BioSysBio:abstracts/2007/iGEM2006 Imperial College

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Engineering a synthetic molecular oscillator based on the lotka volterra dynamic model

Author(s): I. CoLi Team 2006
Affiliations: Imperial College
Contact:email: your_e-mail
Keywords: 'iGEM' 'Biological Oscillator' 'AHL' 'AiiA'


Oscillators and oscillatory systems are ubiquitous in everyday life, from the alternating current electricity that we use to the circadian rhythms that control our sleep and wake cycle. Already, synthetic biology has begun to take on the challenge of creating the first biological computer, starting with ETH Zurich’s 2005 iGEM competition entry for creating a biological NOR logic gate and a two bit counter as well as Harvard’s BioWire design concept to transmit a signal down a length of bacteria. In computers, clocks are used to synchronise the components in order to prevent overflow of information within the system. On a broader scale, these clocks synchronise time around the world and are also used to determine the winner of eBay bids accurate to seconds, perhaps a more recognisable example to our modern life.

Why would we want to create a biological computer? Consider first the human brain, a complex network of cells intercommunicating to create our thoughts and conduct the human body symphoniously. If we can mimic this type of system in other non-neural type cells, we might be able to harness the massive scale parallel computing power inherent to biological systems.

Once we are able to create a biological oscillator, we can then move to synchronise several biological computers paving the way for an internet-like system controlled by bacteria. Further developments in biological to electrical interfacing could mean that communication between electrical devices and biological devices would be seamless. This can potentially integrate the existing infrastructure and novel biological approaches so the current technology would not be drastically displaced, but gradually replaced by biological machines. Moreover, the quest for self-reproducing machines has finally succeeded. Wouldn't it be great if our computers upgraded themselves? Made themselves faster every 30 mintutes? Genetically engineered bacteria indeed have this potential and are only limited by their lifespan and the biological reaction rates. Unfortunately, biological reaction rates are relatively slow when compared to electrical signals, but consider 100 years ago when we knew very little about electricity and how to harness the power of electricity. Biological engineering is at that stage now, and we cannot expect to surpass in a few years the engineering foundations that have been perfected throughout the ages.

Stable biological oscillations are seen to be produced with accuracy in predator-prey relationships, where we assume an exponential growth of prey and insatiable predators. The Lotka-Voltarra model for predator-prey interaction can be implemented given certain assumptions and given that we are able to find biological equivalents to predator and prey. Of course, a molecular predator-prey system would have different assumptions and thus different equations, but the fundamental predator-prey relationship can still hold. The assumptions and adaptations to the Lotka-Volterra system will be discussed further in the modelling document. Once we find molecules that can act similarly to predator-prey interactions, the next step is to successfully implement the system into bacteria!

Design of Biological Oscillator

Our design focused on implementing predator-prey molecular interactions into E. coli cells. In order to have population wide control and not just single cell oscillations, the team decided to use N-acyl homoserine lactone (AHL) synthesis and degradation pathways. The team wanted to mimic Lotka-Volterra interactions as much as possible so certain assumptions had to be taken into consideration. First, the L-V model assumes that there is an exponential increase in prey and that prey do not die on their own accord. Second, the predator must "eat" the prey and it's "productivity" is determined by how many prey it eats. Finally, the predator have a fixed death rate.

The first assumption was considered and implemented as a positive feedback loop to produce AHL in the "prey cell". A Lux R and a LuxI protein coding region was attached to a pLuxR promoter. Inherent noise in the system would cause both LuxR and LuxI to be produced. The LuxI would then catalyse AHL production leading, which would feed back into the system leading to an exponential increase of AHL. However, as biological resources are limited, the exponential increase eventually stops giving way to a steady state level of AHL. This is where AiiA, an AHL-lactonase and our predator molecule, has a pivotal role. AiiA will limit the amount of AHL in the cell by continuously "eating" the prey molecules, keeping the concentration of AHL away from steady state. However, before we implement the prey cell into our oscillator, we would like to exert some control in order to prevent the AHL concentration from reaching steady state prematurely. Several methods were devised. First, a RNA sequence called a riboswitch was designed such that the addition of theophylline would trigger the exponential feedback mechanism. The sequence coding for the riboswitch was placed in between the pLux promoter and the LuxR protein coding region, such that any leaky expression would produce the riboswitch and prevent further transcription from occuring. In its native state, the riboswitch sequence has a sticky end that will bind to the DNA sequence preventing it from being transcribed. Theophylline acts as an aptamer to change the conformation of the riboswitch, enabling the DNA sequence to be exposed, thus leading to protein expression. The second method of control was the Cre/Lox system, whereby non-coding regions of DNA were inserted in between the promoter and the protein coding region. Similar to the riboswitch, this prevents the transcription of DNA and maintains the baseline level of AHL. A second plasmid is inserted which codes for a specific restriction enzyme that will remove the non-coding region of DNA. This other plasmid is controlled by a LacI promoter, such that IPTG induction will cause its expression. This will result in the DNA being cleaved and subsequent protein expression. Also taken into consideration was the monocystronic versus polycistronic efficiency. Two test constructs were designed to investigate into which construct would provide the most exponential surge of AHL (to match as closely as possible to the Lotka-Volterra model).

But how is our predator production controlled? The team decided that a two cell system, one producing AHL and the other producing AiiA, would lead to the best population wide oscillations, perhaps also enabling control over the amplitude and frequency of the oscillations as well. As the AHL molecules are released into the surrounding solution, it is the signal by which the other cell knows to begin production of AiiA. In a population dynamics sense, the number of sheep (AHL) available will determine the growth of foxes (AiiA). Thus, our design contained LuxR and AiiA protein coding regions regulated by a pLuxR promoter. Again, the team hoped that leaky expression of LuxR would enable the feedback mechanism to start working once AHL was introduced into the system from the prey cells.

According to the extensive modelling and the similarities between the biological oscillator and the Lotka-Volterra model, a sinusoidal theoretical output was predicted that would continue for more than 10 oscillations. Moreover, by changing certain key parameters, the frequency and amplitude could easily be changed. However, tweaking biological parameters in living systems has posed a serious problem, and should be the investigation of a future project.


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