# Oscillator Circuits

The aim of synthetic biology is to design and synthesize biological networks that perform desired funtions in a predictable manner. A significant chunk of workin synthetic biology has focused on the construction of two important type of networks: switches and oscillators. Synthetic biology is at the intersection of biology, engineering and computational mathematics. Consequently, there are two distinct aspects to the design, analysis and implementation of a synthetic circuit: in-silico and in-vivo validation. Under the in-silico paradigm, we forego the specific implementational details, rather we are focused on the abstract mathematical model and the dynamical behavior such a model allows. While for in-vivo analysis, we work on identyfing the specific biological components that can be used to implement the identified topology for the synthetic network. Here, we look at both these aspects for the Danino Oscillator [4].

Figure (number intro1) shows some topologies which are known to show oscillatory behavior [8]:

- Goodwin Oscillator
- Repressilator
- Amplified negative feedback oscillator
- Fussenegger Oscillator

We’ll give a very brief overview of the Goodwin and the Amplified negative feed- back oscillators . The Danino Oscillator is essentially a quorum sensing version of the Amplified negative feedback oscillator.

**Goodwin Oscillator -**This was the first synthetic genetic oscillator to be studied. It consists of a single gene with negative autoregulation. Models suggest that oscillations occur in the goodwin oscillator if repression is mod- elled by a nonlinear Hill function with a high cooperativity coefficient [3]. Further, this oscillator has been shown to have a robust time period.**Amplified negative feedback oscillator**Leaving aside the biological im- plementation, this abstract topology is the one used in the Danino Oscillator.Under this architecture, the activator gene A activates it’s own repressor gene B. In the Daanino oscillator there is a latent phase when both the activator and repressor accumulate, thus allowing large amplitudes to be achived for this configuration.The qualitative behavior of this oscillator is discussed in the modelling section using the mathematical model suggested in [4]. One crucial benefit that the Danino oscillator has over this topology is the prop- erty of quorum sensing; the AHL molecule can diffuse across the cell mem- brane and be exchange with neighbouring cells. This offers a mechanism to synchronize the oscillators.