CH391L/S14/Oscillation

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Oscillations

Oscillations are very useful in many regards. For example, oscillations can be used to transfer information quickly through the use of waves. Oscillations, however, are not limited to physical vibrations, but can rather be thought of as the periodic transition between two, or more, states. A circadian rhythm, for instance, is an example of a biological oscillation.

Entertainment is defined as the systematic process of synchronization of the biological network. Oscillators often respond to external stimuli at some point in their cycle, and if these stimuli are strong compared to the strength of the oscillation, then the oscillation can be driven by the stimulus.

A positive feedback loop is one in which the output of the system further induces the system to perform its function (for instance, if a few sheep in a heard start running, they will cause other sheep to start running, which will cause more sheep to start running, and so on). A negative feedback loop is the opposite, in which the output of the system inhibits the system from repeating the function.

Biochemical Oscillators

Novák et al states that biological oscillators have to have four basic requirements in order to function properly: “negative feedback, time delay, sufficient ‘nonlinearity’ of the reaction kinetics and proper balancing of the timescales of opposing chemical reactions.” [1, 2] Nonlinearity of the system refers to how the characteristic equation for the system should be structured, specifically, differential equation used to describe the reaction mechanism ought to follow the general form Nonlineardiffeq.png. Components of metabolic systems such as glycolysis, AMP production, and the horseradish peroxidase reaction were the first discovered biological oscillators (discovered in the 1950s and ‘60s). [1, 2]


The Repressilator

(source: http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html) The Repressilator network is shown on the left, and the reporter plasmid is shown on the right.

Michael B. Elowitz and Stanislas Leibler were the first to design a synthetic network that produces oscillatory behaviors, termed “the Repressilator.” Their paper on the study, “A synthetic oscillatory network of transcriptional regulators,” was published in Nature Magazine in 2000. This paper was groundbreaking to the field of synthetic biology as it was one of the first synthetic networks designed to execute a particular function. As shown in figure 1, the Repressilator has three the repressor genes (tetR-lite, lac-lite, and λ cl-lite) coded for on a plasmid. The system oscillates between three states. In one state, the tetR gene binds to the tet01 binding site, inhibiting the production of λ cl-lite. This state therefor immediately produces the second state of the system, for without the presence of λ cl-lite, lacl-lite can be produced as the λ promoter site is left uninhibited. Lacl then represses the transcription of tetR by binding to the PL lac01 promoter site. This then leads to the third state of the system, for since tetR is not coded for, the PLtet01 promoter site is left uninhibited, and λ ct-lite can be coded for and repress the production of lacl-lite. This brings the system back to the first state described. The period of oscillation in the Repressilator was far greater than the time between cell divisions. This, however, did not hinder the ability of the oscillator to function properly, as the cell clones essentially picked up where the parent cell left off and continued the oscillation. While this study was significant in at it was among the first synthetically devised biological system which performed a predicted function, it was shown to be unstable and produced a lot of noise. [3].


Dual Feedback Oscillator Circuit

(source: http://www.ncbi.nlm.nih.gov/pubmed/18971928) The dual oscillator circuit's network. Note the positive and negative feedback loops.
(source: http://www.ncbi.nlm.nih.gov/pubmed/18971928) As shown, the oscillation periods are a function of IPTG, Temperature, Cell Doubling Period, and Arabinose


A study published in Nature by Sticker et al demonstrated a more robust oscillator that is both tunable and has fast oscillatory periods (around 13 minutes in length). It achieves this robustness by implementing both a positive feedback loop and a negative feedback loop. The intricacy of the design of the network lies in the implementation of a hybrid promoter site that is used to promote gene expression of all three genes used in the oscillator.

The araC gene produces Arabinose, which promotes the transcription of araC, yemGFP and lacI. Note that the fact that Arabinose is used to promote its own synthesis is a positive feedback loop. LacI then transcribes IPTG, which represses the expression of all three genes (including itself). Note that IPTG represses LacI transcription, which is an example of a negative feedback loop. SsrA degradation tags were added to each gene to decrease the lifetime of proteins.

Oscillatory periods could be controlled by temperature, as at lower temperatures the system produced higher oscillatory periods, while at higher temperatures the system produced lower oscillatory periods. Further control over the period of oscillation could be done by increasing the presence of Arabinose or IPTG. [4]


Basics behind mathematical models for oscillations

Allmath.png (Image on left: http://hyperphysics.phy-astr.gsu.edu/hbase/images/oscda13.gif) The image on the left shows what a damped, over damped, and critically damped system look like.



Future Directions

Creating stable biological oscillators has advanced the field of synthetic biology, and further efforts to increase complexity and robustness of oscillators will enable the creation of biological circuits that can execute complex functions. Biochemical oscillations are steady in nature, and thus ought to remain steady when synthetically derived.

iGEM

The 2012 Fudan Lux team created a biological oscillator that was able to synchronize oscillations between multiple cells by the use of light. This is useful, as it allowed for cell to cell communication and synchronization which is present in the behavior of a lot of organisms. [5]
(source: http://2012.igem.org/wiki/index.php?title=Team:Fudan_Lux/biowave&oldid=237302) The oscillator the Fudan team designed in 2012

The 2013 KU team modeled an oscillating system in which all bacterium in the culture experience synchronized oscillations. Using the concept quorum sensing mechanisms, they were able to create a model for a system in which all the cells in a population produce beta-farnesenesynthase in periodic intervals, through the use of extracellular biochemicals. [6]


References

  1. ák2008 Novak, B. "Design principles of biochemical oscillators." Nat Rev Mol Cell Biol. (2008) [Nov]
    Requirements for biological systems to oscillate.
  2. Elowitz, M. "A synthetic oscillatory network of transcriptional regulators." Nature 403, 335-338 (2000) [Elowitz2000]
    The Represcilator
  3. Sticker, J. "A fast, robust and tunable synthetic gene oscillator." Nature 456, 516-519 (2008) [Sticker2008]
    Dual Feedback Oscillator
  4. http://2012.igem.org/wiki/index.php?title=Team:Fudan_Lux/biowave&oldid=237302 [Fudan2012]
    Fudan 2012 iGEM project
  5. http://2013.igem.org/Team:KU_Leuven/Project/Oscillator/Design [KU2013]
    The KU synthetic oscillator design