Sudoku

Introduction System Modeling Lab note Experiment Result Reference

System

First, we begin by preparing E.coli corresponding to each cell number. Then we make them “decide” what number they should differentiate into. Notably, spatial distribution is lost while the bacteria are in the process of solving Sudoku. Instead, spatial information is represented by a genetic identity assigned to each bacterium. In fact, the solving process is not performed on a 4×4 grid, but instead in a flask where we mix bacteria possessing all 16 types of genetic spatial identity. In this mixture, the puzzle is solved as a result of inter-bacterial interaction. (We will explain this later in detail.)

So, how do the bacteria “decide” what number they become? Let’s look at the figure. The number in the cell 1-1 is not yet decided. There are bacteria differentiated as 1 in the same line, 3 in the same row, and 2 in the same block, so the bacteria in the cell 1-1 should differentiate into number 4. In this way, bacteria which are not assigned a number from the beginning have to decide number they differentiate into by judging the identity of other bacteria. The 4C3 leak-switch we suggest enables such a system.

Let us explain this switch in detail. First, this switch has to output the number it did not receive when they receive the other three numbers. For example, when the switch receives the numbers 1, 2 and 3, it outputs the number 4, and when it receives the numbers 2, 3 and 4, it outputs 1. This switch must work despite the numbers not being received in a set order, or being received more than once. In other words, it is required that the switch outputs a signal only after receiving three numbers, regardless of the order of reception. This is the “4C3 leak-switch”.

So what is it, in physical terms, what we have been calling “numbers”? The numbers 1 through 4 are represented by 4 different kinds of recombinases. Bacteria communicate with each other by transmitting RNA encoding these recombinases, which are packaged in virus vectors. Look at the figure again. This communication system must be one that only conveys information between bacteria possessing identities of the same row, column or block. In this figure, bacteria with the identity 1-1 needs to differentiate to “1”. Therefore they should not receive information from bacteria with the identity 4-4 prompting others not to differentiate to “1”. The signal virus system together with the antisense RNA system enables such restricted communication to take place. We will discuss these systems in detail below.

The overall systems therefore works are follows:

1. 1. The 4C3 leak-switch designates what number bacteria differentiate into.
2. 2. The signal virus transmits this information to other bacteria.
3. 3. The antisense RNA system restricts exchange of information to that between bacteria possessing identities of the same row, column or block.

Now we examine each of these systems in detail.

4C3 leak-switch

4C3 leak switch_1

4C3 leak switch_2

The 4C3 leak-switch is a switch which receives three number signals and outputs number signal that it did not receive, regardless of the order of reception. In fact, number signals are mRNA encoding homologous recombinases. When three types of mRNA encoidng the recombinases enter E.coli, the switch turns on and transcription of the recombinase that it did not receive begins. 4C3 leak-switch is composed of a promoter, the cre protein coding region and four terminators in between. Each terminator is flanked on both sides by the recognition sequence of a homologous recombinase, and the terminator is excised following expression of the recombinase. Therefore when the E.coli do not receive a number signal, they have four terminators, when they receive one number signal, they have three terminators, and so on. Importantly, bacteria are able to differentiate only after they receive three number signals. 4C3 leak-switch, as the name implies, is a switch that makes use of transcriptional leakage. We assembled the sequence so that when there is more than one terminator, cre protein is not expressed but it is when there is only one. In addition, a recombinase coding sequence flanking the terminator is excised at the same time. Therefore, when the recombinase A coding sequence is excised, terminator A is also excised. As a result, after a cell receives the number signals 1, 2 and 3, only recombinase 4 coding sequence remains. Each cre protein expressed in this way irreversibility excises the sequence between the lox sites independently of the other species of cre proteins. In the example above, mRNA coding recombinase 4 corresponding to the answer of this particular puzzle, is transcribed. In conclusion, The 4C3 leak-switch begins transcription of the recombinase that it did not receive begins after receiving three signals.

Genotype Specific Signal Transmitting Virus

Transcription of MS2 phage & location sequence

The mRNA coding the homologous recombinases has two additional sequences. First, they contain a Loading sequence to the MS2 phage which enables the mRNA to be attached to the coat protein of MS2 phage. This MS2 phage is the carrier that transfers the number signal to other bacteria. These phage are only synthesized after recombination takes place, therefore preventing undifferentiated bacteria from emitting a number signal precociously. Secondly, they contain a location sequence which assigns a cell number to the bacterium. We will explain this in detail later. In conclusion,
4C3 leak-switch turns on
→ transcription of mRNA coding homologous recombinase
→ production of MS2 phage protein　
→ phage with the number signal and location sequence attached
is produced. In this way, differentiated E.coli produces phage with a number signal and location sequence and conveys this information to other bacteria.

Antisense RNA

Infection of signal virus.

The final component of our system, the antisense RNA system, restricts which bacteria are able to receive which number signals. The phage infect all bacteria, so there needs to be a way for the infected bacteria to shunt away mRNA not targeted to them. This is realized because bacteria represented each cell number transcribes a unique set of antisense RNA. This RNA is antisense to the location sequences included in the mRNA transferred by the phage. Each bacterium has a set of antisense RNA corresponding to the location sequence of bacteria from which they do not want to receive a signal. These antisense RNA attach to the mRNA, preventing transcription, allowing blockage of irrelevant number signals. For instance, bacteria with identity 1-1 do not want to receive number signals from 1-1, 2-3, 2-4, 3-2, 3-3, 3-4, 4-2, 4-3, 4-4. Therefore, bacteria with identity 1-1 constitutively transcribes RNA antisense to the location sequence of these nine cell numbers and as a result do not receive the number signals from these cells. Thus this system disables bacteria to receive number signals not targeted to them, although the phage infect all bacteria.

Selective translational suppression.

The construct of selective translational suppression.

Visualization of results

The construct to visualize results.

Until now, we explained how bacteria solve Sudoku but you may be wondering how we determine the results. Currently, the differentiations status of bacteria depends on which recombinase they possess. We need to convert this information into a visible form to do this, we created detection bacteria which we plated on a 4×4grid. When these bacteria come in contact with the signal viruses, they are able to receive number signals and fluoresce a different color depending on the signal they receive. So, these bacteria recognize the type of number signal (the type of homologous recombinase) and express the corresponding fluorescent protein. Once a signal enters the detection bacteria, fluorescent proteins are expressed in a similar way to the signal viruses expressed previously. As shown, a fluorescent protein coding sequence is placed downstream of the terminator, enabling it to be excised when the terminator is excised. Therefore, after three rounds of excision, only one fluorescent protein will remain. The remaining protein is expressed and its color signals to us which number it has differentiated into. For example, when 1-1 cell outputs number 1, only recombinase 1 is transcribed in the detection bacteria, which excises the terminator between the recognition sequences of recombinase 1 and expresses Green Fluorescent Protein.