We will be using signaling parts from quorum sensing systems of various bacteria to implement intracellular communication between bacterial colonies of different 'colors'. 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.

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 protein encoded by the 'Receiver' binds the signals, forming a complex which in turn can bind to and upregulate transcription from specific promoter.

To test the effectiveness of our signaling system, we will first test the Receivers by attaching a GFP coding unit (rbs + protein coding region + terminator) behind the Receiver's AHL-activated promoter. We will then directly add chemically-derived AHL into culture solutions of these 'Test Receivers' and look for GFP fluorescence which will indicate that transcription has been activated by AHL.

Following that, we will test the Senders by using the above Receivers. We can determine the amount of AHL produced by the Senders by comparing transcription activity induced by the Senders in relation to AHL-induced trancription activity.

Once both Sender and Receiver function has been confirmed and characterized, we will then attempt to characterize the function of the whole system in a way that relates to our intended usage. We will spot two colonies, one of Senders and one of Receivers, on a soft agar plate and determine the maximum distance that the Senders can successfully activate the Receivers. Of course, this will only work if the AHL molecules can effectively diffuse through the agar medium.

Under construction

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 (1)
We then applied it and converted it which gave us the equation (2) and (3), each representing the diffusion of the cell(or colony) and the autoinducer. These two equations were the bases of our program.

...(2)
...(3)

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

・・・(4)
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

・・・(5)
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.

・・・(6)
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.
・・・(7)

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 0.7329[h^-1].

fig_model.1 growth curve

The diffusion coefficient of the cell is, by definition,
・・・(8)
where v_cell, the average speed of a cell, is 0.02 mm/h(=72,000 μm/h) and T, the average random walk time, is 1s. So in conclusion the diffusion coefficient of the cell is 0.0833 μm²/h [2].

The diffusion coefficient of serine is known as 1.0×10^-3 mm²/sec(=0.00278 μm²/h). 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=0.218 μm²/h

D_3OC6HSL=0.195 μm²/h

D_3OC12HSL=0.169 μm²/h

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.

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.

[1]H.C.Berg, D.A.Brown, Chemtaxis in Esherichia coli analysed by three-dimensional traking, Nature 239.

[2]H.C.Berg, Random Walks in Biology, Princeton University Press, 1983.