In this year’s project, we use mathematics model to demonstrate the functional proof of the artificial biological system we designed. We focus on the two essential parts in our gene circuits, which are ribosome switches and double integrase sites. Apart from these two parts, the RNA-based gene silencing expression is also demonstrated in both of two models.

1 Integrase sites model

figure 2: GFP level trend as KT (rate for Bxb1 to switch from ‘on’ state to ‘off’ state ) increases.

From figure 2, we can see it saturates when KT reaches the value of 1e5/(M*M*min).

Figure 3: The relationship between time and GFP （ KT=1e5/(M*M*min，km(lac)=5nM/min.)

In figure 3, we can concluded that GFP level reaches its final stable value at about 600 minutes(10h). And this time is not sensitive to KT and km(lac).

Figure 4: The relationship between time and GFP （ KT=1e5/(M*M*min，km(lac)=5nM/min.)

Figure 5: The relationship between time and GFP （KT=1/(M*M*min，km(lac)=5nM/min.)

Figure 6: The relationship between time and GFP （KT=1e7/(M*M*min，km(lac)=100nM/min.)

Figure 7: The relationship between P(T(Bxb1)off) and KT

Figure 8: The relationship between lg[P(T(Bxb1)off)] and KT

The relationship of P(T(Bxb1)off) with KT is almost identical to that of [GFP] with KT. So we can conclude that [GFP] is proportional to P(T(Bxb1)off).

Figure 9: The relationship between GFP and km(lac)

It is clearly that GFP level decreases as km(lac) increases, but saturates when km(lac) is too large or too small. But the reference value lies in the unsaturated scope. This indicates that the inhibition of transcription of lacl activates the expression of GFP.

Figure 10: The relationship between lg(km(lac)) and P(T(Bxb1)off)(lac)

So the figure 10 verified that GFP is proportional to P(T(Bxb1)off) .

Figure 11: The relationship between GFP and km(lac)

After we get experimental data(abscissa), we should corresponding to the ordinata to find out whether the trend in range, if within the range, it means our experiments are correct, otherwise it is necessary to continue the experiment to get correct data.

fugure12:The relationship between lg(kt) and lg(GFP)

We keep kt1(for Bxb1)and kt1(for FimE) the same, and vary them in the scope we used before. We find that the GFP output changes with kt1 and kt2 in a similar way compared to the independent gene circuits.

Figure13:The relationship between GFP and t.

Kt1=Kt2=1/(M*M*min) km(lac)=km(tet)=5e-5nM/min

Figure14: The relationship between GFP and t. Kt1=Kt2=1e7/(M*M*min) km(lac)=km(tet)=100nM/min

The morphology of the reaction curve is not obviously affected by these two parameters.

Figure15:The relationship between lg(kt)and p(T(off))

Figure16:The relationship between lg(kt)and lg(P(T(off)))

The relationship of P(Toff) with kt is almost identical to that of GFP with kt. So we can conclude that GFP is proportional to P(Toff).(Here two kt and two P(Toff))s are both the same.

Figure17: The relationship between GFP and lg(km)

GFP level decerases as km increases, but saturates when km is too large or too small.But the reference value lies in the unsaturated scope. This indicates that the inhibition of transcription of Lacl and tetR activates the expression of GFP.

The results of the model are simulated with MATLAB software, then discussed the results. By setting up a k-value interval, calculated the relationship between KT and GFP level, we concluded GFP level are increasing as value of k increasing, when KT = 1e5, GFP level in steady stage. In figure 3, we can concluded that GFP level reaches its final stable value at about 600 minutes(10h). And this time is not sensitive to KT and km(lac). When changed kt and km(lac), the relationship between GFP level and time in common. GFP level decreases as km(lac) increases, but saturates when km(lac) is too large or too small. But the reference value lies in the unsaturated scope. This indicates that the inhibition of transcription of Lacl activates the expression of GFP. Figure 10 verified that GFP is proportional to P(T(Bxb1)off). Not only can we concluded the FimE has influenced on GFP level, but also as same as Bxb1 from figure.

2 Lock-Key Model

Figure18:The noise floor of bacterial fluid

Figure19: The GFP expression of FimE was caused by the reverse action of the enzyme.

Figure19: The GFP expression of FimE was caused by the reverse action of the enzyme.

Figure 20: The GFP expression of between FimE and lock-key systerm were caused by the reverse action of the enzyme.

Figure 21: The comparison between figure19 and figure20

Figure 22: The GFP level of different mir155 concentration inducing

The results of the model are simulated with MATLAB software, then discussed the results. The value of GFP induced by mir155 is regarded as signal and the one without inducing is regarded as noise floor. From the figure 21, we can conclude that the system equipped with Lock and Key part has the higher signal to noise ratio (SNR) than the one without Lock and Key part. And Lock and Key part significantly reduce the background noise of detection. From the figure 22, we can conclude the Lock and Key part will not influence the linearity of detection and the correlation between GFP and concentration of mir155 is correct according to the figure.

For more details of model: https://2016.igem.org/Team:BIT/Model