Creating an oscillating system

Already existing genetic oscillators and their limits

Designing a simple genetic network that presents an oscillatory behavior is one of the first challenge synthetic biology overcame. More or less successfully. We can count more than ten synthetic genetic oscillators that have varied period and mechanisms. [http://www.ncbi.nlm.nih.gov/pubmed/16604190?ordinalpos=2&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Raúl GUANTES and Juan F. POYATOS (2006)] studied the most simple oscillators composed of two elements while [http://www.ncbi.nlm.nih.gov/pubmed/10659856?ordinalpos=10&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Michael B. ELOWITZ and Stanislas LEIBLER (2000)] designed the more complex "repressilator" (Table 1), to quote only the best known.

Tab 1. Two examples of genetic oscillators. A : a simple oscillator composed of two elements. B : the repressilator. (Legend : Green arrow : Activation. Red blunt arrow : Inhibition)

Both oscillators work : we can observe oscillations but only a limited number of cycles. Actually, they always reach a steady-state because the degradation/dilution rate is often too low : at the end of each cycle, the conditions are not exactly the initial conditions. Experimentally, the longer is the period the more cycles we can observe.

Design of our genetic oscillator : The Feed Forward Loop

We want to design a simple oscillator that oscillates during as many cycles as possible. We propose a system based on an oscillator composed of two elements (Network 1) on which we added a delay at the end of each cycle.

Network 1. Simple oscillator composed of two elements

Uri ALON described genetic network motifs that generate a delay. Those motifs are the type 1 coherent Feed Forward Loop (C1-FFL).

Definition of a FFL Fig. 1 : Structure of a type 1 coherent Feed Forward Loop A Feed-Forward Loop is a genetic network composed of three nodes. This strong network motif is composed of a transcription factor X that regulates a second transcription factor, Y, and both X and Y regulate Z (Figure 1). The different types of FFL Depending on the type of regulations between the different nodes, we can define eight types of FFL that can be classified into two groups : coherent and incoherent FFLs. In coherent FFLs, the indirect path has the same overall sign as the direct path. The most abundant FFL is the type-1 coherent FFL (C1-FFL) (Figure 1). The type 1 coherent Feed Forward Loop with an OR gate introduces a delay after the extinction of the signal Fig. 2 : The C1-FFL with OR logic in the flagella system of E. coli. Fig. 3 : Promoter dynamics after an OFF step of X, in the presence of Y. The results are shown for the wild-type bacterium, and for a bacterium in which the gene for Fli1 was deleted from the genome. The FFL generates a delay after an OFF step of X In addition to the signs of the edges, to understand the dynamics of the FFL, we must also know how the inputs from the two regulators X and Y are integrated at the promoter of the gene Z. Uri ALON considers that there are two biologically reasonable logic functions : "AND" logic, in which both X and Y activities are need to be high in order to turn on Z expression and "OR" logic in which either X or Y is sufficient (Figure 2). If the input function of the promoter of the gene Z is "OR", Z is expressed when X activity is high. There is no delay following the expression of X. But when X is not expressed anymore, its concentration decreases and reach the activation threshold of Y and Z. Y is not expressed anymore but as the concentration decreases, Z is still expressed. The OR-gate C1-FFL allow the gene Z to be expressed about one more hour after the gene X is OFF. (Figure 3) Bibliography : [http://www.nature.com/ng/journal/v31/n1/abs/ng881.html Shen-Orr et al. (2002)] [http://www.ncbi.nlm.nih.gov/pubmed/14607112?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Mangan et al. (2003)] [http://www.ncbi.nlm.nih.gov/pubmed/14530388?ordinalpos=2&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Mangan et al. (2003)] [http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=16729041 Kalir et al. (2005)]

We will use one of those network to increase the run of each period and permit more oscillations (Network 2).

Network 2. Our oscillator : a C1-FFL increase the length of each period

Implementation of the core system

[http://www.ncbi.nlm.nih.gov/pubmed/16729041?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Shiraz Kalir et al. (2004)] studied the complex network of gene that lead to the synthesis of E. coli flagella. A C1-FFL is present in this network.

• X is flhDC, the master regulator of the synthesis of the flagella. It is associated to its natural promoter.
• Y is fliA, another transcription factor that regulates the expression of a large amount of flagellar genes. fliA is also associated with its natural promoter.
• For Z, we need a protein that inhibits the expression of flhDC.

We considered two possibilities. First of all, we planned to use tetR, and the appropriate promoter before flhDC. But, once again, in a concern to use as many "natural" BioBricks, we decided to use proteins that naturally inhibits the expression of flhDC, such as envZ and ompR. The mechanism of inhibition is quite well-known. envZ phosphorylates OmpR which becomes active. OmpR-P strongly inhibits the expression of flhDC. [http://www.ncbi.nlm.nih.gov/pubmed/18193944?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DefaultReportPanel.Pubmed_RVDocSum Antoine Giraud et al.(2008)] discribed a specific mutant, envZ* that phosphorylates very efficiently ompR. We chose envZ* for Z because it introduces another delay, as envZ* works through over-phophorylation of ompR, which in turns represses flhDC. For Z promoter, we chose one of the promoter controlling the expression of one of the flagellar gene that are regulated by both FliA and FlhDC. We chose the promoter of FlhB because it is the gene that is lastly activated. As a consequence, it increases the length of each cycle. Of course, to make the oscillations observable, we decided to put EnvZ and GFP under the control of the same promoter.

Network 3. Final Design of the core system.

Limits of our network

Intuitively, it seems that there is a range of parameters that permit oscillations. However, an analysis of the core system highlighted the fact that it could hardly have an oscillating dynamics (Graph 1).

Among the alternatives we studied, the system that could most probably oscillate is the third module that uses the quorum sensing to produce both a delay and the synchronization at the population level.