Team:Tsinghua/Model
Ⅰ. Simulation for Phase Separation System
In order to use theoretical caculation to guide experiment, we try to interpret our mathematical models in a visual version by design some virtual experiments and computer simulations. It is well known that, phase separation is a thermodynamic process which follows complex nonelinear physical law. To achieve precise but economical numerical calculation, we use Cahn-Hilliard equation and simplify some details in 2-dimensional simulation. And try a particle model as our 3-dimensional simulation. We also try artificial light-induce in our simulation.
Two-Dimensional Simulation
This part of our work is based on well-known Cahn-Hilliard equation, whose standard mathematical representation shows as follows:
In this formula, variable D is a diffusion coefficient, whose unit is 𝜇m2/ms，c is the concentration of the fluid. By referring to online open-source code, we utilize a time marching method to the equation. It can save a lot of time and provide a convenient data which is easy to visualize. The data is presented with four subplots. The top two plots show the solution as a function of space. The lower left plot shows a cross section of the solution, and the lower right plot shows a portion of the power spectrum of the solutions cosine transformation.
while D=1
while D=0.5
while D=0.1
while D=0.02
Expansion to three-dimensional space
In order to more realistically reflect the phase separation process in the cell, we simulated the phase separation process in the 3D grid space. The particles are set to move randomly within the three-dimensional grid space. When particles are gathered, the probability that they will separate at the next moment is inversely proportional to the strength of the interaction between them. Therefore, when particles have mutual attraction, they eventually tend to be in a state of being gathered into clusters. As shown in the following animation, the particles in the image on the right are set to have a stronger interaction than the particles in the image on the left. The difference in phase separation ability can be found in the simulation animation.
Without light-induce
Light-induce
To the best of our knowledge, this simulation is the first to apply three-dimensional random walks to phase separation simulations, although it is more qualitative than quantitative. It gives a well-considered interpretation of photo-activated phase separation, that is, light changes the conformation of the protein and then changes the strength of the interaction between proteins, thereby affecting the phase separation state.
