Team:Waseda/IFFL
IFFL Modeling
Multi IFFL
In the incoherent feed forward loop(Fig 4-2-1), the expressions of each gene: x,y, and z are formulated as the differential-equation (1), (2) and (3).
Table 4-2-1 description of each parameter of IFFL
| Variables | Description | unit |
|---|---|---|
| [x] | Concentration of protein x | µM |
| [y] | Concentration of protein y | µM |
| [z] | Concentration of protein z | µM |
| Parameters | Description | unit |
|---|---|---|
| a1 | Maximum expression rate of protein X | µM/min |
| a2 | Mamimum expression rate of protein Y, when promoter of z is activated by protein X | µM/min |
| αx | Mamimum expression rate of protein Z, when promoter of z is activated by protein X | µM/min |
| αy | Mamimum expression rate of z, when promoter of protein Z is activated by protein Y | µM/min |
| K1 | x concentration at which the expression rate of y is half of α2 | µM |
| Kx | x concentration at which the expression rate of y is half of αx | µM |
| Ky | x concentration at which the expression rate of y is half of αy | µM |
| βk(k=1,x,y) | Hill coefficient | - |
| dk(k=x,y,z) | Degradation rate | /min |
We designed an expanded IFFL system containing two target genes (Z1,Z2) each of which with different peak time to the other. We call this Multi -target- IFFL, or Multi IFFL. By adjusting the parameters for each activation and repression, we can provide a time difference in the generation of each pulse. To check whether the designed multi-target IFFL can really generate two pulses with a time delay, we extensively searched for parameter space for the system.
We first investigated how the concentration of Z changes over time when the parameters Kx and Ky are changed independently in Formula (3). When searching, we varied Kx and Ky from 1 to 1000 every 100 and other parameters were fixed as shown on Table-4-2-2, Table-4-2-3 respectively.
Table 4-2-2 Fixed parameters in the Kx search
| parameter | value |
|---|---|
| ax | 4000 |
| βx | 1 |
| βy | 2 |
| Ky | 50 |
Table 4-2-3 Fixed parameters in the Ky search
| parameter | value |
|---|---|
| ax | 4000 |
| βx | 1 |
| βy | 2 |
| Kx | 8 |
Next, we constructed a heatmap to check how much time (t) of the pulse peak is delayed as we simultaneously changed the parameters Kx and Ky in the formula (3). Fig. 4-2-4 is the results. Other parameters are fixed as shown on Table 4-2-4.
Table.4-2-4 parameter set to AHL-R protein crosstalk
| parameter | value |
|---|---|
| ax | 4000 |
| βx | 1 |
| βy | 2 |
Furthermore, in order to evaluate the balance of the pulse shape, we calculated the ratio of the peak concentration to the following steady-state concentration for each parameter and presented it in a heat map. This is called the ratio heatmap. (Fig 4-2-5)
Based on these two indicators, we multiplied the cross heatmap by the value of the time heatmap and the ratio heatmap for each parameter to find out which parameter has both time difference and balance, comprehensively .To make this cross heatmap, we subtracted a certain constant number of time values from the time heatmap because we have to make the time delay above a certain level. If the time heatmap is negative, it is treated as 0. This is called time processed heatmap. Fig 4-2-6 is the time processed heat map, calculated by subtracting 4 from the all values of the time heatmap.
We selected the optimal parameter for the multi IFFL in the resulting match heatmap as the one with the highest score. Two pulses were generated using the optimal parameter in practice (Fig 4-2-7)(Table 4-2-5, 4-2-6). Yellow indicates the temporal variation of the concentration of Z1 and green indicates that of Z2. As a result, we succeeded in creating pulses with a time difference.
Table 4-2-5
| parameter | value |
|---|---|
| αx | 2500 |
| βx | 1 |
| βy | 2 |
| kx | 8 |
| ky | 10 |
| dz | 1 |
Table 4-2-6
| parameter | value |
|---|---|
| αx | 3500 |
| βx | 1 |
| βy | 2 |
| kx | 650 |
| ky | 600 |
| dz | 2 |
