". If either A or B is true, the statement is said to be true. The only time this statement will be false is when both A and B are false. This is the meaning of the OR operation.
 
-
An OR gate accepts two binary inputs, where a 1 represents "true" and a 0 represents "false". The output of the OR gate is also binary, and similarly represents either "true" or "false".
+
====Using logic gates to make an adder====
-
To illustrate,
+
Given two binary inputs A and B, their sum can be computed by passing these inputs through various logic gates. The process is illustrated in Figures 4 and 5.
-
0 OR 0 = 0
+
<table style="border-width:0px:vertical-align:middle;width:100%">
 +
<tr>
 +
  <td>
 +
    [[Image:Half-adder.png|left|thumb|300px|Figure 4: Half-adder circuit diagram]]
 +
  </td>
 +
  <td>
 +
    [[Image:Full-adder.png|left|thumb|300px|Figure 5: Full-adder circuit diagram]]
 +
  </td>
 +
</tr>
 +
</table>
 +
<br clear="all" />
-
1 OR 0 = 0 OR 1 = 1
+
===DNA as Logic Gates===
 +
Our project focuses on using DNA as logic gates. The output of a logical operation is the protein product of a certain gene; the inputs are external stimuli that cause allosteric changes in the conformation of proteins that can induce or inhibit transcription by acting on promoter elements. Whether or not the gene is turned 'on' or 'off' depends on the logic gate implemented.
-
1 OR 1 = 1
+
For two inputs, the "presence" or "absence" of input A and the "presence" or "absence" of protein B (both representing 0 or 1 as inputs) would result in an output of either the "presence" or "absence" of protein X (where "presence" and "absence" should be read as high and low intensity/concentration, respectively).
-
====XOR Gate====
+
For example, consider a regulated gene G that codes for protein X. By default, the gene is not expressed (to be precise, there is a low basal level of expression that we can disregard). If the inputs A and B are on and together can turn on expression of gene G, the expressed protein X represents the output of an AND gate. This is the type of approach used to construct our biological adder.
-
XOR is an abbreviation for "exclusive OR". The XOR gate is similar to the OR gate, the only difference being that it will return false if both inputs are true.
+
==Project Details==
-
For example,
+
===Input and Output===
-
1 XOR 0 = 1
+
<table style="border-width:0px;width:100%;vertical-align:text-bottom">
 +
<tr>
 +
  <td>
-
1 XOR 1 = 0
+
As a half-adder, our device requires two binary inputs; the possible 1 and 0 values of these inputs are represented by the presence and absence of two stimuli. For the first input, the presence of red light represents a 0 and the absence represents a 1. For the second input, the absence of tetracycline represents a 0 and the presence represents a 1.
-
====AND gate====
+
We chose to use light as an input because it does not require altering the media, it can be turned on and off rapidly, and it has extremely high resolution and accuracy. The red light will be detected by Cph8, the previously used Cph1/EnvZ fusion protein. 
-
The AND gate will return 1 (true) '''only if both the inputs are 1 (true)'''. Otherwise, it will return a 0.
+
Tetracycline was used as a second input since it inactivates the repressor TetR, thereby derepressing expression at the PtetR locus.
-
To illustrate,
+
Depending on the result of the calculation, the bacteria will produce either red fluorescent protein (RFP), green fluorescent protein (GFP), or neither. A diagram of the biological half adder in culture is shown above, depicting the possible outcomes for each combination of inputs.
-
0 AND 0 = 0
+
</td>
 +
<td>
 +
[[Image:UW_biology_schematic_diagram.PNG|none|thumbnail|center|500px|Inputs and Output of the Biological Half-Adder]]
 +
</td>
 +
</tr>
 +
</table>
-
1 AND 0 = 0 AND 1 = 0
 
-
1 AND 1 = 1
+
===Molecular Mechanism===
-
====NOT gate====
+
As components of a natural quorum sensing system, LuxR and LuxI proteins are ideal for producing the AND logic function required to create 1-bit half-adder. LuxR enhances transcription at Plux when activated by an inducer produced by LuxI. The expression of both LuxR and LuxI is therefore necessary to "turn on" the promoter Plux. LasR and LasI have analogous roles in another quorum sensing system, and contribute to the XOR logic function in our design. Below is a diagram showing all of the gene constructs that are involved in the biological half adder (these will ultimately be included on a single plasmid, but are here shown separately for ease of explanation).
-
The NOT gate accepts one input, and simply switches its value.
 
-
NOT 1 = 0
+
[[Image:GeneDesignHA.jpg|none|thumbnail|center|500px|Gene Diagram for the Half Adder Construction]]
-
NOT 0 = 1
 
-
====Using logic gates to make an adder====
+
The products in the first, third, and fifth constructs are always produced while the other constructs are controlled by various proteins that either induce or inhibit the production of the proteins that these genes encode.
-
Given two binary inputs A and B, their sum can be computed by passing these inputs through various logic gates. The process is illustrated in Figures 4 and 5.
+
<br clear="all">
-
[[Image:Half-adder.png|left|thumb|300px|Figure 4: Half-adder circuit diagram]][[Image:Full-adder.png|left|thumb|300px|Figure 5: Full-adder circuit diagram]]<br clear="all" />
+
The behaviour of the half-adder can be described by four possible cases which are simulated in the genetic system as follows:
-
===DNA as Logic Gates===
+
<table style="border: 1px solid gray;text-align:left">
-
The focus of our project revolves around using DNA as logic gates. In essence, the output of a logical operation is the chemical produced by a certain gene, and the inputs are external stimuli that modify the conformation of proteins, which act on the promoters of the genes to induce or inhibit transcription depending on the specific logic gate implemented.
+
<tr><td rowspan="2" style="border-bottom: 1px solid gray;padding-bottom:10px">[[Image:Tube00.jpg]]</td><th style="font-size:medium">Case 1: 0 + 0 = 0</th></tr>
 +
<tr><td style="border-bottom: 1px solid gray;">
 +
This is achieved through the presence of red light and absence of tetracycline.
 +
 +
In the absence of tetracycline, the TetR repressor protein that is constitutively being produced by the third construct will bind to the operator on the fourth construct preventing the production of LasR and LuxR.  
-
For example, consider a positively regulated gene G that codes for protein X. By default, the gene is not expressed. If the inputs A and B are on and inducing protein activity that turns on G, the expressed protein represents the output of an AND gate. The inputs would be the "presence" or "absence" of A and the "presence" or "absence" of B (both representing 0 and/or 1 as inputs), and the output would be the "presence" or "absence" of X (where "presence" and "absence" should be read as high and low intensity/concentration, respectively).
+
In the presence of red light, the complex formed by Cph8, Ho1, and PcyA is inactivated and thus cannot activate OmpR to act on the Pomp promoter. Without OmpR, the proteins LasR and LuxI will not be produced.  
-
This is the type of approach used to construct our biological adder. Further details are given under the Project Details section.
+
The protein LasR is required for the production of Green Fluroescent Protein (GFP). For Red Fluroescent Protein (RFP) to be produced, the proteins LuxI and LuxR must both be present in the cell.  
-
==Project Details==
+
In the absence of LasR, LuxI, and LuxR, neither of the reporter genes RFP or GFP will be produced.
-
===Inputs===
+
Consequently, there will not be any output (i.e., no colour produced), representing a result of 0 for the computation.
-
As a half-adder, our cells require two binary inputs. We chose to use the presence or absence of red light as one input, and the presence or absence of the chemical tetracycline as another. For the first input, the presence of red light represents a 0 and the absence represents a 1. For the second input, the absence of tetracycline represents a 0 and the presence represents a 1.
+
</td></tr>
 +
<tr><td rowspan="2" style="border-bottom: 1px solid gray;padding-bottom:10px">[[Image:Tube10.jpg]]</td><th style="font-size:medium">Case 2: 1 + 0 = 1</th></tr>
 +
<tr><td style="border-bottom: 1px solid gray;">
 +
This is achieved through the absence of both red light and tetracycline.
-
We chose to use light as an input for the reasons that it does not require altering the media, it can be turned on and off rapidly, and it has extremely high resolution and accuracy. The red light will be detected by the previously used Cph1/EnvZ fusion protein ([http://partsregistry.org/Part:BBa_I15010 BBa_I15010]).
+
In the absence of tetracycline, the TetR repressor binds to the operator on the fourth construct preventing the production of LasR and LuxR.
-
Tetracycline was used as a second input since it binds to the tetR repressor ultimately allowing for the production of the Green Fluorescent Protein (GFP) or Red Fluorescent Protein (RFP). It also will not interfere with the constitutive promoter and can be easily controlled.
+
In the absence of red light, however, the components Cph8, Ho1, and PcyA will combine to form a complex to activate ompR. This complex will bind to the promoter of the second construct activating the production of the proteins LasR and LuxI.
-
===Output===
+
Since the LasR protein is now present, it can be activated by the constitutively produced LasI to turn on the promoter of the sixth construct and induce the production of GFP.
-
Depending on the result of the calculation, the bacteria will produce either red fluorescent protein (RFP), green fluorescent protein (GFP), or neither. The possible outcomes are as follows:
+
-
No Tetracycline & No red light ==> 0+0 ==> nothing
+
However, the presence of the LuxI protein alone is insufficient to activate the production of RFP.
-
No Tetracycline & Red light ==> 0+1 ==> GFP
+
Consequently, the output is green.
 +
</td></tr>
 +
<tr><td rowspan="2" style="border-bottom: 1px solid gray;padding-bottom:10px">[[Image:Tube01.jpg]]</td><th style="font-size:medium">Case 3: 0 + 1 = 1</th></tr>
 +
<tr><td style="border-bottom: 1px solid gray;">
 +
This case is similar to Case 2. This is achieved through the presence of both red light and tetracycline.
 +
 +
In the presence of red light, the proteins Cph8, Ho1, and PcyA do not activate ompR. Thus, nothing acts on the promoter in the second construct to induce the production of the LasR and LuxI proteins.
-
Tetracycline & No red light 1+0 ==> GFP
+
When tetracycline is present, tetracycline binds to the repressor protein TetR, which causes a conformational change to TetR and prevents it  from binding to the operator on the fourth construct. This allows the proteins LasR and LuxR to be produced.
-
Tetracycline & red light ==> 1+1 ==> RFP
+
The LasR protein then acts on the promter of the last construct inducing the production of GFP. However, LuxR alone cannot induce the production RFP, so only GFP is produced.
 +
Consequently, the output is green.
 +
</td></tr>
 +
<tr><td rowspan="2">[[Image:Tube11.jpg]]</td><th style="font-size:medium">Case 4: 1 + 1 = 10</th></tr>
 +
<tr><td>
 +
This is achieved through the absence of red light and the presence of tetracycline.
-
A diagram of the biological half adder in culture is shown below. It shows all outputs given all possible inputs.
+
In the absence of red light, the proteins Cph8, Ho1, and PcyA combine to form a complex that activates OmpR. This complex then binds to the promoter of the third construct and induces the production of the LasR and LuxI proteins.  
-
[[Image:UW_biology_schematic_diagram.PNG|none|thumbnail|center|500px|Input and Outputs of the Biological Half Adder]]
+
In the presence of tetracycline, TetR undergoes a conformational change that prevents it from binding to the operator of the fourth construct. As a result, LasR and LuxR proteins are produced.
-
===Schematic Diagram===
+
Since the proteins LuxI and LuxR are present, they induce the production of the cI repressor protein and RFP under the Plux promoter. The cI repressor protein then binds to the operator of the sixth construct, inhibiting the production of GFP.
-
[[Image:Design schematic.jpg|none|thumbnail|center|500px|Schematic Design of Biological Half-Adder]]
+
-
===Gene Diagram===
+
Consequently, the output is red.
-
[[Image:GeneDesignHA.jpg|none|thumbnail|center|500px|Gene Diagram for the Half Adder Construction]]
+
</td></tr></table>
-
 
+
<center>  
-
<div style="text-align:center" >
+
   [[Waterloo | Home ]] | [[Project | Project]] | [[Modelling | Mathematical Modelling]] | [[Construction_and_Testing | Construction and Testing]] | [[Future_Work | Future Work]]  
-
   [[Waterloo | Home ]]  
+
</center>
-
</div>
+

Latest revision as of 03:58, 27 October 2007

Contents

Background

Binary Addition

Decimal
(Base 10)
Binary
(Base 2)
0
00
1
01
2
10
3
11
4
100
5
101
6
110

When working in binary, only two digits are used: 0 and 1. A single binary digit is called a bit. Counting proceeds as: To add two binary numbers, the process is much the same as adding two decimal (ordinary) numbers, except that instead of carrying when two digits add to ten, carrying must be performed when two digits add to two. In other words, 0 + 1 adds to 1, but 1 + 1 adds to 0 with a carry of 1, which gives 10 (just as in decimal 1 + 9 would add to 0 with a carry of 1, to give 10). A complete list of the possibilities is as follows:

000.jpg

Here is an example of long addition:

222.jpg

Half-Adder vs. Full-Adder

Figure 1: Half-Adder Truth Table
Figure 2: Full Adder Truth Table

Any construct designed to add two numbers will either be a half-adder or a full-adder. A half-adder can only add together two single digits, whereas a full-adder is needed to add two numbers consisting of more than one digit.


For example, a half-adder could perform the addition 1 + 0 = 1, or 1 + 1 = 10, but it would take a full-adder to be able to perform 1100101 + 100101.

In terms of implementation, a half-adder accepts two inputs (the two digits to be summed) and returns two outputs (the "sum bit" and the "carry bit"). To add 1 + 1, the two inputs would each be 1, the sum bit would be 0, and the carry bit would be 1. A full list of the possibilities is shown in Figure 1.


A full-adder is merely a half-adder that accepts an extra input; namely, the carry bit from another full-adder. Each full-adder is responsible for adding one pair of corresponding digits from the two numbers to be added, and it must add to that the carry bit from the previous full-adder. The full-adder will output the resulting sum bit and carry bit, and the process will continue until all the digits have been added. Such a chain of full-adders is called a ripple carry adder. See Figure 2 for a full list of possibilities.

Logic Gates and Implementing an Adder

A logic gate performs a logical operation on one or more logic inputs and produces a logic output. Usually the inputs and outputs are binary, meaning they each have a value of either 0 or 1. Also, it is often useful to think of of 0 as representing "false", and 1 as representing "true". A list of relevant logic gates is as follows:

  • OR gate
  • XOR gate
  • AND gate
  • NOT gate

For the following explanations, A and B represent statements that can be either true or false.

Operator Condition Truth Table
a OR b If a, b, or both are true UW Or TABLE.jpg
a XOR b If a and b are different UW XOR TABLE.jpg
AND If both are true UW And TABLE.jpg
NOT a If a is false UW NOT TABLE.jpg


Using logic gates to make an adder

Given two binary inputs A and B, their sum can be computed by passing these inputs through various logic gates. The process is illustrated in Figures 4 and 5.

Figure 4: Half-adder circuit diagram
Figure 5: Full-adder circuit diagram


DNA as Logic Gates

Our project focuses on using DNA as logic gates. The output of a logical operation is the protein product of a certain gene; the inputs are external stimuli that cause allosteric changes in the conformation of proteins that can induce or inhibit transcription by acting on promoter elements. Whether or not the gene is turned 'on' or 'off' depends on the logic gate implemented.

For two inputs, the "presence" or "absence" of input A and the "presence" or "absence" of protein B (both representing 0 or 1 as inputs) would result in an output of either the "presence" or "absence" of protein X (where "presence" and "absence" should be read as high and low intensity/concentration, respectively).

For example, consider a regulated gene G that codes for protein X. By default, the gene is not expressed (to be precise, there is a low basal level of expression that we can disregard). If the inputs A and B are on and together can turn on expression of gene G, the expressed protein X represents the output of an AND gate. This is the type of approach used to construct our biological adder.

Project Details

Input and Output

As a half-adder, our device requires two binary inputs; the possible 1 and 0 values of these inputs are represented by the presence and absence of two stimuli. For the first input, the presence of red light represents a 0 and the absence represents a 1. For the second input, the absence of tetracycline represents a 0 and the presence represents a 1.

We chose to use light as an input because it does not require altering the media, it can be turned on and off rapidly, and it has extremely high resolution and accuracy. The red light will be detected by Cph8, the previously used Cph1/EnvZ fusion protein.

Tetracycline was used as a second input since it inactivates the repressor TetR, thereby derepressing expression at the PtetR locus.

Depending on the result of the calculation, the bacteria will produce either red fluorescent protein (RFP), green fluorescent protein (GFP), or neither. A diagram of the biological half adder in culture is shown above, depicting the possible outcomes for each combination of inputs.

Inputs and Output of the Biological Half-Adder


Molecular Mechanism

As components of a natural quorum sensing system, LuxR and LuxI proteins are ideal for producing the AND logic function required to create 1-bit half-adder. LuxR enhances transcription at Plux when activated by an inducer produced by LuxI. The expression of both LuxR and LuxI is therefore necessary to "turn on" the promoter Plux. LasR and LasI have analogous roles in another quorum sensing system, and contribute to the XOR logic function in our design. Below is a diagram showing all of the gene constructs that are involved in the biological half adder (these will ultimately be included on a single plasmid, but are here shown separately for ease of explanation).


Gene Diagram for the Half Adder Construction


The products in the first, third, and fifth constructs are always produced while the other constructs are controlled by various proteins that either induce or inhibit the production of the proteins that these genes encode.


The behaviour of the half-adder can be described by four possible cases which are simulated in the genetic system as follows:

Tube00.jpgCase 1: 0 + 0 = 0

This is achieved through the presence of red light and absence of tetracycline.

In the absence of tetracycline, the TetR repressor protein that is constitutively being produced by the third construct will bind to the operator on the fourth construct preventing the production of LasR and LuxR.

In the presence of red light, the complex formed by Cph8, Ho1, and PcyA is inactivated and thus cannot activate OmpR to act on the Pomp promoter. Without OmpR, the proteins LasR and LuxI will not be produced.

The protein LasR is required for the production of Green Fluroescent Protein (GFP). For Red Fluroescent Protein (RFP) to be produced, the proteins LuxI and LuxR must both be present in the cell.

In the absence of LasR, LuxI, and LuxR, neither of the reporter genes RFP or GFP will be produced.

Consequently, there will not be any output (i.e., no colour produced), representing a result of 0 for the computation.

Tube10.jpgCase 2: 1 + 0 = 1

This is achieved through the absence of both red light and tetracycline.

In the absence of tetracycline, the TetR repressor binds to the operator on the fourth construct preventing the production of LasR and LuxR.

In the absence of red light, however, the components Cph8, Ho1, and PcyA will combine to form a complex to activate ompR. This complex will bind to the promoter of the second construct activating the production of the proteins LasR and LuxI.

Since the LasR protein is now present, it can be activated by the constitutively produced LasI to turn on the promoter of the sixth construct and induce the production of GFP.

However, the presence of the LuxI protein alone is insufficient to activate the production of RFP.

Consequently, the output is green.

Tube01.jpgCase 3: 0 + 1 = 1

This case is similar to Case 2. This is achieved through the presence of both red light and tetracycline.

In the presence of red light, the proteins Cph8, Ho1, and PcyA do not activate ompR. Thus, nothing acts on the promoter in the second construct to induce the production of the LasR and LuxI proteins.

When tetracycline is present, tetracycline binds to the repressor protein TetR, which causes a conformational change to TetR and prevents it from binding to the operator on the fourth construct. This allows the proteins LasR and LuxR to be produced.

The LasR protein then acts on the promter of the last construct inducing the production of GFP. However, LuxR alone cannot induce the production RFP, so only GFP is produced.

Consequently, the output is green.

Tube11.jpgCase 4: 1 + 1 = 10

This is achieved through the absence of red light and the presence of tetracycline.

In the absence of red light, the proteins Cph8, Ho1, and PcyA combine to form a complex that activates OmpR. This complex then binds to the promoter of the third construct and induces the production of the LasR and LuxI proteins.

In the presence of tetracycline, TetR undergoes a conformational change that prevents it from binding to the operator of the fourth construct. As a result, LasR and LuxR proteins are produced.

Since the proteins LuxI and LuxR are present, they induce the production of the cI repressor protein and RFP under the Plux promoter. The cI repressor protein then binds to the operator of the sixth construct, inhibiting the production of GFP.

Consequently, the output is red.

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