Team:NUDT CHINA/Modeling

Fig. 1 Cascade Regulatory Framework Fig. 2 Cascade Regulatory Pathway in DNA

According the cascade regulatory framework (Fig. 1) to solve the shortest path problem, we can build the cascade regulatory path in the plasmid of E.coli (Fig. 2). Now, we divide the whole cascade regulatory pathway into five units, which share same structures and similar properties (Fig. 3). Every unit can perform three common behaviours, i.e. promotion, transcription and translation. Usually, we can combine the process of promotion and translation when building and calculating the mathematic model of cascade regulatory. After combination, it is reasonable to assume that the transcriptional rate is in direct proportion to the extent of promotion. So we now get five easier units which can achieve two separated functions: promotion & transcription and translation.

The logic of the cascade regulation is:

• the translation of this cascade is regulated by the product (protein) of the upstream cascade;
• and identically, the product (protein) of this cascade regulates the translation of the downstream.

In addition, we need to take the temporal degradation of mRNA and protein into account.

I. Analyses of Cascade Regulatory Pathway

• the concentration of promoter binding sites in unit i is $D\_i$;
• the concentration of upstream promoter protein in unit i is $P\_i(t)$;
• the concentration of mrna in unit i is $R\_i(t)$;
• the concentration of product protein in unit i is $X\_i(t)$;
• the hill coefficient of promotion in unit i is $n\_i$;
• the dissociation constant in unit i is .

Content

Here is the detailed explain for our project.

Overall project summary

Recent years, there were some researches aiming to solve specific mathematical problems using synthetic biology, one of which even shed lights on the possibility of solving Hamilton Problem in engineered bacteria. Inspired by them, we are trying to design and construct gene circuits to deal with other problem in graph theory. What we want to prove is that the organism have potential for computation as long as they are designed appropriately.

Project Details

SPP-for-short problem asks the shortest pathway between two given points in a directed graph. We came up with an idea to translate this shortest of space into quickest of time with the help of transcriptional cascades in Escherichia coli. That is to say that we build gene circuits to encode a directed graph where each nodes and edges within are represented by certain promoters and TFs respectively. Then a proof-of-concept experiment in vivo was carried to confirm the validation of this design.

Materials and Methods

We used several parts from iGEM registry and constructed five new parts and devices. The experiments involved are basic ones in gene engineering including gene amplification and expression; polymerase chain reaction; electrophoresis etc.

The Experiments

Results

We designed a series of genetic circuits in Escherichia coli forming a regulatory network in order to translate the form of mathematical problem from geometrical graph into biological structure. The nodes and arrows are marked by well-assigned promoters and transcription factors (TFs) respectively. The promoter of destination node in SPP is followed by a green fluorescent protein (GFP) as a reporter. In this way, the connections among nodes in a directed graph are simulated by transcriptional regulation network. The temporal ordering of the fluorescent protein expression in bacteria reflects distance differences among varied paths, in which an individual bacteria clone containing the shortest pathway encoded gene would show fluorescent earlier than the others. In the following one bit knock-out process, we verified the phenotype which showed fluorescent earlier resulted from the genotype that represented the shortest pathway solution, shedding lights on that our encoding system functioned as expected with linear computation complexity and this approach is theoretically proved feasible.

Data analysis

Conclusions

The bio-computing method we have come up with is a brand-new way to solve the SPP problem effectively. Based on the standardization principals and abstraction strategies of synthetic biology, the results also validated synthetic biology as a valuable approach to biological engineering. In the discussion concerning its augmentability, the potential value and superiority of solving NPC problems can be observed when combining metabolism pathway modification engineering.