Difference between revisions of "Team:Aalto-Helsinki/Modeling synergy"
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<p>To compare between enzymes being close together and not being close together, the model simulates enzyme reactions inside a cell. The model behaves stochastically, and needs to be ran multiple times to ensure reliable results, as its results will vary according to pseudorandom variables.</p> | <p>To compare between enzymes being close together and not being close together, the model simulates enzyme reactions inside a cell. The model behaves stochastically, and needs to be ran multiple times to ensure reliable results, as its results will vary according to pseudorandom variables.</p> | ||
− | <p>The model is a computer program made with Python that simulates a space filled with enzymes and substrates which react with each other. A simplified flowchart of the program is presented on the side, see Fig. | + | <p>The model is a computer program made with Python that simulates a space filled with enzymes and substrates which react with each other. A simplified flowchart of the program is presented on the side, see <a href="#fig2">Fig. 2.</a></p> |
− | <figure style="float:right;"> | + | <figure id="fig2" style="float:right;margin-bottom:2%;margin-left:1%;" > |
<img src="https://static.igem.org/mediawiki/2015/4/48/Aalto-Helsinki_particle_model_flowchart.png" style="width:400px;margin-top:40px;" /> | <img src="https://static.igem.org/mediawiki/2015/4/48/Aalto-Helsinki_particle_model_flowchart.png" style="width:400px;margin-top:40px;" /> | ||
− | <figcaption><b>Figure | + | <figcaption><b>Figure 2:</b> Flowchart of the model </figcaption> |
</figure> | </figure> | ||
<p>Now, let’s go through the different phases of the simulation:</p> | <p>Now, let’s go through the different phases of the simulation:</p> | ||
− | <p>Initialization: The program loads a settings file filled with information concerning the simulation, and creates a simulation according these specifications. With this file the user can, for example, specify the length of the simulation, the different substrates with their amounts and masses, as well as the different enzymes and the types of substrates and products they either consume or produce.</p> | + | <p><b>Initialization:</b> The program loads a settings file filled with information concerning the simulation, and creates a simulation according these specifications. With this file the user can, for example, specify the length of the simulation, the different substrates with their amounts and masses, as well as the different enzymes and the types of substrates and products they either consume or produce.</p> |
− | <p>Particle movement: The model moves particles according to Brownian motion in water. With particles of this size the governing attribute these particles have is their radius.</p> | + | <p><b>Particle movement:</b> The model moves particles according to Brownian motion in water. With particles of this size the governing attribute these particles have is their radius.</p> |
<p>The movement of particles under the influence of Brownian motion follows a normal distribution. According to ____, the mean squared displacement of particles experiencing Brownian motion is proportional to the time interval: \[ \left( | r(t + dt) - r(t) |^2 \right) = 2 \cdot d \cdot D \cdot dt \] where \( r(t)\) is the position of the particle, \(d\) is the number of dimensions, \(D\) is the diffusion coefficient and \(dt\) is time interval. For us to generate correct brownian motion for our particles, we need to scale the normal distribution with a factor \[ k = \sqrt{D \cdot d \cdot dt}. \] For our simulation, \( d=2\) and \( dt\) is a time interval defined by the user. \( D\) or the diffusion coefficient is calculated from the Einstein relation: \[ D = \mu k_BT \] where \(k_B\) is the Boltzmann’s constant and \( T\) is the temperature, and \( \mu \) is the particle’s mobility: \[ \mu = \frac{1}{6 \pi \eta r} \] where \( \eta \) is the dynamic viscosity of the fluid and \( r\) is the particle’s radius.</p> | <p>The movement of particles under the influence of Brownian motion follows a normal distribution. According to ____, the mean squared displacement of particles experiencing Brownian motion is proportional to the time interval: \[ \left( | r(t + dt) - r(t) |^2 \right) = 2 \cdot d \cdot D \cdot dt \] where \( r(t)\) is the position of the particle, \(d\) is the number of dimensions, \(D\) is the diffusion coefficient and \(dt\) is time interval. For us to generate correct brownian motion for our particles, we need to scale the normal distribution with a factor \[ k = \sqrt{D \cdot d \cdot dt}. \] For our simulation, \( d=2\) and \( dt\) is a time interval defined by the user. \( D\) or the diffusion coefficient is calculated from the Einstein relation: \[ D = \mu k_BT \] where \(k_B\) is the Boltzmann’s constant and \( T\) is the temperature, and \( \mu \) is the particle’s mobility: \[ \mu = \frac{1}{6 \pi \eta r} \] where \( \eta \) is the dynamic viscosity of the fluid and \( r\) is the particle’s radius.</p> | ||
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− | <p>Reactions: The simulation considers that a reaction is possible only when a right type of substrate and a right type of enzyme are close enough to react. When this happens, the simulation randomly decides if the reaction actually took place with user-defined probability. If the reaction happened, the simulation changes the substrate to the enzyme’s product and makes both the substrate and enzyme unable to react for a short amount of time.</p> | + | <p><b>Reactions:</b> The simulation considers that a reaction is possible only when a right type of substrate and a right type of enzyme are close enough to react. When this happens, the simulation randomly decides if the reaction actually took place with user-defined probability. If the reaction happened, the simulation changes the substrate to the enzyme’s product and makes both the substrate and enzyme unable to react for a short amount of time.</p> |
− | <p>Data logging: the program collects only one type of data, and that is the particle numbers of each substrate at each point in time that the simulation runs. This makes it possible to make figures of the reactions and to determine the different reaction rates.</p> | + | <p><b>Data logging:</b> the program collects only one type of data, and that is the particle numbers of each substrate at each point in time that the simulation runs. This makes it possible to make figures of the reactions and to determine the different reaction rates.</p> |
− | <p>Post-Simulation tasks: | + | <p><b>Post-Simulation tasks:</b> |
After the simulation, the program creates a data file from the simulation data it gathered. This data file has data about the amounts of substrates at each point in time.</p> | After the simulation, the program creates a data file from the simulation data it gathered. This data file has data about the amounts of substrates at each point in time.</p> | ||
Revision as of 07:37, 4 September 2015