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From 2012.igem.org

Preperation

Simplification

 

We simplify our abstract model as a pathway A -> B -> C. Enzyme one (E1) catalyzes the reaction A -> B and enzyme two (E2) catalyzes the reaction B -> C. The reaction equation is:

 

 

Molecular motion is continuous and complex so that it is difficult to model precisely. As a simplification, it is reasonable to discretize the continuous time as discrete steps and simplify the molecular Brownian motion as three-dimensional random walking. With this simplification, we can approximately observe the process of reaction and the reaction rate. Therefore, we present algorithms to simulate the process of molecular reaction dynamically and intuitionally.

 

Assumptions

 

1. The container is a cube and we assumed a unit. The edge of the cube is an integral multiple of one unit.

2. The cube is in a grid pattern and all the molecules are at the grid intersections.

3. The molecular motion is random walking in three dimensions.

4. The molecule cannot cross the edge of the cube.

 

Algorithm:

 

In order to simulate the molecular motion and verify the fact that a RNA scaffold with two enzymes can speed reactions of the pathway, we simplify the complex realistic situation as a simple and virtual three dimensional world.

 

Initial state: All the molecules including A, E1 and E2 are randomly scattered at the intersections

Step 1: Check if there is A and E1 at the same intersection. If there, B is generated and A disappears.

Step 2: Check if there is B and E2 at the same intersection. If there, C is generated and B disappears.

Step 3: All the molecules are randomly walking one unit. If the molecule is going to across the border, it will be still and does not have a walk. Then, go back to step 1.

 

Implementation

 

We use the Matlab programming to construct the model and implement this algorithm, presenting the results using both data and 3D figures.