Difference between revisions of "Team:Aalto-Helsinki/Modeling synergy"
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− | <h1>Synergy | + | <h1>Synergy model</h1> |
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<p>As such, this problem is quite difficult and would undoubtedly need a lot of research. Instead, we decided to simplify the situation: Could we simulate enzymes and substrates as particles in a cell and model enzyme reactions by simulating their interactions with each other?</p> | <p>As such, this problem is quite difficult and would undoubtedly need a lot of research. Instead, we decided to simplify the situation: Could we simulate enzymes and substrates as particles in a cell and model enzyme reactions by simulating their interactions with each other?</p> | ||
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+ | <p>It just so happens that we can do that. So we did. Our modeling team created a model using Python called the synergy model, as it models the effect of having different enzymes working together.</p> | ||
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− | <h2>The | + | <h2>The Model</h2> |
<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> | ||
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<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><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 <a | + | <p>The movement of particles under the influence of Brownian motion follows a normal distribution. According to <a href="http://advancedlab.org/mediawiki/index.php/Simulating_Brownian_Motion" target="_blank">this reference</a>, 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 set the standard deviation of the normal distribution to \[ k = \sqrt{D \cdot d \cdot dt}, \]which is equal to scaling the distribution by k. 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>Getting the radius of the particles is a bit trickier. To calculate this, we <a href="https://2015.igem.org/Team:Aalto-Helsinki/Modeling_micelle">use the same method as in our Micelle modeling</a>. Based on the information in <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055910/">this paper</a> we can calculate the enzymes’ radii from their mass. | + | <p>Getting the radius of the particles is a bit trickier. To calculate this, we <a href="https://2015.igem.org/Team:Aalto-Helsinki/Modeling_micelle">use the same method as in our Micelle modeling</a>. Based on the information in <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055910/" target="_blank">this paper</a> we can calculate the enzymes’ radii from their mass. |
Proteins' approximate density is 1.37 g/ml. Thus, the specific partial volume (or inverse density) is 0.73 ml/g. From this, we can calculate that the volume of an enzyme mainly consisting of amino acids is \[V(nm^3)=\frac{0.73\tfrac{cm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^{23} \tfrac{Da}{g}} M(Da).\] Then, if we approximate the enzymes as spheres with a volume \( V(r) = \frac{4}{3} \pi r^3 \), we can calculate the enzymes' radii:\[R_{min(nm)} = \left( \frac{3V}{4\pi} \right)^{1/3}\ = \left( \frac{3\cdot \frac{0.73\tfrac{cm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^{23} \tfrac{Da}{g}}}{4\pi} \right)^{1/3} \cdot \left( M(Da) \right) ^{1/3} | Proteins' approximate density is 1.37 g/ml. Thus, the specific partial volume (or inverse density) is 0.73 ml/g. From this, we can calculate that the volume of an enzyme mainly consisting of amino acids is \[V(nm^3)=\frac{0.73\tfrac{cm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^{23} \tfrac{Da}{g}} M(Da).\] Then, if we approximate the enzymes as spheres with a volume \( V(r) = \frac{4}{3} \pi r^3 \), we can calculate the enzymes' radii:\[R_{min(nm)} = \left( \frac{3V}{4\pi} \right)^{1/3}\ = \left( \frac{3\cdot \frac{0.73\tfrac{cm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^{23} \tfrac{Da}{g}}}{4\pi} \right)^{1/3} \cdot \left( M(Da) \right) ^{1/3} | ||
= 0.066 \cdot (M(Da))^{1/3} \] For substrates this is not so easy. To simplify the situation we used the same method for calculating the approximate radii for the substrates as well, based on their molar mass.</p> | = 0.066 \cdot (M(Da))^{1/3} \] For substrates this is not so easy. To simplify the situation we used the same method for calculating the approximate radii for the substrates as well, based on their molar mass.</p> | ||
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<p>Settings with both joined enzymes and no joined enzymes were used to get the results presented. In addition to this, the model was tested with settings with competing enzymes to better represent the real-world scenario inside <i>E. coli</i>, where there are multiple competing enzymes consuming butyraldehyde.</p> | <p>Settings with both joined enzymes and no joined enzymes were used to get the results presented. In addition to this, the model was tested with settings with competing enzymes to better represent the real-world scenario inside <i>E. coli</i>, where there are multiple competing enzymes consuming butyraldehyde.</p> | ||
− | <p>The simulation space was set to represent a cross section of an <i>E. coli</i> bacteria. Time resolution of the simulations was set to 1 µs. The simulations considered the initial substrate’s concentration to be constant. The reaction probabilities for different enzymes were set at 15%. Total elapsed simulation time was 0.1 s. The amount of competing enzymes varied from 0% to 1500% of the other enzymes’ amounts between simulations. The other enzymes’ amounts were not varied between simulations. The simulation setting files are available <a href="https://static.igem.org/mediawiki/2015/7/72/Aalto-Helsinki_synergy_model_simulation_data.zip">here</a>.</p> | + | <p>The simulation space was set to represent a cross section of an <i>E. coli</i> bacteria. Time resolution of the simulations was set to 1 µs. The simulations considered the initial substrate’s concentration to be constant. The reaction probabilities for different enzymes were set at 15%. Total elapsed simulation time was 0.1 s. The amount of competing enzymes varied from 0% to 1500% of the other enzymes’ amounts between simulations. The other enzymes’ amounts were not varied between simulations. The simulation setting files are available <a href="https://static.igem.org/mediawiki/2015/6/66/Aalto-Helsinki_synergy_model_setting_files.zip">here</a>. The data files that were gotten from the simulations are available <a href="https://static.igem.org/mediawiki/2015/7/72/Aalto-Helsinki_synergy_model_simulation_data.zip">here</a>. The simulation itself can be downloaded <a href="https://static.igem.org/mediawiki/2015/f/f2/Aalto-Helsinki_synergy_model.zip">here</a>.</p> |
<p>The simulation results indicate that simulations with joined enzymes as opposed to unjoined enzymes achieved higher product creation rates. When more competing enzymes were present in the simulation, the difference between joined and unjoined enzymes became more apparent. In some simulations, joined enzymes got up to 400% reaction rate as opposed to non-joined enzymes. In most simulations, joined enzyme reaction rate changed between 150% and 400% of unjoined enzyme reaction rate, depending on how much competing enzymes there were. In all of the simulations joined enzymes performed as well or better than unjoined enzymes.</p> | <p>The simulation results indicate that simulations with joined enzymes as opposed to unjoined enzymes achieved higher product creation rates. When more competing enzymes were present in the simulation, the difference between joined and unjoined enzymes became more apparent. In some simulations, joined enzymes got up to 400% reaction rate as opposed to non-joined enzymes. In most simulations, joined enzyme reaction rate changed between 150% and 400% of unjoined enzyme reaction rate, depending on how much competing enzymes there were. In all of the simulations joined enzymes performed as well or better than unjoined enzymes.</p> | ||
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<figure style="margin-bottom:2%;"> | <figure style="margin-bottom:2%;"> | ||
<img src="https://static.igem.org/mediawiki/2015/e/e9/Aalto-Helsinki_Synergy_model_timecourse_0_80_300.png" style="max-width:100%;" /> | <img src="https://static.igem.org/mediawiki/2015/e/e9/Aalto-Helsinki_Synergy_model_timecourse_0_80_300.png" style="max-width:100%;" /> | ||
− | <figcaption><b>Figure 3:</b>Time course of | + | <figcaption><b>Figure 3:</b>Time course of end product amounts with both joined and unjoined enzymes and different amounts of competition.</figcaption> |
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<p>The model has some virtues. One of these is that the model is quite lightweight, and can simulate thousands of particles with the resources of a single machine in a reasonable time. The model is also quite flexible, and can be easily configured through the use of its settings file, in which the user can choose both the general settings concerning the simulation space and timescale as well as set the enzymes and substrates that are relevant to the reactions using a human readable file.</p> | <p>The model has some virtues. One of these is that the model is quite lightweight, and can simulate thousands of particles with the resources of a single machine in a reasonable time. The model is also quite flexible, and can be easily configured through the use of its settings file, in which the user can choose both the general settings concerning the simulation space and timescale as well as set the enzymes and substrates that are relevant to the reactions using a human readable file.</p> | ||
− | <p>All in all, the model can be useful if it's remembered that its predictions should be viewed as guidelines only, and if one remembers the simplifications made in the enzymes’ function. </p> | + | <p style="margin-bottom:0;padding-bottom:10%;">All in all, the model can be useful if it's remembered that its predictions should be viewed as guidelines only, and if one remembers the simplifications made in the enzymes’ function. </p> |
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Latest revision as of 06:41, 17 September 2015