MODELLING

Our modelling in this project has several aims:

• To find the amount of DPP-IV reduction reached when the system reaches equilibrium
• To find a way to control the level of DPP-IV reduction
• To find the minimum number of RdRps, replicons, etc to be initially transfected into the cell, which are required to achieve a steady state for the system
• To find out how long does it take for the system to reach equilibrium
• To find out the level of reduction we need to treat diabetes
• To find out how stable the system is (i.e. will the system only work in very specific situations, or in lots of different systems?)

We are currently using Simbiology in Matlab and Copasi to model the system. We are currently adapting several different models, which come from research into HCV replicons, to our system. If our models can be made to fit our experiments well, we may extend our project to try and find a way to control the level of DPP-IV which is reduced. In addition modelling the system will allow it to be better optimised in the future, and optimum values for constants such as the strength of the ribosome binding sites, and the number of siRNAs produced by each degradation, so that the effect of our biobrick can be optimised.

We are currently using Simbiology in Matlab and Copasi to model the system. We are currently adapting several different models, which come from research into HCV replicons, to our system. If our models can be made to fit our experiments well, we may extend our project to try and find a way to control the level of DPP-IV which is reduced. In addition modelling the system will allow it to be better optimised in the future, and optimum values for constants such as the strength of the ribosome binding sites, and the number of siRNAs produced by each degradation, so that the effect of our biobrick can be optimised.

Initially we determined that our system should reach some equilibrium after a certain amount of time. This is because firstly, HCV is a successful virus, so the replicons should not completely degrade away as time goes to infinity. Secondly, since there are only a finite amount of resources within the cell, the number of replicons in the system cannot keep increasing forever. This means either the number of replicons must tend towards a certain constant (constant with respect to time), or the number of replicons should tend towards oscillations.

\begin{eqnarray} \label{system1} \frac{dm}{dt} &=& \alpha_m - \beta_m m - k_s ms \\ \label{system2} \frac{ds}{dt} &=& \alpha_s - \beta_s s - p_s k_s ms - k_r sr \\ \label{system3} \frac{dr}{dt} &=& \alpha_r - \beta_r r - p_r k_r sr \end{eqnarray}