University of Calgary



Membrane Computing Modelling
Differential Equation Modelling


We've reached modelling, the fifth stop on our tour! We've looked in to two different methods of modelling our system: Differential Equation Based Modelling and Membrane Computing. Here, you can explore the similarities and differences, as well as the functions of each method. As well, you can find the results of our characterization of the signalling pathway. Once you're done, we'll move on to the Second Life component of the project HERE.

The aim of the modelling aspect of our project is to develop simulations that would enable us to predict the behavior of the Autoinducer-2 (AI-2) signalling system. For example, in our system, knowing of the optimal LuxPQ concentration within the periplasmic space for the bacteria to function is crucial, and if one attempted to find the optimal level of LuxPQ in the lab, the cost of experiment would rise and it would take days and months to figure out. With an accurate model, however, we would be able to predict the optimal level of LuxPQ within a matter of seconds, which would result in a cheaper and much efficient experiment. This year, we decided to model our system in two different ways: Membrane Computing and Differential Equation Based Modelling, and through them, we seek to answer different questions, as noted below:

Membrane Computing
Membrane computing is a specific branch in computer sciences that focuses on acquiring computational models form the structure and functionality of cells. The knowledge from how cells in tissues are organized, distributed and parallel computing models, as well as compartmentalization and basic data structures can be developed. Compartments are important, especially when representing biological systems because it allows the organization of structures in a hierarchical way. Membranes from a cellular sense, acts as a barrier that divides organelles from their environment and they involved reactions that take place within the compartments of the cell. This allows the compartments to communicate between cells and the environment. Many different types of modelling such as the P system have been developed to model different systems. Ultimately, the goal of membrane computing is to advance our knowledge in bacterial communication in nature by examining individual behaviour of each bacterium. Two goals are developed for the membrane computing team:

1. Using the AHL signalling system that was investigated heavily by the 2008 wetlab iGEM team, basic interactions between agents are explored.
2. Using the AI-2 signalling system developed this year, a computational model will be built.

Through the development of these models, the reactions and their parallel effects can be monitored.

Differential Equation Based Modelling
System characterization is essential for understanding the effects of specific conditions and inputs by simulation. By using results that are collected from modelling and simulation, optimizations through experimental means are reduced. The combination of mathematics and engineering principles, combined with systems biology can potentially solve many complexities in experimental sciences. If a system can be successfully modelled, there is the potential of reducing money and resource allocations to experimental science. As well, through the use of simulation, certain conditions can be applied to optimize certain results. The goals for the mathematical modelling team are:

1. Develop the differential model for the AI-2 signalling system. This will be done in Simbiology, a toolbox in MATLAB that allows individuals to model, design, simulate and analyze different biochemical pathways.
2. Study the effects of varying input to the system.
3. Examine the effects of different synthetic constitutively-active promoters of different strengths.

In nature, biological circuits are robust, which means that their function is insensitive to natural fluctuations in their components. Many engineered circuits can perform a given function, but very few can perform robustly in cells.

Interactions between computing and biology have led to developments in different types of disciplines (mathematical modelling and membrane computing). Membrane computing specifically looks at bacterial communication that happens outside the cell, while the differential equations based modelling concentrates on characterizing and optimizing the compatibility of the signalling system. In hope, these two models can provide a greater understanding of the pathway and emphasize the complexities that are linked with systems biology.