Team:Oxford/Model

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Dry Lab

Description and Assumptions

Modeling Description

Different parts of the project have been modelled for a better understanding of the validity of our proposed solution as well as predicting different aspects of the system. Firstly, a system of non-linear Ordinary Differential Equations was written for all reactions taking place; then, they were solved numerically over 250 seconds to explore and understand both transient and steady-state response of the system. The time-domain analysis of the system was proceeded by looking at steady-state curves and output/input behaviour of the system in the steady state as well as body response dynamics, which gave an overall prediction about the fate of the combined system-body model. Secondly, optimisation and modelling were used to determine the optimum number of base pairs needed for sRNA binding as well as promoters' strength used in transcriptions. Modelling was then taken to the frequency domain for transfer function derivation and cascade controller design. A summary on main areas of our analysis is given here however, a detailed modelling report could be found at the end of the page.

Assumptions

A list of general assumptions is summarised below. It should be noted that more specific assumptions are stated in our modelling report at the end of the page.

  • item Adenosine has been replaced by Adenine as the Hydrolase reaction is believed to be much faster than the body response.
  • item Concentration of Adenine and NO was kept constant for dynamic analysis as there is plenty of these chemicals available outside and inside the cell.
  • item The initial conditions used for time domain analysis correspond to the worst case scenarios.

The Dynamics of the system

Differential Equations and parameters

The dynamic model of both of the pathways were analysed using Simbiology toolbox in Matlab and some of the modelling and parameters are based on the paper "Frequency domain analysis of small non-coding RNAs". The dynamic time domain analysis of the system was done using the combined model in Figure 1 with different initial conditions corresponding to negative and positive pathways separately. It is worth mentioning that data fitting was used to determine some of the parameters. A table of the parameters and data is available in the Appendix of the report. The differential equations describing the systems are as follow.

Section 3

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