Background and overview
An oscillator is a key device in any sequential logic circuit. Its repetitive signal serves for synchronization of events and therefore insuring the correct results of any logical or control operation inside a digital device. While this digitally-accurate concept cannot be directly transferred to biological systems, the nature of this device can still be used to our benefit. As we strive to control processes inside a single or multiple cells this tool could offer help in triggering the selected events in any given order or at any given moment. For ensuring that kind of control, we would need a biological oscillator that would be self-sustaining and would have adjustable frequency.
While experimental work is what counts at the end of the day, modeling of any biological system can help with roughly determining what experimental parameters should be used to achieve the best possible results.
We created two different models of a biological oscillator for that purpose, i.e. Smolen-type oscillator (Smolen et al., 1998) and represillator (Elowitz et al., 2000). Both models have been experimentally tested and extensively modeled based on respective biological processes. Our aim was to investigate in which manner the use of ZNF-based panel of repressors could extend the current experimentally realizable set of oscillators and what additional properties could be achieved. We investigated the validity of some premises of genetic oscillators, such as the requirement for the oligomeric repressors to support nonlinear binding profiles. Additionally, we performed stochastic and deterministic simulations.
How is deterministic approximation different from stochastic?
Deterministic approximation is a mathematical model that follows certain rules and equations without any randomness. It is determined by one or usually more differential equations which produce the same output for a given input every time we run the simulation, meaning that the results for of the same starting parameters will always be the same. Because deterministic system is determined by ordinary differential equations the calculation of the results is actually just a problem of solving this system, which was solved in our case with MATLAB, using the SimBiology toolkit.
On the other hand, the key feature of a stochastic process is certain level of randomness. The evolution of stochastic system is usually determined by a probability distribution. Regardless of the distribution used it is highly unlikely that two results from the same input (initial parameters) would be exactly the same.
All our stochastic models used Poisson distribution for executing reactions at each step of the simulation, which produces slightly different results every time the simulation is run even if the input is the same, making them more natural and representative. In a complex system such as biological oscillator it would be too complex (or even impossible) to take into account every variable present, however using a probability distribution for some of the processes is a good enough approximation of the natural situation. While many different probability distributions are known, the Poisson distribution is the most commonly used distribution when it comes to molecular interaction.
For the calculation of discrete stochastic simulation the Gillespie algorithm (stochastic simulation algorithm - SSA) was used (Gillespie D. T. 2007 Stochastic simulation of chemical kinetics). Two different tools were used for stochastic model, a script written for MATLAB and a freeware program SGNSim (runs on Microsoft windows), that serves for simulation of gene networks ("SGN Sim, a Stochastic Genetic Networks Simulator", A.S.Ribeiro, J.Lloyd-Price, 2007; http://www.cs.tut.fi/~sanchesr/SGN/SGNSim.html ). MATLAB script used a version of SSA algorithm, while SGNSim uses a delayed SSA (SSA that includes delays for transcription and translation).
A distinction was made in simulations of prokaryotic (bacterial) and eukaryotic (mammalian) systems. The main difference is the delay between transcription and translation. While this process is coupled in bacteria there is a large delay in eukaryotic cells due to the RNA maturation and translocation from the nucleus into the cytoplasm.
Deterministic models seem to be more robust. Wide variety of starting parameter values were simulated and most of the results were an oscillating system. On the other hand, stochastic system quickly reaches an equilibrium state if we do not use realistic parameter values. That is why deterministic model was used to compare the results with stochastic simulations, however extensive testing, including difference in prokaryotic and eukaryotic cells, were only done with stochastic model.
Both script file for MATLAB and input file for SGNSim were written by Slovenian iGEM team members.
 Paul Smolen, Douglas A. Baxter and John H. Byrne, Department of Neurobiology and Anatomy, University of Texas, Medical School, Houston, Texas, 1998. Frequency selectivity, multistability, and oscillations emerge from models of genetic regulatory system.
Am J Physiol Cell Physiol 274: 531-542.
 Michael B. Elowitz, Stanislas Leibler, Departments of Molecular Biology and Physics, Princeton University, USA, 2000. A synthetic oscillatory network of transcriptional regulators.
Nature Vol 403: 335-338