Difference between revisions of "Team:Aalto-Helsinki/Modeling synergy"
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<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>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>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 \[ k = \sqrt{D \cdot d \cdot dt} \] | + | <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>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/">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} | + | 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> | ||
Revision as of 09:35, 27 August 2015