Bacteria expressing genes that code for color will form interesting patterns when spotted onto agar plates in appropriate locations and allowed to spread out and intermingle. But what if we could increase the complexity of the patterns formed by implementing intercellular signaling between different groups of bacteria?

We decided to use parts from the natural quorum-sensing mechanisms of various bacteria to implement our intracellular communication system. If it works, we can for example cause two colonies of bacteria to change color or stop moving as they approach each other, hopefully resulting in interesting patterns.

A brief overview of quorum-sensing: Bacteria, such as V. fisheri, coordinate their gene expression through a system in which each bacterial cell produces a limited amount of signaling molecules, called AHL, which diffuse through the medium and reach other bacteria in its vicinity. AHL molecules bind to receptor proteins which in turn bind to specific promoters that then up-regulate downstream transcription activity. When the bacteria reach a certain density, the amount of AHL in the environment (and thus in the cells) will be sufficient to trigger this increase in promoter activity, and the genes downstream of the promoter will be ‘switched’ on.

[include picture of quorum-sensing system]

Currently we are working on 2 distinct groups of parts: 'Senders' and 'Receivers'. 'Senders' code for enzymes that produce AHL signal molecules, which diffuse out of the cell, through the culture medium and into the receiving cell, where a receptor proteins encoded by the 'Receivers' bind the signals, forming a complex which in turn can bind to and up-regulate transcription from their specific promoter.

We assembled the following devices using parts from the iGEM 2009 Spring Distribution:

Senders:
Lux Sender [include link to registry] - produces (Lux-signaling system AHL), includes a double terminator for easy insertion in front or behind any other device/part [include pic of circuit]
Las Sender - same as above, but produces (Las-signaling system AHL)
Rhl Sender
Cin Sender

Receivers:
Lux Receiver [include link to registry] - receives signal from Lux Sender transmitted in the form of (Lux-signaling system AHL), which then activates/upregulates transcription downstream of this device [include pic of circuit]
Las Receiver
Rhl Receiver
Cin Receiver

Test Constructs:
Lux Receiver with GFP attached downstream ("X1") - a GFP coding device [link to registry part] has been attached downstream of the Lux Receiver described above [include pic of circuit]
Las Receiver with GFP attached downstream ("X2")
Rhl Receiver with GFP attached downstream ("X3")
Cin Receiver with GFP attached downstream ("X4")

Of these parts, the receivers are thought to be the most generally useful as any protein coding region can theoretically be attached downstream of them to be triggered upon induction with the appropriate signal sender (or alternatively by addition of the corresponding AHL). Therefore, we tested those parts extensively, using both PCR sequencing to confirm their nucleotide sequences and fluorimetry measurements to check that the test constructs were functioning as planned.

Unfortunately, we did not have time to properly integrate our sensor modules with the color or motility modules to build the final devices that we initially devised. In future years hopefully we will be able to augment our sensors with further improvements as described under the 'Future Works' section below.

Under construction

To make an effective simulation program we regarded the cell's movement as a diffusion. Therefore we applied the fick's second law of diffusion in modeling the cells movement along with the diffusion of autoinducers. Since the law of diffusion is a differential equation(strictly speaking a partial differential equation) the need for a numerical solution was inevitable. We used the finite difference method showen in equation
We then applied it and converted it which gave us the equation (1) and (2), each representing the diffusion of the cell(or colony) and the autoinducer. These two equations were the bases of our program.

...(1)
...(2)

Finite difference method-Expicit method

As mentioned above we used the finite difference method (and also the explicit method). Finite difference methods are widely used numerical methods in solving differential equations, by considering the differential equations as a finite difference equations. We also used the explicit method which calculates the future state of a system by using the current state of the system.

Fick's second law of diffusion can be written as

・・・(3)
where C[normalized amount/μm³] is the concentration, t[s] is the time, x[μm] is the position, and D is the diffusion coefficient in dimensions of [μm²/h].(Normalized　amount is an amount of cell divided by maximum.)

If we apply the finite difference method to the above equation, fick's second law of diffusion can be expressed in a finite difference equation written as

・・・(4)
where the concentration[C] of a substance at a time[t], and at a position [i,j] is represented as C^t_i,j.

In this experiment, for convenience we let Δt=h and Δx=1 but for a more accurate result Δt and Δx can be adjusted.

By applying the explicit method to the above equation again we reach the following equation.

・・・(5)
Since the concentration of the substance can not be lower than zero, every term of the equation must be over zero. So we reach the following condition.
・・・(6)

Determination of the values of parameters

For accurate results, the precise determination of the values of parameters used in the simulation was essential. We had to determine the values of the two diffusion coefficients(the cell and the autoinducer) along with the production rate of the autoinducers and the growth rate of the colony itself.

The growth rate of the colony was measured by experiment which took place in our lab[fig_model.1]. As a result the value of the colony's logarithmic　growth rate μ is 0.0024[s^-1].

fig_model.1 growth curve

The diffusion coefficient of the cell is, by definition,
・・・(7)
where v_cell, the average speed of a cell, is 0.02 mm/h(=20 μm/s) and T, the average random walk time, is 1s. So in conclusion the diffusion coefficient of the cell is 300 μm²/s [2].

The diffusion coefficient of serine is known as 1000 μm²/sec. Since the diffusion coefficient is inversely proportional to the square root of the molecular weight by simple computation we were able to figure out the diffusion coefficients of the autoinducers we used. The autoinducer's diffusion coefficients is as follows[1].

D_C4HSL = 784 μm²/s

D_3OC6HSL = 702 μm²/s

D_3OC12HSL = 607 μm²/s

The production of autoinducers and the growth of E.coli

Since the E.coli used in this experiment has itself an ability to produce autoinducers, a term which considers the cell's production of autoinducers must be contained in the equation. The added equation is shown as it follows.

・・・(8)
where δ is the production rate of the individual cell. Because the autoinducer's amount, produced by the colony increases in proportion to the numbers of individual E.colis, a term of multiplication to the cell's density was added.

The growth rate of the colony is slightly more complex. Since the nutrient of the medium is limited, E.coli's density is finite. So we expressed the colony's grwoth rate by an sigmoid curve.

・・・(9)