Team:Calgary/Modelling/Method

Overview

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• Notebook & Parts

Membrane Computing Modelling

• Introduction
  
• Tutorials
• Results
• Paper

Differential Equation Modelling

• Method
  
• Results
  
• Basic Definitions

The simbiology interface from Matlab was used to simulate the differential equations model. Chemical Kinetic equations were used to build the model for simulation.


Fig : The Reaction of Species A with B to produce C and D


Fig : The Chemical Kinetic Rate Equation

k is the kinetic rate constant. The size of k will determine the speed of the reaction. A smaller value of k will produce a slow reaction rate while a larger value of k will produce a fast reaction rate.

[A] is the amount of reactant A present.

The simulations were run for 50000 seconds . It was considered to be enough time for the system to reach equilibrium after disturbance.

Sundial Solver

The sundial solver (SUNDIALS) was developed so that robust time integrators and non-linear solvers can be easily combined with already existing simulation codes. Minimal information from user is required and this solver allow users to easily supply their own data structures. The Sundials solvers are part of a third-party package developed at Lawrence Livermore National Laboratory. Built-in ordinary differential equation (ODE) solvers (ode45 and ode15s) are also part of the interface. More more information about sundials within Simbiology, please visit the Matlab website.

When sundials solver is selected, the program selects one of the two sundials solvers that suits your model: CVODE or IDA. CVODE is used for systems of ODEs (stiff or nonstiff) and this type of solver is usually used for a model that has no algebraic rules. IDA is a differential-algebraic equation (DAE) solver and it is usually used when there is one more algebraic rules. Since our model incorporates an event (the addition of autoinducer-II (AI-2)), this type of solver was used in our model. More information can be found here: https://computation.llnl.gov/casc/sundials/description/description.html
***Information provided by Matlab website

Rationale

The following initial conditions and k constants are estimated values. The modelling team was unable to find much literature regarding rate constants and initial conditions for our signalling system. With that being said, this model still serves a purpose in understanding the signalling pathway. We were able to demonstrate various trends when AI-2 and expression of specific proteins were adjusted. The output when inputs were changed showed significant trends that may be taken into consideration when the laboratory work is performed. This model provides a good starting place for understanding of the basic signalling system. Further research and work will be dedicated to provide a more accurate model. The main focus for this team is to find significant trends that will effect the AI-2 signalling cascade.

During the past few months, the modelling team developed the AI-2 signalling circuit within Simbiology. The following is a diagram that simplifies the AI-2 signalling cascade with interactions of different species:

AI-2 Signalling System Map Developed

The system was represented by the following reactions. The reactions with double headed arrows have two rate constants(forward/ reverse rate constant). All reactions were assumed to be elementary reactions.