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Switch Modeling - Overview
In our system either inner or outer signals can result in a rearrangement of our protein clusters. These interactions activated by signals can change the distances between enzymes, adjust the reaction rate and then finally alter the production amount. We assume that the random diffusion distance on the membrane is about 50-100 times the distance of our cluster interaction radius, and according to PDE model the concentration deceases with radius.
Working with a chain reaction which has different path ways, after getting a signal, the system will soon recruits our membrane protein parts and alters the dynamic equilibrium of products. In other words, alters the amount and ratio of our final products.
Membrane Switch Model
Enzyme A consumes the primary substrate which has a constant concentration. The products of A (call it α) diffuse in an area of hemisphere. In our switch model, enzyme B and enzyme C all use α as the substrate to produce their products.
Enzymes in the enzyme cluster AB are adjacent to each other, and have a tendency to produce more products that enzyme C. Basic simulation shows that the concentration of substrate α distributes like this:
To illustrate the diffusion behavior and the reaction progress, we assume that enzyme A locates on the center and produce α as the rate of (v_max [A])/(K_m+[A]), and enzyme B and enzyme C occupies the region of Ф1 and Ф2. In the beginning, enzyme B and C share different substrate concentration due to their distance to enzyme A. And enzyme B may produces much more products. Then we give the system a switch signal which can shorten the distance between enzyme A and C. The products of enzyme C rise because it gets more substrate than before. The percentage of these two products
The whole process in membrane switch can be simulated as following:
Discussion
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