Team:HZAU-China/Circuit

If you want to design your own rewirable circuit, you may need more information about how to design. Our design principle can help you to find the pattern that satisfies the specification. Our method is based on the large-scale search.

5.1 ODE sets with matrices

In order to implement large scale calculation, we introduce the ordinary differential equation sets with matrices. The transcription regulatory network can be abstracted into a matrix $R$. We use 1, -1, 0 to stand for three possible gene relationships: activation, repression, no regulation. The elements $r_{ij}$ in $R$ indicates that gene $i$ is regulated by gene $j$. This matrix is used to index the topological structure. For calculation, we need to decompose this matrix into two adjacent matrices to represent activation relationship $R_1$ and repression relationship $R_2$, respectively. According to the matrices, we can use the following equations to simulate the gene expression dynamic. \begin{equation} \begin{split} \left( \begin{array}{c} \frac{d{mRNA}_{x_1}}{dt}\\ \vdots\\ \frac{d{mRNA}_{x_N}}{dt}\\ \end{array} \right) &= R_1 \cdot \left( \begin{array}{c} \frac{\beta_1\cdot x_1^n}{K^n+x_1^n}\\ \vdots\\ \frac{\beta_N\cdot x_N^n}{K^n+x_N^n}\\ \end{array} \right) + R_2 \cdot \left( \begin{array}{c} \frac{\beta_{N+1}\cdot K^n}{K^n+x_1^n}\\ \vdots\\ \frac{\beta_{2N}\cdot K^n}{K^n+x_N^n}\\ \end{array} \right) - I \cdot K_{dm} \cdot \left( \begin{array}{c} {mRNA}_{x_1}\\ \vdots\\ {mRNA}_{x_N}\\ \end{array} \right)\\ \left( \begin{array}{c} \frac{dx_1}{dt}\\ \vdots\\ \frac{dx_N}{dt}\\ \end{array} \right) &= K_{tl}\cdot \left( \begin{array}{c} {mRNA}_{x_1}\\ \vdots\\ {mRNA}_{x_N}\\ \end{array} \right) -K_{dp}\cdot \left( \begin{array}{c} x_1\\ \vdots\\ x_N\\ \end{array} \right) \end{split} \end{equation}

where $I$ is the identity matrix. Then we construct some indexes to quantify our needs. Next, we scan different possible matrices and different parameters and record the indexes. Finally we find the patterns that meet our requirements and choose some specific biobricks to construct our rewirable circuits.

Figure 7: Deterministic simulation of design 1. The state versus time is simulated by scanning the moment of rewiring from 100 min to 900 min. The interval of the transient state we set is 20 min

Figure 8: Stochastic simulation of design 1. The parameter we used is the same as the deterministic model. The simulation is achieved by standard stochastic simulation algorithm (Direct method).