Difference between revisions of "Team:USTC/Model/3"

Introduction

In order to quantitatively analyze the electron transfer rate, a model based on simple symmetric random walk is employed, in which the mtrA, mtrC and CymA proteins are regarded as particles on an infinite cubic lattice. It is assumed that electron transfer happens where proteins of all three kinds are in same position. To run the simulation, this system is initialized with protein positions generated randomly in a uniformly distributed manner with density measured in wet experiment. The interactions between proteins are ignored including physical collision and electrostatic force, and proteins are considered to move with equal probabilities to any one of its immediate neighbors in an arbitrary time step. The total number of times of these proteins overlapping is counted after each simulation and an average is calculated to help us analyze the electron transfer rate.

What were we modeling:

To avoid lots of precise kinetics process and dynamics process, we used Monte Carlo simulation to achieve our goal. In reference[1] and [2], we’ve found that Monte Carlo simulation can actually describe the Brownian motion of the motion of proteins.

At the beginning, we considered a simple simulation of just one particle in an infinite plane to verify the feasibilities of our simulation. This whole process is a Markov process. The coordinate (x,y) of the particle in every step constituted two Markov chains, one for x, the other for y. Figure 1 shows the simulation of a randomly moving.

As a molecule, it would walk randomly in the solution. In our system, we ignored the interaction force between molecules. Because of this approximation, we could use a DLA model to describe the structure of a CdS crystal.

Fig. 1 random walking particle model

To some extent, this simulation lets us know more about the truth of the moving of protein. So we considered this simulation can be used in our model.

In practice, we used a local coordinate on the surface of a bacteria. In this coordinate, spacetime is a Minkowski Space which is a flat spacetime. In this space, firstly we can see that functional mtrC is binding on mtrB which is binding on the extracellular membrane of E.coli. Because of this structure, mtrB can’t move into the periplasm. We regarded mtrC can just move on a 2D plane. As for mtrA, mtrA moves in the periplasm. Because the thickness of periplasm is very smaller than the width of the membrane, we can regard mtrA also moves in a flat plane. At last, CymA is a globulin that binding on the intracellular membranes. Just like mtrB, we also think that the CymA moves on a flat plane.

Because of this approximation, we have figure 2. Figure 2 shows the motion of these proteins. Every protein just moves in a flat plane.

a)

b)

Fig. 2

In order to simulate the real process of the transformation of an electron, we ignored the time which the chemical react cost. The Brownian motion took most of the time of the whole process. So we considered that if a mtrA, mtrC, and CymA move like a line, the electron can be transferred into bacteria. Based on this simulation, we assumed the current I that is a function of time t. So we get a curve of I-t(Figure 3).

Results: