Bacterial chemotaxis, which is universal in E. coli, is defined as migration of bacteria in response to a chemical stimulus. The natural E. coli chemotaxis has limited receptor proteins which can respond to only six kinds of amino acids. Nevertheless, the reprogrammed chemotaxis named pseudotaxis makes the engineered E. coli able to respond to molecules, whose receptor proteins do not exist in classical E. coli, such as IPTG and L-arabinose, etc. 

E. coli have several flagella per cell (4–10 typically), which can rotate in two ways : counterclockwise (CCW) and clockwise (CW).^[1][2] The former aligns the flagella into a single rotating bundle, causing the bacterium to swim in line, while the later breaks the flagella bundle apart such that each flagellum points in a different direction, causing the bacterium to tumble. The motility is determined by the phosphorylation state of CheY protein which is governed by CheZ protein. In the presence of CheZ protein, CheY-P is dephosphorylated and produce CheY, thus CheY leads to the flagellar motor rotating CCW resulting in swimming. In the absence of CheZ, CheY is phosphorylated into CheY-P which can bind to the flagellar switch protein FliM resulting in tumbling (Figure 1).^[2]

Therefore, if no CheZ is expressed (such as E. coli CL-1 with cheZ gene knocked out of genome), CheY-P couldn’t be dephosphorylated so that flagella keep CW, thus E. coli keep tumbling and perform non-motile ability on semi-solid culture medium (Figure 2 left). With enough CheZ expressed, E. coli regain chemotaxis ability on semi-solid culture medium (Figure 2 right). If one kind of molecule (such as IPTG) could stimulate circuit to express CheZ, reprogrammed E. coli will have the tendency to migrate to it. We named the reprogrammed chemotaxis pseudotaxis. Therefore, we are able to reprogram bacterial chemotaxis by knocking cheZ gene out of the wild-type genome to control the expression of cheZ by logic gene circuits. In this case, we can manipulate the motion of the cells and let them form patterns such as conic curves.

Conic curves universally exist in nature and are significant for science research, production and living. For example, many planets’ orbits are elliptical and parabolic antennas are widely employed in telecommunication. Therefore, we can imitate the orbits of celestial bodies by cell bacterial colony, or form conic curves by precise mathematical laws and apply them in practice.

Besides, as aptamers have the potential to respond to almost all kinds of molecules and have already been used to regulate gene expressions such as cheZ to reprogram chemotaxis (Figure 4). We are also developing a new mechanism which combines aptamers with RNA-lock system to regulate the target genes.

Characterizing the circuits we constructed, we combined mathematical modeling with experiments, using modeling to guide experiments and to explain experimental phenomena. We have got reasonable results for a broader range of applications. As we have proved that the chemotaxis of E. coli could be well reprogrammed, we tried to apply reprogrammed chemotaxis into practice. For example, we have already demonstrated that motile ability is positively associated with the expression strength of cheZ, thus we can characterize the activity of promoters and efficiency of RBS. At the same time, we also developed a biosafety system which relies on reprogrammed chemotaxis.

Last but not the least, we applied mathematical principles in our project. Mathematics is the simplest and clearest language, and its value to the development of human civilization is now widely recognized because of its extensive application in science, society and even our daily life. However, the mathematical laws in life sciences are still unclear and even in chaos. Luckily, synthetic biology can overcome these shortcomings on a certain level. Based on this, we design a gene circuit, expecting that mathematical regularities can realize the regulation and control of life activities. We hope our work can inspire people's interests in combining mathematics with synthetic biology.

References

1. http://en.wikipedia.org/wiki/Chemotaxis

2. Topp S, Gallivan J P. Guiding bacteria with small molecules and RNA[J]. Journal of the American Chemical Society, 2007, 129(21): 6807-6811.